--- title: "Dose-Ranging Study" output: rmarkdown::html_vignette vignette: > %\VignetteIndexEntry{Dose-Ranging Study} %\VignetteEncoding{UTF-8} %\VignetteEngine{knitr::rmarkdown} editor_options: markdown: wrap: 72 --- ```{r, include = FALSE} knitr::opts_chunk$set( collapse = TRUE, cache.path = 'cache/doseRanging/', comment = '#>', dpi = 300, out.width = '100%' ) ``` ```{r setup, echo = FALSE, message = FALSE} library(TrialSimulator) library(DoseFinding) library(dplyr) library(kableExtra) set.seed(12345) ``` In this vignette, we implement simulation for a dose-ranging trial under adaptive design. We start from a placebo arm and a treatment arm with highest possible dose. At an interim, if we observe promising results, we add arms with doses in between to inform decision at final analysis. For the sake of simplicity, we assume a binary endpoint of interest. The response rates at doses 0 (placebo), 0.5, 1.5, 2.5, 4 (highest dose) are given by a `sigEmax` model below, where the response rate is assume to be 10% in placebo, and 25% in arm of the highest dose (dose = 4). For further background information, refer to [vignette](https://cran.r-project.org/package=DoseFinding/vignettes/binary_data.html) of the `DoseFinding` package. ```{r flaf} mods <- DoseFinding::Mods(sigEmax = rbind(c(1, 3)), placEff = log(.1/(1 - .1)), maxEff = log(.25/(1 - .25)) - log(.1/(1 - .1)), doses = c(0, 0.5, 1.5, 2.5, 4)) DoseFinding::plotMods(mods, trafo = function(x) 1/(1+exp(-x))) ## response rates on curve x <- DoseFinding::getResp(mods, doses = c(0, 0.5, 1.5, 2.5, 4)) 1 / (1 + exp(-unclass(x))) ``` ## Simulation Settings In our simulation, we assume - the response rates of binary endpoint as | Dose | 0 | 0.5 | 1.5 | 2.5 | 4 | |-------------------|------|------|------|------|------| | Response Rate (%) | 10.0 | 11.2 | 20.8 | 24.1 | 25.0 | - readout time is 1 week. - no dropout. - starting with a placebo arm and a treatment arm of the highest dose (= 4), with a 1:1 randomization ratio. - enroll 5 patients per week for 7 weeks. - an interim is planed when we have collected 30 readouts in total from the two arms. - if z statistic of odds ratio is greater than 1 - add three arms of dose 0.5, 1.5, and 2.5 to trial - enroll 20 patients per week with a randomization ratio 1:2:2:2:1, until in total 150 patients are enrolled in the trial - final analysis is performed when readouts are available for all enrolled patients. - otherwise, stop the trial. ## Define Placebo and High Dose Arms ```{r} ep <- endpoint(name = 'ep', type = 'non-tte', readout = c(ep = 1), generator = rbinom, size = 1, prob = 0.1) pbo <- arm(name = 'dose = 0.0') pbo$add_endpoints(ep) ep <- endpoint(name = 'ep', type = 'non-tte', readout = c(ep = 1), generator = rbinom, size = 1, prob = 0.25) trt4 <- arm(name = 'dose = 4.0') trt4$add_endpoints(ep) ``` ## Define a Trial ```{r} accrual_rate <- data.frame(end_time = c(7, Inf), piecewise_rate = c(5, 20)) trial <- trial(name = '123', n_patients = 150, duration = 14, enroller = StaggeredRecruiter, accrual_rate = accrual_rate, silent = TRUE) trial$add_arms(sample_ratio = c(1, 1), pbo, trt4) trial ``` ```{r go_nogo, echo=FALSE} go_nogo <- function(data){ ## candidate models for MCPMod doses <- c(0, 0.5, 1.5, 2.5, 4) candidates <- Mods(emax = c(.25, 1), sigEmax = rbind(c(1, 3), c(2.5, 4)), betaMod = c(1.1, 1.1), placEff = log(.1/(1 - .1)), maxEff = log(.25/(1 - .25)) - log(.1/(1 - .1)), doses = doses) fit <- glm(ep ~ factor(arm) + 0, data = data, family = binomial) mu_hat <- coef(fit) S_hat <- vcov(fit) ## multiple contrast test test <- DoseFinding::MCTtest(dose = doses, mu_hat, S = S_hat, models = candidates, type = "general") ## model averaging model <- DoseFinding::maFitMod(dose = doses, mu_hat, S = S_hat, models = c("emax", "sigEmax", "betaMod")) ## predict response rate per dose prd <- predict(model, summaryFct = median, doseSeq = doses) ## convert to scale of probability prd_rate <- 1 / (1 + exp(-prd)) ## go/no-go rule: MCP test p-value < 0.05 and estimated effect > 10% ifelse(min(attr(test$tStat, 'pVal')) < .05 & max(prd_rate - prd_rate[1]) > .1, 'go', 'no-go') } ``` ```{r action_at_interim, echo=FALSE} action_at_interim <- function(trial){ ## get data snapshot locked_data <- trial$get_locked_data('interim') ## compare two arms ## Risk difference = response rate in high dose - response rate in placebo fit <- fitLogistic(ep ~ arm, placebo = 'dose = 0.0', data = locked_data, alternative = 'greater', scale = 'risk difference') ## for summary of early termination trial$save(value = fit$z, name = 'z_value') trial$save(value = ifelse(fit$z > 1.64, 'add dose arms', 'stop trial'), name = 'interim_decision') ## create three dose arms ep <- endpoint(name = 'ep', type = 'non-tte', readout = c(ep = 1), generator = rbinom, size = 1, prob = .112) trt1 <- arm(name = 'dose = 0.5') trt1$add_endpoints(ep) ep <- endpoint(name = 'ep', type = 'non-tte', readout = c(ep = 1), generator = rbinom, size = 1, prob = .208) trt2 <- arm(name = 'dose = 1.5') trt2$add_endpoints(ep) ep <- endpoint(name = 'ep', type = 'non-tte', readout = c(ep = 1), generator = rbinom, size = 1, prob = .241) trt3 <- arm(name = 'dose = 2.5') trt3$add_endpoints(ep) ## add three new arms to trial trial$add_arms(sample_ratio = c(2, 2, 2), trt1, trt2, trt3) } ``` ```{r action_at_final, echo=FALSE} action_at_final <- function(trial){ locked_data <- trial$get_locked_data('final') trial$save(value = go_nogo(locked_data), name = 'decision') } ``` ## Define Milestones and Actions Two milestones are triggered when 30 and 150 readouts are collected, respectively. Note that the 30 readouts are from the placebo and the highest dose arm, while the 150 readouts are from all five arms. ```{r} interim <- milestone(name = 'interim', when = eventNumber(endpoint = 'ep', n = 30), action = action_at_interim) final <- milestone(name = 'final', when = eventNumber(endpoint = 'ep', n = 150), action = action_at_final) ``` In the action function `action_at_interim()`, we don't actually terminate the trial in simulation but always add dose arms. Instead, we save the z statistic for summary later, e.g., computing the proportion of early termination. ```{r ref.label='action_at_interim', eval=FALSE} ``` At final analysis, we analyze data from all five arms using MCPMod. It calls a helper function `go_nogo()` which can be found in the Appendix below. ```{r ref.label='action_at_final', eval=FALSE} ``` ## Execute a Trial After registering the two milestones with a listener, we simulate a single trial using `controller$run()`. We can see that more patients are randomized to the three newly added arms after interim, reflecting the new randomization ratio 1:2:2:2:1. ```{r message=FALSE} listener <- listener() listener$add_milestones(interim, final) controller <- controller(trial, listener) controller$run(n = 1, plot_event = TRUE) ``` In this trial, the z statistic at interim is relatively low (`r round(controller$get_output('z_value'), 2)`), thus is early terminated even if in simulation we keep going with three newly added dose arms. ```{r} output <- controller$get_output() output %>% kable(escape = FALSE) %>% kable_styling(bootstrap_options = "striped", full_width = FALSE, position = "left") %>% scroll_box(width = "100%") ``` We can call `controller$run(n = 10)` to simulate additional trials. in the function `action_at_final()`, the go/no-go decision (`decision` in output) is determined under the assumption that the dose has been expanded, regardless of the interim evidence—this simplification is made solely for the convenience of simulation. However, the overall probability of a `"go"` should incorporate the interim results—specifically, the trial must not be stopped at interim (i.e., `interim_decision == "add dose arms"`), and the function `go_nogo()` must return `"go"` at the final analysis. ```{r eval=FALSE, message=FALSE} ## important: reset before calling run() again controller$reset() controller$run(n = 10, plot_event = FALSE, silent = TRUE) res <- controller$get_output() ``` ```{r echo=FALSE} res <- TrialSimulator:::getDoseRangingOutput() ``` ```{r} res %>% kable(escape = FALSE) %>% kable_styling(bootstrap_options = "striped", full_width = FALSE, position = "left") %>% scroll_box(width = "100%") ``` ```{r message=FALSE} ## Number of overall Go sum(res$interim_decision == 'add dose arms' & 'decision' == 'go') ## Number of early trial termination sum(res$interim_decision == 'stop trial') ``` ## Appendix: Code of Helper Function For completeness, the full code of the helper functions `go_nogo()` is included below, which informs go/no-go decision at the end of the trial. ```{r ref.label='go_nogo', eval=FALSE} ```