Time-Aggregation Bias in Continuous-Time Hazard-Rate Models

In analyses of event-history data, the estimators for the parameters of the process (i. e., of the hazard rate) typically assume that the available measures of time are continuous. The assumption that time is exactly or continuously measured is rarely met. Instead, researchers typically know that the amount of time spent in a state lies between, say, j 1 and j months, but not the exact time within that window. Researchers then customarily set the duration in the state equal to j and treat this as the exact duration. Or, if censoring occurred between j 1 and j, they set the censoring time equal to j. These practices give rise to some bias in the estimates, called time-aggregation bias. In this paper I address two issues in connection with timeaggregation bias. First, I discuss the size of the bias when an estimator based on exact measurements of durations is applied to grouped measurements of durations. Second, I discuss how one can minimize the time-aggregation bias when using an estimator that assumes exact measurements of durations. This amounts to asking the following question: If an event occurred between duration j 1 and j, what is the optimal choice for the assigned duration t? Or, if censoring occurred between j 1