Subgroup identification in clinical trials via the predicted individual treatment effect

Abstract

Identifying subgroups of treatment responders through the different phases of clinical trials has the potential to increase success in drug development. Recent developments in subgroup analysis consider subgroups that are defined in terms of the predicted individual treatment effect, i.e. the difference between the predicted outcome under treatment and the predicted outcome under control for each individual, which in turn may depend on multiple biomarkers. In this work, we study the properties of different modelling strategies to estimate the predicted individual treatment effect. We explore linear models and compare different estimation methods, such as maximum likelihood and the Lasso with and without randomized response. For the latter, we implement confidence intervals based on the selective inference framework to account for the model selection stage. We illustrate the methods in a dataset of a treatment for Alzheimer disease (normal response) and in a dataset of a treatment for prostate cancer (survival outcome). We also evaluate via simulations the performance of using the predicted individual treatment effect to identify subgroups where a novel treatment leads to better outcomes compared to a control treatment.

Fig 1. Estimates and confidence intervals for (A) standardized coefficients in the score and (B) four selected subjects (for models that include other covariates besides sex and age, they were set to the mean on the dataset for those covariates).

Fig 2. Average coverage of the confidence intervals for the PITE in (A) the null case and (B) the predictive case.

The solid line at 95% indicates the target coverage and the bands (dotted lines below and above) indicate ±1.96 standard error for the simulations.

Fig 3. Sensitivity and specificity for (A) the null case and (B) the predictive case.

The reduced method is not shown in this figure since the confidence intervals do not meet the desired coverage and the point estimate is the same as for the reduced-Scheffe method. In the null case, it is not possible to calculate sensitivity as no subjects have a positive PITE.

Fig 4. Estimates and confidence intervals for A. the coefficients in the score, and B. the first 10 subjects in the dataset.

The ‘full’ legend corresponds to the full model without model selection, the ‘Lasso’ model implements model selection through shrinkage and Selective Inference to derive the confidence intervals, while the ‘reduced’ corresponds to the usual cox model using only the predictors that are selected by the Lasso, but without conditioning on the selection.

Fig 5

(A) PITE and confidence intervals for combination of levels of variables selected by the Lasso. (B) Identified subgroups by regions of the covariate space.

Fig 6. Average coverage of the confidence intervals for the PITE in (A) the null case and (B) the predictive case.

The solid line at 95% indicates the target coverage and the bands (dotted lines below and above) indicate ±1.96 standard error for the simulations.

Fig 7. Sensitivity and specificity for (A) the null case and (B) the predictive case when using a survival outcome.