Refining estimates of prescription durations by using observed covariates in pharmacoepidemiological databases: an application of the reverse waiting time distribution

Pharmacoepidemiol Drug Saf. 2017 Aug;26(8):900-908. doi: 10.1002/pds.4216. Epub 2017 May 3.


Purpose: The study aimed to develop an automated method to estimate prescription durations in pharmacoepidemiological studies that may depend on patient and redemption characteristics.

Methods: We developed an estimation algorithm based on maximum likelihood estimation for the reverse waiting time distribution (WTD), which is the distribution of time from the last prescription of each patient within a time window to the end of the time window. The reverse WTD consists of two distinctly different components: one component for prevalent users and one for patients stopping treatment. We extended the model to allow parameters of the reverse WTD to depend on linear combinations of covariates to obtain estimates and confidence intervals for percentiles of the inter-arrival density (time from one prescription to the subsequent). We applied the method to redemptions of warfarin, using the amount of drug filled, patient sex and patient age as covariates.

Results: The estimated prescription durations increased with redeemed amount and age. Women generally had longer prescription durations, which increased more with age than men. For 70-year-old women redeeming 300+ pills, we predicted a 95th percentile of the inter-arrival density of 225 (95%CI: 201, 249) days. For 50-year-old men redeeming 100 pills, the corresponding prediction was 97 (88, 106) days.

Conclusions: The algorithm allows estimation of prescription durations based on the reverse WTD, which can depend upon observed covariates. Statistical uncertainty intervals and tests allow statistical inference on the influence of observed patient and prescription characteristics. The method may replace ad hoc decision rules. Copyright © 2017 John Wiley & Sons, Ltd.

Keywords: covariates; maximum likelihood; parametric modelling; pharmacoepidemiology; prescription durations; reverse waiting time distribution.

MeSH terms

  • Adolescent
  • Adult
  • Aged
  • Aged, 80 and over
  • Anticoagulants / therapeutic use
  • Child
  • Child, Preschool
  • Databases, Factual / statistics & numerical data*
  • Databases, Factual / trends
  • Drug Prescriptions / statistics & numerical data*
  • Female
  • Humans
  • Infant
  • Infant, Newborn
  • Likelihood Functions
  • Male
  • Middle Aged
  • Pharmacoepidemiology / statistics & numerical data*
  • Pharmacoepidemiology / trends
  • Time Factors
  • Warfarin / therapeutic use
  • Young Adult


  • Anticoagulants
  • Warfarin