Time to event and drop-out model

Dear NM-users. I am modeling the preventive effect of a drug by using a time-to-event approach (time to get a new parasite infection after treatment). Patients were treated once a month for 3 months, with a scheduled follow-up 1 month after the last treatment (and again if they were symptomatic during 2 additional months of follow-up) The PK has been modeled and fixed for the TTE-model. A constant hazard with sigmoid Emax drug effect was used to explain the time-to-new infection with a good RSEs and reasonable parameter estimates. However, in this study, the dropout events are not randomly distributed. After the third month (after last treatment), 30% of all patients dropped out and did not come back for the 1st follow-up visit (the average dropout rate is about 2% each month). Many of the patients (50%) that came back after the 1st follow-up visit had acquired a new infection. I therefore believe that many of the patients that were lost did not have an infection. I am wondering if I need/how to model the drop-outs or in any way compensate for the fact that only patients without infections dropped out? I would also like to ask if anyone know how to diagnose TTE-models (except VPCs)? Your comments and help is most appreciated. Thank you and Best Regards Palang Chotsiri PhD-student in Pharmacometrics Mahidol-Oxford Tropical Medicine Research Unit, Bangkok 10400, THAILAND

Dear Palang, Thanks for sharing your experience. It seems you are facing a case of informative drop-out. It may be valuable to model it indeed, in order to maximize the information supporting your model and avoid a bias after 3 months based on non-randomly remaining patients when determining whether your hazard is time-varying or time-constant. One way to model it would be to have the drop-out hazard be driven by the infection hazard (itself a function of exposure). But the question you are trying to answer with modelling should also be taken into account when deciding what to focus your modelling effort on. That said, it seems that the design is challenging, the resolution of your data (monthly) is rather coarse (though apparently an Emax was picked up with good RSEs) risking overparameterization (and I didn't understand whether there were placebo patients or not). Regarding the evaluation, simulation-based diagnostics, i.e. VPC, are, I think, the preferred way to diagnose TTE models. Internal and possibly external evaluation should be carried out to check the simulation properties of your model. There are several types of VPCs that can be useful though. I can think of the gold standard Kaplan-Meier plot, showing the proportion of IDs not experiencing the event versus time, and I'm guessing that currently it performs well only until 3 months. But the increasingly common discrete data type plot representing the proportion of individuals (not) experiencing the event versus exposure would be a good tool too to diagnose the drug effect part. Residual-based diagnostics have also been presented, more specifically the Cox-Snell plot. I am sure other NMusers have more insights. Good luck with your model. Best regards, Elodie ________________________________ Elodie L. Plan, Ph.D., Researcher Pharmacometric Research Group Uppsala University, Sweden +46-7-22-81-39-07