Package 'precmed'

Description

Compute the area between curves (ABC) for each scoring method in the "precmed" object. This should be run only after results of catecv() have been obtained.

Usage

abc(x, ...)

## Default S3 method:
abc(x, ...)

Arguments

Details

The ABC is the area between a validation curve and the overall ATE in the validation set. It is calculated for each scoring method separately. Higher ABC values are preferable as they indicate that more treatment effect heterogeneity is captured by the scoring method. Negative values of ABC are possible if segments of the validation curve cross the overall ATE line. The ABC is calculated with the auc() in utility.R with a natural cubic spline interpolation. The calculation of the ABC is always based on validation curves based on 100 proportions equally spaced from min(prop.cutoff) to max(prop.cutoff).

The ABC is a metric to help users select the best scoring method in terms of capturing treatment effect heterogeneity in the data. It should be used in complement to the visual inspection of the validation curves in the validation set in plot().

Value

Returns a matrix of numeric values with number of columns equal to the number cross-validation iteration and number of rows equal to the number of scoring methods in x.

References

Zhao, L., Tian, L., Cai, T., Claggett, B., & Wei, L. J. (2013). Effectively selecting a target population for a future comparative study. Journal of the American Statistical Association, 108(502), 527-539.

See Also

catecv() function and plot(), boxplot() methods for "precmed" objects.

Examples

# Count outcome
cv_count <- catecv(response = "count",
                   data = countExample,
                   score.method = "poisson",
                   cate.model = y ~ age + female + previous_treatment +
                                previous_cost + previous_number_relapses +
                                offset(log(years)),
                   ps.model = trt ~ age + previous_treatment,
                   higher.y = FALSE, cv.n = 5, verbose = 1)

# ABC of the validation curves for each method and each CV iteration
abc(cv_count)

# Survival outcome
library(survival)
cv_surv <- catecv(response = "survival",
                  data = survivalExample,
                  score.method = c("poisson", "randomForest"),
                  cate.model = Surv(y, d) ~ age + female + previous_cost +
                               previous_number_relapses,
                  ps.model = trt ~ age + previous_treatment,
                  higher.y = FALSE,
                  cv.n = 5)

# ABC of the validation curves for each method and each CV iteration
abc(cv_surv)

Description

Compute the area between curves (ABC) for each scoring method in the "precmed" object. This should be run only after results of catecv() have been obtained.

Usage

## S3 method for class 'precmed'
abc(x, ...)

Arguments

Details

The ABC is the area between a validation curve and the overall ATE in the validation set. It is calculated for each scoring method separately. Higher ABC values are preferable as they indicate that more treatment effect heterogeneity is captured by the scoring method. Negative values of ABC are possible if segments of the validation curve cross the overall ATE line. The ABC is calculated with the auc() in utility.R with a natural cubic spline interpolation. The calculation of the ABC is always based on validation curves based on 100 proportions equally spaced from min(prop.cutoff) to max(prop.cutoff).

The ABC is a metric to help users select the best scoring method in terms of capturing treatment effect heterogeneity in the data. It should be used in complement to the visual inspection of the validation curves in the validation set in plot().

Value

Returns a matrix of numeric values with number of columns equal to the number cross-validation iteration and number of rows equal to the number of scoring methods in x.

References

Zhao, L., Tian, L., Cai, T., Claggett, B., & Wei, L. J. (2013). Effectively selecting a target population for a future comparative study. Journal of the American Statistical Association, 108(502), 527-539.

See Also

catecv() function and plot(), boxplot() methods for "precmed" objects.

Examples

# Count outcome
cv_count <- catecv(response = "count",
                   data = countExample,
                   score.method = "poisson",
                   cate.model = y ~ age + female + previous_treatment +
                                previous_cost + previous_number_relapses +
                                offset(log(years)),
                   ps.model = trt ~ age + previous_treatment,
                   higher.y = FALSE, cv.n = 5, verbose = 1)

# ABC of the validation curves for each method and each CV iteration
abc(cv_count)

# Survival outcome
library(survival)
cv_surv <- catecv(response = "survival",
                  data = survivalExample,
                  score.method = c("poisson", "randomForest"),
                  cate.model = Surv(y, d) ~ age + female + previous_cost +
                               previous_number_relapses,
                  ps.model = trt ~ age + previous_treatment,
                  higher.y = FALSE,
                  cv.n = 5)

# ABC of the validation curves for each method and each CV iteration
abc(cv_surv)

Description

Check arguments Catered to all types of outcome Apply at the beginning of pmcount(), cvcount(), drcount.inference(), catefitsurv(), catecvsurv(), and drsurv.inference()

Usage

arg.checks(
  fun,
  response,
  data,
  followup.time = NULL,
  tau0 = NULL,
  surv.min = NULL,
  ipcw.method = NULL,
  ps.method,
  minPS,
  maxPS,
  higher.y = NULL,
  score.method = NULL,
  abc = NULL,
  prop.cutoff = NULL,
  prop.multi = NULL,
  train.prop = NULL,
  cv.n = NULL,
  error.max = NULL,
  max.iter = NULL,
  initial.predictor.method = NULL,
  tree.depth = NULL,
  n.trees.rf = NULL,
  n.trees.boosting = NULL,
  B = NULL,
  Kfold = NULL,
  plot.gbmperf = NULL,
  error.maxNR = NULL,
  max.iterNR = NULL,
  tune = NULL,
  n.boot = NULL,
  plot.boot = NULL,
  interactions = NULL
)

Arguments

Value

Nothing. Will stop if arguments are incorrect.

Description

Check arguments that are common to all types of outcome USed inside arg.checks()

Usage

arg.checks.common(
  fun,
  ps.method,
  minPS,
  maxPS,
  higher.y = NULL,
  abc = NULL,
  prop.cutoff = NULL,
  prop.multi = NULL,
  B = NULL,
  Kfold = NULL,
  plot.gbmperf = NULL,
  tree.depth = NULL,
  n.trees.boosting = NULL,
  error.maxNR = NULL,
  max.iterNR = NULL,
  tune = NULL,
  train.prop = NULL,
  cv.n = NULL,
  error.max = NULL,
  max.iter = NULL,
  n.boot = NULL,
  plot.boot = NULL
)

Arguments

Value

Nothing. Will stop if arguments are incorrect.

Description

Doubly robust estimator of the average treatment effect between two treatments, which is the rate ratio for count outcomes, the restricted mean time lost ratio for survival outcomes and the mean difference for continuous outcome. Bootstrap is used for inference.

Usage

atefit(
  response,
  data,
  cate.model,
  ps.model,
  ps.method = "glm",
  ipcw.model = NULL,
  ipcw.method = "breslow",
  minPS = 0.01,
  maxPS = 0.99,
  followup.time = NULL,
  tau0 = NULL,
  surv.min = 0.025,
  interactions = TRUE,
  n.boot = 500,
  seed = NULL,
  verbose = 0
)

Arguments

Details

For count response, see details in atefitcount(). For survival response, see details in atefitsurv().

Value

For count response, see description of outputs in atefitcount(). For survival response, see description of outputs in atefitsurv().

Examples

# Count outcome
output <- atefit(response = "count",
                 data = countExample,
                 cate.model = y ~ age + female + previous_treatment +
                              previous_cost + previous_number_relapses +
                              offset(log(years)),
                 ps.model = trt ~ age + previous_treatment,
                 n.boot = 50,
                 seed = 999)
output
plot(output)



# Survival outcome
tau0 <- with(survivalExample,
                 min(quantile(y[trt == "drug1"], 0.95), quantile(y[trt == "drug0"], 0.95)))

output2 <- atefit(response = "survival",
                  data = survivalExample,
                  cate.model = survival::Surv(y, d) ~ age + female +
                        previous_cost + previous_number_relapses,
                        ps.model = trt ~ age + previous_treatment,
                  tau0 = tau0,
                  seed = 999)
output2
plot(output2)

Description

Doubly robust estimator of the average treatment effect between two treatments, which is the rate ratio for count outcomes. Bootstrap is used for inference.

Usage

atefitcount(
  data,
  cate.model,
  ps.model,
  ps.method = "glm",
  minPS = 0.01,
  maxPS = 0.99,
  interactions = TRUE,
  n.boot = 500,
  seed = NULL,
  verbose = 0
)

Arguments

Details

This helper function estimates the average treatment effect (ATE) between two treatment groups in a given dataset. The ATE is estimated with a doubly robust estimator that accounts for imbalances in covariate distributions between the two treatment groups with inverse probability treatment weighting. For count outcomes, the estimated ATE is the estimated rate ratio between treatment 1 versus treatment 0.

Value

Return an item of the class atefit with the following elements:

• log.rate.ratio: A vector of numeric values of the estimated ATE (expressed as a log rate ratio of trt=1 over trt=0), the bootstrap standard error, the lower and upper limits of 95% confidence interval, and the p-value.

• rate0: A numeric value of the estimated rate in the group trt=0.

• rate1: A numeric value of the estimated rate in the group trt=1.

• trt.boot: Estimated log rate ratios in each bootstrap sample.

• warning: A warning message produced if the treatment variable was not coded as 0 or 1. The key to map the original coding of the variable to a 0-1 coding is displayed in the warning to facilitate the interpretation of the remaining of the output.

Examples

output <- atefitcount(data = countExample,
                      cate.model = y ~ age + female + previous_treatment +
                                   previous_cost + previous_number_relapses +
                                   offset(log(years)),
                      ps.model = trt ~ age + previous_treatment,
                      verbose = 1, n.boot = 50, seed = 999)
output
plot(output)

Description

Doubly robust estimator of the average treatment effect between two treatments, which is the rate ratio of treatment 1 over treatment 0 for count outcomes. Bootstrap is used for inference.

