Revisiting the sequence symmetry analysis design

The purpose of this paper is to re-examine the sequence symmetry analysis (SSA) in a mathematical framework to improve the understanding and use of the design. The mathematical properties of the crude, null-effects, and adjusted sequence ratios (SR) are analyzed in the presence of prescription time-trends and unmeasured time-invariant confounding. The theoretical results are illustrated in a simulation study. The crude SR can be interpreted as an estimator of the hazard ratio (HR) of treatment when the allowed time between initiation of the treatment and the outcome drug is small. The HR can easily be estimated flexibly as a function of covariates, such as age and sex, using logistic regression. The crude SR implicitly adjusts for unmeasured time-invariant confounding, whereas the null-effects SR, and thereby the adjusted SR, make little sense unless treatment and outcome are strictly independent. The use of the adjusted SR should be abandoned. Another design should be used if it is infeasible to require treatment and outcome sufficiently close. The crude SR can be modeled flexibly with logistic regression to estimate covariate-dependent HRs or at least to test whether the HR depends on covariates.