On the design and analysis of clinical trials with correlated outcomes

The convention in clinical trials is to regard outcomes as independently distributed, possibly conditional on covariates, but in some situations they may be correlated. For example, in infectious diseases, correlation may be induced if participants have contact with a common infectious source, or share hygienic tips that prevent infection. This paper discusses the design and analysis of randomized clinical trials that allow arbitrary correlation among all randomized participants. This perspective generalizes the traditional perspective of strata, where patients are exchangeable within strata, and independent across strata. For theoretical work, we focus on the test of no treatment effect μ1 − μ0 = 0 when the n dimensional vector of outcomes follows a Gaussian distribution with known n × n covariance matrix Σ, where the half randomized to treatment (placebo) have mean response μ1(μ0). We show how the new test corresponds to familiar tests in simple situations for independent, exchangeable, paired, and clustered data. We also discuss the design of trials where Σ is known before or during randomization of patients and evaluate randomization schemes based on such knowledge. We provide two complex examples to illustrate the method, one for a study of 23 family clusters with cardiomyopathy, and the other where the malaria attack rates vary within households and clusters of households in a Malian village.