Usage

atefitmean(
  data,
  cate.model,
  ps.model,
  ps.method = "glm",
  minPS = 0.01,
  maxPS = 0.99,
  interactions = TRUE,
  n.boot = 500,
  plot.boot = FALSE,
  seed = NULL,
  verbose = 0
)

Arguments

Details

This helper function estimates the average treatment effect (ATE) between two treatment groups in a given dataset specified by y, trt, x.cate, x.ps, time. The ATE is estimated with a doubly robust estimator that accounts for imbalances in covariate distributions between the two treatment groups with inverse probability treatment weighting. For count outcomes, the estimated ATE is the estimated rate ratio between treatment 1 versus treatment 0. Both original and log-transformed ATEs are returned, as well as the rate in either treatment group. If inference = TRUE, the variability of the estimated rate ratio is also calculated using bootstrap. Additional variability outputs include standard error of the log rate ratio, 95% confidence interval of the rate ratio, p-value, and a histogram of the log rate ratio.

Value

Return a list of 8 elements:

• log.rate.ratio: A numeric value of the estimated log rate ratio.

• se.boot.log.rate.ratio: A numeric value of the bootstrap standard error of log rate ratio.

• rate.ratio: A numeric value of the estimated rate ratio.

• rate.ratio0: A numeric value of the estimated rate in the group trt=0.

• rate.ratio1: A numeric value of the estimated rate in the group trt=1.

• rate.ratio.CIl: A numeric value of the lower limit 95% bootstrap confidence interval for estimated rate ratio.

• rate.ratio.CIu: A numeric value of the upper limit 95% bootstrap confidence interval for estimated rate ratio.

• pvalue: A numeric value of the p-value derived from the bootstrapped values based on a Chi-squared distribution.

• warning: A warning message produced if the treatment variable was not coded as 0/1. The key to map the original coding of the variable to a 0/1 key is displayed in the warning to facilitate the interpretation of the remaining of the output.

• plot: If plot.boot is TRUE, a histogram displaying the distribution of the bootstrapped log rate ratios. The red vertical reference line in the histogram represents the estimated log rate ratio.

Examples

# This module is not implemented yet!

Description

Doubly robust estimator of the average treatment effect between two treatments, which is the restricted mean time lost ratio for survival outcomes. Bootstrap is used for inference.

Usage

atefitsurv(
  data,
  cate.model,
  ps.model,
  ps.method = "glm",
  ipcw.model = NULL,
  ipcw.method = "breslow",
  minPS = 0.01,
  maxPS = 0.99,
  followup.time = NULL,
  tau0 = NULL,
  surv.min = 0.025,
  n.boot = 500,
  seed = NULL,
  verbose = 0
)

Arguments

Details

This helper function estimates the average treatment effect (ATE) for survival data between two treatment groups in a given dataset. The ATE is estimated with a doubly robust estimator that accounts for imbalances in covariate distributions between the two treatment groups with inverse probability treatment and censoring weighting. For survival outcomes, the estimated ATE is the estimated by RMTL ratio between treatment 1 versus treatment 0. The log-transformed ATEs and log-transformed adjusted hazard ratios are returned, as well as the estimated RMST in either treatment group. The variability of the estimated RMTL ratio is calculated using bootstrap. Additional outputs include standard error of the log RMTL ratio, 95% confidence interval, p-value, and a histogram of the bootstrap estimates.

Value

Return an object of class atefit with 6 elements:

• rmst1: A vector of numeric values of the estimated RMST, bootstrap standard error, lower and upper limits of 95% confidence interval, and the p-value in the group trt=1.

• rmst0: A vector of numeric values of the estimated RMST, bootstrap standard error, lower and upper limits of 95% confidence interval, and the p-value in the group trt=0.

• log.rmtl.ratio: A vector of numeric values of the estimated log RMTL ratio of trt=1 over trt=0, bootstrap standard error, lower and upper limits of 95% confidence interval, and the p-value.

• log.hazard.ratio: A vector of numeric values of the estimated adjusted log hazard ratio of trt=1 over trt=0, bootstrap standard error, lower and upper limits of 95% confidence interval, and the p-value.

• trt.boot: Estimates of rmst1, rmst0, log.rmtl.ratio and log.hazard.ratio in each bootstrap sample.

• warning: A warning message produced if the treatment variable was not coded as 0/1. The key to map the original coding of the variable to a 0/1 key is displayed in the warning to facilitate the interpretation of the remaining of the output.

Examples

library(survival)
tau0 <- with(survivalExample,
             min(quantile(y[trt == "drug1"], 0.95), quantile(y[trt == "drug0"], 0.95)))

output <- atefitsurv(data = survivalExample,
                     cate.model = Surv(y, d) ~ age + female +
                                  previous_cost + previous_number_relapses,
                     ps.model = trt ~ age + previous_treatment,
                     tau0 = tau0,
                     n.boot = 50,
                     seed = 999,
                     verbose = 1)
output
plot(output)

Description

This function computes the area under the curve for two vectors where one corresponds to the x values and the other corresponds to the y values. It supports both linear and spline interpolation.

Usage

auc(
  x,
  y,
  from = min(x, na.rm = TRUE),
  to = max(x, na.rm = TRUE),
  type = c("linear", "spline"),
  subdivisions = 100,
  ...
)

Arguments

Value

A numeric value representing the area under the curve.

Description

Split the given dataset into balanced training and validation sets (within a pre-specified tolerance) Balanced means 1) The ratio of treated and controls is maintained in the training and validation sets 2) The covariate distributions are balanced between the training and validation sets

Usage

balance.split(
  y,
  trt,
  x.cate,
  x.ps,
  time,
  minPS = 0.01,
  maxPS = 0.99,
  train.prop = 3/4,
  error.max = 0.1,
  max.iter = 5000
)

Arguments

Value

A list of 10 objects, 5 training and 5 validation of y, trt, x.cate, x.ps, time: y.train - observed outcome in the training set; vector of size m (observations in the training set) trt.train - treatment received in the training set; vector of size m coded as 0/1 x.cate.train - baseline covariates for the outcome model in the training set; matrix of dimension m by p.cate x.ps.train - baseline covariates (plus intercept) for the propensity score model in the training set; matrix of dimension m by p.ps + 1 time.train - log-transformed person-years of follow-up in the training set; vector of size m y.valid - observed outcome in the validation set; vector of size n-m trt.valid - treatment received in the validation set; vector of size n-m coded as 0/1 x.cate.valid - baseline covariates for the outcome model in the validation set; matrix of dimension n-m by p.cate x.ps.valid - baseline covariates (plus intercept) for the propensity score model in the validation set; matrix of dimension n-m by p.ps + 1 time.valid - log-transformed person-years of follow-up in the validation set; vector of size n-m

Description

Split the given dataset into balanced training and validation sets (within a pre-specified tolerance) Balanced means 1) The ratio of treated and controls is maintained in the training and validation sets 2) The covariate distributions are balanced between the training and validation sets

Usage

balancemean.split(
  y,
  trt,
  x.cate,
  x.ps,
  minPS = 0.01,
  maxPS = 0.99,
  train.prop = 3/4,
  error.max = 0.1,
  max.iter = 5000
)

Arguments

Value

A list of 10 objects, 5 training and 5 validation of y, trt, x.cate, x.ps, time: y.train - observed outcome in the training set; vector of size m (observations in the training set) trt.train - treatment received in the training set; vector of size m coded as 0/1 x.cate.train - baseline covariates for the outcome model in the training set; matrix of dimension m by p.cate x.ps.train - baseline covariates (plus intercept) for the propensity score model in the training set; matrix of dimension m by p.ps + 1 y.valid - observed outcome in the validation set; vector of size n-m trt.valid - treatment received in the validation set; vector of size n-m coded as 0/1 x.cate.valid - baseline covariates for the outcome model in the validation set; matrix of dimension n-m by p.cate x.ps.valid - baseline covariates (plus intercept) for the propensity score model in the validation set; matrix of dimension n-m by p.ps + 1 bestid.valid - id for the validation set by the best split; vector of size n-m

Description

Split the given time-to-event dataset into balanced training and validation sets (within a pre-specified tolerance) Balanced means 1) The ratio of treated and controls is maintained in the training and validation sets 2) The covariate distributions are balanced between the training and validation sets

Usage

balancesurv.split(
  y,
  d,
  trt,
  x.cate,
  x.ps,
  x.ipcw,
  yf = NULL,
  train.prop = 3/4,
  error.max = 0.1,
  max.iter = 5000
)

Arguments

Value

A list of 14 objects, 7training and 7 validation of y, trt, x.cate, x.ps, x.ipcw, time, yf: y.train - observed survival or censoring time in the training set; vector of size m (observations in the training set) d.train - event indicator in the training set; vector of size m coded as 0/1 trt.train - treatment received in the training set; vector of size m coded as 0/1 x.cate.train - baseline covariates for the outcome model in the training set; matrix of dimension m by p.cate x.ps.train - baseline covariates (plus intercept) for the propensity score model in the training set; matrix of dimension m by p.ps + 1 x.ipcw.train - baseline covariates for inverse probability of censoring in the training set; matrix of dimension m by p.ipw yf.train - follow-up time in the training set; if known, vector of size m; if unknown, yf == NULL y.valid - observed survival or censoring time in the validation set; vector of size n-m d.valid - event indicator in the validation set; vector of size n-m coded as 0/1 trt.valid - treatment received in the validation set; vector of size n-m coded as 0/1 x.cate.valid - baseline covariates for the outcome model in the validation set; matrix of dimension n-m by p.cate x.ps.valid - baseline covariates (plus intercept) for the propensity score model in the validation set; matrix of dimension n-m by p.ps + 1 x.ipcw.valid - baseline covariates for inverse probability of censoring in the validation set; matrix of dimension n-m by p.ipw yf.valid - follow-up time in the training set; if known, vector of size n-m; if unknown, yf == NULL

Description

Provides box plots which depict distributions of estimated ATEs for each multi-category subgroup in the validation set across all cross-validation iterations. The subgroups are mutually exclusive and are categorized by the CATE score percentiles (prop.multi specified in catecv() or catecvmean()). Box plots of mutually exclusive subgroups are constructed separately by scoring method specified in catecv(). This should be run only after results of catecv() or catecvmean()) have been obtained.

