The Incubation Period of Acute Retroviral Syndrome as a Multistep Process: A Parametric Survival Analysis

A long duration of acute retroviral syndrome (ARS) and a short incubation of ARS (IncARS) are independent predictors of a fast progression to AIDS. The first objective of this study was to validate previous estimates of IncARS by comparing durations between health care workers (HCWs) accidentally infected by HIV and individuals infected by other routes (non-health care workers [N-HCWs]). The second objective was to use parametric survival models to generate hypotheses on various steps occurring during the IncARS. Data from a prospective cohort of patients with documented ARS and from individuals with ARS as the result of accidental exposure to HIV were analyzed. Nonparametric and parametric survival models were used to describe the incubation of ARS. No differences were found for the median IncARS between 34 HCWs (21.5 days) and 70 N-HCWs (21.5 days) (log-rank test, P = 0.72). According to survival models, IncARS can be modeled with a gamma and/or lognormal model with means of 26.4 days and 26.7 days, respectively. The gamma model suggests that 3 sequential stages are present during the IncARS, which is compatible with basic science investigations identifying crossing of the epithelial barrier by the virus, the virus-host cell interactions, and the viral systemic dissemination.

The duration of the acute retroviral syndrome (ARS) and that of its incubation period (IncARS) have been associated with the progression of HIV disease.¹ The IncARS is the time elapsed between HIV infection and onset of ARS. A long ARS and a short IncARS were independent predictors of a rapid progression to AIDS.¹ These results might not be valid if the duration of IncARS was measured with error as a result of the uncertain date of infection. Conversely, the date of HIV exposure is known more precisely when the infection occurs among health care workers (HCWs).²

To validate the IncARS reported previously,¹ we first compared the distributions of IncARS duration between HCWs and individuals infected by another route using a nonparametric survival model. We then used parametric survival models³ to suggest pathogenic hypotheses based on the model that best fitted the data. Parametric survival models have been used to describe the incubation of infectious diseases,⁴ cancer,^5,6 genetic diseases,⁷ or drug-induced diseases⁸ and have been helpful for generating hypotheses on determinants of incubation. Because IncARS is a stage of HIV infection not well known in human beings, our objective was to bring in additional information suggested by a biostatistical approach.

MATERIALS AND METHODS

Patients

Health Care Workers

The data on 34 HCWs were extracted from an extensive review of Ippolito et al,² who reported 94 worldwide cases of HIV infection after occupational exposure. The selection of the 34 individuals was based on the individuals having reliable dates of HIV exposure and onset of ARS reported in the article (Cited Here...).²

Non-Health Care Workers

The data on 70 non-health care workers (N-HCWs) with ARS and a reliable date of HIV infection were analyzed. These patients are a subgroup of a larger prospective cohort of Swiss and Australian individuals infected between 1985 and 1995 and described in detail previously.^1,9 The presumed date of HIV infection was reported at the time of presentation of symptoms of ARS by self-report and completed by a physician interview.¹

The IncARS was defined as the time in days elapsed between the date of HIV infection and the date of ARS onset. No other HIV exposure occurred between this date and the date of ARS onset according to the patients' statements. Patients were asked about the date of infection at the time they presented with symptoms of ARS. The clinical features of ARS were collected on standardized collection forms in the 2 centers.⁹

Biologic Diagnosis

Health Care Workers

The cases of occupational HIV infection were documented by percutaneous exposure or mucocutaneous exposure, with a confirmed seroconversion or with similar strains being isolated from the patient source and infected HCWs.²

Non-Health Care Workers

The biologic criteria of ARS were (1) the presence of p24 antigenemia (n = 58) in patients with negative or indeterminate enzyme-linked immunoassay (ELISA) serology; (2) 2 bands on Western blot analysis, 1 of which corresponded to the env gene (gp 160, gp 120, or gp 41; n = 3) with negative or indeterminate ELISA serology; or 3) a negative HIV-1 ELISA test followed by a positive test within 6 months (median: 85 days, range: 4-188 days, n = 9). Infection with HIV was confirmed for all patients by Western blot analysis. All patients had a positive anti-HIV-1 antibody test during the follow-up period.

