Package 'snSMART' reference manual

Title:	Small N Sequential Multiple Assignment Randomized Trial Methods
Description:	Consolidated data simulation, sample size calculation and analysis functions for several snSMART (small sample sequential, multiple assignment, randomized trial) designs under one library. See Wei, B., Braun, T.M., Tamura, R.N. and Kidwell, K.M. "A Bayesian analysis of small n sequential multiple assignment randomized trials (snSMARTs)." (2018) Statistics in medicine, 37(26), pp.3723-3732 <doi:10.1002/sim.7900>.
Authors:	Sidi Wang [aut], Kelley Kidwell [aut], Michael Kleinsasser [cre]
Maintainer:	Michael Kleinsasser <[email protected]>
License:	GPL (>= 2)
Version:	0.2.4
Built:	2024-10-17 05:29:07 UTC
Source:	CRAN

BJSM for snSMART (3 active treatments/placebo and 2 dose level) with binary outcome

Description

This function implements the BJSM (Bayesian Joint Stage Modeling) method which borrows information across both stages to estimate the individual response rate of each treatment/dose level in a snSMART design with binary outcomes.

Usage

BJSM_binary(
  data,
  prior_dist,
  pi_prior,
  normal.par,
  beta_prior,
  n_MCMC_chain = 1,
  n.adapt,
  BURN.IN = 100,
  thin = 1,
  MCMC_SAMPLE,
  ci = 0.95,
  six = TRUE,
  DTR = TRUE,
  jags.model_options = NULL,
  coda.samples_options = NULL,
  verbose = FALSE,
  ...
)

## S3 method for class 'summary.BJSM_binary'
print(x, ...)

## S3 method for class 'BJSM_binary'
print(x, ...)

## S3 method for class 'summary.BJSM_dose_binary'
print(x, ...)

## S3 method for class 'BJSM_dose_binary'
print(x, ...)
BJSM_binary(
  data,
  prior_dist,
  pi_prior,
  normal.par,
  beta_prior,
  n_MCMC_chain = 1,
  n.adapt,
  BURN.IN = 100,
  thin = 1,
  MCMC_SAMPLE,
  ci = 0.95,
  six = TRUE,
  DTR = TRUE,
  jags.model_options = NULL,
  coda.samples_options = NULL,
  verbose = FALSE,
  ...
)

## S3 method for class 'summary.BJSM_binary'
print(x, ...)

## S3 method for class 'BJSM_binary'
print(x, ...)

## S3 method for class 'summary.BJSM_dose_binary'
print(x, ...)

## S3 method for class 'BJSM_dose_binary'
print(x, ...)

Arguments

`data`	trial data with 4 columns: `treatment_stageI, response_stageI, treatment_stageII` and `response_stageII`. Missing data is allowed in stage 2.
`prior_dist`	for 3 active treatment design: vector of three values ("prior distribution for `pi`", "prior distribution for `beta0`", "prior distribution for `beta1`"). User can choose from "gamma", "beta", "pareto". e.g. prior_dist = c("beta", "beta", "pareto"); for dose level design: vector of two values ("prior distribution for `pi_P`", "prior distribution for `beta`")
`pi_prior`	for 3 active treatment design: vector of six values (a, b, c, d, e, f), where a and b are the parameter `a` and parameter `b` of the prior distribution for `pi_1A`, c and d are the parameter `a` and parameter `b` of the prior distribution for `pi_1B`, and e and f are the parameter `a` and parameter `b` of the prior distribution for `pi_1C`. for dose level design: vector of two values (a, b). `a` is the parameter `a` of the prior distribution for `pi` (response rate) of placebo. `b` is the parameter `b` of the prior distribution for `pi` of placebo. Please check the `Details` section for more explanation
`normal.par`	for dose level design: vector of two values (normal.mean, normal.var). our function assumes that the logarithm of treatment effect ratio follows a Gaussian prior distribution $N(\mu, \sigma^2)$ , that is $log(\pi_L/\pi_P)~N(normal.mean, normal.var)$ , and $log(\pi_H/\pi_P)~N(normal.mean, normal.var)$ . `normal.mean` is the mean of this Gaussian prior. `normal.var` is the variance of this Gaussian prior distribution
`beta_prior`	for 3 active treatment design: vector of four values (a, b, c, d). `a` is the value of parameter `a` of the prior distribution for linkage parameter `beta_0` or `beta_0m`, `b` is the value of parameter `b` of the prior distribution for linkage parameter `beta_0` or `beta_0m`. `c` is the value of parameter `a` of the prior distribution for linkage parameter `beta_1` or `beta_1m`. `d` is the value of parameter `b` of the prior distribution for linkage parameter `beta_1` or `beta_1m`. for dose level design: vector of two values (a, b). `a` is the parameter `a` of the prior distribution for linkage parameter `beta`. `b` is the parameter b of the prior distribution for linkage parameter `beta`. Please check the `Details` section for more explanation
`n_MCMC_chain`	number of MCMC chains, default to 1.
`n.adapt`	the number of iterations for adaptation
`BURN.IN`	number of burn-in iterations for MCMC
`thin`	thinning interval for monitors
`MCMC_SAMPLE`	number of iterations for MCMC
`ci`	coverage probability for credible intervals, default = 0.95
`six`	TRUE or FALSE. If TRUE, will run the six beta model (allow for estimating `beta_0m` and `beta_1m` values that differ among different treatments m), if FALSE will run the two beta model. default = TRUE. Only need to specify this for 3 active treatment design.
`DTR`	TRUE or FALSE. If TRUE, will also return the expected response rate of dynamic treatment regimens. default = TRUE. Only need to specify this for 3 active treatment design.
`jags.model_options`	a list of optional arguments that are passed to `jags.model()` function.
`coda.samples_options`	a list of optional arguments that are passed to `coda.samples()` function.
`verbose`	TRUE or FALSE. If FALSE, no function message and progress bar will be printed.
`...`	further arguments. Not currently used.
`x`	object to summarize.

