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 ensure patient safety during trial conduct by supporting dose-escalation decisions. In addition, the model can support estimation of the Maximum Tolerated Dose (MTD) in adaptive Bayesian dose-escalation designs.

Whereas traditional dose escalation designs, such as the 3+3 design, base the dosing decisions on predefined rules about the number of DLTs in the last one or two cohorts at the current dose, model-based designs such as those using Bayesian Logistic Regression Models (BLRMs) endeavor to model the dose-toxicity relationship as a continuous curve, and allow the model to guide dosing decisions. In this way, all available data contributes to the dosing decisions. Furthermore, extensions to the BLRM approach can support inclusion of available additional data on the compound(s) involved. The additional data can be either historical data collected prior trial conduct or concurrent data, which is collected during trial conduct in the context of another trial/context.

The package supports incorporation of additional data through a Meta-Analytic-Combined (MAC) framework [1]. Within the MAC model the heterogeneous sources of data are assigned to groups and information is shared across groups through a hierarchical model structure. For any given group this leads to borrowing strength from all other groups while discounting the information from other groups. The amount of discounting (or down-weighting) is determined by the heterogeneity. A group is commonly defined to be a trial, but that must not necessarily hold.

The key assumption of the hierarchical model is the exchangability assumption between the groups. There are two independent mechanisms in the package which aim at relaxing the exchangability assumption:

• Differential discounting: Groups are assigned to different strata. While the overall hierarchical mean stays the same, the heterogeneity between groups is allowed to be different between strata. Each group must be assigned to a single stratum only.

• EXchangeable/Non-EXchangeable (EX/NEX) model for each group: With EXNEX each group is modelled as being exchangeable with some probability and is allowed to have it’s own group-specific estimate as if the group is not exchangeable with the remainder of the data.

Both techniques are rather advanced and are not discussed further in this introduction.

In the following we illustrate first a very common use case of historical information only and then consider concurrent data in addition. In particular, we will discuss a trial evaluating a combination of two drugs whenever historical information is available on each drug individually from separate trials. This example will be expanded by using in addition concurrent data on one of the drugs and on their combination.

Note on terminology: While in the literature (see [1], [2], and [4]) the term stratum refers to a trial commonly, OncoBayes2 deviates here and uses the term group instead. This is more in line with hierarchical modeling terminology. The term stratum is used to define a higher level grouping structure. That is, every group is assigned to a single stratum within OncoBayes2. This higher level grouping (groups of groups) is necessary whenever differential discounting is used. By convention OncoBayes2 assigns any group to the stratum “all” whenever no stratum is assigned for a group.

## Load involved packages
library(dplyr)   ## for mutate
library(tidyr)   ## defines expand_grid
library(tibble)  ## for tibbles
library(ggplot2) ## for plotting

Example use-case: Dual combination trial with historical information

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"

However, we will first consider only the dual combination trial AB and it’s historical data and add concurrent data at a later stage.

kable(drug_info_combo2)

dose_info <- filter(dose_info_combo2, group_id == "trial_AB",
                    drug_A %in% c(3,6), drug_B %in% c(0,400, 800))
kable(dose_info)

combo2_trial_setup <- blrm_trial(
  data = hist_combo2,
  drug_info = drug_info_combo2,
  dose_info = dose_info
)

combo2_trial_start <- blrm_trial(
  data = hist_combo2,
  drug_info = drug_info_combo2,
  dose_info = dose_info,
  simplified_prior = TRUE,
  EXNEX_comp=FALSE,
  EX_prob_comp_hist=1,
  EX_prob_comp_new=1
)

prior_summary(combo2_trial_start) # not run here

kable(summary(combo2_trial_start, "dose_prediction"), digits = 2)

kable(summary(combo2_trial_start, "ewoc_check"), digits = 3)

candidate_starting_dose <- summary(combo2_trial_start, "dose_info") %>%
  filter(drug_A == 3, drug_B == 400) %>%
  crossing(num_toxicities = 0, num_patients = 3:6)

pp_summary <- summary(combo2_trial_start, interval_prob = c(-1, 0, 1, 6), predictive = TRUE,
                      newdata = candidate_starting_dose)

kable(bind_cols(select(candidate_starting_dose, num_patients),
                select(pp_summary, ends_with("]"))), digits = 3)

new_cohort <- tibble(group_id = "trial_AB",
                     drug_A = 3,
                     drug_B = 400,
                     num_patients = 5,
                     num_toxicities = 1)

combo2_trial_update <- update(combo2_trial_start, add_data = new_cohort)

kable(summary(combo2_trial_update, "dose_prediction"), digits = 2)

kable(summary(combo2_trial_update, "newdata_prediction",
              newdata = tibble(group_id = "trial_AB",
                               drug_A = 4.5,
                               drug_B = c(400, 600, 800))), digits = 2)