Statistical Analysis

The continuous variables are reported by mean, median, and standard deviation (SD), and the categoric variables are reported as frequencies and percentages. The IncARS was treated as the survival time between infection and the occurrence of the event defined as the onset of ARS. The Kaplan-Meier survival analysis was used for description. Four parametric survival models were then fitted to the distribution of IncARS. The parametric survival models are each described by a specific probability density function³ that is applied to the observed data. Parametric values were estimated using the maximum likelihood method. A statistical test was used to assess the goodness-of-fit of a parametric model. Four models of increasing complexity were tested. The simplest is the exponential, with constant hazard over time. The second is the Weibull, the hazard of which increases or decreases continuously with time. The third and fourth models represent different stepwise processes: the third is a gamma function involving a number of independent steps, the hazard of which is the same between all steps and is constant over time, and the fourth is the lognormal, the multisteps of which occur randomly among individuals. The statistical underpinning of each model is expanded in the Cited Here.... The IncARS was stratified in 20 strata with at least 5 patients per strata for goodness-of-fit calculations, based on a χ² test with N-K-1 degrees of freedom (N for the number of strata comparisons, K for the number of distribution-descriptive estimated parameters). The statistical threshold of significance was P = 0.05.

RESULTS

Health Care Workers

Few demographic characteristics were available from the report by Ippolito et al.² Eighteen patients were female, 1 was male, and gender was not reported for 15. The mean IncARS was 27.4 days, and the median was 21.5 days [range: 11-75 days].

Non-Health Care Workers

Thirty-one patients were from Geneva, and 39 were from Sydney. Patients were predominantly men (91%), with a mean age of 30.6 years. The presumed route of HIV infection was homosexual contact for 53 patients (76%), heterosexual contact for 11 patients (16%), drug injection for 2 patients (3%), and another route for 4 patients (5%). The mean IncARS was 25.8 days, with a median of 21.5 days (range: 5-70 days), and did not differ by center (P = 0.15).

Survival Models

Figure 1 depicts the absence of difference in survival distribution between the 2 groups (log-rank test, P = 0.72). The data for the 2 groups were combined in subsequent analyses because of the similarity of descriptive parameters and survival distributions. Table 1 shows the parameter estimates and the goodness-of-fit of survival models applied to the total population. The models best describing the data were the gamma and lognormal distributions. According to these, the mean IncARS is 26.4 days (γ/λ) and the SD is 14.6 days (γ^1/2/λ) (gamma distribution), or 26.7 days (exp[λ + 0.5 γ²]) and 18.4 days (([exp[γ²]-1]*exp[2λ + γ²])^1/2) (lognormal distribution).

Table 1

Figure 1

Figure 2 shows the 4 models fitted to the data and the common Kaplan-Meier curve. The lognormal model is the closest to the Kaplan-Meier curve, which corresponds to the result of the goodness-of-fit test.

Figure 2

DISCUSSION

The first objective of this study was to validate the duration of IncARS of N-HCWs using data from HCWs accidentally infected by HIV. The similarity of the 2 survival distributions suggests that patients infected through the sexual route or after injection of drugs might provide a reliable date of HIV exposure and that IncARS was the same for the 2 groups. We cannot exclude the possibility that this subgroup of patients might be biased toward individuals quite aware of HIV disease and risky behaviors, however.

We found that the parametric models that best fit the data are the gamma and lognormal models. Comparing the exponential with the other 3 models is not entirely fair, however, because the exponential has only 1 parameter; it is therefore expected that the 2-parameter models would agree more closely with the data. Nevertheless, the small P value can help to rule out the exponential; it would therefore seem that IncARS is not a random event with constant incidence density over time. Rather, IncARS would seem to result from a more complex process, and among them, the Weibull model comes first. The Weibull model can represent a homogeneous disease process, the hazard of which increases with time. According to the χ² value, however, it provides the weakest fit to the data.

The gamma and lognormal models best fit the data given their small χ² values. Both involve complex mechanisms. The gamma model is a compound of exponentials standing for hypothetic multiple steps leading to ARS. The number of steps can be read as the value of the shape parameter (rounded). The lognormal model is also based on a step process, with the steps occurring randomly among individuals such that the number of steps varies between individuals. If we suppose that the various steps are represented by the multiplication of HIV, there will be a few individuals whose invasion will take a long time to occur (right skewness) and a much larger number with a shorter incubation period. Unfortunately, the data cannot discriminate between both models. Be that as it may, onset of ARS seems to result from a multistep process.