Details

The individual response rate is regarded as a permanent feature of the treatment. The second stage outcome is modeled conditionally on the first stage results linking the first and second stage response probabilities through linkage parameters. The first stage response rate is denoted as $\pi_m$ for treatment $m$ . In the two $\beta$ model, the second stage response rate for first stage responders is equal to $\beta_1\pi_m$ . For nonresponders to treatment $m$ in the first stage who receive treatment $m'$ in the second the stage, the second stage response rate in the second stage is equal to $\beta_0\pi_{m'}$ . In the six $\beta$ model, the second stage response rate of the first stage responders to treatment m is denoted by $\beta_{1m}\pi_m$ , and the second stage response rate of the non-responders to first stage treatment $m$ who receive treatment $m'$ in the second stage is denoted by $\beta_{0m}\pi_{m'}$ . All the $\beta$ s are linkage parameters.

Please refer to the paper listed under reference section for standard snSMART trial design and detailed definition of parameters.

Note that this package does not include the JAGS library, users need to install JAGS separately. Please check this page for more details: https://sourceforge.net/projects/mcmc-jags/

Value

`posterior_sample`	an `mcmc.list` object generated through the `coda.samples()` function, which includes posterior samples of the link parameters and response rates generated through the MCMC process
`pi_hat_bjsm`	estimate of response rate/treatment effect
`se_hat_bjsm`	standard error of the response rate
`ci_pi_A(P)`, `ci_pi_B(L)`, `ci_pi_C(H)`	x% credible intervals for treatment A(P), B(L), C(H)
`diff_AB(PL)`, `diff_BC(LH). diff_AC(PH)`	estimate of differences between treatments A(P) and B(L), B(L) and C(H), A(P) and C(H)
`ci_diff_AB(PL)`, `ci_diff_BC(LH)`, `ci_diff_AC(PH)`	x% credible intervals for the estimated differences between treatments A(P) and B(L), B(L) and C(H), A(P) and C(H)
`se_AB(PL)`, `se_BC(LH)`, `se_AC(PH)`	standard error for the estimated differences between treatments A(P) and B(L), B(L) and C(H), A(P) and C(H)
`beta0_hat`, `beta1_hat`	linkage parameter `beta0` and `beta1` estimates
`se_beta0_hat`, `se_beta1_hat`	standard error of the estimated value of linkage parameter `beta0` and `beta1`
`ci_beta0_hat`, `ci_beta1_hat`	linkage parameter `beta0` and `beta1` credible interval
`pi_DTR_est`	expected response rate of dynamic treatment regimens (DTRs)
`pi_DTR_se`	standard error for the estimated DTR response rate
`ci_pi_AB`, `ci_pi_AC`, `ci_pi_BA`, `ci_pi_BC`, `ci_pi_CA`, `ci_pi_CB`	x% credible intervals for the estimated DTR response rate

References

Wei, B., Braun, T.M., Tamura, R.N. and Kidwell, K.M., 2018. A Bayesian analysis of small n sequential multiple assignment randomized trials (snSMARTs). Statistics in medicine, 37(26), pp.3723-3732. URL: doi:10.1002/sim.7900

Chao, Y.C., Trachtman, H., Gipson, D.S., Spino, C., Braun, T.M. and Kidwell, K.M., 2020. Dynamic treatment regimens in small n, sequential, multiple assignment, randomized trials: An application in focal segmental glomerulosclerosis. Contemporary clinical trials, 92, p.105989. URL: doi:10.1016/j.cct.2020.105989

Fang, F., Hochstedler, K.A., Tamura, R.N., Braun, T.M. and Kidwell, K.M., 2021. Bayesian methods to compare dose levels with placebo in a small n, sequential, multiple assignment, randomized trial. Statistics in Medicine, 40(4), pp.963-977. URL: doi:10.1002/sim.8813

Examples

mydata <- data_binary

BJSM_result <- BJSM_binary(
  data = mydata, prior_dist = c("beta", "beta", "pareto"),
  pi_prior = c(0.4, 1.6, 0.4, 1.6, 0.4, 1.6), beta_prior = c(1.6, 0.4, 3, 1),
  n_MCMC_chain = 1, n.adapt = 1000, MCMC_SAMPLE = 2000, ci = 0.95,
  six = TRUE, DTR = TRUE, verbose = FALSE
)


BJSM_result2 <- BJSM_binary(
  data = mydata, prior_dist = c("beta", "beta", "pareto"),
  pi_prior = c(0.4, 1.6, 0.4, 1.6, 0.4, 1.6), beta_prior = c(1.6, 0.4, 3, 1),
  n_MCMC_chain = 1, n.adapt = 10000, MCMC_SAMPLE = 60000, ci = 0.95,
  six = FALSE, DTR = FALSE, verbose = FALSE
)

summary(BJSM_result)
summary(BJSM_result2)


data <- data_dose
BJSM_dose_result <- BJSM_binary(
  data = data_dose, prior_dist = c("beta", "gamma"),
  pi_prior = c(3, 17), normal.par = c(0.2, 100), beta_prior = c(2, 2),
  n_MCMC_chain = 2, n.adapt = 1000, MCMC_SAMPLE = 6000, ci = 0.95, verbose = FALSE
)

summary(BJSM_dose_result)

mydata <- data_binary

BJSM_result <- BJSM_binary(
  data = mydata, prior_dist = c("beta", "beta", "pareto"),
  pi_prior = c(0.4, 1.6, 0.4, 1.6, 0.4, 1.6), beta_prior = c(1.6, 0.4, 3, 1),
  n_MCMC_chain = 1, n.adapt = 1000, MCMC_SAMPLE = 2000, ci = 0.95,
  six = TRUE, DTR = TRUE, verbose = FALSE
)


