Guiding Oncology Dose-Escalation Trials

Introduction

The OncoBayes2 package provides flexible functions for Bayesian meta-analytic modeling of the incidence of Dose Limiting Toxicities (DLTs) by dose level, under treatment regimes involving any number of combination partners. Such models may be used to support dose-escalation decisions and estimation of the Maximum Tolerated Dose (MTD) in adaptive Bayesian dose-escalation designs.

The package supports incorporation of historical data through a Meta-Analytic-Combined (MAC) framework [1], which stratifies these heterogeneous sources of information through a hierarchical model. Additionally, it allows the use of EXchangeable/Non-EXchangeable (EX/NEX) priors to manage the amount of information-sharing across subgroups of historical and/or concurrent sources of data.

Example use-case

Consider the application described in Section 3.2 of [1], in which the risk of DLT is to be studied as a function of dose for two drugs, drug A and drug B. Historical information on the toxicity profiles of these two drugs is available from single agent trials trial_A and trial_B. The historical data for this example is available in an internal data set.

kable(hist_combo2)

The objective is to aid dosing and dose-escalation decisions in a future trial, trial_AB, in which the drugs will be combined. Additionally, another investigator-initiated trial IIT will study the same combination concurrently. Note that these as-yet-unobserved sources of data are included in the input data as unobserved factor levels. This mechanism allows us to specify a joint meta-analytic prior for all four sources of historical and concurrent data.

levels(hist_combo2$group_id)

## [1] "trial_A"  "trial_B"  "IIT"      "trial_AB"

## Load involved packages
library(RBesT)  ## defines logit function
library(dplyr)  ## for mutate
library(tidyr)  ## defines crossing

## Design parameters ---------------------

dref <- c(3, 960)
num_comp <- 2 # two investigational drugs
num_inter <- 1 # one drug-drug interaction needs to be modeled
num_groups <- nlevels(hist_combo2$group_id) # four groups of data
num_strata <- 1 # no stratification needed

## abbreviate labels (wait for prior_summary)
options(OncoBayes2.abbreviate.min=8)

## disables abbreviations (default)
#options(OncoBayes2.abbreviate.min=0)

## STRONGLY RECOMMENDED => uses 4 cores
options(mc.cores=4)

## Model fit -----------------------------

blrmfit <- blrm_exnex(
  cbind(num_toxicities, num_patients - num_toxicities) ~
    1 + I(log(drug_A / dref[1])) |
    1 + I(log(drug_B / dref[2])) |
    0 + I(drug_A/dref[1] * drug_B/dref[2]) |
    group_id,
  data = hist_combo2,
  prior_EX_mu_mean_comp = matrix(
    c(logit(0.1), 0, # hyper-mean of (intercept, log-slope) for drug A
      logit(0.1), 0), # hyper-mean of (intercept, log-slope) for drug B
    nrow = num_comp,
    ncol = 2,
    byrow = TRUE
  ),
  prior_EX_mu_sd_comp = matrix(
    c(3.33, 1, # hyper-sd of mean mu for (intercept, log-slope) for drug B
      3.33, 1), # hyper-sd of mean mu for (intercept, log-slope) for drug B
    nrow = num_comp,
    ncol = 2,
    byrow = TRUE
  ),
  prior_EX_tau_mean_comp = matrix(
    c(log(0.25), log(0.125),
      log(0.25), log(0.125)),
    nrow = num_comp,
    ncol = 2,
    byrow = TRUE
  ),
  prior_EX_tau_sd_comp = matrix(
    c(log(4) / 1.96, log(4) / 1.96,
      log(4) / 1.96, log(4) / 1.96),
    nrow = num_comp,
    ncol = 2,
    byrow = TRUE
  ),
  prior_EX_mu_mean_inter = 0,
  prior_EX_mu_sd_inter = 1.121,
  prior_EX_tau_mean_inter = matrix(log(0.125), nrow = num_inter, ncol = num_strata),
  prior_EX_tau_sd_inter = matrix(log(4) / 1.96, nrow = num_inter, ncol = num_strata),
  prior_is_EXNEX_comp = rep(TRUE, num_comp),
  prior_is_EXNEX_inter = rep(FALSE, num_inter),
  ## historical data is 100% EX
  ## new data only 80% EX
  prior_EX_prob_comp = matrix(c(1.0, 1.0,
                                1.0, 1.0,
                                0.8, 0.8,
                                0.8, 0.8),
                              nrow = num_groups,
                              ncol = num_comp,
                              byrow=TRUE),
  prior_EX_prob_inter = matrix(1, nrow = num_groups, ncol = num_inter),
  prior_tau_dist = 1
)

prior_summary(blrmfit) # not run here

newdata <- crossing(
  group_id = c("trial_AB"),
  drug_A = c(0, 3, 4.5, 6),
  drug_B = c(0, 400, 600, 800)
)
newdata$group_id <- factor(newdata$group_id, levels(hist_combo2$group_id))

newdata <- crossing(
  group_id = factor(c("trial_AB"), levels(hist_combo2$group_id)),
  drug_A = c(0, 3, 4.5, 6),
  drug_B = c(0, 400, 600, 800)
)

summ_stats <- summary(blrmfit, 
                      newdata = newdata,
                      prob = 0.95,
                      interval_prob = c(0, 0.16, 0.33, 1))

kable(cbind(newdata, summ_stats), digits = 3)

