Using secondary outcome to sharpen bounds for treatment harm rate in characterizing heterogeneity

Abstract

In a clinical trial, statistical reports are typically concerned about the mean difference in two groups. Now there is increasing interest in the heterogeneity of the treatment effect, which has important implications in treatment evaluation and selection. The treatment harm rate (THR), which is defined by the proportion of people who has a worse outcome on the treatment compared to the control, was used to characterize the heterogeneity. Since THR involves the joint distribution of the two potential outcomes, it cannot be identified without further assumptions even in the randomized trials. We can only derive the simple bounds with the observed data. But the simple bounds are usually too wide. In this paper, we use a secondary outcome that satisfies the monotonicity assumption to tighten the bounds. It is shown that the bounds we derive cannot be wider than the simple bounds. We also construct some simulation studies to assess the performance of our bounds in finite sample. The results show that a secondary outcome, which is more closely related to the primary outcome, can lead to narrower bounds. Finally, we illustrate the application of the proposed bounds in a randomized clinical trial of determining whether the intensive glycemia could reduce the risk of development or progression of diabetic retinopathy.

Computation of The Mann-Whitney Effect under Parametric Survival Copula Models

“…In future work, we will examine the method of computing p without parametric assumptions. Another extension is to include covariates or secondary outcomes in the model, which help obtain narrow bounds for treatment effects ( [43]). Another limitation is that only one-parameter copulas are implemented.…”

Computation of the Mann–Whitney Effect under Parametric Survival Copula Models

“…The anticipated challenge of nonparametric approach is that the empirical copula, which is a nonparametric approach to copula models, is often nonsmooth and not a genuine copula. Another extension is to include covariates or secondary outcomes, including time-varying effects in the model, which helps obtain narrow bounds for treatment effects [54][55][56]. Another limitation is that only one-parameter bivariate copulas and noninformative censoring were implemented.…”

Assessing The Treatment Effect Heterogeity with a Latent Variable

“…Under the assumption that subjects are exchangeable within blocks and that the withinblock probabilities are constant across blocks, they estimated the bounds and provided the variances for the estimators. Alternatively, Yin and Zhou [18] used a secondary outcome to obtain tighter bounds under the monotonicity, transitivity and causal necessity assumptions.…”