Analysis of interval-censored longitudinal data with application to onco-haematology

The analysis of repeated measurements on a biomarker, either alone or jointly with the analysis of time to the event of interest, is an area of active research. Nevertheless, we are not yet able to deal in complete generality with these complex data, which frequently consist of error-prone, sparse and intermittent values. In many cancer studies, they arise in the framework of clinical trials and thus their relationship with prognosis is a primary focus. In such a setting, the Cox model is regarded as the standard technique for analysis. The aim of this work is to illustrate an alternative approach to the analysis of studies in which the biomarker values are complicated by interval censoring and an event occurs when the biomarker itself passes a certain threshold. We propose a linear mixed model with a Gaussian stochastic process that allows for interval-censored data and can be used both to track the biomarker trajectory and to estimate the probability of event occurrence. It is developed within the classic approach to longitudinal data analysis that was previously adapted for left-censored data, only. We apply this method to a study on the minimal residual disease (MRD) in childhood leukaemia. MRD is an interval-censored measurement of residual leukaemic cells that was scheduled at 9 time-points during treatment. The aim is to investigate the relationship between MRD and the disease process. Relapse, the event of interest, may conveniently be represented as MRD over a pre-defined threshold. Our focus is on modelling the probability of relapse conditional on MRD observed prior to it. Results show that the approach is promising as it allows proper description of the data, while maintaining flexibility of modelling, feasibility of computations and interpretability of results.