Sampling Biases in Analyses of Prescription Durations

Background: Determining prescription duration is a first step in most studies with information on drug exposure obtained from pharmacoepidemiologic databases. In statistical process theory, it is well-known that the sampling frame may bias estimates of the interarrival distribution (IAD) governing the gap time from event to event. These effects have received limited attention in pharmacoepidemiology, where prescription duration is often estimated from the distribution of gap times between dispensings. Including all gap times, individuals with shorter gap times will contribute relatively more observations (downward bias), and longer observation windows will include more individuals with a treatment stop (upward bias). The Waiting Time Distribution (WTD) is a validated procedure for estimation of prescription duration and thus used for reference.

Objectives: To estimate the bias when using individual's observed gap times between dispensings to estimate prescription durations.

Methods: We obtained information on prescription redemptions of warfarin in 2013-2014 at pharmacies in Southern Denmark (1.2 million inhabitants) captured in Odense PharmacoEpidemiological Database (OPED). In the first approach, we sampled all gap times ignoring censored gap times. Secondly, we included censored gap times. Finally, we sampled one, possibly censored, gap time for each individual. All approaches were applied to a one year period (2013) and a two year period (2013 and 2014). For each approach, we estimated the median and 90th percentile of the sampled distribution. Reference percentiles were estimated with the reverse WTD using one random index date per individual sampled in 2014 and a one year observation period before the index date. The reverse WTD used a log-Normal recurrence distribution.

Results: The reverse WTD estimated a median of 60.6 (95% CI: 59.1; 62.1) days and a 90th percentile of 116.2 (114.1; 118.4) days. When all uncensored gap times observed in a one year period were used, the median was 55 (54; 55) days and the 90th percentile 103 (103;104) days. Using a two year period, estimates increased to 56 and 111 days. Including censored gap times, the median and 90th percentile was estimated at 59 and 134 days (one year period) and 60 and 135 days (two year period). When one random, possibly censored, gap time was used for each patient, only the median at 74 days could be estimated with a one year period; with a two year period the estimates were 63 (4.0% relative bias) and 127 days (9.3% relative bias).

Conclusions: Using all gap times induced downward bias, whereas using only a single random gap time per patient caused upward bias. The length of the observation period affected bias magnitude. Simple approaches to estimating prescription durations cannot be recommended.