BJSM_result2 <- BJSM_binary(
  data = mydata, prior_dist = c("beta", "beta", "pareto"),
  pi_prior = c(0.4, 1.6, 0.4, 1.6, 0.4, 1.6), beta_prior = c(1.6, 0.4, 3, 1),
  n_MCMC_chain = 1, n.adapt = 10000, MCMC_SAMPLE = 60000, ci = 0.95,
  six = FALSE, DTR = FALSE, verbose = FALSE
)

summary(BJSM_result)
summary(BJSM_result2)


data <- data_dose
BJSM_dose_result <- BJSM_binary(
  data = data_dose, prior_dist = c("beta", "gamma"),
  pi_prior = c(3, 17), normal.par = c(0.2, 100), beta_prior = c(2, 2),
  n_MCMC_chain = 2, n.adapt = 1000, MCMC_SAMPLE = 6000, ci = 0.95, verbose = FALSE
)

summary(BJSM_dose_result)

BJSM continuous (snSMART with three active treatments and a continuous outcome design)

Description

BJSM (Bayesian Joint Stage Modeling) method that borrows information across both stages to estimate the individual response rate of each treatment (with continuous outcome and a mapping function).

Usage

BJSM_c(
  data,
  xi_prior.mean,
  xi_prior.sd,
  phi3_prior.sd,
  n_MCMC_chain,
  n.adapt,
  MCMC_SAMPLE,
  ci = 0.95,
  n.digits,
  thin = 1,
  BURN.IN = 100,
  jags.model_options = NULL,
  coda.samples_options = NULL,
  verbose = FALSE,
  ...
)

## S3 method for class 'BJSM_c'
summary(object, ...)

## S3 method for class 'summary.BJSM_c'
print(x, ...)

## S3 method for class 'BJSM_c'
print(x, ...)
BJSM_c(
  data,
  xi_prior.mean,
  xi_prior.sd,
  phi3_prior.sd,
  n_MCMC_chain,
  n.adapt,
  MCMC_SAMPLE,
  ci = 0.95,
  n.digits,
  thin = 1,
  BURN.IN = 100,
  jags.model_options = NULL,
  coda.samples_options = NULL,
  verbose = FALSE,
  ...
)

## S3 method for class 'BJSM_c'
summary(object, ...)

## S3 method for class 'summary.BJSM_c'
print(x, ...)

## S3 method for class 'BJSM_c'
print(x, ...)

Arguments

`data`	trial ddatset with columns: `id, trt1` (treatment 1), `stage1outcome, stay` (stay = 1 if patient stay on the same treatment in stage 2, otherwise stay = 0), `trt2` (treatment 2), `stage2outcome`
`xi_prior.mean`	a 3-element vector of mean of the prior distributions (normal distribution) for `xi`s (treatment effect). Please check the `Details` section for more explaination
`xi_prior.sd`	a 3-element vector of standard deviation of the prior distributions (normal distribution) for `xi`s (treatment effect). Please check the `Details` section for more explaination
`phi3_prior.sd`	standard deviation of the prior distribution (folded normal distribution) of `phi3` (if the patient stays on the same treatment, `phi3` is the cumulative effect of stage 1 that occurs on the treatment longer term). Please check the `Details` section for more explaination
`n_MCMC_chain`	number of MCMC chains, default to 1
`n.adapt`	the number of iterations for adaptation
`MCMC_SAMPLE`	number of iterations for MCMC
`ci`	coverage probability for credible intervals, default = 0.95
`n.digits`	number of digits to keep in the final estimation of treatment effect
`thin`	thinning interval for monitors
`BURN.IN`	number of burn-in iterations for MCMC
`jags.model_options`	a list of optional arguments that are passed to `jags.model()` function.
`coda.samples_options`	a list of optional arguments that are passed to `coda.samples()` function.
`verbose`	TRUE or FALSE. If FALSE, no function message and progress bar will be printed.
`...`	further arguments. Not currently used.
`object`	object to summarize.
`x`	object to print

Details

section 2.2.1 and 2.2.2 of the paper listed under reference provides a detailed description of the assumptions and prior distributions of the model.

Note that this package does not include the JAGS library, users need to install JAGS separately. Please check this page for more details: https://sourceforge.net/projects/mcmc-jags/

Value

posterior_sample

an mcmc.list object generated through the coda.samples() function, which includes posterior samples of the link parameters and response rates generated through the MCMC process

mean_estimate

BJSM estimate of each parameter:

phi1 - lingering effect of the first treatment
phi3 - if the patient stays on the same treatment, phi3 is the cumulative effect of stage 1 that occurs on the treatment longer term
xi_j - the expected effect of treatment j, j = 1, 2, 3 in the first stage
V1,V2 are the variance-covariance matrix of the multivariate distribution. V1 is for patients who stay on the same treatment, and V2 is for patients who switch treatments. This allows those who stay on the same treatment to have a different correlation between stage one stage two outcomes than those who switch treatments.

