| Title: | Bayesian Set of Best Dynamic Treatment Regimes and Sample Size in SMARTs for Binary Outcomes |
|---|---|
| Description: | Permits determination of a set of optimal dynamic treatment regimes and sample size for a SMART design in the Bayesian setting with binary outcomes. Please see Artman (2020) <arXiv:2008.02341>. |
| Authors: | William Artman [aut, cre] |
| Maintainer: | William Artman <[email protected]> |
| License: | GPL-3 |
| Version: | 2.0.0 |
| Built: | 2024-11-21 06:08:42 UTC |
| Source: | https://github.com/cran/SMARTbayesR |
Computes the embedded dynamic treatment regime specific log-odds ratios.
LogOR( response_prob = c(0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8), stage_one_trt_one_response_prob = 0.6, stage_one_trt_two_response_prob = 0.3, stage_one_trt_three_response_prob = 0.4, design = "general" )LogOR( response_prob = c(0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8), stage_one_trt_one_response_prob = 0.6, stage_one_trt_two_response_prob = 0.3, stage_one_trt_three_response_prob = 0.4, design = "general" )
response_prob |
the probability of response for each of embedded treatment sequences. In the case of the design 1 SMART, there are 6, for the general design there are 8, and for Design-3 there are 9 embedded treatment sequences. |
stage_one_trt_one_response_prob |
the probability of response to stage-1 treatment given stage-1 treatment one. |
stage_one_trt_two_response_prob |
the probability of response to stage-1 treatment given stage-1 treatment two. |
stage_one_trt_three_response_prob |
the probability of response to stage-1 treatment given stage-1 treatment three (for design-3 only) |
design |
which SMART design: design-1 (ENGAGE-type), general, or design-3. |
The embedded dynamic treatment regime specific log-OR.
Computes the embedded dynamic treatment regime specific log risk-ratios.
LogRR( response_prob = c(0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8), stage_one_trt_one_response_prob = 0.6, stage_one_trt_two_response_prob = 0.3, stage_one_trt_three_response_prob = 0.4, design = "general" )LogRR( response_prob = c(0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8), stage_one_trt_one_response_prob = 0.6, stage_one_trt_two_response_prob = 0.3, stage_one_trt_three_response_prob = 0.4, design = "general" )
response_prob |
the probability of response for each of the embedded treatment sequences. In the case of the design 1 SMART there are 6, for the general design there are 8, and for design-3 there are 9. |
stage_one_trt_one_response_prob |
the probability of response to stage-1 treatment given stage-1 treatment one. |
stage_one_trt_two_response_prob |
the probability of response to stage-1 treatment given stage-1 treatment two. |
stage_one_trt_three_response_prob |
the probability of response to stage-1 treatment given stage-1 treatment three (for design-3 only) |
design |
which SMART design: design-1 (ENGAGE-type), general, or design-3 |
The embedded dynamic treatment regime specific log-Risk Ratios.
Compute simultaneous upper credible intervals from draws of embedded dynamic treatment regime probabilities given by the function argument “thetadraws”.
MCBUpperLimits(thetadraws, alpha = 0.05, design = "design-1", type = "log-OR")MCBUpperLimits(thetadraws, alpha = 0.05, design = "design-1", type = "log-OR")
thetadraws |
draws of the embedded dynamic treatment regimes. |
alpha |
the probability of excluding the true best EDTR from the set of best. |
design |
specifies to which SMART design to apply function: either design-1, general, or design-3. |
type |
summary statistic: log-OR, log-RR, or RD |
Upper 1-alpha level simultaneous credible interval limits for the embedded dynamic treatment regimes.
dat <- SimDesign1(sample_size=250, response_prob = c(0.5,0.9,0.3,0.7,0.5,0.8), stage_one_trt_one_response_prob = 0.7, stage_one_trt_two_response_prob = 0.4) x <- PosteriorTrtSeqProb(niter = 1000, dat, design = "design-1") thetadraws <- PosteriorEDTRProbs(x, design = "design-1") MCBUpperLimits(thetadraws, alpha = 0.05, design = "design-1", type = "log-OR")dat <- SimDesign1(sample_size=250, response_prob = c(0.5,0.9,0.3,0.7,0.5,0.8), stage_one_trt_one_response_prob = 0.7, stage_one_trt_two_response_prob = 0.4) x <- PosteriorTrtSeqProb(niter = 1000, dat, design = "design-1") thetadraws <- PosteriorEDTRProbs(x, design = "design-1") MCBUpperLimits(thetadraws, alpha = 0.05, design = "design-1", type = "log-OR")
Apply Robins' G-computation formula to compute the embedded dynamic treatment regime draws from as a weighted average of treatment sequence and stage-1 response probability draws.
If design is "design-1", then compute for Design 1 SMART with 6 embedded treatment sequences and 4 embedded dynamic treatment regimes.
If design is "general", then compute for General SMART with 8 embedded treatment sequences and 8 embedded dynamic treatment regimes.
