Joint models for longitudinal and survival data are a class of models that jointly analyse an outcome repeatedly observed over time such as a bio-marker and associated event times. These models are useful in two practical applications; firstly focusing on survival outcome whilst accounting for time varying covariates measured with error and secondly focusing on the longitudinal outcome while controlling for informative censoring. Interest on the estimation of these joint models has grown in the past two and half decades. However, minimal effort has been directed towards developing diagnostic assessment tools for these models. The available diagnostic tools have mainly been based on separate analysis of residuals for the longitudinal and survival sub-models which could be sub-optimal. In this thesis we make four contributions towards the body of knowledge. We first developed influence diagnostics for the shared parameter joint model for longitudinal and survival data based on Cook's statistics. We evaluated the performance of the diagnostics using simulation studies under different scenarios. We then illustrated these diagnostics using real data set from a multi-center clinical trial on TB pericarditis (IMPI). The second contribution was to implement a variance shift outlier model (VSOM) in the two-stage joint survival model. This was achieved by identifying outlying subjects in the longitudinal sub-model and down-weighting before the second stage of the joint model. The third contribution was to develop influence diagnostics for the multivariate joint model for longitudinal and survival data. In this setting we considered two longitudinal outcomes, square root CD4 cell count which was Gaussian in nature and antiretroviral therapy (ART) uptake which was binary. We achieved this by extending the univariate case i based on Cook's statistics for all parameters. The fourth contribution was to implement influence diagnostics in joint models for longitudinal and survival data with multiple failure types (competing risk). Using IMPI data set we considered two competing events in the joint model; death and constrictive pericarditis. Using simulation studies and IMPI dataset the developed diagnostics identified influential subjects as well as observations. The performance of the diagnostics was over 98% in simulation studies. We further conducted sensitivity analyses to check the impact of influential subjects and/or observations on parameter estimates by excluding them and re-fitting the joint model. We observed subtle differences, overall in the parameter estimates, which gives confidence that the initial inferences are credible and can be relied on. We illustrated case deletion diagnostics using the IMPI trial setting, these diagnostics can also be applied to clinical trials with similar settings. We therefore make a strong recommendation to analysts to conduct influence diagnostics in the joint model for longitudinal and survival data to ascertain the reliability of parameter estimates. We also recommend the implementation of VSOM in the longitudinal part of the two-stage joint model before the second stage