ci_estimate

x% credible interval for each parameter. By default round to 2 decimal places, if more decimals are needed, please access the results by ⁠[YourResultName]$ci_estimates$CI_low⁠ or ⁠[YourResultName]$ci_estimates$CI_high⁠

References

Hartman, H., Tamura, R.N., Schipper, M.J. and Kidwell, K.M., 2021. Design and analysis considerations for utilizing a mapping function in a small sample, sequential, multiple assignment, randomized trials with continuous outcomes. Statistics in Medicine, 40(2), pp.312-326. URL: doi:10.1002/sim.8776

Examples

trialData <- trialDataMF

BJSM_result <- BJSM_c(
  data = trialData, xi_prior.mean = c(50, 50, 50),
  xi_prior.sd = c(50, 50, 50), phi3_prior.sd = 20, n_MCMC_chain = 1,
  n.adapt = 1000, MCMC_SAMPLE = 5000, BURIN.IN = 1000, ci = 0.95, n.digits = 5, verbose = FALSE
)

summary(BJSM_result)
print(BJSM_result)
trialData <- trialDataMF

BJSM_result <- BJSM_c(
  data = trialData, xi_prior.mean = c(50, 50, 50),
  xi_prior.sd = c(50, 50, 50), phi3_prior.sd = 20, n_MCMC_chain = 1,
  n.adapt = 1000, MCMC_SAMPLE = 5000, BURIN.IN = 1000, ci = 0.95, n.digits = 5, verbose = FALSE
)

summary(BJSM_result)
print(BJSM_result)

Dataset with binary outcomes

Description

sample synthetic dataset of snSMART (3 active treatment) with binary outcomes

Usage

data_binary
data_binary

Format

This data frame contains the following columns:

treatment_stageI: treatment received in stage 1 - possible values: 1 (placebo), 2, 3
response_stageI: whether patients respond to stage 1 treatment - possible values: 0 (nonresponder), 1 (responder)
treatment_stageII: treatment received in stage 2 - possible values: 2, 3
response_stageII: whether patients respond to stage 2 treatment - possible values: 0 (nonresponder), 1 (responder)

Examples

mydata <- data_binary
LPJSM_result <- LPJSM_binary(data = mydata, six = TRUE, DTR = TRUE)

mydata <- data_binary
LPJSM_result <- LPJSM_binary(data = mydata, six = TRUE, DTR = TRUE)

Dose Level dataset with binary outcomes

Description

sample synthetic dataset of snSMART (dose level treatment) with binary outcomes

Usage

data_dose
data_dose

Format

This data frame contains the following columns:

treatment_stageI: treatment received in stage 1 - possible values: 1 (placebo), 2, 3
response_stageI: whether patients respond to stage 1 treatment - possible values: 0 (nonresponder), 1 (responder)
treatment_stageII: treatment received in stage 2 - possible values: 2, 3
response_stageII: whether patients respond to stage 2 treatment - possible values: 0 (nonresponder), 1 (responder)

Examples

mydata <- data_dose
BJSM_dose_result <- BJSM_binary(
  data = data_dose, prior_dist = c("beta", "gamma"),
  pi_prior = c(3, 17), normal.par = c(0.2, 100), beta_prior = c(2, 2),
  n_MCMC_chain = 2, n.adapt = 100, MCMC_SAMPLE = 2000, ci = 0.95
)

mydata <- data_dose
BJSM_dose_result <- BJSM_binary(
  data = data_dose, prior_dist = c("beta", "gamma"),
  pi_prior = c(3, 17), normal.par = c(0.2, 100), beta_prior = c(2, 2),
  n_MCMC_chain = 2, n.adapt = 100, MCMC_SAMPLE = 2000, ci = 0.95
)

BJSM method for interim analysis and final analysis of group sequential trial design

Description

After obtain real trial data, this function can be used to decide which arm to drop in an interim analysis or provide a full final analysis.

Usage

group_seq(
  data,
  interim = TRUE,
  drop_threshold_pair = NULL,
  prior_dist,
  pi_prior,
  beta_prior,
  MCMC_SAMPLE,
  n.adapt,
  thin = 1,
  BURN.IN = 100,
  n_MCMC_chain,
  ci = 0.95,
  DTR = TRUE,
  jags.model_options = NULL,
  coda.samples_options = NULL,
  verbose = FALSE,
  ...
)

## S3 method for class 'summary.group_seq'
print(x, ...)

## S3 method for class 'group_seq'
print(x, ...)
group_seq(
  data,
  interim = TRUE,
  drop_threshold_pair = NULL,
  prior_dist,
  pi_prior,
  beta_prior,
  MCMC_SAMPLE,
  n.adapt,
  thin = 1,
  BURN.IN = 100,
  n_MCMC_chain,
  ci = 0.95,
  DTR = TRUE,
  jags.model_options = NULL,
  coda.samples_options = NULL,
  verbose = FALSE,
  ...
)