Usage

## S3 method for class 'precmed'
boxplot(
  x,
  ylab = NULL,
  plot.hr = FALSE,
  title = waiver(),
  theme = theme_classic(),
  ...
)

Arguments

Details

boxplot() takes in outputs from catecv() and generates the box plots of estimated ATEs for multi-category subgroups of the validation set. The box plots together with the overall ATE reference line can help compare the scoring methods' ability to distinguish subgroups of patients with different treatment effects.

For a given scoring method, box plots showing increasing or decreasing trends across the multi-category subgroups indicate presence of treatment effect heterogeneity (and the ability of the scoring method to capture it). On the contrary, box plots which are relatively aligned across the multi-category subgroups indicate absence of treatment effect heterogeneity (or the inability of the scoring method to capture it).

Value

Returns sets of box plots, one set for each scoring method, over each of the multi-category subgroups. A gray horizontal dashed line of the overall ATE is included as a reference.

References

Yadlowsky, S., Pellegrini, F., Lionetto, F., Braune, S., & Tian, L. (2020). Estimation and validation of ratio-based conditional average treatment effects using observational data. Journal of the American Statistical Association, 1-18. DOI: 10.1080/01621459.2020.1772080.

See Also

plot and abc() for "precmed" objects.

Examples

# Count outcome
eval_1 <- catecv(response = "count",
                 data = countExample,
                 score.method = "poisson",
                 cate.model = y ~ age + female + previous_treatment +
                                  previous_cost + previous_number_relapses +
                                  offset(log(years)),
                 ps.model = trt ~ age + previous_treatment,
                 higher.y = FALSE,
                 cv.n = 5)

boxplot(eval_1, ylab = "Rate ratio of drug1 vs drug0 in each subgroup")

# Survival outcome
library(survival)
tau0 <- with(survivalExample,
             min(quantile(y[trt == "drug1"], 0.95), quantile(y[trt == "drug0"], 0.95)))
eval_2 <- catecv(response = "survival",
                 data = survivalExample,
                 score.method = c("poisson", "randomForest"),
                 cate.model = Surv(y, d) ~ age + female + previous_cost +
                                           previous_number_relapses,
                 ps.model = trt ~ age + previous_treatment,
                 initial.predictor.method = "randomForest",
                 ipcw.model = ~ age + previous_cost + previous_treatment,
                 tau0 = tau0,
                 higher.y = TRUE,
                 cv.n = 5,
                 seed = 999)

boxplot(eval_2, ylab = "RMTL ratio of drug1 vs drug0 in each subgroup")

Description

Provides (doubly robust) estimation of the average treatment effect (ATE) for count, survival or continuous outcomes in nested and mutually exclusive subgroups of patients defined by an estimated conditional average treatment effect (CATE) score via cross-validation (CV).

Usage

catecv(
  response,
  data,
  score.method,
  cate.model,
  ps.model,
  ps.method = "glm",
  init.model = NULL,
  initial.predictor.method = NULL,
  ipcw.model = NULL,
  ipcw.method = "breslow",
  minPS = 0.01,
  maxPS = 0.99,
  followup.time = NULL,
  tau0 = NULL,
  higher.y = TRUE,
  prop.cutoff = seq(0.5, 1, length = 6),
  prop.multi = c(0, 1/3, 2/3, 1),
  abc = TRUE,
  train.prop = 3/4,
  cv.n = 10,
  error.max = 0.1,
  max.iter = 5000,
  surv.min = 0.025,
  xvar.smooth.score = NULL,
  xvar.smooth.init = NULL,
  tree.depth = 2,
  n.trees.rf = 1000,
  n.trees.boosting = 200,
  B = 3,
  Kfold = 5,
  error.maxNR = 0.001,
  max.iterNR = 150,
  tune = c(0.5, 2),
  seed = NULL,
  plot.gbmperf = TRUE,
  verbose = 0
)

Arguments

Details

For count response, see details in catecvcount(). For survival response, see details in catecvsurv(). For continuous response, see details in catecvmean().

Value

For count response, see description of outputs in catecvcount(). For survival response, see description of outputs in catecvsurv(). For continuous response, see description of outputs in catecvmean().

References

Yadlowsky, S., Pellegrini, F., Lionetto, F., Braune, S., & Tian, L. (2020). Estimation and validation of ratio-based conditional average treatment effects using observational data. Journal of the American Statistical Association, 1-18. DOI: 10.1080/01621459.2020.1772080.

See Also

catefit() function and boxplot(), abc methods for "precmed" objects.

Examples

cate_1 <- catecv(response = "count",
                 data = countExample,
                 score.method = "poisson",
                 cate.model = y ~ age + female + previous_treatment +
                              previous_cost + previous_number_relapses +
                              offset(log(years)),
                 ps.model = trt ~ age + previous_treatment,
                 higher.y = FALSE, cv.n = 5, seed = 999, verbose = 1)

plot(cate_1, ylab = "RMTL ratio of drug1 vs drug0 in each subgroup")
boxplot(cate_1, ylab = "RMTL ratio of drug1 vs drug0 in each subgroup")
abc(cate_1)

# Survival outcome
library(survival)
tau0 <- with(survivalExample,
             min(quantile(y[trt == "drug1"], 0.95), quantile(y[trt == "drug0"], 0.95)))

cate_2 <- catecv(response = "survival",
                 data = survivalExample,
                 score.method = c("poisson", "randomForest"),
                 cate.model = Surv(y, d) ~ age + female + previous_cost +
                              previous_number_relapses,
                 ps.model = trt ~ age + previous_treatment,
                 initial.predictor.method = "randomForest",
                 ipcw.model = ~ age + previous_cost + previous_treatment,
                 tau0 = tau0,
                 higher.y = TRUE,
                 surv.min = 0.025,
                 cv.n = 5,
                 seed = 999)

plot(cate_2, ylab = "RMTL ratio of drug1 vs drug0 in each subgroup")
boxplot(cate_2, ylab = "RMTL ratio of drug1 vs drug0 in each subgroup")
abc(cate_2)

Description

Provides doubly robust estimation of the average treatment effect (ATE) in nested and mutually exclusive subgroups of patients defined by an estimated conditional average treatment effect (CATE) score via cross-validation (CV). The CATE score can be estimated with up to 5 methods among the following: Poisson regression, boosting, two regressions, contrast regression, and negative binomial (see score.method).

Usage

catecvcount(
  data,
  score.method,
  cate.model,
  ps.model,
  ps.method = "glm",
  initial.predictor.method = "boosting",
  minPS = 0.01,
  maxPS = 0.99,
  higher.y = TRUE,
  prop.cutoff = seq(0.5, 1, length = 6),
  prop.multi = c(0, 1/3, 2/3, 1),
  abc = TRUE,
  train.prop = 3/4,
  cv.n = 10,
  error.max = 0.1,
  max.iter = 5000,
  xvar.smooth = NULL,
  tree.depth = 2,
  n.trees.boosting = 200,
  B = 3,
  Kfold = 5,
  error.maxNR = 0.001,
  max.iterNR = 150,
  tune = c(0.5, 2),
  seed = NULL,
  plot.gbmperf = TRUE,
  verbose = 0,
  ...
)

Arguments

Details

The CATE score represents an individual-level treatment effect expressed as a rate ratio for count outcomes. It can be estimated with boosting, Poisson regression, negative binomial regression, and the doubly robust estimator two regressions (Yadlowsky, 2020) applied separately by treatment group or with the other doubly robust estimator contrast regression (Yadlowsky, 2020) applied to the entire data set.

Internal CV is applied to reduce optimism in choosing the CATE estimation method that captures the most treatment effect heterogeneity. The CV is applied by repeating the following steps cv.n times:

1. Split the data into a training and validation set according to train.prop. The training and validation sets must be balanced with respect to covariate distributions and doubly robust rate ratio estimates (see error.max).

2. Estimate the CATE score in the training set with the specified scoring method.

3. Predict the CATE score in the validation set using the scoring model fitted from the training set.

4. Build nested subgroups of treatment responders in the training and validation sets, separately, and estimate the ATE within each nested subgroup. For each element i of prop.cutoff (e.g., prop.cutoff[i] = 0.6), take the following steps:

   1. Identify high responders as observations with the 60% (i.e., prop.cutoff[i]x100%) highest (if higher.y = TRUE) or lowest (if higher.y = FALSE) estimated CATE scores.

   2. Estimate the ATE in the subgroup of high responders using a doubly robust estimator.

   3. Conversely, identify low responders as observations with the 40% (i.e., 1 - prop.cutoff[i]x100%) lowest (if higher.y = TRUE) or highest (if higher.y = FALSE) estimated CATE scores.

   4. Estimate the ATE in the subgroup of low responders using a doubly robust estimator.

5. If abc = TRUE, calculate the area between the ATE and the series of ATEs in nested subgroups of high responders in the validation set.

6. Build mutually exclusive subgroups of treatment responders in the training and validation sets, separately, and estimate the ATE within each subgroup. Mutually exclusive subgroups are built by splitting the estimated CATE scores according to prop.multi.