# set up two scenarios at the starting dose level
# store them as data frames in a named list
scenarios <- expand_grid(
  group_id  = "trial_AB",
  drug_A = 3,
  drug_B = 800,
  num_patients = 3,
  num_toxicities = 0:2
) %>% split(1:3) %>% setNames(paste0(0:2, "/3 DLTs"))

candidate_doses <- expand_grid(
  group_id = "trial_AB",
  drug_A = c(3, 4.5),
  drug_B = c(600, 800)
)

scenario_inference <- lapply(scenarios, function(scenario_newdata) {
  # refit the model with each scenario's additional data
  scenario_fit <- update(combo2_trial_update, add_data = scenario_newdata)
  # summarize posterior at candidate doses
  summary(scenario_fit, "newdata_prediction", newdata = candidate_doses)
}) %>%
  bind_rows(.id="Scenario")

Continuation of example: Using concurrent data

In the example of [1], at the time of completion of the first stage of trial_AB, the following additional data was observed.

trial_AB_data <- filter(codata_combo2, group_id == "trial_AB", cohort_time==1)
kable(trial_AB_data)

These data are easily incorporated into the model using another call to update, as below.

combo2_trial_histdata <- update(combo2_trial_start, add_data = trial_AB_data)

However, during the first stage of trial_AB, the trial_A studying drug A did continue and collected more data on the drug A dose-toxicity relationship:

trial_A_codata <- filter(codata_combo2, group_id == "trial_A", cohort_time==1)
kable(trial_A_codata)

Wthin the MAC framework we may simply add the concurrent data to our overall model which yields refined predictions for future cohorts.

combo2_trial_codata <- update(combo2_trial_histdata, add_data = trial_A_codata)

To compare the effect of co-data in this case it is simplest to visualize the interval probabilities as predicted by the model for the different data constellations. Here we use the function plot_toxicity_intervals_stacked to explore the dose-toxicity relationship in a continuous manner in terms of the dose.

plot_toxicity_intervals_stacked(combo2_trial_histdata,
                                newdata=mutate(dose_info, dose_id=NULL, stratum_id="all"),
                                x = vars(drug_B),
                                group = vars(drug_A),
                                facet_args = list(ncol = 1)
) + ggtitle("Trial AB with historical data only")

plot_toxicity_intervals_stacked(combo2_trial_codata,
                                newdata=mutate(dose_info, dose_id=NULL, stratum_id="all"),
                                x = vars(drug_B),
                                group = vars(drug_A),
                                facet_args = list(ncol = 1)
) + ggtitle("Trial AB with historical and concurrent data on drug A")

As we can observe, the additional data on drug A moves the maximal admissible dose allowed by EWOC towards higher doses for drug B whenever drug A is 6 mg. This reflects that drug A has been observed to be relatively safe, since no DLT was observed for a number of doses.

In the example of [1], during the conduct of the second stage of the trial_AB an additional external data source from a new trial became available. This time it is stemming from another trial which is an investigator-initiated trial IIT of the same combination. Numerous toxicities were observed in this concurrent study as stage 2 of trial_AB.

trial_AB_stage_2_codata <- filter(codata_combo2, cohort_time==2)
kable(trial_AB_stage_2_codata)

As before, through the MAC framework, these data can influence the model summaries for trial_AB. We leave it to the reader to explore the differences in the co-data (combined historical and concurrent data) vs the historical data only approach.

To conclude we present a graphical summary of the dose-toxicity relationship for the dual combination trial for the final data constellation. Note that we use the data option of update here to ensure that we use an entirely new dataset which includes all data collected; so this includes historical, trial and concurrent data:

combo2_trial_final <- update(combo2_trial_start, data = codata_combo2)

As final summary we consider the 75% quantile of the probability for a DLT at all dose combinations. Whenever the 75% quantile exceeds 33%, then the EWOC criterion is violated and the dose is too toxic.

grid_length <- 25

dose_info_plot_grid <- expand_grid(stratum_id = "all",
                                   group_id = "trial_AB",
                                   drug_A=seq(min(dose_info_combo2$drug_A), max(dose_info_combo2$drug_A), length.out=grid_length),
                                   drug_B=seq(min(dose_info_combo2$drug_B), max(dose_info_combo2$drug_B), length.out=grid_length))


dose_info_plot_grid_sum <- summary(combo2_trial_final,
                                   newdata=dose_info_plot_grid,
                                   prob=0.5)

ggplot(dose_info_plot_grid_sum, aes(drug_A, drug_B, z = !!as.name("75%"))) +
  geom_contour_filled(breaks=c(0, 0.1, 0.16, 0.33, 1)) +
  scale_fill_brewer("Quantile Range", type="div", palette = "RdBu", direction=-1) +
  ggtitle("DLT Probability 75% Quantile")

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.

[5] Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., Bürkner, P. C. (2021). Rank-Normalization, Folding, and Localization: An Improved (\(\hat{R}\)) for Assessing Convergence of MCMC, Bayesian Analysis, 16 (2), 667–718. https://doi.org/10.1214/20-BA1221

Session Info

sessionInfo()

## R version 4.1.0 (2021-05-18)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 20.04.5 LTS
## 
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## LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.9.0
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## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
## [1] ggplot2_3.3.5    tibble_3.1.3     tidyr_1.1.3      dplyr_1.0.8     
## [5] knitr_1.33       OncoBayes2_0.8-9
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## loaded via a namespace (and not attached):
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