## S3 method for class 'summary.group_seq'
print(x, ...)

## S3 method for class 'group_seq'
print(x, ...)

Arguments

`data`	dataset should include 8 columns: `time.1st.trt` (first treatment starts time), `time.1st.resp` (first response time), `time.2nd.trt` (second treatment starts time), `time.2nd.resp` (second response time), `trt.1st` (treatment arm for first treatment), `resp.1st` (response for first treatment), `trt.2nd` (treatment arm for second treatment), `resp.2nd` (response for second treatment) data yet to be observed should be marked as "`NA`"
`interim`	indicates whether user is conducting an interim analysis via BJSM (`interim` = TRUE) or an final analysis via BJSM (`interim` = FALSE)
`drop_threshold_pair`	a vector of 2 values (`drop_threshold_tau_l`, `drop_threshold_psi_l`). Both `drop_threshold_tau_l` and `drop_threshold_psi_l` should be between 0 and 1. only assign value to this parameter when `interim = TRUE`. See the details section for more explanation
`prior_dist`	vector of three values ("prior distribution for `pi`", "prior distribution for `beta0`", "prior distribution for `beta1`"), user can choose from "gamma", "beta", "pareto". e.g. prior_dist = c("beta", "beta", "pareto")
`pi_prior`	vector of six values (a, b, c, d, e, f), where a and b are the parameter `a` and parameter `b` of the prior distribution for `pi_1A`, c and d are the parameter `a` and parameter `b` of the prior distribution for `pi_1B`, and e and f are the parameter `a` and parameter `b` of the prior distribution for `pi_1C`. Please check the `Details` section for more explanation
`beta_prior`	vector of four values (`beta0_prior.a`, `beta0_prior.b`, `beta1_prior.a`, `beta1_prior.c`). `beta0_prior.a` is the parameter a of the prior distribution for linkage parameter `beta0`. `beta0_prior.b` is the parameter b of the prior distribution for linkage parameter `beta0`. `beta1_prior.a` is the parameter a of the prior distribution for linkage parameter `beta1`. `beta1_prior.c` is the parameter b of the prior distribution for linkage parameter `beta1`. Please check the `Details` section for more explanation
`MCMC_SAMPLE`	number of iterations for MCMC
`n.adapt`	the number of iterations for adaptation
`thin`	thinning interval for monitors
`BURN.IN`	number of burn-in iterations for MCMC
`n_MCMC_chain`	number of MCMC chains, default to 1
`ci`	coverage probability for credible intervals, default = 0.95. only assign value to this parameter when `interim = FALSE`.
`DTR`	if TRUE, will also return the expected response rate of dynamic treatment regimens. default = TRUE. only assign value to this parameter when `interim = FALSE`.
`jags.model_options`	a list of optional arguments that are passed to `jags.model()` function.
`coda.samples_options`	a list of optional arguments that are passed to `coda.samples()` function.
`verbose`	TRUE or FALSE. If FALSE, no function message and progress bar will be printed.
`...`	further arguments. Not currently used.
`x`	object to summarize.

Details

For gamma distribution, prior.a is the shape parameter r, prior.b is the rate parameter lambda. For beta distribution, prior.a is the shape parameter a, prior.b is the shape parameter b. For pareto distribution, prior.a is the scale parameter alpha, prior.b is the shape parameter c (see jags user manual). The individual response rate is regarded as a permanent feature of the treatment. The second stage outcome is modeled conditionally on the first stage results linking the first and second stage response probabilities through linkage parameters.

(paper provided in the reference section, section 2.2.2 Bayesian decision rules. drop_threshold_tau_l and drop_threshold_psi_l correspond to $tau_l$ and $psi_l$ respectively)

Please refer to the paper listed under reference section for detailed definition of parameters. Note that this package does not include the JAGS library, users need to install JAGS separately. Please check this page for more details: https://sourceforge.net/projects/mcmc-jags/

Value

if interim = TRUE, this function returns either 0 - no arm is dropped, or A/B/C - arm A/B/C is dropped

if interim = FALSE, this function returns:

`posterior_sample`	an `mcmc.list` object generated through the `coda.samples()` function, which includes posterior samples of the link parameters and response rates generated through the MCMC process
`pi_hat_bjsm`	estimate of response rate/treatment effect
`se_hat_bjsm`	standard error of the response rate
`ci_pi_A`, `ci_pi_B`, `ci_pi_C`	x% credible intervals for treatment A, B, C
`diff_AB`, `diff_BC. diff_AC`	estimate of differences between treatments A and B, B and C, A and C
`ci_diff_AB`, `ci_diff_BC`, `ci_diff_AC`	x% credible intervals for the differences between treatments A and B, B and C, A and C
`se_AB`, `se_BC`, `se_AC`	standard error for the differences between treatments A and B, B and C, A and C
`beta0_hat`, `beta1_hat`	linkage parameter `beta0` and `beta1` estimates
`se_beta0_hat`, `se_beta1_hat`	standard error of the estimated value of linkage parameter `beta0` and `beta1`
`ci_beta0_hat`, `ci_beta1_hat`	linkage parameter `beta0` and `beta1` credible interval
`pi_DTR_est`	expected response rate of dynamic treatment regimens (DTRs)
`pi_DTR_se`	standard error for the estimated DTR response rate
`ci_pi_AB`, `ci_pi_AC`, `ci_pi_BA`, `ci_pi_BC`, `ci_pi_CA`, `ci_pi_CB`	x% credible intervals for the estimated DTR response rate

References

Chao, Y.C., Braun, T.M., Tamura, R.N. and Kidwell, K.M., 2020. A Bayesian group sequential small n sequential multiple‐assignment randomized trial. Journal of the Royal Statistical Society: Series C (Applied Statistics), 69(3), pp.663-680. URL: doi:10.1111/rssc.12406

