The role of statistics in human immunodeficiency virus research

The following papers in this issue of Statistics in Society were among those presented to a special meeting on `Statistical issues in HIV research' held at the Royal Statistical Society in London on May 16th, 1997. Since the beginning of the acquired immune de®ciency syndrome (AIDS) epidemic in developed countries, statistical and mathematical methods have played a considerable role in a variety of areas of research on the human immunode®ciency virus (HIV). These include the analysis of epidemiological patterns and studies of the natural history and clinical course of HIV-related disease, the prediction of future trends and the design of trials and programmes for intervention and surveillance (Brookmeyer and Gail, 1986; May and Anderson, 1987). For example, the so-called `back-calculation' methods employed to make short-term projections of AIDS and HIV case numbers 1 to a few years into the future have used longitudinal data on the incidence of AIDS together with observations and assumptions about the incubation period distribution to calculate the number of people infected with HIV in past time intervals (Day, 1996; Cox et al., 1989). In North America and Europe such projections have been fairly reliable during the exponential growth phase of the epidemic and hence have been of value to health care planners in assessing future needs. Mathematical models of the transmission dynamics of the virus have been of use in helping to interpret observed patterns and in dissecting out the in ̄uence of dierent processes, particularly components of sexual behaviour, on temporal changes in HIV prevalence and incidence. Examples include highlighting the non-linear shape of the epidemic, where incidence ®rst rises and then declines from its peak, even in the absence of interventions to reduce transmission, emphasizing the role of networks of sexual partners in inducing multipeaked epidemics as the virus spreads from high to low risk segments of the population, and determining the eect of ̄uctuations in viraemia (which equates in part to infectiousness) over the incubation period of AIDS on the shape and duration of the epidemic (Anderson and May, 1988; Jaquez et al., 1988; Anderson, 1988). Statistical methods have also played a material role in the design and evaluation of interventions to limit the rate of spread of HIV and the analysis and interpretation of markers of the rate at which infected patients progress to AIDS (O'Brien et al., 1996). Few large scale intervention trials with appropriate evaluation have been completed to date, but a good example is that by Hayes and co-workers which was designed to assess the eect of the treatment of sexually transmitted diseases (STDs) as a method of reducing HIV transmission (Hayes et al., 1995). Many dierent markers of progression to AIDS have been evaluated but the two of choice at present are quantitative scores of viraemia and CD4+ cell counts (O'Brien et al., 1996). A variety of models have been developed to describe progression including stochastic frameworks depicting the movement of patients via a series of classes de®ned on the basis of CD4+ cell counts (Longini et al., 1991). These models have proved to be helpful in the evaluation of dierent programmes of chemotherapy.