Time-dependent Robust Joint Modelling: Analysing a wealth of longitudinal outliers

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Joint modelling is a sophisticated technique that allows one to simultaneously analyse the evolution, over time, of repeated measurements from individuals and the impact this has on the time to a particular event of interest. Commonly, it is applied to medical applications where patients are observed over time with the aim of investigating how and why their responses change to treatment and how this affects their survival. From this, it is evident that such approaches can be applied to a vast array of research questions, from cancer research to the analysis of chronic diseases such as heart disease, diabetes, stroke, to name but a few. As a result of this advantage, the volume of research publications utilising joint models has exploded in the last few decades. Despite this, however, only limited research efforts have been directed at investigating one of the key assumptions of these models: that the random terms within these models follow normal distributional assumptions. This prevailing assumption of normality is detrimentally impacted when longitudinal outliers are present. Simple removal of these outliers will not only reduce sample size but, more importantly, would exclude important cases which commonly guide innovation in biomedical sciences; it is typically the analysis of outlying cases which tell us more about disease progression. Instead, this research will advance robust joint modelling techniques which both restrict the impact of outliers, providing more accurate and precise estimates to be obtained, and allow a high level of precision in the identification of such outliers for further exploration.However, this research area is in its infancy with the volume of work to date on robust joint modelling being currently somewhat limited. This is due to the potentially restrictive assumptions of the current methodology for these models i.e. that the impact of outliers is constant, unchanging over time. There are no established theoretical tools for handling such a situation, an undesirable situation that will be rectified through this research. To do so, I will develop a novel methodology, the time-varying outlier impacts (TOI) approach, which will allow the degree at which outliers are down weighed to change over time. Doing so, will allow more realistic scenarios to be modelled using such techniques, for example, modelling patients reaction to starting a new treatment, accounting for the fact that it will take time for them to adjust to the new treatment, which could result in outlying measurements being taken from such patients or all measurements taken from the patient outlying from the trends of the population.Another reason for limited research utilising robust joint modelling techniques is the lack of available software to fit such models. It has only been in recent years, since the introduction of the JM software package in R in 2008, that software has become available to fit standard joint models. Each of these joint modelling software packages have normal distributional assumptions for the random terms and thus cannot handle the analysis of data which contains longitudinal outliers, providing biased and imprecise estimates in the presence of outliers. This issue will also be alleviated through the work undertaken in this project through the development of a software package in R for robust joint modelling that will utilise the newly developed TOI approach.