If design is "design-3", then compute for Design 3 SMART with 9 embedded treatment sequences and 6 embedded dynamic treatment regimes.
PosteriorEDTRProbs(x, design = "design-1")PosteriorEDTRProbs(x, design = "design-1")
x |
A data frame consisting of draws from the posterior of the end of study response probabilities of each treatment sequence and of stage-1 response probabilities for each stage-1 treatment |
design |
Which SMART design to compute the posterior draws for: "design-1" or "general" or "design-3". |
For the General SMART design, x should have columns p_1, p_2, p_3, p_4, p_5, p_6, p_7, p_8, s1, and s2.
For the Design-1 SMART, x should have columns p_1, p_2, p_3, p_4, p_5, p_6, s1, and s2.
For the design-3 SMART, x should have columns
p_1, p_2, p_3, p_4, p_5, p_6, p_7, p_8, p_9 s1, s2, and s3
These are the posterior draws of the response probabilities for each treatment sequence and stage-1 response probability draws.
s1 contains the draws of the stage-1 response probability for the first treatment, s2 is analogous for the second treatment and s3 for the third treatment.
Matrix of EDTR specific posterior response probability draws at the end of the study There will be 4 columns for design-1, 8 columns for design general, and 6 columns for design-3 each corresponding to an EDTR. The number of rows will be the same as that of x.
dat <- SimDesign1(sample_size=250, response_prob = c(0.5,0.9,0.3,0.7,0.5,0.8), stage_one_trt_one_response_prob = 0.7, stage_one_trt_two_response_prob = 0.4) x <- PosteriorTrtSeqProb(niter = 1000, dat, design = "design-1") PosteriorEDTRProbs(x, design = "design-1")dat <- SimDesign1(sample_size=250, response_prob = c(0.5,0.9,0.3,0.7,0.5,0.8), stage_one_trt_one_response_prob = 0.7, stage_one_trt_two_response_prob = 0.4) x <- PosteriorTrtSeqProb(niter = 1000, dat, design = "design-1") PosteriorEDTRProbs(x, design = "design-1")
Draws from the posterior of the treatment sequence response probabilities.
PosteriorTrtSeqProb(niter, dat, design = "design-1")PosteriorTrtSeqProb(niter, dat, design = "design-1")
niter |
the number of posterior draws. |
dat |
a data frame (see Details). |
design |
an indicator of which SMART design, design-1, general, or design-3. |
dat should contain the following columns:
y, the end of study binary response indicator
a1, the stage-1 treatment assignment indicator
s, the end of stage-1 binary response indicator
Additionally, for design-1 and design-3 it should contain a2, the stage-2 treatment assignment indicator
For the general design, it should contain
a2r, stage-2 treatment assignment for responders to stage-1 treatment.
a2nr, stage-2 treatment assignment for non-responders to stage-1 treatment.
Posterior draws of the probability of response at the end of the study for each embedded treatment sequence and the posterior draws of the probability of response at the end of stage-1 for each stage-1 treatment.
dat <- SimDesign1(sample_size=250, response_prob = c(0.5,0.9,0.3,0.7,0.5,0.8), stage_one_trt_one_response_prob = 0.7, stage_one_trt_two_response_prob = 0.4) PosteriorTrtSeqProb(niter = 1000, dat, design = "design-1")dat <- SimDesign1(sample_size=250, response_prob = c(0.5,0.9,0.3,0.7,0.5,0.8), stage_one_trt_one_response_prob = 0.7, stage_one_trt_two_response_prob = 0.4) PosteriorTrtSeqProb(niter = 1000, dat, design = "design-1")
This function computes the power for a sequential multiple assignment randomized trial (SMART) of one of three designs: "design-1" or "general" or "design-3".
PowerBayesian( design = "design-1", sample_size = 100, response_prob = c(0.5, 0.9, 0.3, 0.7, 0.5, 0.8), stage_one_trt_one_response_prob = 0.7, stage_one_trt_two_response_prob = 0.5, stage_one_trt_three_response_prob = 0.4, type = "log-OR", threshold, alpha = 0.05 )PowerBayesian( design = "design-1", sample_size = 100, response_prob = c(0.5, 0.9, 0.3, 0.7, 0.5, 0.8), stage_one_trt_one_response_prob = 0.7, stage_one_trt_two_response_prob = 0.5, stage_one_trt_three_response_prob = 0.4, type = "log-OR", threshold, alpha = 0.05 )
design |
specifies for which SMART design to calculate the power: design-1, general, or design-3. |
sample_size |
the total SMART study sample size. |
response_prob |
a vector of probabilities of response for each of embedded treatment sequences. In the case of design 1, there are 6, for general design there are 8, and for design-3 there are 9 |
stage_one_trt_one_response_prob |
the probability of response to stage-1 treatment for first stage-1 treatment. |
stage_one_trt_two_response_prob |
the probability of response to stage-1 treatment for second stage-1 treatment. |
stage_one_trt_three_response_prob |
the probability of response to stage-1 treatment for third stage-1 treatment (for design-3 only). |
type |
specifies log-OR, RD or log-RR. |
threshold |
minimum detectable difference between each EDTR and the best |
alpha |
probability of excluding optimal embedded dynamic treatment regime |
The power to exclude embedded dynamic treatment regimes bigger than threshold from the set of best.