Examples

mydata <- groupseqDATA_look1

result1 <- group_seq(
  data = mydata, interim = TRUE, drop_threshold_pair = c(0.5, 0.4),
  prior_dist = c("beta", "beta", "pareto"), pi_prior = c(0.4, 1.6, 0.4, 1.6, 0.4, 1.6),
  beta_prior = c(1.6, 0.4, 3, 1), MCMC_SAMPLE = 6000, n.adapt = 1000, n_MCMC_chain = 1
)

summary(result1)


mydata <- groupseqDATA_full
result2 <- group_seq(
  data = mydata, interim = FALSE, prior_dist = c("beta", "beta", "pareto"),
  pi_prior = c(0.4, 1.6, 0.4, 1.6, 0.4, 1.6),
  beta_prior = c(1.6, 0.4, 3, 1), MCMC_SAMPLE = 6000, n.adapt = 1000,
  n_MCMC_chain = 1, ci = 0.95, DTR = TRUE
)

summary(result2)

mydata <- groupseqDATA_look1

result1 <- group_seq(
  data = mydata, interim = TRUE, drop_threshold_pair = c(0.5, 0.4),
  prior_dist = c("beta", "beta", "pareto"), pi_prior = c(0.4, 1.6, 0.4, 1.6, 0.4, 1.6),
  beta_prior = c(1.6, 0.4, 3, 1), MCMC_SAMPLE = 6000, n.adapt = 1000, n_MCMC_chain = 1
)

summary(result1)


mydata <- groupseqDATA_full
result2 <- group_seq(
  data = mydata, interim = FALSE, prior_dist = c("beta", "beta", "pareto"),
  pi_prior = c(0.4, 1.6, 0.4, 1.6, 0.4, 1.6),
  beta_prior = c(1.6, 0.4, 3, 1), MCMC_SAMPLE = 6000, n.adapt = 1000,
  n_MCMC_chain = 1, ci = 0.95, DTR = TRUE
)

summary(result2)

Group sequential full data

Description

sample synthetic dataset of group sequential trial design snSMART, can be used for final analysis

Usage

groupseqDATA_full
groupseqDATA_full

Format

This data frame contains the following columns:

time.1st.trt: first treatment time
time.1st.resp: first response time
time.2nd.trt: second treatment time
time.2nd.resp: second response time
trt.1st: treatment arm for first treatment
resp.1st: response for first treatment
trt.2nd: treatment arm for second treatment
resp.2nd: response for second treatment

Examples

mydata <- groupseqDATA_full
result2 <- group_seq(
  data = mydata, interim = FALSE, prior_dist = c(
    "beta", "beta", "pareto"
  ), pi_prior = c(0.4, 1.6, 0.4, 1.6, 0.4, 1.6),
  beta_prior = c(1.6, 0.4, 3, 1), MCMC_SAMPLE = 6000, n.adapt = 1000,
  n_MCMC_chain = 1, ci = 0.95, DTR = TRUE
)
mydata <- groupseqDATA_full
result2 <- group_seq(
  data = mydata, interim = FALSE, prior_dist = c(
    "beta", "beta", "pareto"
  ), pi_prior = c(0.4, 1.6, 0.4, 1.6, 0.4, 1.6),
  beta_prior = c(1.6, 0.4, 3, 1), MCMC_SAMPLE = 6000, n.adapt = 1000,
  n_MCMC_chain = 1, ci = 0.95, DTR = TRUE
)

Group sequential data look 1

Description

sample synthetic dataset of group sequential trial design snSMART, can be used for interim analysis

Usage

groupseqDATA_look1
groupseqDATA_look1

Format

This data frame contains the following columns:

time.1st.trt: first treatment time
time.1st.resp: first response time
time.2nd.trt: second treatment time
time.2nd.resp: second response time
trt.1st: treatment arm for first treatment
resp.1st: response for first treatment
trt.2nd: treatment arm for second treatment
resp.2nd: response for second treatment

Examples

mydata <- groupseqDATA_look1

result1 <- group_seq(
  data = mydata, interim = TRUE, drop_threshold_pair = c(0.5, 0.4),
  prior_dist = c("beta", "beta", "pareto"), pi_prior = c(0.4, 1.6, 0.4, 1.6, 0.4, 1.6),
  beta_prior = c(1.6, 0.4, 3, 1), MCMC_SAMPLE = 6000, n.adapt = 1000, n_MCMC_chain = 1
)

mydata <- groupseqDATA_look1

result1 <- group_seq(
  data = mydata, interim = TRUE, drop_threshold_pair = c(0.5, 0.4),
  prior_dist = c("beta", "beta", "pareto"), pi_prior = c(0.4, 1.6, 0.4, 1.6, 0.4, 1.6),
  beta_prior = c(1.6, 0.4, 3, 1), MCMC_SAMPLE = 6000, n.adapt = 1000, n_MCMC_chain = 1
)

LPJSM for snSMART with binary outcomes (3 active treatments or placebo and two dose level)

Description

A joint-stage regression model (LPJSM) is a frequentist modeling approach that incorporates the responses of both stages as repeated measurements for each subject. Generalized estimating equations (GEE) are used to estimate the response rates of each treatment. The marginal response rates for each DTR can also be obtained based on the GEE results.

Usage

LPJSM_binary(data, six = TRUE, DTR = TRUE, ...)

## S3 method for class 'LPJSM_binary'
summary(object, ...)

## S3 method for class 'summary.LPJSM_binary'
print(x, ...)

## S3 method for class 'LPJSM_binary'
print(x, ...)
LPJSM_binary(data, six = TRUE, DTR = TRUE, ...)

## S3 method for class 'LPJSM_binary'
summary(object, ...)

## S3 method for class 'summary.LPJSM_binary'
print(x, ...)

## S3 method for class 'LPJSM_binary'
print(x, ...)

Arguments

`data`	dataset with columns named as `treatment_stageI`, `response_stageI`, `treatment_stageII` and `response_stageII`
`six`	if TRUE, will run the six beta model, if FALSE will run the two beta model. Default is `six = TRUE`
`DTR`	if TRUE, will also return the expected response rate and its standard error of dynamic treatment regimens
`...`	optional arguments that are passed to `geepack::geeglm()` function.
`object`	object to print
`x`	object to summarize.

