Recovery of the Baseline Incidence Density in Censored Time-to-Event Analysis

Abstract Time-to-event analyses are often concerned with the effects of explanatory factors on the underlying incidence density, but since there is no intrinsic interest in the form of the incidence density itself, a proportional hazards model is used. When part of the purpose of the analysis is to use actual cumulative incidence for simulation, or for providing informative visual displays of the results, an estimate of the baseline incidence density is required. The usual method for estimating the baseline hazards in Cox’s proportional hazards analysis yields values that are of little use, and furthermore no standard deviations of the estimates (SDEs) are available. In this article we present an alternative approach to recovering an estimate of the baseline incidence density that yields smooth estimates as well as smooth estimates of SDEs. We illustrate the method on a large dataset of inter-visit times for individuals in a diabetes registry, and indicate how it can be used to incorporate different baseline incidence densities in the analysis of different subgroups. Keywords: proportional hazards, exponential regression, survival analysis, diabete