Package 'sleev'

Performs cross-validation to calculate the average predicted log likelihood for the linear2ph function. This function can be used to select the B-spline basis that yields the largest average predicted log likelihood.

Description

Performs cross-validation to calculate the average predicted log likelihood for the linear2ph function. This function can be used to select the B-spline basis that yields the largest average predicted log likelihood.

Usage

cv_linear2ph(
  Y_unval = NULL,
  Y = NULL,
  X_unval = NULL,
  X = NULL,
  Z = NULL,
  Bspline = NULL,
  data = NULL,
  nfolds = 5,
  MAX_ITER = 2000,
  TOL = 1e-04,
  verbose = FALSE
)

Arguments

Y_unval	Specifies the column of the error-prone outcome that is continuous. Subjects with missing values of Y_unval are omitted from the analysis. This argument is required.
Y	Specifies the column that stores the validated value of Y_unval in the second phase. Subjects with missing values of Y are considered as those not selected in the second phase. This argument is required.
X_unval	Specifies the columns of the error-prone covariates. Subjects with missing values of X_unval are omitted from the analysis. This argument is required.
X	Specifies the columns that store the validated values of X_unval in the second phase. Subjects with missing values of X are considered as those not selected in the second phase. This argument is required.
Z	Specifies the columns of the accurately measured covariates. Subjects with missing values of Z are omitted from the analysis. This argument is optional.
Bspline	Specifies the columns of the B-spline basis. Subjects with missing values of Bspline are omitted from the analysis. This argument is required.
data	Specifies the name of the dataset. This argument is required.
nfolds	Specifies the number of cross-validation folds. The default value is 5. Although nfolds can be as large as the sample size (leave-one-out cross-validation), it is not recommended for large datasets. The smallest value allowable is 3.
MAX_ITER	Specifies the maximum number of iterations in the EM algorithm. The default number is 2000. This argument is optional.
TOL	Specifies the convergence criterion in the EM algorithm. The default value is 1E-4. This argument is optional.
verbose	If TRUE, then show details of the analysis. The default value is FALSE.

Value

avg_pred_loglike	Stores the average predicted log likelihood.
pred_loglike	Stores the predicted log likelihood in each fold.
converge	Stores the convergence status of the EM algorithm in each run.

Examples

rho = 0.3
  p = 0.3
  n = 100
  n2 = 40
  alpha = 0.3
  beta = 0.4
   
  ### generate data
  simX = rnorm(n)
  epsilon = rnorm(n)
  simY = alpha+beta*simX+epsilon
  error = MASS::mvrnorm(n, mu=c(0,0), Sigma=matrix(c(1, rho, rho, 1), nrow=2))
   
  simS = rbinom(n, 1, p)
  simU = simS*error[,2]
  simW = simS*error[,1]
  simY_tilde = simY+simW
  simX_tilde = simX+simU
   
  id_phase2 = sample(n, n2)
   
  simY[-id_phase2] = NA
  simX[-id_phase2] = NA
   
  # cubic basis
  nsieves = c(5, 10)
  pred_loglike = rep(NA, length(nsieves))
  for (i in 1:length(nsieves)) {
      nsieve = nsieves[i]
      Bspline = splines::bs(simX_tilde, df=nsieve, degree=3, 
        Boundary.knots=range(simX_tilde), intercept=TRUE)
      colnames(Bspline) = paste("bs", 1:nsieve, sep="")
      # cubic basis
     
      data = data.frame(Y_tilde=simY_tilde, X_tilde=simX_tilde, Y=simY, X=simX, Bspline)
      ### generate data
     
      res = cv_linear2ph(Y="Y", X="X", Y_unval="Y_tilde", X_unval="X_tilde", 
        Bspline=colnames(Bspline), data=data, nfolds = 5)
      pred_loglike[i] = res$avg_pred_loglik
    }
   
  data.frame(nsieves, pred_loglike)

---

Sieve maximum likelihood estimator (SMLE) for two-phase linear regression problems

Description

Performs efficient semiparametric estimation for general two-phase measurement error models when there are errors in both the outcome and covariates.