Value

Returns a list containing the following components saved as a "precmed" object:

• ate.poisson: A list of results output if score.method includes 'poisson':

  • ate.est.train.high.cv: A matrix of numerical values with length(prop.cutoff) rows and cv.n columns. The ith row/jth column cell contains the estimated ATE in the nested subgroup of high responders defined by CATE score above (if higher.y = TRUE) or below (if higher.y = FALSE) the prop.cutoff[i]x100% percentile of the estimated CATE score in the training set in the jth cross-validation iteration.

  • ate.est.train.low.cv: A matrix of numerical values with length(prop.cutoff) - 1 rows and cv.n columns. The ith row/jth column cell contains the estimated ATE in the nested subgroup of low responders defined by CATE score below (if higher.y = TRUE) or above (if higher.y = FALSE) the prop.cutoff[i]x100% percentile of the estimated CATE score in the training set in the jth cross-validation iteration.

  • ate.est.valid.high.cv: Same as ate.est.train.high.cv, but in the validation set.

  • ate.est.valid.low.cv: Same as ate.est.train.low.cv, but in the validation set.

  • ate.est.train.group.cv: A matrix of numerical values with length(prop.multi) - 1 rows and cv.n columns. The jth column contains the estimated ATE in length(prop.multi) - 1 mutually exclusive subgroups defined by prop.multi in the training set in jth cross-validation iteration.

  • ate.est.valid.group.cv: Same as ate.est.train.group.cv, but in the validation set.

  • abc.valid: A vector of numerical values of length cv.n. The ith element returns the ABC of the validation curve in the ith cross-validation iteration. Only returned if abc = TRUE.

• ate.boosting: A list of results similar to ate.poisson output if score.method includes 'boosting'.

• ate.twoReg: A list of results similar to ate.poisson output if score.method includes 'twoReg'.

• ate.contrastReg: A list of results similar to ate.poisson output if score.method includes 'contrastReg'. This method has an additional element in the list of results:

  • converge.contrastReg.cv: A vector of logical value of length cv.n. The ith element indicates whether the algorithm converged in the ith cross-validation iteration.

• ate.negBin: A list of results similar to ate.poisson output if score.method includes 'negBin'.

• props: A list of 3 elements:

  • prop.onlyhigh: The original argument prop.cutoff, reformatted as necessary.

  • prop.bi: The original argument prop.cutoff, similar to prop.onlyhigh but reformatted to exclude 1.

  • prop.multi: The original argument prop.multi, reformatted as necessary to include 0 and 1.

• overall.ate.valid: A vector of numerical values of length cv.n. The ith element contains the ATE in the validation set of the ith cross-validation iteration, estimated with the doubly robust estimator.

• overall.ate.train: A vector of numerical values of length cv.n. The ith element contains the ATE in the training set of the ith cross-validation iteration, estimated with the doubly robust estimator.

• fgam: The formula used in GAM if initial.predictor.method = 'gam'.

• higher.y: The original higher.y argument.

• abc: The original abc argument.

• cv.n: The original cv.n argument.

• response: The type of response. Always 'count' for this function.

• formulas:A list of 3 elements: (1) cate.model argument, (2) ps.model argument and (3) original labels of the left-hand side variable in ps.model (treatment) if it was not 0/1.

References

Yadlowsky, S., Pellegrini, F., Lionetto, F., Braune, S., & Tian, L. (2020). Estimation and validation of ratio-based conditional average treatment effects using observational data. Journal of the American Statistical Association, 1-18.. DOI: 10.1080/01621459.2020.1772080.

See Also

plot.precmed(), boxplot.precmed(), abc() methods for "precmed" objects, and catefitcount() function.

Examples

catecv <- catecvcount(data = countExample,
                      score.method = "poisson",
                      cate.model = y ~ age + female + previous_treatment +
                                   previous_cost + previous_number_relapses +
                                   offset(log(years)),
                      ps.model = trt ~ age + previous_treatment,
                      higher.y = FALSE,
                      cv.n = 5,
                      seed = 999,
                      plot.gbmperf = FALSE,
                      verbose = 1)

plot(catecv, ylab = "Rate ratio of drug1 vs drug0 in each subgroup")
boxplot(catecv, ylab = "Rate ratio of drug1 vs drug0 in each subgroup")
abc(catecv)

Description

Provides doubly robust estimation of the average treatment effect (ATE) in nested and mutually exclusive subgroups of patients defined by an estimated conditional average treatment effect (CATE) score via cross-validation (CV). The CATE score can be estimated with up to 6 methods among the following: Linear regression, boosting, two regressions, contrast regression, random forest and generalized additive model (see score.method).

Usage

catecvmean(
  data,
  score.method,
  cate.model,
  ps.model,
  ps.method = "glm",
  init.model = NULL,
  initial.predictor.method = "boosting",
  minPS = 0.01,
  maxPS = 0.99,
  higher.y = TRUE,
  prop.cutoff = seq(0.5, 1, length = 6),
  prop.multi = c(0, 1/3, 2/3, 1),
  abc = TRUE,
  train.prop = 3/4,
  cv.n = 10,
  error.max = 0.1,
  max.iter = 5000,
  xvar.smooth.score = NULL,
  xvar.smooth.init = NULL,
  tree.depth = 2,
  n.trees.rf = 1000,
  n.trees.boosting = 200,
  B = 3,
  Kfold = 6,
  plot.gbmperf = TRUE,
  error.maxNR = 0.001,
  tune = c(0.5, 2),
  seed = NULL,
  verbose = 0,
  ...
)

Arguments

Details

The CATE score represents an individual-level treatment effect for continuous data, estimated with boosting, linear regression, random forest, generalized additive model and the doubly robust estimator (two regressions, Yadlowsky, 2020) applied separately by treatment group or with the other doubly robust estimators (contrast regression, Yadlowsky, 2020) applied to the entire data set.

Internal CV is applied to reduce optimism in choosing the CATE estimation method that captures the most treatment effect heterogeneity. The CV is applied by repeating the following steps cv.n times:

1. Split the data into a training and validation set according to train.prop. The training and validation sets must be balanced with respect to covariate distributions and doubly robust rate ratio estimates (see error.max).

2. Estimate the CATE score in the training set with the specified scoring method.

3. Predict the CATE score in the validation set using the scoring model fitted from the training set.

4. Build nested subgroups of treatment responders in the training and validation sets, separately, and estimate the ATE within each nested subgroup. For each element i of prop.cutoff (e.g., prop.cutoff[i] = 0.6), take the following steps:

   1. Identify high responders as observations with the 60% (i.e., prop.cutoff[i]x100%) highest (if higher.y = TRUE) or lowest (if higher.y = FALSE) estimated CATE scores.

   2. Estimate the ATE in the subgroup of high responders using a doubly robust estimator.

   3. Conversely, identify low responders as observations with the 40% (i.e., 1 - prop.cutoff[i]x100%) lowest (if higher.y = TRUE) or highest (if higher.y = FALSE) estimated CATE scores.

   4. Estimate the ATE in the subgroup of low responders using a doubly robust estimator.

5. Build mutually exclusive subgroups of treatment responders in the training and validation sets, separately, and estimate the ATE within each subgroup. Mutually exclusive subgroups are built by splitting the estimated CATE scores according to prop.multi.

6. If abc = TRUE, calculate the area between the ATE and the series of ATEs in nested subgroups of high responders in the validation set.

Value

Returns a list containing the following components saved as a "precmed" object:

• ate.gaussian: A list of results output if score.method includes 'gaussian':

  • ate.est.train.high.cv: A matrix of numerical values with length(prop.cutoff) rows and cv.n columns. The ith column/jth row cell contains the estimated ATE in the nested subgroup of high responders defined by CATE score above (if higher.y = TRUE) or below (if higher.y = FALSE) the prop.cutoff[j]x100% percentile of the estimated CATE score in the training set in the ith cross-validation iteration.

  • ate.est.train.low.cv: A matrix of numerical values with length(prop.cutoff) - 1 rows and cv.n columns. The ith column/jth row cell contains the estimated ATE in the nested subgroup of low responders defined by CATE score below (if higher.y = TRUE) or above (if higher.y = FALSE) the prop.cutoff[j]x100% percentile of the estimated CATE score in the training set in the ith cross-validation iteration.

  • ate.est.valid.high.cv: Same as ate.est.train.high.cv, but in the validation set.

  • ate.est.valid.low.cv: Same as ate.est.train.low.cv, but in the validation set.

  • ate.est.train.group.cv: A matrix of numerical values with length(prop.multi) - 1 rows and cv.n columns. The ith column contains the estimated ATE in length(prop.multi) - 1 mutually exclusive subgroups defined by prop.multi in the training set in ith cross-validation iteration.

  • ate.est.valid.group.cv: Same as ate.est.train.group.cv, but in the validation set.

  • abc.valid: A vector of numerical values of length cv.n, The ith element returns the ABC of the validation curve in the ith cross-validation iteration. Only returned if abc = TRUE.

• ate.boosting: A list of results similar to ate.gaussian output if score.method includes 'boosting'.

• ate.twoReg: A list of results similar to ate.gaussian output if score.method includes 'twoReg'.

• ate.contrastReg: A list of results similar to ate.gaussian output if score.method includes 'contrastReg'.

• ate.randomForest: A list of ATE output measured by the RMTL ratio if score.method includes 'randomForest':

• ate.gam: A list of results similar to ate.gaussian output if score.method includes 'gam'.

• props: A list of 3 elements:

  • prop.onlyhigh: The original argument prop.cutoff, reformatted as necessary.

  • prop.bi: The original argument prop.cutoff, similar to prop.onlyhigh but reformatted to exclude 1.

  • prop.multi: The original argument prop.multi, reformatted as necessary.

• overall.ate.train: A vector of numerical values of length cv.n. The ith element contains the ATE in the training set of the ith cross-validation iteration, estimated with the doubly robust estimator.

• overall.ate.valid: A vector of numerical values of length cv.n. The ith element contains the ATE in the validation set of the ith cross-validation iteration, estimated with the doubly robust estimator.

