a Department of Medical Statistics, University of Nijmegen, The Netherlands.
b Department of Public Health, Municipal Health Service, Amsterdam, The Netherlands.
c British Columbia Centre for Excellence in HIV/AIDS, St. Paul's Hospital, Vancouver, BC, Canada.
d Department of Community Health and Epidemiology, Dalhousie University, Halifax, NS, Canada.
e Department of Health Care and Epidemiology, University of British Columbia, Vancouver, BC, Canada.
Reprint requests to: JCM Hendriks, Department of Medical Statistics, University of Nijmegen, PO Box 9101, NL-6500 HB Nijmegen, The Netherlands.
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Abstract |
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Methods The CD4-based stage of an individual at each visit was determined using smoothed data. For each cohort and in each calendar time period, a CD4-based Markov model with death as the absorbing stage was fitted to the data. The parameters in this model were estimated using the method of maximum likelihood and confidence intervals were calculated using bootstrap methods.
Results A total of 509 homosexual men participating in the VLAS were included in this study, providing 5356 visits. Some 292 men developed AIDS before 1 January 1997 and 239 died before this date. In all, 232 of the 239 deaths were AIDS related. Thirty-seven per cent of all visits were related to treatment. A total of 543 homosexual men participating in the ACS were included in this study, providing 10 043 visits; 277 men developed AIDS before 1 January 1997 and 250 died before this date. The date of AIDS diagnosis was known for 225 of the 250 deaths. Twenty per cent of all visits were related to treatment. We found that in both cohort studies the stage-specific waiting times were longer in the low CD4-based stages (stages 4, 5 and 6: i.e. CD4 count <500 cells per mm3) after March 1990 compared to waiting times before March 1990. The increase in mean waiting time in these stages with low CD4 count was 21%, 33% and 53%, respectively in the ACS and 20%, 2% and 29% in the VLAS. Because waiting times alone are not exclusive for progression in a reversible model we also calculated the stage-specific median incubation periods till death. Men spent considerably longer in these CD4-based stages after March 1990 compared to before March 1990.
Conclusions Data from these population-based cohort studies showed that HIV disease progression in the calendar period where treatment was administered was slower for individuals in stages with low CD4 counts. We found no evidence for shortening of the incubation period that may have appeared from increasing virulence of the HIV in the population.
Keywords HIV disease progression, incubation period distribution, CD4 count, trends in waiting time, homosexual men, Markov model
Accepted 4 November 1999
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Introduction |
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Survival techniques have been used to estimate the incubation period from seroincident cohort studies, possibly after imputing seroprevalent data. However, using a Markov model full use of the data of a seroprevalent cohort is made, and in addition progression through stages of HIV infection are estimated. The Markov assumption is in agreement with the property of biological systems that the present state of the system is most predictive for progression. An advantage of studying staged disease progression is that only short study periods are needed, i.e. short relative to the long incubation period (median 810 years10). Short study periods are especially of interest when (temporal) time trends or the effect of treatment are studied.
Markers of immune function are the main indicators for HIV disease progression and from these, CD4 T-cell count is widely accepted as the best marker for disease progression. Even in the presence of viral load measurements, CD4 cell count is a significant predictor of disease progression.11 Subsequently, stages of the incubation period to AIDS (i.e. the time from infection, approximated by the date of HIV seroconversion, to a diagnosis of AIDS) can be defined by ranges of CD4 cell count. The waiting time of a stage is the time spent in that stage before going to another stage.
The purpose of this study was to investigate secular trends in waiting times in CD4-based stages of HIV disease progression by calendar time. Stages of CD4 cell count in a reversible continuous-time Markov model in two calendar time intervals in a cohort of homosexual men in Vancouver and in a cohort of homosexual men in Amsterdam were used. March 1990 was chosen a priori as the cutoff point because antiretroviral treatment was generally available at that time and its use became widespread. Consequently, these calendar time intervals were characterized by low and high percentages of participants for whom treatment was administered. In addition, data from two cohort studies were used because, next to secular trends, there may be geographical differences in progression times due to underlying geographical variation in viral strains and in virulence. If this was not the case, our study gained significant power because of the repeated confirmation of results.
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Materials and Methods |
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The Vancouver Lymphadenopathy-AIDS Study (VLAS), was started in November 1982 and had enrolment until December 1984. Both HIV-negative and HIV-positive men were followed at intervals of 36 months until 1986 and annual visits occurred thereafter. In all 5356 visits from 509 homosexual men were included in this study. Some 292 men developed AIDS before 1 January 1997 and 239 died before this date, whereas 232 had a known date of AIDS diagnosis. Thirty-seven per cent of all visits of the asymptomatic HIV-positive men were related to treatment with the potential to delay the onset of AIDS: 10% to AZT alone, 21% to AZT and additional treatment (i.e. PCP prophylaxis, DDC, DDI) and 6% to treatment other than AZT.
The Amsterdam cohort study on HIV and AIDS (ACS) started in December 1984, and has ongoing enrolment and follow-up of both HIV-negative and HIV-positive homosexual men. The HIV-positive men were followed at intervals of 3 months. In all, 10 043 visits from 543 homosexual men were included in this study and 277 men developed AIDS before 1 January 1997; 250 died before this date, whereas 225 had a known date of an AIDS diagnosis. Twenty per cent of all visits of the asymptomatic HIV-positive men were related to treatment with the potential to delay onset of AIDS: 13% to AZT alone, 5% to AZT and additional treatment (i.e. PCP prophylaxis, DDC, DDI) and 2% to treatment other than AZT.
