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Using secondary outcome to sharpen bounds for treatment harm rate in characterizing heterogeneity
Author(s) -
Yin Yunjian,
Cai Zheng,
Zhou XiaoHua
Publication year - 2018
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.201700049
Subject(s) - outcome (game theory) , monotonic function , randomized controlled trial , harm , clinical trial , sample size determination , selection (genetic algorithm) , simple (philosophy) , medicine , econometrics , computer science , mathematics , statistics , artificial intelligence , psychology , mathematical economics , mathematical analysis , social psychology , philosophy , epistemology
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.