• higher.y: The original higher.y argument.

• abc: The original abc argument.

• cv.n: The original cv.n argument.

• response: The type of response. Always 'continuous' for this function.

• formulas:A list of 3 elements: (1) cate.model argument, (2) ps.model argument and (3) original labels of the left-hand side variable in ps.model (treatment) if it was not 0/1.

References

Yadlowsky, S., Pellegrini, F., Lionetto, F., Braune, S., & Tian, L. (2020). Estimation and validation of ratio-based conditional average treatment effects using observational data. Journal of the American Statistical Association, 1-18. DOI: 10.1080/01621459.2020.1772080.

See Also

plot.precmed(), boxplot.precmed(), abc() methods for "precmed" objects, and catefitmean() function.

Examples

# Not implemented yet!

Description

Provides doubly robust estimation of the average treatment effect (ATE) by the RMTL (restricted mean time lost) ratio in nested and mutually exclusive subgroups of patients defined by an estimated conditional average treatment effect (CATE) score via cross-validation (CV). The CATE score can be estimated with up to 5 methods among the following: Random forest, boosting, poisson regression, two regressions, and contrast regression (see score.method).

Usage

catecvsurv(
  data,
  score.method,
  cate.model,
  ps.model,
  ps.method = "glm",
  initial.predictor.method = "randomForest",
  ipcw.model = NULL,
  ipcw.method = "breslow",
  minPS = 0.01,
  maxPS = 0.99,
  followup.time = NULL,
  tau0 = NULL,
  higher.y = TRUE,
  prop.cutoff = seq(0.5, 1, length = 6),
  prop.multi = c(0, 1/3, 2/3, 1),
  abc = TRUE,
  train.prop = 3/4,
  cv.n = 10,
  error.max = 0.1,
  max.iter = 5000,
  surv.min = 0.025,
  tree.depth = 2,
  n.trees.rf = 1000,
  n.trees.boosting = 200,
  B = 3,
  Kfold = 5,
  error.maxNR = 0.001,
  max.iterNR = 150,
  tune = c(0.5, 2),
  seed = NULL,
  plot.gbmperf = TRUE,
  verbose = 0
)

Arguments

Details

The CATE score represents an individual-level treatment effect expressed as the restricted mean survival time (RMTL) ratio) for survival outcomes. It can be estimated with boosting, Poisson regression, random forest, and the doubly robust estimator two regressions (Yadlowsky, 2020) applied separately by treatment group or with the other doubly robust estimator contrast regression (Yadlowsky, 2020) applied to the entire data set.

Internal CV is applied to reduce optimism in choosing the CATE estimation method that captures the most treatment effect heterogeneity. The CV is applied by repeating the following steps cv.n times:

1. Split the data into a training and validation set according to train.prop. The training and validation sets must be balanced with respect to covariate distributions and doubly robust RMTL ratio estimates (see error.max).

2. Estimate the CATE score in the training set with the specified scoring method.

3. Predict the CATE score in the validation set using the scoring model fitted from the training set.

4. Build nested subgroups of treatment responders in the training and validation sets, separately, and estimate the ATE within each nested subgroup. For each element i of prop.cutoff (e.g., prop.cutoff[i] = 0.6), take the following steps:

   1. Identify high responders as observations with the 60% (i.e., prop.cutoff[i]x100%) highest (if higher.y = FALSE) or lowest (if higher.y = TRUE) estimated CATE scores.

   2. Estimate the ATE in the subgroup of high responders using a doubly robust estimator.

   3. Conversely, identify low responders as observations with the 40% (i.e., 1 - prop.cutoff[i]x100%) lowest (if higher.y = FALSE) or highest (if higher.y = TRUE) estimated CATE scores.

   4. Estimate the ATE in the subgroup of low responders using a doubly robust estimator.

5. If abc = TRUE, calculate the area between the ATE and the series of ATEs in nested subgroups of high responders in the validation set.

6. Build mutually exclusive subgroups of treatment responders in the training and validation sets, separately, and estimate the ATE within each subgroup. Mutually exclusive subgroups are built by splitting the estimated CATE scores according to prop.multi.

Value

Returns a list containing the following components saved as a "precmed" object:

• ate.randomForest: A list of ATE output measured by the RMTL ratio if score.method includes 'randomForest':

  • ate.est.train.high.cv: A matrix of numerical values with length(prop.cutoff) rows and cv.n columns. The ith column/jth row cell contains the estimated ATE in the nested subgroup of high responders defined by CATE score above (if higher.y = FALSE) or below (if higher.y = TRUE) the prop.cutoff[j]x100% percentile of the estimated CATE score in the training set in the ith cross-validation iteration.

  • ate.est.train.low.cv: A matrix of numerical values with length(prop.cutoff) - 1 rows and cv.n columns. TThe ith column/jth row cell contains the estimated ATE in the nested subgroup of low responders defined by CATE score below (if higher.y = FALSE) or above (if higher.y = TRUE) the prop.cutoff[j]x100% percentile of the estimated CATE score in the training set in the ith cross-validation iteration.

  • ate.est.valid.high.cv: Same as ate.est.train.high.cv, but in the validation set.

  • ate.est.valid.low.cv: Same as ate.est.train.low.cv, but in the validation set.

  • ate.est.train.group.cv: A matrix of numerical values with length(prop.multi) - 1 rows and cv.n columns. The ith column contains the estimated ATE in length(prop.multi) - 1 mutually exclusive subgroups defined by prop.multi in the training set in ith cross-validation iteration.

  • ate.est.valid.group.cv: Same as ate.est.train.group.cv, but in the validation set.

  • abc.valid: A vector of numerical values of length cv.n, The ith element returns the ABC of the validation curve in the ith cross-validation iteration. Only returned if abc = TRUE.

• ate.boosting: A list of results similar to ate.randomForest output if score.method includes 'boosting'.

• ate.poisson: A list of results similar to ate.randomForest output if score.method includes 'poisson'.

• ate.twoReg: A list of results similar to ate.randomForest output if score.method includes 'twoReg'.

• ate.contrastReg: A list of results similar to ate.randomForest output if score.method includes 'contrastReg'. This method has an additional element in the list of results:

  • converge.contrastReg.cv: A vector of logical value of length cv.n. The ith element indicates whether the algorithm converged in the ith cross-validation iteration.

• hr.randomForest: A list of adjusted hazard ratio if score.method includes 'randomForest':

  • hr.est.train.high.cv: A matrix of numerical values with length(prop.cutoff) rows and cv.n columns. The ith column/jth row cell contains the estimated HR in the nested subgroup of high responders defined by CATE score above (if higher.y = FALSE) or below (if higher.y = TRUE) the prop.cutoff[j]x100% percentile of the estimated CATE score in the training set in the ith cross-validation iteration.

  • hr.est.train.low.cv: A matrix of numerical values with length(prop.cutoff) - 1 rows and cv.n columns. TThe ith column/jth row cell contains the estimated HR in the nested subgroup of low responders defined by CATE score below (if higher.y = FALSE) or above (if higher.y = TRUE) the prop.cutoff[j]x100% percentile of the estimated CATE score in the training set in the ith cross-validation iteration.

  • hr.est.valid.high.cv: Same as hr.est.train.high.cv, but in the validation set.

  • hr.est.valid.low.cv: Same as hr.est.train.low.cv, but in the validation set.

  • hr.est.train.group.cv: A matrix of numerical values with length(prop.multi) - 1 rows and cv.n columns. The ith column contains the estimated HR in length(prop.multi) - 1 mutually exclusive subgroups defined by prop.multi in the training set in ith cross-validation iteration.

  • hr.est.valid.group.cv: Same as hr.est.train.group.cv, but in the validation set.

• hr.boosting: A list of results similar to hr.randomForest output if score.method includes 'boosting'.

• hr.poisson: A list of results similar to hr.randomForest output if score.method includes 'poisson'.

• hr.twoReg: A list of results similar to hr.randomForest output if score.method includes 'twoReg'.

• hr.contrastReg: A list of results similar to hr.randomForest output if score.method includes 'contrastReg'.

• props: A list of 3 elements:

  • prop.onlyhigh: The original argument prop.cutoff, reformatted as necessary.

  • prop.bi: The original argument prop.cutoff, similar to prop.onlyhigh but reformatted to exclude 1.

  • prop.multi: The original argument prop.multi, reformatted as necessary to include 0 and 1.

• overall.ate.train: A vector of numerical values of length cv.n. The ith element contains the ATE (RMTL ratio) in the training set of the ith cross-validation iteration, estimated with the doubly robust estimator.

• overall.hr.train: A vector of numerical values of length cv.n. The ith element contains the ATE (HR) in the training set of the ith cross-validation iteration.

• overall.ate.valid: A vector of numerical values of length cv.n. The ith element contains the ATE (RMTL ratio) in the validation set of the ith cross-validation iteration, estimated with the doubly robust estimator.

• overall.hr.valid: A vector of numerical values of length cv.n. The ith element contains the ATE (HR) in the validation set of the ith cross-validation iteration.

• errors/warnings: A nested list of errors and warnings that were wrapped during the calculation of ATE. Errors and warnings are organized by score.method and position in the CV flow.

• higher.y: The original higher.y argument.

• abc: The original abc argument.

• cv.n: The original cv.n argument.

• response: The type of response. Always 'survival' for this function.

• formulas:A list of 3 elements: (1) cate.model argument, (2) ps.model argument and (3) original labels of the left-hand side variable in ps.model (treatment) if it was not 0/1.

References

Yadlowsky, S., Pellegrini, F., Lionetto, F., Braune, S., & Tian, L. (2020). Estimation and validation of ratio-based conditional average treatment effects using observational data. Journal of the American Statistical Association, 1-18.. DOI: 10.1080/01621459.2020.1772080.

