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) generall y experience a decline in their CD4 cell count (a count of certain whi te blood cells). We describe the use of quantile regression methods to analyse longitudinal data on CD4 cell counts from 1300 patients who p articipated in clinical trials that compared two therapeutic treatment s: zidovudine and didanosine. It is of scientific interest to determin e any treatment differences in the CD4 cell counts over a short treatm ent period. However, the analysis of the CD4 data is complicated by dr op-outs: patients with lower CD4 cell counts at the base-line appear m ore likely to drop out at later measurement occasions. Motivated by th is example, we describe the use of 'weighted' estimating equations in quantile regression models for longitudinal data with drop-outs. In pa rticular, the conventional estimating equations for the quantile regre ssion parameters are weighted inversely proportionally to the probabil ity of drop-out. This approach requires the process generating the mis sing data to be estimable but makes no assumptions about the distribut ion of the responses other than those imposed by the quantile regressi on model. This method yields consistent estimates of the quantile regr ession parameters provided that the model for drop-out has been correc tly specified. The methodology proposed is applied to the CD4 cell cou nt data and the results are compared with those obtained from an 'unwe ighted' analysis. These results demonstrate how an analysis that fails to account for drop-outs can mislead.