Bayesian approach to meta-analysis with joint modelling of longitudinal and time-to-event outcomes in dementia and subtypes

Meta-analysis is a statistical approach that combines results from published literature in order to obtain an overall grand mean effect estimate. The main problem that affects meta-analysis is publication bias; the first part of this thesis thus seeks to address this problem. This work goes further to address heterogeneity which affects the mean effect being evaluated due to the combination of different studies. Meta-analyses of cognitive decline, Alzheimers disease, vascular dementia and all causes of dementia are undertaken to evaluate the effect of physical activity on these diseases. Dementia is an organic disorder, related to the physical deterioration of the human brain tissue that is detected after a number of medical examinations. The relationship between exercise and the risk of developing cognitive decline is further evaluated using data from the Osteoporotic Fracture Study in the United States. Meta-analytic data is obtained and used as a prior information to the secondary data. The final part of this thesis looks at a study in dementia where measurements are collected on death of participants in addition to other covariates over a period of time. These types of repeated measurements collected from each individual over time violate a number of statistical models assumptions, especially when the interest is to determine the risk factors that affect the study outcome. The aim of this approach is to examine and use these measurements to predict dementia patients probability of survival in the future. Copas selection model which was developed to assess and account for publication bias is implemented in this research. One major disadvantage of this model is that, it relies on a number of sensitivity analysis which results in many effect size estimates with even a single meta-analytic data. In order to overcome the problems of the Copas selection model, a new Bayesian prior known as triangular prior has been developed and used to fit the parameters of the Copas model via a probability distribution. The developed prior is assessed through sensitivity analysis with comparison to other priors. It is also applied to antidepressant meta-analytic dataset. The newly developed prior is further applied to a meta-analyses of dementia and its subtypes. In order to control for the heterogeneity (between-study variation), a proposed Bayesian non-parametric modelling is implemented via a Dirichlet Process. A power prior is also proposed and applied to the meta-analytic (historical) data that is used as a prior to determine whether exercise has any effect on cognitive decline. The power prior is transformed into probabilistic values out of which posterior estimates are obtained. To analyse the repeated measurements and the time to event data in order to assess their effect on dementia, we propose to use a joint modelling approach. The proposed modelling framework involves the standard and extended relative risk models as well as linear mixed effects sub-models on the repeated measures of the longitudinal covariate. The results from the simulations indicate that the triangular prior should be used. The estimated number of studies was similar to that of the frequentist trim and fill method. Our analysis reveal a protective effect of 21% for high physical activity on all cause dementia with an odds ratio of 0.79, 95% Credible Interval (CI) (0.69,0.88), a higher and better protective effect of 38% for Alzheimer’s disease with an odds ratio of 0.62, 95% CI (0.49,0.75), a 33% for cognitive decline with odds ratio of 0.67, 95% CI (0.55, 0.78) and a non-protective effect for vascular dementia of 0.92, 95% CI (0.62, 1.30). Statistically significant results were obtained when the informative prior formulated from the meta-analytic data was used at face value for higher against lowest with odds of 0.69 95% CI (0.58, 0.80) and moderate against lowest 0.63 95% CI (0.50, 0.79) physical activity. The joint modelling approach found a strong relationship between the 3MS scores and the risk of mortality, where every unit decrease in 3MS scores results in a 1.135 (13%) increased risk of death via cognitive impairment with a 95% CI of (1.056, 1.215). The triangular prior is a better alternative prior to use. The prior gives an overall or grand mean effect that is far better than conducting several sensitivity analysis. The implementation of the Dirichlet process in the meta-analyses overcomes the problem of heterogeneity. In evaluating the effect of exercise on cognitive decline with the power prior, it becomes clear that elderly women who engage in moderate exercise will have a reduced risk of developing cognitive decline. In the joint modelling of the longitudinal measurements, the results show that a decrease in 3MS scores has a significant increase risk of mortality due to cognitive impairment when implemented via the joint model but insignificant under the standard relative risk model.

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