Usage

linear2ph(
  Y_unval = NULL,
  Y = NULL,
  X_unval = NULL,
  X = NULL,
  Z = NULL,
  Bspline = NULL,
  data = NULL,
  hn_scale = 1,
  noSE = FALSE,
  TOL = 1e-04,
  MAX_ITER = 1000,
  verbose = FALSE
)

Arguments

Y_unval	Column name of the error-prone or unvalidated continuous outcome. Subjects with missing values of Y_unval are omitted from the analysis. This argument is required.
Y	Column name that stores the validated value of Y_unval in the second phase. Subjects with missing values of Y are considered as those not selected in the second phase. This argument is required.
X_unval	Specifies the columns of the error-prone covariates. Subjects with missing values of X_unval are omitted from the analysis. This argument is required.
X	Specifies the columns that store the validated values of X_unval in the second phase. Subjects with missing values of X are considered as those not selected in the second phase. This argument is required.
Z	Specifies the columns of the accurately measured covariates. Subjects with missing values of Z are omitted from the analysis. This argument is optional.
Bspline	Specifies the columns of the B-spline basis. Subjects with missing values of Bspline are omitted from the analysis. This argument is required.
data	Specifies the name of the dataset. This argument is required.
hn_scale	Specifies the scale of the perturbation constant in the variance estimation. For example, if hn_scale = 0.5, then the perturbation constant is $0.5n^{-1/2}$, where $n$ is the first-phase sample size. The default value is 1. This argument is optional.
noSE	If TRUE, then the variances of the parameter estimators will not be estimated. The default value is FALSE. This argument is optional.
TOL	Specifies the convergence criterion in the EM algorithm. The default value is 1E-4. This argument is optional.
MAX_ITER	Maximum number of iterations in the EM algorithm. The default number is 1000. This argument is optional.
verbose	If TRUE, then show details of the analysis. The default value is FALSE.

Value

coefficients	Stores the analysis results.
sigma	Stores the residual standard error.
covariance	Stores the covariance matrix of the regression coefficient estimates.
converge	In parameter estimation, if the EM algorithm converges, then converge = TRUE. Otherwise, converge = FALSE.
converge_cov	In variance estimation, if the EM algorithm converges, then converge_cov = TRUE. Otherwise, converge_cov = FALSE.

References

Tao, R., Mercaldo, N. D., Haneuse, S., Maronge, J. M., Rathouz, P. J., Heagerty, P. J., & Schildcrout, J. S. (2021). Two-wave two-phase outcome-dependent sampling designs, with applications to longitudinal binary data. Statistics in Medicine, 40(8), 1863–1876. https://doi.org/10.1002/sim.8876

See Also

cv_linear2ph() to calculate the average predicted log likelihood of this function.

Examples

rho = -.3
 p = 0.3
 hn_scale = 1
 nsieve = 20

 n = 100
 n2 = 40
 alpha = 0.3
 beta = 0.4
 set.seed(12345)

 ### generate data
 simX = rnorm(n)
 epsilon = rnorm(n)
 simY = alpha+beta*simX+epsilon
 error = MASS::mvrnorm(n, mu=c(0,0), Sigma=matrix(c(1, rho, rho, 1), nrow=2))
 
 simS = rbinom(n, 1, p)
 simU = simS*error[,2]
 simW = simS*error[,1]
 simY_tilde = simY+simW
 simX_tilde = simX+simU
 
 id_phase2 = sample(n, n2)
 
 simY[-id_phase2] = NA
 simX[-id_phase2] = NA
 
 # # histogram basis
 # Bspline = matrix(NA, nrow=n, ncol=nsieve)
 # cut_x_tilde = cut(simX_tilde, breaks=quantile(simX_tilde, probs=seq(0, 1, 1/nsieve)), 
 #   include.lowest = TRUE)
 # for (i in 1:nsieve) {
 #     Bspline[,i] = as.numeric(cut_x_tilde == names(table(cut_x_tilde))[i])
 # }
 # colnames(Bspline) = paste("bs", 1:nsieve, sep="")
 # # histogram basis
 
 # # linear basis
 # Bspline = splines::bs(simX_tilde, df=nsieve, degree=1,
 #   Boundary.knots=range(simX_tilde), intercept=TRUE)
 # colnames(Bspline) = paste("bs", 1:nsieve, sep="")
 # # linear basis
 
 # # quadratic basis
 # Bspline = splines::bs(simX_tilde, df=nsieve, degree=2, 
 #   Boundary.knots=range(simX_tilde), intercept=TRUE)
 # colnames(Bspline) = paste("bs", 1:nsieve, sep="")
 # # quadratic basis
 
 # cubic basis
 Bspline = splines::bs(simX_tilde, df=nsieve, degree=3, 
   Boundary.knots=range(simX_tilde), intercept=TRUE)
 colnames(Bspline) = paste("bs", 1:nsieve, sep="")
 # cubic basis
 
 data = data.frame(Y_tilde=simY_tilde, X_tilde=simX_tilde, Y=simY, X=simX, Bspline)

 res = linear2ph(Y="Y", X="X", Y_unval="Y_tilde", X_unval="X_tilde", 
   Bspline=colnames(Bspline), data=data, hn_scale=0.1)

---

Sieve maximum likelihood estimator (SMLE) for two-phase logistic regression problems

Description

This function returns the sieve maximum likelihood estimators (SMLE) for the logistic regression model from Lotspeich et al. (2021).