See Also

catefitsurv() function and boxplot(), abc methods for "precmed" objects.

Examples

library(survival)

tau0 <- with(survivalExample,
             min(quantile(y[trt == "drug1"], 0.95), quantile(y[trt == "drug0"], 0.95)))

catecv <- catecvsurv(data = survivalExample,
                     score.method = "poisson",
                     cate.model = Surv(y, d) ~ age + female + previous_cost +
                                               previous_number_relapses,
                     ps.model = trt ~ age + previous_treatment,
                     initial.predictor.method = "logistic",
                     ipcw.model = ~ age + previous_cost + previous_treatment,
                     tau0 = tau0,
                     higher.y = TRUE,
                     cv.n = 5, seed = 999, verbose = 1)

# Try:
plot(catecv, ylab = "RMTL ratio of drug1 vs drug0 in each subgroup")
boxplot(catecv, ylab = "RMTL ratio of drug1 vs drug0 in each subgroup")
abc(catecv)

Description

Provides singly robust and doubly robust estimation of CATE score for count, survival and continuous data with up the following scoring methods among the following: Random forest (survival, continuous only), boosting, poisson regression (count, survival only), two regressions, contrast regression, negative binomial regression (count only), linear regression (continuous only), and generalized additive model (continuous only).

Usage

catefit(
  response,
  data,
  score.method,
  cate.model,
  ps.model,
  ps.method = "glm",
  init.model = NULL,
  initial.predictor.method = NULL,
  ipcw.model = NULL,
  ipcw.method = "breslow",
  minPS = 0.01,
  maxPS = 0.99,
  followup.time = NULL,
  tau0 = NULL,
  higher.y = TRUE,
  prop.cutoff = seq(0.5, 1, length = 6),
  surv.min = 0.025,
  xvar.smooth.score = NULL,
  xvar.smooth.init = NULL,
  tree.depth = 2,
  n.trees.rf = 1000,
  n.trees.boosting = 200,
  B = 3,
  Kfold = 5,
  error.maxNR = 0.001,
  max.iterNR = 150,
  tune = c(0.5, 2),
  seed = NULL,
  plot.gbmperf = TRUE,
  verbose = 0,
  ...
)

Arguments

Details

For count response, see details in catefitcount(). For survival response, see details in catefitsurv().

Value

For count response, see description of outputs in catefitcount(). For survival response, see description of outputs in catefitsurv().

References

Yadlowsky, S., Pellegrini, F., Lionetto, F., Braune, S., & Tian, L. (2020). Estimation and validation of ratio-based conditional average treatment effects using observational data. Journal of the American Statistical Association, 1-18. DOI: 10.1080/01621459.2020.1772080.

See Also

catecv()

Examples

# Count outcome
fit_1 <- catefit(response = "count",
                 data = countExample,
                 score.method = "poisson",
                 cate.model = y ~ age + female + previous_treatment +
                                  previous_cost + previous_number_relapses +
                                  offset(log(years)),
                 ps.model = trt ~ age + previous_treatment,
                 higher.y = TRUE,
                 seed = 999)

coef(fit_1)


# Survival outcome
library(survival)
tau0 <- with(survivalExample,
                 min(quantile(y[trt == "drug1"], 0.95), quantile(y[trt == "drug0"], 0.95)))

fit_2 <- catefit(response = "survival",
                 data = survivalExample,
                 score.method = c("poisson", "boosting", "randomForest"),
                 cate.model = Surv(y, d) ~ age + female + previous_cost +
                                           previous_number_relapses,
                 ps.model = trt ~ age + previous_treatment,
                 initial.predictor.method = "logistic",
                 ipcw.model = ~ age + previous_cost + previous_treatment,
                 tau0 = tau0, higher.y = TRUE, seed = 999, n.cores = 1)

coef(fit_2)

Description

Provides singly robust and doubly robust estimation of CATE score with up to 5 scoring methods among the following: Poisson regression, boosting, two regressions, contrast regression, and negative binomial.

Usage

catefitcount(
  data,
  score.method,
  cate.model,
  ps.model,
  ps.method = "glm",
  initial.predictor.method = "boosting",
  minPS = 0.01,
  maxPS = 0.99,
  higher.y = TRUE,
  prop.cutoff = seq(0.5, 1, length = 6),
  xvar.smooth = NULL,
  tree.depth = 2,
  n.trees.boosting = 200,
  B = 3,
  Kfold = 5,
  error.maxNR = 0.001,
  max.iterNR = 150,
  tune = c(0.5, 2),
  seed = NULL,
  plot.gbmperf = FALSE,
  verbose = 0,
  ...
)

Arguments

Details

The CATE score represents an individual-level treatment effect, estimated with either Poisson regression, boosting or negative binomial regression applied separately by treatment group or with two doubly robust estimators, two regressions and contrast regression (Yadlowsky, 2020) applied to the entire dataset.

catefitcount() provides the coefficients of the CATE score for each scoring method requested through score.method. Currently, contrast regression is the only method which allows for inference of the CATE coefficients by providing standard errors of the coefficients. The coefficients can be used to learn the effect size of each variable and predict the CATE score for a new observation.

catefitcount() also provides the predicted CATE score of each observation in the data set, for each scoring method. The predictions allow ranking the observations from potentially high responders to the treatment to potentially low or standard responders.

The estimated ATE among nested subgroups of high responders are also provided by scoring method. Note that the ATEs in catefitcount() are derived based on the CATE score which is estimated using the same data sample. Therefore, overfitting may be an issue. catecvcount() is more suitable to inspect the estimated ATEs across scoring methods as it implements internal cross validation to reduce optimism.

Value

Returns a list containing the following components:

• ate.poisson: A vector of numerical values of length prop.cutoff containing the estimated ATE in nested subgroups (defined by prop.cutoff) constructed based on the estimated CATE scores with poisson regression. Only provided if score.method includes 'poisson'.

• ate.boosting: Same as ate.poisson, but with the nested subgroups based the estimated CATE scores with boosting. Only provided if score.method includes 'boosting'.

• ate.twoReg: Same as ate.poisson, but with the nested subgroups based the estimated CATE scores with two regressions. Only provided if score.method includes 'twoReg'.

• ate.contrastReg: Same as ate.poisson, but with the nested subgroups based the estimated CATE scores with contrast regression. Only provided if score.method includes 'contrastReg'.

• ate.negBin: Same as ate.poisson, but with the nested subgroups based the estimated CATE scores with negative binomial regression. Only provided if score.method includes 'negBin'.

• score.poisson: A vector of numerical values of length n (number of observations in data) containing the estimated log-CATE scores according to the Poisson regression. Only provided if score.method includes 'poisson'.

• score.boosting: Same as score.poisson, but with estimated log-CATE score according to boosting. Only provided if score.method includes 'boosting'.

• score.twoReg: Same as score.poisson, but with estimated log-CATE score according to two regressions. Only provided if score.method includes 'twoReg'.

• score.contrastReg: Same as score.poisson, but with estimated log-CATE score according to contrast regression. Only provided if score.method includes 'contrastReg'.

• score.negBin: Same as score.poisson, but with estimated log-CATE score according to negative binomial regression. Only provided if score.method includes 'negBin'.

• fit: Additional details on model fitting if score.method includes 'boosting' or 'contrastReg':

  • result.boosting: Details on the boosting model fitted to observations with treatment = 0 ($fit0.boosting) and to observations with treatment = 1 ($fit1.boosting). Only provided if score.method includes 'boosting'.

  • result.contrastReg$sigma.contrastReg: Variance-covariance matrix of the estimated log-CATE coefficients in contrast regression. Only provided if score.method includes 'contrastReg'.

• coefficients: A data frame with the coefficients of the estimated log-CATE score by score.method. The data frame has number of rows equal to the number of covariates in cate.model and number of columns equal to length(score.method). If score.method includes 'contrastReg', the data frame has an additional column containing the standard errors of the coefficients estimated with contrast regression. 'boosting' does not have coefficient results because tree-based methods typically do not express the log-CATE as a linear combination of coefficients and covariates.

References

Yadlowsky, S., Pellegrini, F., Lionetto, F., Braune, S., & Tian, L. (2020). Estimation and validation of ratio-based conditional average treatment effects using observational data. Journal of the American Statistical Association, 1-18. DOI: 10.1080/01621459.2020.1772080.

See Also

catecvcount()

Examples

fit <- catefitcount(data = countExample,
                    score.method = "poisson",
                    cate.model = y ~ age + female + previous_treatment +
                                 previous_cost + previous_number_relapses +
                                 offset(log(years)),
                    ps.model = trt ~ age + previous_treatment,
                    higher.y = FALSE,
                    seed = 999, verbose = 1)

Description

Provides singly robust and doubly robust estimation of CATE score with up to 6 scoring methods among the following: Linear regression, boosting, two regressions, contrast regression, random forest and generalized additive model.

Usage

catefitmean(
  data,
  score.method,
  cate.model,
  ps.model,
  ps.method = "glm",
  init.model = NULL,
  initial.predictor.method = "boosting",
  minPS = 0.01,
  maxPS = 0.99,
  higher.y = TRUE,
  prop.cutoff = seq(0.5, 1, length = 6),
  xvar.smooth.score = NULL,
  xvar.smooth.init = NULL,
  tree.depth = 2,
  n.trees.rf = 1000,
  n.trees.boosting = 200,
  B = 3,
  Kfold = 6,
  plot.gbmperf = FALSE,
  error.maxNR = 0.001,
  tune = c(0.5, 2),
  seed = NULL,
  verbose = 0,
  ...
)

Arguments

Details

The CATE score represents an individual-level treatment effect, estimated with either linear regression, boosting, random forest and generalized additive model applied separately by treatment group or with two doubly robust estimators, two regressions and contrast regression (Yadlowsky, 2020) applied to the entire dataset.

catefitmean() provides the coefficients of the CATE score for each scoring method requested through score.method. Currently, contrast regression is the only method which allows for inference of the CATE coefficients by providing standard errors of the coefficients. The coefficients can be used to learn the effect size of each variable and predict the CATE score for a new observation.

catefitmean() also provides the predicted CATE score of each observation in the data set, for each scoring method. The predictions allow ranking the observations from potentially high responders to the treatment to potentially low or standard responders.

