PubMed · 2795452
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P Duesberg. 1989. Does HIV cause AIDS?. https://pubmed.ncbi.nlm.nih.gov/2795452/
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Longitudinal data are commonly analysed using mixed-effects models in which the population growth curve and individual subjects' growth curves are assumed to be known functions of time. Frequently, polynomial functions are assumed. In practice, however, polynomials may not fit the data and a mechanistic model that could suggest a non-linear function might not be known. Recent, more flexible approaches to these data approximate the underlying population mean curve or the individual subjects' curves using smoothing splines or kernel-based functions. I apply the local likelihood estimation method of Tibshirani and Hastie and estimate smooth population and individual growth curves by assuming that they are approximately linear or quadratic functions of time within overlapping neighbourhoods. This method requires neither complete data, nor that measurements are made at the same time points for each individual. For descriptive purposes, this approach is easy to implement with standard software. Inference for the resulting curve is facilitated by the theory of estimating equations. I illustrate the methods with data sets containing longitudinal measurements of serum neopterin in an AIDS clinical trial, measurements of ultrafiltration rates of high flux membrane dialysers for haemodialysis, and measurements of the volume of air expelled by individuals.
A revised assessment of the HIV/AIDS incubation period has been made, based on an updated operational model that includes a very short early period of high infectivity, following recent work by Jacquez et al. and using AIDS incidence data from the San Francisco Department of Public Health, plus data on AIDS incidence and HIV prevalence in a specially recruited cohort from the San Francisco City Clinic. The incubation period has, approximately, a suitably scaled gamma distribution with 14 degrees of freedom and mean 12.8 (SE 0.2) years. This information is essential in interpreting data from other areas and regions where AIDS incidence figures only are available, and is in particular intended for applications to several countries in Europe.