Estimating medication stopping fraction and real-time prevalence of drug use in pharmaco-epidemiologic databases. An application of the reverse waiting time distribution

Pharmacoepidemiol Drug Saf. 2017 Aug;26(8):909-916. doi: 10.1002/pds.4217. Epub 2017 May 4.


Purpose: To introduce the reverse waiting time distribution (WTD) and show how it can be used to estimate stopping fractions and real-time prevalence of treatment in pharmacoepidemiological studies.

Methods: The reverse WTD is the distribution of time from the last dispensed prescription of each patient within a time window to the end of it. It is a mirrored version of the ordinary WTD, which considers the first dispensed prescription of patients within a time window. Based on renewal process theory, the reverse WTD can be analyzed as an ordinary WTD with maximum likelihood estimation. Based on Danish prescription data for NSAIDs, warfarin, bendroflumethiazide and levothyroxine in the years 2013 and 2014, we compared estimates from the reverse WTD to those of the ordinary WTD regarding prevalence, stopping fractions and the 80th percentiles of the inter-arrival distributions.

Results: The fraction of all users in 2013 stopping treatment varied from 73.1% (NSAID) to 9.3% (levothyroxine). Comparing prevalence estimates of the reverse WTD at the end of 2013 with those of the ordinary WTD at the start of 2014, relative differences did not exceed 4.8%. For the estimated 80th percentiles of the inter-arrival distribution, differences did not exceed 3.3%.

Conclusions: The reverse WTD allows estimation of the aggregated fraction of users stopping treatment and prevalence, especially when the WTD reliably separates current users from users who have stopped treatment. It may replace ad-hoc decision rules for automated implementations, and it yields estimates of real-time prevalence. Copyright © 2017 John Wiley & Sons, Ltd.

Keywords: maximum likelihood; parametric modeling; pharmacoepidemiology; prevalence; treatment stopping; waiting time distribution.

MeSH terms

  • Anti-Inflammatory Agents, Non-Steroidal / administration & dosage
  • Anti-Inflammatory Agents, Non-Steroidal / adverse effects
  • Databases, Factual / statistics & numerical data*
  • Drug Prescriptions / statistics & numerical data*
  • Humans
  • Likelihood Functions
  • Pharmacoepidemiology / statistics & numerical data*
  • Prevalence
  • Thyroxine / administration & dosage
  • Thyroxine / adverse effects
  • Time Factors


  • Anti-Inflammatory Agents, Non-Steroidal
  • Thyroxine