Background: Case-control studies based on pharmaco-epidemiological databases typically use decision rules to determine exposure status from information on dates of prescription redemptions, although this induces misclassification. The reverse Waiting Time Distribution has been suggested as a likelihood based model to estimate the latent exposure status, and we therefore suggest to extend this into a joint likelihood based model, which incorporates both the latent exposure status and the exposure-outcome association. This will achieve consistency and efficiency of the estimates, i.e. they can be expected to be asymptotically unbiased and have optimal precision.
Methods: We established a joint likelihood for the observed case-control status and last prescription redemption before the index date. The likelihood combines the ordinary logistic regression likelihood and the reverse Waiting Time Distribution, and allows inclusion of covariates in both parts to adjust for observed confounders. We conducted a simulation study of the new model and standard models based on decision rules for exposure and the probability of being exposed, respectively, to assess the relative bias and variability of estimates. Lastly, we applied the models to a case-control study on use of nonsteroidal anti-inflammatory drugs and risk of upper-gastrointestinal bleeding.
Results: In simulation studies the new model had low relative bias (< 1.4%) and largely retained nominal coverage probabilities (90.2% to 95.1% of nominal 95% confidence intervals), also when moderate misspecification was introduced. All standard methods generally had substantial bias (-21.1% to 17.0%) and low coverage probabilities (0.0% to 68.9%). When analyzing the empirical case-control study, the new method estimated the effect of nonsteroidal anti-inflammatory drugs on risk of with upper-gastrointestinal bleeding hospitalization to 2.52 (1.59 - 3.45), whereas the other methods had estimates ranging from 3.52 (2.19 - 5.65) to 5.17 (2.40 - 11.11).
Conclusions: Unlike standard methods, the proposed model gave nearly unbiased estimates with adequate coverage probabilities in simulation studies. The developed model demonstrates the potential for the reverse Waiting Time Distribution to be integrated with existing likelihood based analyses in pharmacoepidemiological studies.
Keywords: Case–control study; Maximum likelihood; Parametric modelling; Pharmacoepidemiology; Reverse waiting time distribution.