Time-Aggregation Bias in Hazard-Rate Models with Covariates

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Abstract
This article elaborates the results found in Petersen (1991) by discussing how to minimize time-aggregation bias in hazard-rate models with measured covariates. It first considers a model with a single categorical covariate with h categories. It derives analytically the bias of the estimator that assumes the durations are exactly measured, when the durations are in fact rounded up to the nearest integer. Second, the article conducts both large-and small-sample Monte Carlo studies for several estimators of the covariate effects in the presence of time aggregation. There are three central findings. (1) It is shown that the likelihood that adjusts for the grouped nature of the duration measures recaptures the parameters very well. (2) The estimator that assumes that the durations are exactly measured, when they in fact are rounded up to the nearest integer, is biased in several ways. (3) The estimator that uses the midpoint adjustment suffers from the same weaknesses as the estimator that rounds up to the nearest integer, but to a lesser degree.