The estimated ATE among nested subgroups of high responders are also provided by scoring method. Note that the ATEs in catefitmean() are derived based on the CATE score which is estimated using the same data sample. Therefore, overfitting may be an issue. catefitmean() is more suitable to inspect the estimated ATEs across scoring methods as it implements internal cross validation to reduce optimism.

Value

Returns a list containing the following components:

• ate.gaussian: A vector of numerical values of length prop.cutoff containing the estimated ATE in nested subgroups (defined by prop.cutoff) constructed based on the estimated CATE scores with Poisson regression. Only provided if score.method includes 'gaussian'.

• ate.boosting: Same as ate.gaussian, but with the nested subgroups based the estimated CATE scores with boosting. Only provided if score.method includes 'boosting'.

• ate.twoReg: Same as ate.gaussian, but with the nested subgroups based the estimated CATE scores with two regressions. Only provided if score.method includes 'twoReg'.

• ate.contrastReg: Same as ate.gaussian, but with the nested subgroups based the estimated CATE scores with contrast regression. Only provided if score.method includes 'contrastReg'.

• ate.randomForest: Same as ate.gaussian, but with the nested subgroups based the estimated CATE scores with random forest. Only provided if score.method includes 'gam'.

• ate.gam: Same as ate.gaussian, but with the nested subgroups based the estimated CATE scores with generalized additive model. Only provided if score.method includes 'gam'.

• score.gaussian: A vector of numerical values of length n (number of observations in data) containing the estimated CATE scores according to the linear regression. Only provided if score.method includes 'gaussian'.

• score.boosting: Same as score.gaussian, but with estimated CATE score according to boosting. Only provided if score.method includes 'boosting'.

• score.twoReg: Same as score.gaussian, but with estimated CATE score according to two regressions. Only provided if score.method includes 'twoReg'.

• score.contrastReg: Same as score.gaussian, but with estimated CATE score according to contrast regression. Only provided if score.method includes 'contrastReg'.

• score.randomForest: Same as score.gaussian, but with estimated CATE score according to random forest. Only provided if score.method includes 'randomForest'.

• score.gam: Same as score.gaussian, but with estimated CATE score according to generalized additive model. Only provided if score.method includes 'gam'.

• fit: Additional details on model fitting if score.method includes 'boosting' or 'contrastReg':

  • result.boosting: Details on the boosting model fitted to observations with treatment = 0 ($fit0.boosting) and to observations with treatment = 1 ($fit1.boosting). Only provided if score.method includes 'boosting'.

  • result.randomForest: Details on the boosting model fitted to observations with treatment = 0 ($fit0.randomForest) and to observations with treatment = 1 ($fit1.randomForest). Only provided if score.method includes 'randomForest'.

  • result.gam: Details on the boosting model fitted to observations with treatment = 0 ($fit0.gam) and to observations with treatment = 1 ($fit1.gam). Only provided if score.method includes 'gam'.

  • result.contrastReg$sigma.contrastReg: Variance-covariance matrix of the estimated CATE coefficients in contrast regression. Only provided if score.method includes 'contrastReg'.

• coefficients: A data frame with the coefficients of the estimated CATE score by score.method. The data frame has number of rows equal to the number of covariates in cate.model and number of columns equal to length(score.method). If score.method includes 'contrastReg', the data frame has an additional column containing the standard errors of the coefficients estimated with contrast regression. 'boosting', 'randomForest', 'gam' do not have coefficient results because these methods do not express the CATE as a linear combination of coefficients and covariates.

References

Yadlowsky, S., Pellegrini, F., Lionetto, F., Braune, S., & Tian, L. (2020). Estimation and validation of ratio-based conditional average treatment effects using observational data. Journal of the American Statistical Association, 1-18. DOI: 10.1080/01621459.2020.1772080.

See Also

catecvmean() function

Description

Provides singly robust and doubly robust estimation of CATE score for survival data with up to 5 scoring methods among the following: Random forest, boosting, poisson regression, two regressions, and contrast regression.

Usage

catefitsurv(
  data,
  score.method,
  cate.model,
  ps.model,
  ps.method = "glm",
  initial.predictor.method = "randomForest",
  ipcw.model = NULL,
  ipcw.method = "breslow",
  minPS = 0.01,
  maxPS = 0.99,
  followup.time = NULL,
  tau0 = NULL,
  higher.y = TRUE,
  prop.cutoff = seq(0.5, 1, length = 6),
  surv.min = 0.025,
  tree.depth = 2,
  n.trees.rf = 1000,
  n.trees.boosting = 200,
  B = 3,
  Kfold = 5,
  plot.gbmperf = TRUE,
  error.maxNR = 0.001,
  max.iterNR = 100,
  tune = c(0.5, 2),
  seed = NULL,
  verbose = 0,
  ...
)

Arguments

Details

The CATE score represents an individual-level treatment effect for survival data, estimated with random forest, boosting, Poisson regression, and the doubly robust estimator (two regressions, Yadlowsky, 2020) applied separately by treatment group or with the other doubly robust estimators (contrast regression, Yadlowsky, 2020) applied to the entire data set.

catefitsurv() provides the coefficients of the CATE score for each scoring method requested through score.method. Currently, contrast regression is the only method which allows for inference of the CATE coefficients by providing standard errors of the coefficients. The coefficients can be used to learn the effect size of each variable and predict the CATE score for a new observation.

catefitsurv() also provides the predicted CATE score of each observation in the data set, for each scoring method. The predictions allow ranking the observations from potentially high responders to the treatment to potentially low or standard responders.

The estimated ATE among nested subgroups of high responders are also provided by scoring method. Note that the ATEs in catefitsurv() are derived based on the CATE score which is estimated using the same data sample. Therefore, overfitting may be an issue. catecvsurv() is more suitable to inspect the estimated ATEs across scoring methods as it implements internal cross validation to reduce optimism.

Value

Returns an object of the class catefit containing the following components:

• ate.randomForest: A vector of numerical values of length prop.cutoff containing the estimated ATE by the RMTL ratio in nested subgroups (defined by prop.cutoff) constructed based on the estimated CATE scores with random forest method. Only provided if score.method includes 'randomForest'.

• ate.boosting: Same as ate.randomForest, but with the nested subgroups based the estimated CATE scores with boosting. Only provided if score.method includes 'boosting'.

• ate.poisson: Same as ate.randomForest, but with the nested subgroups based the estimated CATE scores with poisson regression. Only provided if score.method includes 'poisson'.

• ate.twoReg: Same as ate.randomForest, but with the nested subgroups based the estimated CATE scores with two regressions. Only provided if score.method includes 'twoReg'.

• ate.contrastReg: Same as ate.randomForest, but with the nested subgroups based the estimated CATE scores with contrast regression. Only provided if score.method includes 'contrastReg'.

• hr.randomForest: A vector of numerical values of length prop.cutoff containing the adjusted hazard ratio in nested subgroups (defined by prop.cutoff) constructed based on the estimated CATE scores with random forest method. Only provided if score.method includes 'randomForest'.

• hr.boosting: Same as hr.randomForest, but with the nested subgroups based the estimated CATE scores with boosting. Only provided if score.method includes 'boosting'.

• hr.poisson: Same as hr.randomForest, but with the nested subgroups based the estimated CATE scores with poisson regression. Only provided if score.method includes 'poisson'.

• hr.twoReg: Same as hr.randomForest, but with the nested subgroups based the estimated CATE scores with two regressions. Only provided if score.method includes 'twoReg'.

• hr.contrastReg: Same as hr.randomForest, but with the nested subgroups based the estimated CATE scores with contrast regression. Only provided if score.method includes 'contrastReg'.

• score.randomForest: A vector of numerical values of length n (number of observations in data) containing the estimated log-CATE scores according to random forest. Only provided if score.method includes 'randomForest'.

• score.boosting: Same as score.randomForest, but with estimated log-CATE score according to boosting. Only provided if score.method includes 'boosting'.

• score.poisson: Same as score.randomForest, but with estimated log-CATE score according to the Poisson regression. Only provided if score.method includes 'poisson'.

• score.twoReg: Same as score.randomForest, but with estimated log-CATE score according to two regressions. Only provided if score.method includes 'twoReg'.

• score.contrastReg: Same as score.randomForest, but with estimated log-CATE score according to contrast regression. Only provided if score.method includes 'contrastReg'.

• fit: Additional details on model fitting if score.method includes 'randomForest', 'boosting' or 'contrastReg':

  • result.randomForest: Details on the random forest model fitted to observations with treatment = 0 ($fit0.rf) and to observations with treatment = 1 ($fit1.rf). Only provided if score.method includes 'randomForest'.

  • result.boosting: Details on the boosting model fitted to observations with treatment = 0, ($fit0.boosting) and ($fit0.gam) and to observations with treatment = 1, ($fit1.boosting) and ($fit1.gam). Only provided if score.method includes 'boosting'.

  • result.contrastReg$converge.contrastReg: Whether the contrast regression algorithm converged or not. Only provided if score.method includes 'contrastReg'.