Staged Markov model
We modelled HIV disease progression using a continuous-time Markov model with eight stages (Figure 1). Stages 16 are transient states defined by ranges of the number of CD4+ cells, as used previously.1316 This scheme has been successful in dividing the incubation period into relatively even periods in cohort studies of homosexual men14 and injecting drug users.16 Stage 7 was a transient state defined by being diagnosed with AIDS (using the 1987 Centers for Disease Control and Prevention [CDC] AIDS case definition12), and stage 8 (the only absorbing state in our model) corresponded to death. Our model allowed transitions between adjacent CD4 stages, an AIDS diagnosis directly from the last three CD4-based stages, and transition from an AIDS diagnosis to death. Consequently, the model was specified by 14 transition parameters (
ij's), indicating the instantaneous hazard of moving between stages. For example,
47 was the instantaneous hazard of an AIDS diagnosis (stage 7) from stage 4 (CD4: 351500 cells/mm3).
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The model parameters ('s) were estimated using maximum likelihood methods.17 The distributions of the times that each stage was first entered (first passage times) were generated from 10 000 simulations using the estimated
's and exponential waiting times. To account for both the variability introduced by the smoothing step and the variability in the data, we calculated confidence intervals for the
's and median first passage times using the bootstrap procedure. Specifically, first we sampled with replacement from the members of the study population and, second, we constructed bootstrap replicates for each individual of this new dataset by sampling from the set of observed residuals. The sampled residual was added to the observed value, and then the data were re-smoothed. This procedure was repeated 200 times, resulting in 200 replicate datasets. The model was fit to each replicate dataset, and bootstrap confidence intervals were obtained using the percentiles' method.18 We also calculated the expected number of stages visited before an AIDS diagnosis as a measure of how well the staged CD4 model predicted disease progression.
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Results |
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Plots of the measured and the smoothed CD4 count of an individual, as presented in Hendriks et al.,14 clearly reveal that the smoother effectively removes the noise. The CD4-based stage of an individual at each visit was determined using smoothed CD4 count. Table 1 shows the number of observed transitions from each stage to any other stage between two subsequent visits in both cohort studies in each time period. Although exact comparison of these numbers between both cohorts was not possible, because the intervals between two successive visits are different, one may conclude from Table 1
that the pattern in both cohort studies was similar. The differences that appeared in the relative frequencies per stage or in the mean number of months between two visits were likely due to the differences in study design. The time-continuous staged model as presented in Figure 1
was fitted to these data (using smoothed CD4 count). This model does not allow direct transitions from stages other than 7 (AIDS) to death. So, this limited number of transitions (Table 1
) is forced through stage 7.
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Table 2 shows the percentage of visits in each stage that were related to treatment by calendar time interval for each cohort separately. Although treatment in both cohorts was similar before March 1990, as expected, treatment increased considerably after this time and even more so in the VLAS. Note that these percentages in the VLAS overestimate the actual number of visits related to treatment. In contrast to the ACS, visits are counted when they occurred after start of treatment. This may lead to subtle differences where treatment was (temporarily) stopped.
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Discussion |
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The breakpoint March 1990 was arbitrarily chosen in that it was (1) near halfway data collection, (2) the treatment given in the first interval was limited and (3) the calendar time intervals were long enough to have consistent results from this method of analysis. Using these conditions any other cutoff point, say within one year of the cutoff point used, gave similar results.
In our model we did not allow progression directly from a CD4-based stage to death, assuming that these cases were unobserved AIDS cases. This may be so, because the time since the last visit was on average more than 3 years and only limited information about AIDS-related causes of death were available for these cases. It should also be noted that municipal and national registries were used to complete these data. Finally, omitting these data gave similar results.
The VLAS participants were recruited about 2 years earlier than the participants in the ACS and the VLAS was designed, unlike the cohort in Amsterdam, to be a closed cohort study. Thus, there could be subtle differences between the cohorts with respect to factors that may affect the progression rates, but these factors may be difficult to identify. One of these differences was the relatively short waiting times in stage 1 in the VLAS after March 1990 and in the ACS before March 1990. One may argue that this resulted from the changing patterns of the number of seroconverters in secular time. Since HIV-negative men were followed in both cohorts, ageing may explain this difference in the VLAS. Although, this may be less in the ACS since it is not a (completely) closed cohort study. Also, from this point of view one may expect a relative short number of seroconverters in the ACS in the early years of this study. However, the pattern of number of visits per stage in each calendar time interval was similar to the overall pattern in the ACS. To overcome these differences, we studied the changes in the incubation period by studying the changes in the incubation time from either stage to death. We used death as the endpoint rather then an AIDS diagnosis, as this is not subject to change in definition like AIDS diagnosis is.
These data from the cohort in Amsterdam provided information on the changes in progression rates in a population-based cohort, possibly indicating changes in progression rates in the population from which this cohort was drawn. However, these changes may be overestimated as, for instance, the men participating in the cohort study may have better access to therapy than other homosexual and bisexual men.
Several studies have suggested that there have been no major changes in the incubation period up to 19911992.2123 Our findings were in agreement with other studies that report an extension in the time from seroconversion to death in more recent years.13 There is little doubt that improved treatment and prophylaxis for HIV-related diseases are the underlying cause. Given that this observed extension occurred in the early years of implementation of triple combination therapies, even greater delay in progression is to be expected in the future.
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Acknowledgments |
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References |
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