Usage

logistic2ph(
  Y_unval = NULL,
  Y = NULL,
  X_unval = NULL,
  X = NULL,
  Z = NULL,
  Bspline = NULL,
  data = NULL,
  hn_scale = 1,
  noSE = FALSE,
  TOL = 1e-04,
  MAX_ITER = 1000,
  verbose = FALSE
)

Arguments

Y_unval	Column name of the error-prone or unvalidated binary outcome. This argument is required.
Y	Column name that stores the validated value of Y_unval in the second phase. Subjects with missing values of Y are considered as those not selected in the second phase. This argument is required.
X_unval	Specifies the columns of the error-prone covariates. This argument is required.
X	Specifies the columns that store the validated values of X_unval in the second phase. Subjects with missing values of X are considered as those not selected in the second phase. This argument is required.
Z	Specifies the columns of the accurately measured covariates. This argument is optional.
Bspline	Specifies the columns of the B-spline basis. This argument is required.
data	Specifies the name of the dataset. This argument is required.
hn_scale	Specifies the scale of the perturbation constant in the variance estimation. For example, if hn_scale = 0.5, then the perturbation constant is $0.5n^{-1/2}$, where $n$ is the first-phase sample size. The default value is 1. This argument is optional.
noSE	If TRUE, then the variances of the parameter estimators will not be estimated. The default value is FALSE. This argument is optional.
TOL	Specifies the convergence criterion in the EM algorithm. The default value is 1E-4. This argument is optional.
MAX_ITER	Maximum number of iterations in the EM algorithm. The default number is 1000. This argument is optional.
verbose	If TRUE, then show details of the analysis. The default value is FALSE.

Value

coefficients	Stores the analysis results.
outcome_err_coefficients	Stores the outcome error model results.
Bspline_coefficients	Stores the final B-spline coefficient estimates.
covariance	Stores the covariance matrix of the regression coefficient estimates.
converge	In parameter estimation, if the EM algorithm converges, then converge = TRUE. Otherwise, converge = FALSE.
converge_cov	In variance estimation, if the EM algorithm converges, then converge_cov = TRUE. Otherwise, converge_cov = FALSE.
converge_msg	In parameter estimation, if the EM algorithm does not converge, then converged_msg is a string description.

References

Lotspeich, S. C., Shepherd, B. E., Amorim, G. G. C., Shaw, P. A., & Tao, R. (2021). Efficient odds ratio estimation under two-phase sampling using error-prone data from a multi-national HIV research cohort. Biometrics, biom.13512. https://doi.org/10.1111/biom.13512

---

Mock VCCC dataset.

Description

A simulated dataset constructed to imitate the Vanderbilt Comprehensive Care Clinic (VCCC) patient records, which have been fully validated and therefore contain validated and unvalidated versions of all variables. The VCCC cohort is a good candidate for the purpose of illustration. The data presented in this section are a mocked-up version of the actual data due to confidentiality, but the data structure and features, such as mean and variability, closely resemble the real dataset.

Usage

mock.vccc

Format

A data frame with 2087 rows and 8 variables:

ID

patient ID

VL_unval

viral load at antiretroviral therapy (ART) initiation, error-prone outcome, continuous

VL_val

viral load at antiretroviral therapy (ART) initiation, validated outcome, continuous

ADE_unval

having an AIDS-defining event (ADE) within one year of ART initiation, error-prone outcome, binary

ADE_val

having an AIDS-defining event (ADE) within one year of ART initiation, validated outcome, binary

CD4_unval

CD4 count at ART initiation, error-prone covariate, continuous

CD4_val

CD4 count at ART initiation, validated covariate, continuous

prior_ART

whether patient is ART naive at enrollment, error-free covariate, binary

Sex

sex of patient, 1 indicates male and 0 indicates female & error-free covariate, binary

Age

age of patient, error-free covariate, continuous

Source

https://www.vanderbilthealth.com/clinic/comprehensive-care-clinic

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