# set up two scenarios at the starting dose level
# store them as data frames in a named list
scenarios <- crossing(
  group_id  = factor("trial_AB", levels(hist_combo2$group_id)),
  drug_A = 3,
  drug_B = 400,
  num_patients      = 3,
  num_toxicities      = 1:2
) %>% split(1:2) %>% setNames(paste(1:2, "DLTs"))

candidate_doses <- crossing(
  group_id = factor("trial_AB", levels(hist_combo2$group_id)),
  drug_A = c(3, 4.5),
  drug_B = 400
)

scenario_inference <- lapply(scenarios, function(scenario_newdata){
  
  # refit the model with each scenario's additional data
  scenario_fit <- update(blrmfit, add_data = scenario_newdata)
  
  # summarize posterior at candidate doses
  scenario_summ <- summary(scenario_fit,
                           newdata = candidate_doses,
                           interval_prob = c(0, 0.16, 0.33, 1))
  
  cbind(candidate_doses, scenario_summ)
  
})

Continuation of example

In the example of [1], at the time of completion of trial_AB, the complete historical and concurrent data are as follows.

kable(codata_combo2)

Numerous toxicities were observed in the concurrent IIT study. Through the MAC framework, these data can influence the model summaries for trial_AB. Note that we use the update function differently than before, since we specify the entire data-set now we use the data argument.

final_fit <- update(blrmfit, data = codata_combo2)

summ <- summary(final_fit, newdata, prob = c(0.5, 0.95), interval_prob = c(0,0.33,1))

final_summ_stats <- cbind(newdata, summ) %>%
    mutate(EWOC=1*`(0.33,1]`<=0.25)

ggplot(final_summ_stats,
       aes(x=factor(drug_B), colour=EWOC)) +
    facet_wrap(~drug_A, labeller=label_both) +
    scale_y_continuous(breaks=c(0, 0.16, 0.33, 0.4, 0.6, 0.8, 1.0)) +
    coord_cartesian(ylim=c(0,0.8)) +
    geom_hline(yintercept = c(0.16, 0.33),
               linetype = "dotted") +
    geom_pointrange(aes(y=`50%`, ymin=`2.5%`, ymax=`97.5%`)) +
    geom_linerange(aes(ymin=`25%`, ymax=`75%`), size=1.5) +
    ggtitle("DLT Probability", "Shown is the median (dot), 50% CrI (thick line) and 95% CrI (thin line)") +
    ylab(NULL) + 
    xlab("Dose Drug B [mg]")

References

[1] Neuenschwander, B., Roychoudhury, S., & Schmidli, H. (2016). On the use of co-data in clinical trials. Statistics in Biopharmaceutical Research, 8(3), 345-354.

[2] Neuenschwander, B., Wandel, S., Roychoudhury, S., & Bailey, S. (2016). Robust exchangeability designs for early phase clinical trials with multiple strata. Pharmaceutical statistics, 15(2), 123-134.

[3] Neuenschwander, B., Branson, M., & Gsponer, T. (2008). Critical aspects of the Bayesian approach to phase I cancer trials. Statistics in medicine, 27(13), 2420-2439.

[4] Neuenschwander, B., Matano, A., Tang, Z., Roychoudhury, S., Wandel, S. Bailey, Stuart. (2014). A Bayesian Industry Approach to Phase I Combination Trials in Oncology. In Statistical methods in drug combination studies (Vol. 69). CRC Press.

Session Info

sessionInfo()

## R version 3.6.1 (2019-07-05)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 16.04.6 LTS
## 
## Matrix products: default
## BLAS:   /usr/lib/libblas/libblas.so.3.6.0
## LAPACK: /usr/lib/lapack/liblapack.so.3.6.0
## 
## locale:
## [1] C
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
## [1] tidyr_1.0.0      dplyr_0.8.3      RBesT_1.4-0      ggplot2_3.2.1   
## [5] knitr_1.25       OncoBayes2_0.5-3 Rcpp_1.0.2      
## 
## loaded via a namespace (and not attached):
##  [1] rstan_2.19.2       tidyselect_0.2.5   xfun_0.10         
##  [4] purrr_0.3.3        colorspace_1.4-1   vctrs_0.2.0       
##  [7] htmltools_0.4.0    stats4_3.6.1       loo_2.1.0         
## [10] yaml_2.2.0         rlang_0.4.0        pkgbuild_1.0.6    
## [13] pillar_1.4.2       withr_2.1.2        glue_1.3.1        
## [16] matrixStats_0.55.0 lifecycle_0.1.0    plyr_1.8.4        
## [19] stringr_1.4.0      munsell_0.5.0      gtable_0.3.0      
## [22] mvtnorm_1.0-11     codetools_0.2-16   evaluate_0.14     
## [25] inline_0.3.15      callr_3.3.2        ps_1.3.0          
## [28] parallel_3.6.1     bayesplot_1.7.0    highr_0.8         
## [31] rstantools_2.0.0   scales_1.0.0       backports_1.1.5   
## [34] checkmate_1.9.4    StanHeaders_2.19.0 abind_1.4-5       
## [37] gridExtra_2.3      digest_0.6.21      stringi_1.4.3     
## [40] processx_3.4.1     grid_3.6.1         cli_1.1.0         
## [43] tools_3.6.1        magrittr_1.5       lazyeval_0.2.2    
## [46] tibble_2.1.3       Formula_1.2-3      crayon_1.3.4      
## [49] pkgconfig_2.0.3    zeallot_0.1.0      ellipsis_0.3.0    
## [52] prettyunits_1.0.2  ggridges_0.5.1     assertthat_0.2.1  
## [55] rmarkdown_1.16     R6_2.4.0           compiler_3.6.1