PowerBayesian( design = "design-1", sample_size = 100, response_prob = c(0.5, 0.9, 0.3, 0.7, 0.5, 0.8), stage_one_trt_one_response_prob = 0.7, stage_one_trt_two_response_prob = 0.5, type="log-OR", threshold=0.2 ) PowerBayesian( design = "general", sample_size = 250, response_prob = c(0.5, 0.9, 0.7, 0.2, 0.3, 0.8, 0.4, 0.7), stage_one_trt_one_response_prob = 0.7, stage_one_trt_two_response_prob = 0.5, type="log-OR", threshold=0.2 )PowerBayesian( design = "design-1", sample_size = 100, response_prob = c(0.5, 0.9, 0.3, 0.7, 0.5, 0.8), stage_one_trt_one_response_prob = 0.7, stage_one_trt_two_response_prob = 0.5, type="log-OR", threshold=0.2 ) PowerBayesian( design = "general", sample_size = 250, response_prob = c(0.5, 0.9, 0.7, 0.2, 0.3, 0.8, 0.4, 0.7), stage_one_trt_one_response_prob = 0.7, stage_one_trt_two_response_prob = 0.5, type="log-OR", threshold=0.2 )
Computes the embedded dynamic treatment regime specific risk differences with the best.
RD( response_prob = c(0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8), stage_one_trt_one_response_prob = 0.6, stage_one_trt_two_response_prob = 0.3, stage_one_trt_three_response_prob = 0.4, design = "general" )RD( response_prob = c(0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8), stage_one_trt_one_response_prob = 0.6, stage_one_trt_two_response_prob = 0.3, stage_one_trt_three_response_prob = 0.4, design = "general" )
response_prob |
the probability of response for each of embedded treatment sequences. In the case of the design 1 SMART, there are 6, for the general design there are 8, and for design-3, there are 9. |
stage_one_trt_one_response_prob |
the probability of response to stage-1 treatment given stage-1 treatment one. |
stage_one_trt_two_response_prob |
the probability of response to stage-1 treatment given stage-1 treatment two. |
stage_one_trt_three_response_prob |
the probability of response to stage-1 treatment given stage-1 treatment three (for design-3 only) |
design |
which SMART design: design-1 or general. |
The embedded dynamic treatment regime specific risk differences.
This function simulates a SMART with Design 1.
SimDesign1( sample_size = 250, response_prob = c(0.5, 0.5, 0.5, 0.8, 0.7, 0.5), stage_one_trt_one_response_prob = 0.7, stage_one_trt_two_response_prob = 0.4 )SimDesign1( sample_size = 250, response_prob = c(0.5, 0.5, 0.5, 0.8, 0.7, 0.5), stage_one_trt_one_response_prob = 0.7, stage_one_trt_two_response_prob = 0.4 )
sample_size |
the total sample size |
response_prob |
a vector of probabilities of response for each of the 6 embedded treatment sequences. |
stage_one_trt_one_response_prob |
the probability of response to first stage-1 treatment. |
stage_one_trt_two_response_prob |
the probability of response to second stage-1 treatment. |
a data frame with treatment response indicators for each stage of treatment, a1 and a2, end of stage-1 response indicator s, and final outcome y.
dat <- SimDesign1(sample_size=250, response_prob = c(0.5,0.9,0.3,0.7,0.5,0.8), stage_one_trt_one_response_prob = 0.7, stage_one_trt_two_response_prob = 0.4)dat <- SimDesign1(sample_size=250, response_prob = c(0.5,0.9,0.3,0.7,0.5,0.8), stage_one_trt_one_response_prob = 0.7, stage_one_trt_two_response_prob = 0.4)
The SMARTbayesR package allows computation of a set of optimal embedded dynamic treatment regimes for a SMART. Furthermore, it allows power to be calculated for sample size determination.
SimDesign1 simulates a design-1 type SMART
PosteriorTrtSeqProb draws from the posterior of the probabilities of response for each embedded treatment sequence and stage-1 response probabilities.
PosteriorEDTRProbs converts treatment sequence end of study response probabilities, stage-1 response probabilities into end of study embedded dynamic treatment regime response probabilities.
MCBUpperLimits calculates simultaneous credible intervals which determines the set of optimal dynamic treatment regimes
LogOR computes the log-OR between each embedded dynamic treatment regime and the best.
LogRR computes the log-RR between each embedded dynamic treatment regime and the best.
RD computes the risk difference between each embedded dynamic treatment regime and the best.
PowerBayesian computes the power in a SMART to exclude embedded dynamic treatment regimes inferior to the best by a specified amount.
Please see Artman (2020) <arXiv:2008.02341> for details about the methodology.