Assessing the heterogeneity of treatment effects via potential outcomes of individual patients

Abstract

There is growing interest in understanding the heterogeneity of treatment effects (HTE), which has important implications in treatment evaluation and selection. The standard approach to assessing HTE (i.e. subgroup analyses based on known effect modifiers) is informative about the heterogeneity between subpopulations but not within. It is arguably more informative to assess HTE in terms of individual treatment effects, which can be defined by using potential outcomes. However, estimation of HTE based on potential outcomes is challenged by the lack of complete identifiability. The paper proposes methods to deal with the identifiability problem by using relevant information in baseline covariates and repeated measurements. If a set of covariates is sufficient for explaining the dependence between potential outcomes, the joint distribution of potential outcomes and hence all measures of HTE will then be identified under a conditional independence assumption. Possible violations of this assumption can be addressed by including a random effect to account for residual dependence or by specifying the conditional dependence structure directly. The methods proposed are shown to reduce effectively the uncertainty about HTE in a trial of human immunodeficiency virus.

Keywords: Causal inference; Conditional independence; Copula; Counterfactual; Random effect; Sensitivity analysis.

Fig. 1

Possible values of the cell probabilities in Table 1 as functions of the log-odds ratio, log{π₁₁π₀₀/(π₀₁π₁₀)} for fixed marginal probabilities π₁₊ = 0.225 and π₊₁ = 0.575 as estimated from the MOTIVATE study (see Section 4 for details): , π₀₀;— — —, π₀₁; · · · · · ·, π₁₀; · — · —, π₁₁

Fig. 2

Sensitivity analysis for the MOTIVATE study of Section 4 based on a random-effect model (|, conservative 97.5% lower confidence bound for ${\sigma }_U^2$, which is obtained as 12.2 from a GLMM analysis (see Section 4 for details)): point estimates ( , — — —, · — · —, · · · · · · ·) and 95% confidence intervals ( , — — —, · — · —, · · · · · · ·) for π₀₀ ( ),π₀₁(— — —),π₁₀(· · · · · · ·) and π₁₁ (· — · —)

Fig. 3

Sensitivity analysis for the MOTIVATE study of Section 4 based on the conditional odds ratio ρ(X) defined by equation (6): point estimates ( , — — —, · — · —, · · · · · · ·) and 95% confidence intervals ( , — — —, ·— · —, ·· · · · ·) for π₀₀ ( ), π₀₁ (— — —), π₁₀ (· · · · · · ·) and π₁₁ (· — · —), as functions of ρ(X) ≡ ρ