Omnibus Tests of The Martingale Assumption in The Analysisof Recurrent Failure Time Data

The Andersen-Gill multiplicative intensity(MI) model is well-suited to the analysis of recurrent failuretime data. The fundamental assumption of the MI model is thatthe process M_i(t) for subjects i=1,,n,defined to be the difference between a subject's counting processand compensator, i.e., N_i(t) A_i(t); >0,is a martingale with respect to some filtration. We propose omnibusprocedures for testing this assumption. The methods are basedon transformations of the estimated martingale residual process ^M _i (t) a function of consistent estimatesof the log-intensity ratios and the baseline cumulative hazard.Under a correctly specified model, the expected value of ^M _i (t)is approximately equal to zero with approximately uncorrelatedincrements. These properties are exploited in the proposed testingprocedures. We examine the effects of censoring and covariateeffects on the operating characteristics of the proposed methodsvia simulation. The procedures are most sensitive to the omissionof a time-varying continuous covariate. We illustrate use ofthe methods in an analysis of data from a clinical trial involvingpatients with chronic granulatomous disease.