• coefficients: A data frame with the coefficients of the estimated log-CATE score by score.method. The data frame has number of rows equal to the number of covariates in cate.model and number of columns equal to length(score.method). If score.method includes 'contrastReg', the data frame has an additional column containing the standard errors of the coefficients estimated with contrast regression. 'randomForest' and 'boosting' do not have coefficient results because tree-based methods typically do not express the log-CATE as a linear combination of coefficients and covariates.

• errors/warnings: A nested list of errors and warnings that were wrapped during the calculation of ATE. Errors and warnings are organized by score.method.

References

Yadlowsky, S., Pellegrini, F., Lionetto, F., Braune, S., & Tian, L. (2020). Estimation and validation of ratio-based conditional average treatment effects using observational data. Journal of the American Statistical Association, 1-18. DOI: 10.1080/01621459.2020.1772080.

See Also

catecvsurv()

Examples

library(survival)

tau0 <- with(survivalExample, min(quantile(y[trt == "drug1"], 0.95),
                               quantile(y[trt == "drug0"], 0.95)))

fit <- catefitsurv(data = survivalExample,
                   score.method = "randomForest",
                   cate.model = Surv(y, d) ~ age + female + previous_cost +
                                             previous_number_relapses,
                   ps.model = trt ~ age + previous_treatment,
                   ipcw.model = ~ age + previous_cost + previous_treatment,
                   tau0 = tau0,
                   seed = 999)

coef(fit)

Description

A dataset containing a count outcome, a length of follow-up and 6 baseline covariates

Usage

data(countExample)

Format

A dataframe with 4000 rows (patients) and 9 variables:

age

age at baseline, centered to 48 years old, in years

female

sex, 0 for male, 1 for female

previous_treatment

previous treatment, "drugA", "drugB", or "drugC"

previous_cost

previous medical cost, in US dollars

previous_number_symptoms

previous number of symptoms, "0", "1", or ">=2"

previous_number_relapses

previous number of relapses

trt

current treatment, "drug0" or "drug1"

y

count outcome, current number of relapses

years

length of follow-up, in years

Examples

data(countExample)
str(countExample)
rate <- countExample$y / countExample$years

Description

Estimate restricted mean survival time (RMST) based on Cox regression model

Usage

cox.rmst(y, d, x.cate, xnew, tau0)

Arguments

Value

The estimated RMST for new subjects with covariates xnew; vector of size m.

Description

Data preprocessing Apply at the beginning of pmcount() and cvcount(), after arg.checks()

Usage

data.preproc(
  fun,
  cate.model,
  ps.model,
  data,
  prop.cutoff = NULL,
  prop.multi = NULL,
  ps.method,
  initial.predictor.method = NULL
)

Arguments

Value

A list of 6 elements: - y: outcome; vector of length n (observations) - trt: binary treatment; vector of length n - x.ps: matrix of p.ps baseline covariates (plus intercept); dimension n by p.ps + 1 - x.cate: matrix of p.cate baseline covariates; dimension n by p.cate - time: offset; vector of length n - if fun = "pm": - prop: formatted prop.cutoff - if fun = "cv" - prop.onlyhigh: formatted prop.cutoff with 0 removed if applicable - prop.bi; formatted prop.cutoff with 0 and 1 removed if applicable - prop.multi: formatted prop.multi, starting with 0 and ending with 1

Description

Data preprocessing Apply at the beginning of catefitmean() and catecvmean(), after arg.checks()

Usage

data.preproc.mean(
  fun,
  cate.model,
  init.model,
  ps.model,
  data,
  prop.cutoff = NULL,
  prop.multi = NULL,
  ps.method,
  score.method = NULL,
  initial.predictor.method = NULL
)

Arguments

Value

A list of 6 elements: - y: outcome; vector of length n (observations) - trt: binary treatment; vector of length n - x.ps: matrix of p.ps baseline covariates (plus intercept); dimension n by p.ps + 1 - x.cate: matrix of p.cate baseline covariates; dimension n by p.cate - x.init: matrix of p.init baseline covariates; dimension n by p.init - if fun = "pm": - prop: formatted prop.cutoff - if fun = "cv" - prop.onlyhigh: formatted prop.cutoff with 0 removed if applicable - prop.bi; formatted prop.cutoff with 0 and 1 removed if applicable - prop.multi: formatted prop.multi, starting with 0 and ending with 1

Description

Data preprocessing Apply at the beginning of catefitcount(), catecvcount(), catefitsurv(), and catecvsurv(), after arg.checks()

Usage

data.preproc.surv(
  fun,
  cate.model,
  ps.model,
  ipcw.model = NULL,
  tau0 = NULL,
  data,
  prop.cutoff = NULL,
  prop.multi = NULL,
  ps.method,
  initial.predictor.method = NULL,
  response = "count"
)

Arguments

Value

A list of elements: - y: outcome; vector of length n (observations) - d : the event indicator; vector of length n; only if respone = "survival" - trt: binary treatment; vector of length n - x.ps: matrix of p.ps baseline covariates specified in the propensity score model (plus intercept); dimension n by p.ps + 1 - x.cate: matrix of p.cate baseline covariates specified in the outcome model; dimension n by p.cate - x.ipcw: matrix of p.ipw baseline covarites specified in inverse probability of censoring weighting model; dimension n by p.ipw - time: offset; vector of length n; only if response = "count" - if fun = "catefit": - prop: formatted prop.cutoff - prop.no1: formatted prop.cutoff with 1 removed if applicable; otherwise prop.no1 is the same as prop - if fun = "crossv" - prop.onlyhigh: formatted prop.cutoff with 0 removed if applicable - prop.bi; formatted prop.cutoff with 0 and 1 removed if applicable - prop.multi: formatted prop.multi, starting with 0 and ending with 1

Description

Doubly robust estimator of the average treatment effect between two treatments, which is the rate ratio of treatment 1 over treatment 0 for count outcomes.

Usage

drcount(
  y,
  trt,
  x.cate,
  x.ps,
  time,
  ps.method = "glm",
  minPS = 0.01,
  maxPS = 0.99,
  interactions = TRUE
)

Arguments

Value

Return a list of 4 elements:

• log.rate.ratio: A numeric value of the estimated log rate ratio.

• rate0: A numeric value of the estimated rate in the group trt=0.

• rate1: A numeric value of the estimated rate in the group trt=1.

Description

Doubly robust estimator of the average treatment effect between two treatments, which is the mean difference of treatment 1 over treatment 0 for continuous outcomes.

Usage

drmean(
  y,
  trt,
  x.cate,
  x.ps,
  ps.method = "glm",
  minPS = 0.01,
  maxPS = 0.99,
  interactions = TRUE
)

Arguments

Value

Return a list of 4 elements:

• mean.diff: A numeric value of the estimated mean difference.

• mean.diff0: A numeric value of the estimated mean difference in treatment group 0.

• mean.diff1: A numeric value of the estimated mean difference in treatment group 1.

Description

Doubly robust estimator of the average treatment effect between two treatments, which is the restricted mean time lost (RMTL) ratio of treatment 1 over treatment 0 for survival outcomes.

Usage

drsurv(
  y,
  d,
  x.cate,
  x.ps,
  x.ipcw,
  trt,
  yf = NULL,
  tau0,
  surv.min = 0.025,
  ps.method = "glm",
  minPS = 0.01,
  maxPS = 0.99,
  ipcw.method = "breslow"
)

Arguments

Value

Return a list of 4 elements:

• rmst1: A numeric value of the estimated restricted mean survival time n the group trt = 1.

• rmst0: A numeric value of the estimated restricted mean survival time n the group trt = 0.

• log.rmtl.ratio: A numeric value of the estimated log rmtl ratio.

• log.hazard.ratio: A numeric value of the estimated log hazard ratio.

Description

If only care about the higher subgroup (above cutoff), only need trt.est.high so set onlyhigh to be TRUE Scores are adjusted to the opposite sign if higher.y == FALSE; scores stay the same if higher.y == TRUE; this is because estcount.bilevel.subgroups() always takes the subgroup of the top highest adjusted scores, and higher adjusted scores should always represent high responders of trt=1

Usage

estcount.bilevel.subgroups(
  y,
  x.cate,
  x.ps,
  time,
  trt,
  score,
  higher.y,
  prop,
  onlyhigh,
  ps.method = "glm",
  minPS = 0.01,
  maxPS = 0.99
)

Arguments

Value

ate.est.high: estimated ATEs in the multiple bi-level subgroups that are in the higher-than-cutoff category; vector of size equal to the length of prop; always returned ate.est.low: estimated ATEs in the multiple bi-level subgroups that are in the lower-than-cutoff category; vector of size equal to the length of prop; returned only when onlyhigh == TRUE

Description

Scores are adjusted to the opposite sign if higher.y == FALSE; scores stay the same if higher.y == TRUE; this is because subgroups defined in estcount.multilevel.subgroup() start from the lowest to the highest adjusted scores, and higher adjusted scores should always represent high responders of trt=1

Usage

estcount.multilevel.subgroup(
  y,
  x.cate,
  x.ps,
  time,
  trt,
  score,
  higher.y,
  prop,
  ps.method = "glm",
  minPS = 0.01,
  maxPS = 0.99
)

Arguments

Value

estimated ATEs of all categories in the one multilevel subgroup; vector of size equal to the length of categories in the multilevel subgroup

Description

If only care about the higher subgroup (above cutoff), only need trt.est.high so set onlyhigh to be TRUE. Scores are adjusted to the opposite sign if higher.y == FALSE; scores stay the same if higher.y == TRUE. This is because estcount.bilevel.subgroups() always takes the subgroup of the top highest adjusted scores,and higher adjusted scores should always represent high responders in treatment group 1.

Usage

estmean.bilevel.subgroups(
  y,
  x.cate,
  x.ps,
  trt,
  score,
  higher.y,
  prop,
  onlyhigh,
  ps.method = "glm",
  minPS = 0.01,
  maxPS = 0.99
)

Arguments