Aguirre-Hernandez, Rebeca; (2000) Appraisal of models for the study of disease progression in psoriatic arthritis. Doctoral thesis (Ph.D.), University College London.

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Abstract

The subject of the thesis is the use of models for disease progression in arthritis, with special emphasis on Markov regression models. The first objective of the thesis is to propose a Pearson type goodness of fit test for stationary Markov models with covariates. The grouping technique proposed by Hosmer and Lemeshow for logistic regression models is extended to models with response variables recorded repeatedly over time. This generalization is particularly appropriate for panel data in which different numbers of observations, unequally spaced, are obtained for each sampling unit. Due to the complexity of the theoretical distribution of the test statistic, bootstrap methodology is used to calculate the distribution of the statistic under the null hypothesis. The power of the goodness of fit test is investigated for a particular model using a nested bootstrap algorithm. The proposed test is applied to a data set obtained at the University of Toronto with the objective of identifying prognostic factors for disease progression in psoriatic arthritis (PsA), measured via the number of damaged joints. As the Markov regression model does not fit the PsA data, the second objective of the thesis is to consider potentially better models. A larger data set is analysed for this purpose . Additionally, neither the outcome variable nor the covariates are categorized. Two mixture regression models for longitudinal data are examined to determine if there is statistical evidence supporting the hypothesis that a proportion of individuals never develop damaged joints. The results indicate that a negative binomial regression model without added zeros might provide a reasonable approach. The goodness of fit of this model is examined using bootstrap methodology, comparable to that used for the Markov regression model.

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