Value

a list containing

`GEE_output`	- original output of the GEE (geeglm) model
`pi_hat`	- estimate of response rate/treatment effect
`sd_pi_hat`	- standard error of the response rate
`pi_DTR_hat`	- expected response rate of dynamic treatment regimens (DTRs)
`pi_DTR_se`	- standard deviation of DTR estimates

References

Examples

data <- data_binary

LPJSM_result <- LPJSM_binary(data = data, six = TRUE, DTR = TRUE)

summary(LPJSM_result)

data <- data_binary

LPJSM_result <- LPJSM_binary(data = data, six = TRUE, DTR = TRUE)

summary(LPJSM_result)

Sample size calculation for snSMART with 3 active treatments and a binary outcome

Description

conduct Bayesian sample size calculation for a snSMART design with 3 active treatments and a binary outcome to distinguish the best treatment from the second-best treatment using the Bayesian joint stage model.

Usage

sample_size(pi, beta1, beta0, coverage, power, mu, n, verbose = FALSE)

## S3 method for class 'sample_size'
summary(object, ...)

## S3 method for class 'summary.sample_size'
print(x, ...)

## S3 method for class 'sample_size'
print(x, ...)
sample_size(pi, beta1, beta0, coverage, power, mu, n, verbose = FALSE)

## S3 method for class 'sample_size'
summary(object, ...)

## S3 method for class 'summary.sample_size'
print(x, ...)

## S3 method for class 'sample_size'
print(x, ...)

Arguments

`pi`	a vector with 3 values (`piA`, `piB`, `piC`). `piA` is the the response rate (ranges from 0.01 to 0.99) for treatment A, `piB` is the response rate (ranges from 0.01 to 0.99) for treatment B, `piC` is the response rate (ranges from 0.01 to 0.99) for treatment C
`beta1`	the linkage parameter (ranges from 1.00 to 1/largest response rate) for first stage responders. (A smaller value leads to more conservative sample size calculation because two stages are less correlated)
`beta0`	the linkage parameter (ranges from 0.01 to 0.99) for first stage non-responders. A larger value leads to a more conservative sample size calculation because two stages are less correlated
`coverage`	the coverage rate (ranges from 0.01 to 0.99) for the posterior difference of top two treatments
`power`	the probability (ranges from 0.01 to 0.99) for identify the best treatment
`mu`	a vector with 3 values (`muA`, `muB`, `muC`). `muA` is the prior mean (ranges from 0.01 to 0.99) for treatment A, `muB` is the prior mean (ranges from 0.01 to 0.99) for treatment B, `muC` is the prior mean (ranges from 0.01 to 0.99) for treatment C
`n`	a vector with 3 values (`nA`, `nB`, `nC`). `nA` is the prior sample size (larger than 0) for treatment A. `nB` is the prior sample size (larger than 0) for treatment B. `nC` is the prior sample size (larger than 0) for treatment C
`verbose`	TRUE or FALSE. If FALSE, no function message and progress bar will be printed.
`object`	object to summarize.
`...`	further arguments. Not currently used.
`x`	object to print

Details

Note that this package does not include the JAGS library, users need to install JAGS separately. Please check this page for more details: https://sourceforge.net/projects/mcmc-jags/ This function may take a few minutes to run

Value

`final_N`	the estimated sample size per arm for this snSMART
`critical_value`	critical value based on the provided coverage value
`grid_result`	for each iteration we calculate `l`, where `l` belongs to `{2 * (pi_(1) - pi_(2)), ..., 0.02, 0.01}`; `E(D)`: the mean of the posterior distribution of `D`, , where `D = pi_(1) = pi_(2)`; `Var(D)`: the variance of the posterior distribution of `D`; `N`: the corresponding sample size; and `power`: the resulting power of this iteration

References

Wei, B., Braun, T.M., Tamura, R.N. and Kidwell, K., 2020. Sample size determination for Bayesian analysis of small n sequential, multiple assignment, randomized trials (snSMARTs) with three agents. Journal of Biopharmaceutical Statistics, 30(6), pp.1109-1120. URL: doi:10.1080/10543406.2020.1815032

Examples

## Not run: 
# short running time example
sampleSize <- sample_size(
  pi = c(0.7, 0.5, 0.25), beta1 = 1.4, beta0 = 0.5, coverage = 0.9,
  power = 0.3, mu = c(0.65, 0.55, 0.25), n = c(10, 10, 10)
)

## End(Not run)


sampleSize <- sample_size(
  pi = c(0.7, 0.5, 0.25), beta1 = 1.4, beta0 = 0.5, coverage = 0.9,
  power = 0.8, mu = c(0.65, 0.55, 0.25), n = c(4, 2, 3)
)


## Not run: 
# short running time example
sampleSize <- sample_size(
  pi = c(0.7, 0.5, 0.25), beta1 = 1.4, beta0 = 0.5, coverage = 0.9,
  power = 0.3, mu = c(0.65, 0.55, 0.25), n = c(10, 10, 10)
)

## End(Not run)


sampleSize <- sample_size(
  pi = c(0.7, 0.5, 0.25), beta1 = 1.4, beta0 = 0.5, coverage = 0.9,
  power = 0.8, mu = c(0.65, 0.55, 0.25), n = c(4, 2, 3)
)

Summarizing BJSM fits

Description

summary method for class "BJSM_binary"

Usage

## S3 method for class 'BJSM_binary'
summary(object, ...)
## S3 method for class 'BJSM_binary'
summary(object, ...)

Arguments

`object`	an object of class "`BJSM_binary`", usually, a result of a call to `BJSM_binary`
`...`	further arguments. Not currently used.

