A model-based approach for estimating the mean incubation period of transfusion-associated acquired immunodeficiency syndrome.

Abstract

The incubation period, representing the interval between the date of exposure and the date of diagnosis, can be firmly ascertained in transfusion-associated cases of acquired immunodeficiency syndrome (AIDS). However, because the observation period of all transfusion-infected persons may be short compared with the average incubation period for AIDS, many cases with long incubation periods have not yet been diagnosed. Thus, the simple average of 2.6 years tends to underestimate the true mean. To correct for this underestimation bias, we assumed that the underlying distribution of the incubation periods is a member of a broad class of probability densities. Then, by maximum likelihood techniques, the mean incubation period for transfusion-associated AIDS was estimated to be 4.5 years, with the 90% confidence interval ranging from 2.6 to 14.2 years. The logng incubation period has important consequences for infected individuals and implications for public health intervention and prevention policy.Transfusion-associated acquired immunodeficiency syndrome (AIDS) provides a unique opportunity to study the incubation period ofthis disease because the date ofexposure to the virus can be accurately determined through epidemiologic investigations that identify which blood donor, and donation date, was associated with transmission of infection (1). We define the incubation period as the period from transfusion to the diagnosis of the first opportunistic disease associated with AIDS. The date of diagnosis is used as a closure for this period, rather than the more conventional date ofonset of symptoms, because the earliest symptoms are typically nonspecific and their dates of onset are poorly remembered.During the initial phase of a new disease epidemic, use of the simple average of the incubation periods of the observed cases is subject to two types of bias due to length-biased sampling. One bias can result from any omission of patients who had such short incubation periods that their illnesses went undiagnosed as AIDS before the existence of transfusion-associated AIDS was first recognized; this constitutes left censoring in our sample. As a consequence of this bias, the traditional estimate, the mean incubation periods of the observed cases, might tend to overestimate the true mean. On the other hand, another source of bias can arise from the fact that our sample does not include those exposed persons who will have such long incubation periods that they have not yet been diagnosed; this constitutes right censoring, which might cause the traditional estimate to underestimate the true mean.Our estimate would now suggest that the right censoring exerts a greater impact on the estimate and the simple average tends to represent an underestimation. Moreover, immediately following a period when the rate of exposure is increasing, as certainly was occurring with AIDS during 1978-1984, the degree of underestimation due to the right censoring is even greater, since the absolute number of patients with short incubation perio...

The Effect of Time Distribution Shape on a Complex Epidemic Model

“…Many alternatives have been proposed and used in models, such as the log-normal distribution and Weibull distributions (Medley et al, 1987;Lui et al, 1986). All three have visually similar probability density plots, but differ in key points, particularly in regard to their tails.…”

“…Other time distributions have also been used before, such as uniform, Log-normal, and Weibull (Medley et al, 1987;Lui et al, 1986); the latter two primarily differing in their tails from the gamma distribution. The choice is rather arbitrary, but a discussion is certainly necessary to justify the choice.…”

A modeled time-varying density function for the incubation period of AIDS

“…In particular, the distribution of incubation times between infection with HIV and full-blown AIDS has received a lot of attention in the last few years (see Lui et al 1986, Lui et al 1988, Medley et al 1987, Bachetti and Moss 1990, De Gruttola and Lange 1989, Blythe and Anderson 1988. In the early phase of the epidemic it was quite natural to consider that the distribution of incubation times was characterized by one density function that did not change through time.…”

Statistical and Mathematical Approaches in HIV/AIDS Modeling: A Review

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