Using multiple random index dates with the reverse waiting time distribution improves precision of estimated prescription durations

Purpose: To improve the precision of prescription duration estimates when using the reverse waiting time distribution (rWTD).

Methods: For each patient we uniformly sampled multiple random index dates within a sampling window of length $\delta$ . For each index date, we identified the last preceding prescription redemption, if any, within distance $\delta$ . Based on all pairs of last prescription and index date, we estimated prescription durations using the rWTD with robust variance estimation. In simulation studies with increasing misspecification we investigated bias, root mean square error (RMSE) and coverage probability of the rWTD using multiple index dates (1, 5, 10, and 20). We applied the method to Danish data on warfarin prescriptions from 2013 to 2014 stratifying by and adjusting for sex and age.

Results: In simulation scenarios without misspecification, the relative bias was negligible (-0.04% to 0.01%) and nominal coverage probabilities almost retained (93.8%-95.4%). RMSE decreased with the number of random index dates (e.g., from 1.3 with 1 index date to 0.6 days with 5). With misspecification, the relative bias was higher irrespective of the number of index dates. Precision increased with the number of index dates, and hence coverage probabilities decreased. When estimating durations of warfarin prescriptions in Denmark, precision increased with number of index dates, in particular in strata with few patients (e.g., men 90+ years: width of 95% confidence interval was 16.2 days with 5 index dates versus 35.4 with 1).

Conclusions: Increasing the number of random index dates used with the rWTD improved precision without affecting bias.