Practical issues arising in clustered data: Modified GEE and goodness-of-fit test, overdispersion, and changepoint models

This thesis consists of three articles dealing with methods for analysing clustered data. In the first article a modified generalized estimating equation (GEE) and a goodness-of-fit test for correlated binary responses are developed. The estimating equation is obtained by using a multinomial covariance structure as a working covariance matrix. We here propose a Goodness-of-Marginal-Fit (GOMF) test statistic based on the modified GEEs for the correlated binary data from contingency tables. It is shown that the asymptotic distribution of the GOMF test statistics under the null is a chi-square distribution. The power of the GOMF test is assessed by simulation studies. We illustrate the modified GEEs and the proposed GOMF tests with two examples.; The second article deals with testing for overdispersion in small samples. In toxicological experiments, the number of experimental units is often small. Exact methods for testing and estimation of treatment effects in logistic regression models are available. However, the validity of these methods relies on the binomial assumption. Animal litter effects in toxicological experiments naturally lead to overdispersion, making the binomial assumption untenable. Several tests of that assumption are available. However, those tests rely on large-sample theory, which may not provide a good approximation in smaller samples. An exact test of the binomial assumption is developed in the paper; we develop a conditional likelihood approach for the testing of overdispersion effect based on the multiplicative binomial model. Several examples are used to illustrate our approach.; The third article deals with the analysis of correlated biomarker data in relation to recurrence or progression of disease. An example is the number of CD4 cells that is an important biomarker of disease progression to AIDS in persons infected with HIV. Another example is the use of prostate specific antigen to monitor recurrence of prostate cancer after surgery or radiotherapy treatment. A parametric model that contains a random changepoint in the expected biomarker values is considered. We propose a latent changepoint model (LCM), which posits a latent disease process with random changepoints and an observable surrogate biomarker process. In this paper, estimation through generalized estimating equations is proposed for the LCM. The procedure allows estimation of the biomarker trend over time and the changepoint distribution. The small-sample performance of the estimates for the LCM are investigated using a Monte Carlo simulation study.