Giulia Lestini (1), Etienne Pigeolet (1), Neva Coello (1), Martin Fink (1), Thomas Dumortier (1).
(1) Novartis Pharma AG, Basel, Switzerland
Objectives: Longitudinal observational studies collecting cognitive data can be used to model Alzheimer’s disease progression. Those models cannot be evaluated using standard simulation-based diagnostics given the high dropouts rates as commonly observed in observational studies, even if dropouts happen “at random” [1]. A solution is to develop a dropout model that can be used to adjust the simulation part of simulation-based diagnostics. Here, we present a workflow on how to handle dropouts in these type of studies – from data preparation to model building and diagnostics of the “time to dropout” model.
Methods: Our work is based on longitudinal data collected from three cohort studies (ROS, MAP and MARS) of memory and aging at the Rush Alzheimer’s Disease Center. For the purpose of our analysis we consider a cut-off at 8 years and we define as dropouts those individuals with their last cognitive assessment occurring before year 8. Individuals who have assessments up to 8 years or beyond, are right-censored at 8 years. We propose to model the dropout times using time-to-event analysis with interval censoring. The rationale for this methodology is that the dropout can occur at any time between two subsequent visits. Since visits are not all scheduled at the same time, we stochastically impute the end of the censoring interval based on the information available from the other subjects.
In order to have a first insight about the shape of the dropout baseline hazard, and on the possible relationship between the hazard and some covariates of interest, such as baseline age and baseline cognitive score, we analyse the data using a Cox proportional hazard model, without or with covariates. We then move to parametric modelling, in order to expand the model by accounting for the nonlinearity of the hazard. Baseline covariates are also tested. Time-independent and time-varying Martingales residuals and Kaplan-Meier of the Martingale (predicted cumulative hazard) [2] are produced to assess the quality of the models.
Results: There are 2194 subjects in this analysis data set with 1124 dropping out before year 8. The algorithm that stochastically imputes the end of the censoring interval for a subject who drops out considers records from all subjects with visits in the time range of the last visit of the dropout subject (plus or minus 6 months) and having a follow-up visit. These records are used to derive the respective time intervals “delta” between the selected visits and their subsequent ones. From this set of intervals one delta time is randomly sampled and used to define the right-end of the interval during which the dropout time occurred. This stochastic imputation takes into account the possible differences in time intervals between visits occurring earlier and later during the study. Graphical analysis is used to check unbiased imputation of the right-end time interval.
The cumulative hazard obtained from the Cox proportional hazard model suggests that the hazard of dropping out in the first year and a half is almost zero, and then it constantly increases over time, which translates into fitting an exponential function or a generalized exponential function, such as the Weibull, or a log-logistic function, when moving to parametric modelling.
All parametric models tested show some misfit in the diagnostic plots, with the log-logistic function providing the best fit. When baseline covariates are included additively into this model, the systematic trend observed in the smooth regression line of Martingale residuals disappears, suggesting that the effect of the covariates on the hazard is appropriately specified in the model.
The Kaplan-Meier plot of the Martingale of this model now overlays the shape of an exponential distribution of mean 1 as expected.
Conclusions: This analysis provides a workflow on how to handle dropouts before actually modelling the outcome of interest. Although other algorithms of interval imputation could be used, the one we implemented provides a good approximation of the end of the censoring interval for dropout subjects, allowing for interval censoring time to single event modelling.
References:
[1] Friberg LE, de Greef R, Kerbusch T and Karlsson MO. Modeling and simulation of the time course of asenapine exposure response and dropout patterns in acute schizophrenia. Clin Pharmacol Ther (2009) 86(1):84-91
[2] Collett D. (1994) Modelling survival data in medical research.
Reference: PAGE 28 (2019) Abstr 8907 [www.page-meeting.org/?abstract=8907]
Poster: Methodology - Model Evaluation