A note on scaled Schoenfeld residuals for the proportional hazards model

Grambsch & Therneau (1994) show how Schoenfeld's partial residuals can be used to diagnose the nature of nonproportional hazards in Cox's (1972) model. Each residual is scaled by premultiplying by a time-dependent variance matrix, to obtain estimates of time-varying coefficients. Grambsch & Therneau also suggest an approximation in which each residual is scaled using the average variance matrix. This approximation is widely used. Here we investigate its reliability across a range of possibilities. In many cases this approximation will make very little difference to the estimates. However, in other cases the approximation may change the scaled residuals considerably and result in misleading estimates of time-varying coefficients. Situations in which the approximation is likely to be inappropriate are discussed, and an analysis of the Mayo clinic lung cancer data is presented as an example in which it is not appropriate. Simple alternative guidelines for using Schoenfeld residuals are provided.