The gamma distribution is relevant when the occurrence of an event depends on multiple previous stages. The hazard of transition remains constant over time and between stages, and the event results from the succession of independent subevents.³ In the case of ARS, the simian immunodeficiency virus (SIV) model has clearly shown that acute infection is split in sequential stages corresponding to the transition/passage of the virus through different compartments.¹⁰ The gamma model applied to human beings suggests the successive occurrence of subevents, as has been discussed recently by Pope and Haase.¹¹ That stages were the crossing of the epithelial barrier by the virus, the virus-host cell interactions, and the viral systemic dissemination. The successive stages of acute infection might be a result of the lack of effective host response: first, the absence of an efficient mucous local response; second, the lack of an efficient humoral and cytotoxic response; and, finally, the absence of factors interfering with the lymph node tropism of HIV and body dissemination.

The lognormal distribution suggests the multiplication or growth of HIV during the incubation period.⁴ Then, as proposed by Ruprecht et al,¹⁰ the infection and symptoms of ARS would occur when viral replication reaches a specific threshold. In the case of infection with a large inoculum, as suggested by studies in recipients of contaminated blood products from donors with advanced disease,¹² the viral threshold could be reached faster because of the replication of a larger initial quantity of virus, which might explain a faster progression to AIDS.

Such results can be used by physicians to determine the range of time of HIV exposure and to help search for concomitant unexpected events at onset of ARS that might not at first appear to be related to HIV infection. Also, as suggested by Armenian and Lilienfeld,⁵ the information on incubation of ARS could be useful in planning case-control studies to explore factors associated with some particularities of ARS. A limitation is that the acute pathogenetic mechanisms are supposedly similar for HCWs and N-HCWs. Few results have been published comparing the acute pathogenic mechanisms between different routes of infection, however. In addition, survival distributions are similar.

Even though a multistep process seems to be the most likely mechanism explaining IncARS, one must not put too much confidence on χ² values to pick up the correct model (gamma or lognormal), because this would imply the absence of random or systematic errors, which is not the case here, because data sets are based on different designs and because confounders such as age are not taken into account. Indeed, the lognormal model is widely recognized as robust¹³ and accommodates many different kinds of intervening factors, including population age distribution. Be that as it may, both the lognormal and gamma models can be used to predict the distribution of cases over time.

We have been able to rule out the simple mechanic of the exponential; once an individual is infected, ARS does not occur with uniform incidence density over time. Second, ARS is most likely a stepwise process, whose number could be limited to 3, corresponding to the shape of the gamma model (see Table 1). The multistep process cannot, however, be described in any greater detail, because the gamma and lognormal distributions cannot be differentiated with any confidence.

In summary, we suggest that a multistep model adequately describes the course of IncARS. The gamma model suggests the existence of 3 stages before onset of ARS as described in animal models and suggested for human beings. The investigation of early sequences of events after infection might provide important information applicable to postexposure prophylaxis, early therapy, and vaccine research.

ACKNOWLEDGMENTS

The members of the Swiss HIV Cohort Study are S. Bachmann, M. Battegay, E. Bernasconi, H. Bucher, Ph. Bürgisser, S. Cattacin, M. Egger, P. Erb, W. Fierz, M. Fischer, M. Flepp, A. Fontana, P. Francioli (President of the Swiss HIV Cohort Study, Centre Hospitalier Universitaire Vaudois, Lausanne), H. J. Furrer (Chairman of the Clinical and Laboratory Committee), M. Gorgievski, H. Günthard, B. Hirschel, L. Kaiser, C. Kind, Th. Klimkait, B. Ledergerber, U. Lauper, M. Opravil, F. Paccaud, G. Pantaleo, L. Perrin, J.-C. Piffaretti, M. Rickenbach (Head of Data Center), C. Rudin (Chairman of the Mother and Child Substudy), J. Schüpbach, R. Speck, Ph. Tarr, A. Telenti, A. Trkola, P. Vernazza (Chairman of the Scientific Board), R. Weber, and S. Yerly.