Book Reviews

1. Aitken, C. G. G. Statistics and the Evaluation of Evidence for Forensic Scientists, p. 155
2. Bartholomew, D. J. Uncertain Belief: Is it Rational to be a Christian?, p. 156
3. Conolly, B. and Vajda, S. A Mathematical Kaleidoscope: Applications in Industry, Business and Science, p. 157
4. Dorling, D. A New Social Atlas of Britain, p. 157
5. Fleming, M. C. and Nellis, J. G. International Statistics Sources: Subject Guide to Sources of International Comparative Statistics, vols 1, 2, p. 158
6. Gilks, W. R., Richardson, S. and Spiegelhalter, D. J. ( eds ) Markov Chain Monte Carlo in Practice, p. 158
7. Glasserman, P. and Yao, D. D. Monotone Structure in Discrete Event Systems, p. 159
8. Hernández-Lerna, O. and Lasserre, J. B. Discrete-time Controlled Markov Processes: Basic Optimality Criteria, p. 160
9. Marcoulides, G. A. and Schumacker, R. E. ( eds ) Advanced Structural Equation Modelling: Issues and Techniques, p. 161
10. Rao, C. R. and Toutenberg, H. Linear Models: Least Squares and Alternatives, p. 162
11. Smithers, G. Advanced Modular Mathematics: Pure Mathematics 1; Westover, G. Advanced Modular Mathematics: Statistics 1, p. 163
12. Wickens, T. D. The Geometry of Multivariate Statistics, p. 164     

Quantile Regression Methods for Longitudinal Data with Drop-outs: Application to CD4 Cell Counts of Patients Infected with the Human Immunodeficiency Virus

Patients infected with the human immunodeficiency virus (HIV) generally experience a decline in their CD4 cell count (a count of certain white blood cells). We describe the use of quantile regression methods to analyse longitudinal data on CD4 cell counts from 1300 patients who participated in clinical trials that compared two therapeutic treatments: zidovudine and didanosine. It is of scientific interest to determine any treatment differences in the CD4 cell counts over a short treatment period. However, the analysis of the CD4 data is complicated by drop-outs: patients with lower CD4 cell counts at the base-line appear more likely to drop out at later measurement occasions. Motivated by this example, we describe the use of `weighted' estimating equations in quantile regression models for longitudinal data with drop-outs. In particular, the conventional estimating equations for the quantile regression parameters are weighted inversely proportionally to the probability of drop-out. This approach requires the process generating the missing data to be estimable but makes no assumptions about the distribution of the responses other than those imposed by the quantile regression model. This method yields consistent estimates of the quantile regression parameters provided that the model for drop-out has been correctly specified. The methodology proposed is applied to the CD4 cell count data and the results are compared with those obtained from an `unweighted' analysis. These results demonstrate how an analysis that fails to account for drop-outs can mislead.