Value

Treatment Effects Estimate: a 3 x 5 matrix with columns for the estimated treatment effects, its standard error, coverage probability of its credible interval, lower bound for its credible interval and higher bound for its credible interval
Differences between Treatments: a 3 x 5 matrix with columns for the estimated differences in treatment effects between two treatments, its standard error, coverage probability of its credible interval, lower bound and higher bound of the credible interval
Linkage Parameter Estimate: a 2 x 5 matrix, if the two beta model is fitted, or a 6 x 5 matrix, if the six beta model is fitted, with columns for the estimated linkage parameters
Expected Response Rate of Dynamic Treatment Regimens (DTR): only when DTR = TRUE

Summarizing BJSM fits

Description

summary method for class BJSM_dose_binary

Usage

## S3 method for class 'BJSM_dose_binary'
summary(object, ...)
## S3 method for class 'BJSM_dose_binary'
summary(object, ...)

Arguments

`object`	an object of class `BJSM_dose_binary`, usually, a result of a call to `BJSM_binary`
`...`	further arguments. Not currently used.

Value

Treatment Effects Estimate: a 3 x 5 matrix with columns for the estimated treatment effects, its standard error, coverage probability of its credible interval, lower bound for its credible interval and higher bound for its credible interval
Differences between Treatments: a 3 x 5 matrix with columns for the estimated differences in treatment effects between two treatments, its standard error, coverage probability of its credible interval, lower bound and higher bound of the credible interval
Linkage Parameter Estimate: a 6 x 5 matrix with columns for the estimated linkage parameters

Summarizing BJSM fits

Description

summary method for class "group_seq"

Usage

## S3 method for class 'group_seq'
summary(object, ...)
## S3 method for class 'group_seq'
summary(object, ...)

Arguments

`object`	an object of class "`group_seq`", usually, a result of a call to `group_seq`
`...`	further arguments. Not currently used.

Value

Treatment Effects Estimate: a 3 x 5 matrix with columns for the estimated treatment effects, its standard error, coverage probability of its credible interval, lower bound for its credible interval and higher bound for its credible interval
Differences between Treatments: a 3 x 5 matrix with columns for the estimated differences in treatment effects between two treatments, its standard error, coverage probability of its credible interval, lower bound and higher bound of the credible interval
Linkage Parameter Estimate: a 2 x 5 matrix, if the two beta model is fitted, or a 6 x 5 matrix, if the six beta model is fitted, with columns for the estimated linkage parameters
Expected Response Rate of Dynamic Treatment Regimens (DTR): only when DTR = TRUE

Dataset with continuous outcomes

Description

sample synthetic dataset of snSMART (mapping function) with continuous outcomes

Usage

trialDataMF
trialDataMF

Format

This data frame contains the following columns:

id: participant ID
trt1: treatment received in stage 1 - possible values: 1 (placebo), 2, 3
stage1outcome: a number between 0-100 that represents the stage 1 treatment effect
stay: indicates whether the participant stayed on the same treatment arm in stage 2 - possible values: 0 (didn't stay), 1 (stayed)
trt2: treatment received in stage 2 - possible values: 2, 3
stage2outcome: a number between 0-100 that represents the stage 2 treatment effect

Examples

trialData <- trialDataMF

BJSM_result <- BJSM_c(
  data = trialData, xi_prior.mean = c(50, 50, 50),
  xi_prior.sd = c(50, 50, 50), phi3_prior.sd = 20, n_MCMC_chain = 1,
  n.adapt = 1000, MCMC_SAMPLE = 5000, ci = 0.95, n.digits = 5
)

summary(BJSM_result)
print(BJSM_result)

trialData <- trialDataMF

BJSM_result <- BJSM_c(
  data = trialData, xi_prior.mean = c(50, 50, 50),
  xi_prior.sd = c(50, 50, 50), phi3_prior.sd = 20, n_MCMC_chain = 1,
  n.adapt = 1000, MCMC_SAMPLE = 5000, ci = 0.95, n.digits = 5
)

summary(BJSM_result)
print(BJSM_result)

Package 'snSMART'

Help Index

BJSM for snSMART (3 active treatments/placebo and 2 dose level) with binary outcome

Description

Usage

Arguments

Details

Value

References

See Also

Examples

BJSM continuous (snSMART with three active treatments and a continuous outcome design)

Description

Usage

Arguments

Details

Value

References

Examples

Dataset with binary outcomes

Description

Usage

Format

Examples

Dose Level dataset with binary outcomes

Description

Usage

Format

Examples

BJSM method for interim analysis and final analysis of group sequential trial design

Description

Usage

Arguments

Details

Value

References

Examples

Group sequential full data

Description

Usage

Format

Examples

Group sequential data look 1

Description

Usage

Format

Examples

LPJSM for snSMART with binary outcomes (3 active treatments or placebo and two dose level)

Description

Usage

Arguments

Value

References

See Also

Examples

Sample size calculation for snSMART with 3 active treatments and a binary outcome

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Summarizing BJSM fits

Description

Usage

Arguments

Value

Summarizing BJSM fits

Description

Usage

Arguments

Value

Summarizing BJSM fits

Description

Usage

Arguments

Value

Dataset with continuous outcomes