Regression analysis based on pairwise ordering of patients' clinical histories

Abstract

When a medical treatment influences a variety of outcomes, describing the global effect of treatment can be difficult. Traditional approaches specify how treatment affects each separate outcome. This can be done with separate models for each outcome, or by using a combined multivariate model. Describing the overall effect of a treatment thus requires combining these separate effects in some fashion and can be difficult to explain. In this paper, I specify a regression model for use with multiple outcomes where the outcome histories for each pair of patients are ranked. Pairs of patients with different lengths of follow-up are evaluated solely over the common follow-up interval. The logit of the probability that the outcome for patient i is better than that of patient j is assumed to depend on a linear function of the difference of the covariate vectors (for example, treatment indicators) for persons i and j. Thus covariates directly affect the entire clinical history, rather than directly affecting specific outcomes that comprise the history. The idea is that ranking outcomes is more relevant and interpretable than statistically combining separate effects. An estimating equations approach for estimation is described and an example of a clinical trial involving patients with heart failure is provided.