1 Department of Epidemiology, Bloomberg School of Public Health, Johns Hopkins University, Baltimore, MD
2 Department of Epidemiology, School of Public Health, Harvard University, Boston, MA
3 Department of Molecular Microbiology and Immunology, Bloomberg School of Public Health, Johns Hopkins University, Baltimore, MD
4 Cook County Hospital, Chicago, IL
5 Department of Biostatistics, School of Public Health, Harvard University, Boston, MA
Correspondence to Dr. Stephen Cole, Johns Hopkins Bloomberg School of Public Health, 615 North Wolfe Street, Room E7640, Baltimore, MD 21205 (e-mail: scole{at}jhsph.edu).
Received for publication September 2, 2003. Accepted for publication May 4, 2005.
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ABSTRACT |
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acquired immunodeficiency syndrome; antiretroviral therapy, highly active; bias (epidemiology); causality; CD4 lymphocyte count; confounding factors (epidemiology); HIV
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INTRODUCTION |
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Estimation of the effect of HAART on CD4 evolution is challenging for the following reason. Current treatment guidelines (4, 5
) suggest that physicians use plasma HIV type 1 (HIV-1) RNA level (i.e., viral load) and CD4 cell count to determine the timing of HAART initiation. However, current viral load and CD4 cell count are known predictors of subsequent CD4 cell counts (6
). Therefore, to obtain an unconfounded estimate of the total (i.e., direct and indirect) effect of HAART on CD4 cell count, it is necessary to adjust for viral load and CD4 cell count before HAART initiation. A standard approach is to include past viral load and CD4 cell count as time-varying covariates in a regression model for the mean of the current CD4 cell count, conditional on past treatment and confounder history.
Unfortunately, this standard approach fails because evolving viral load and CD4 cell count are strong intermediate variables on the causal pathway from past HAART treatment to current CD4 cell count. For example, the biologic effect of HAART is known to be largely mediated through its effect on viral load (7): HAART dramatically reduces the load of circulating virus by blocking replication at multiple points in the viral life cycle. Thus, the standard approach can, at best, only estimate the relatively small direct effects of past HAART treatment on current CD4 cell count at time t that are not mediated through the reduction in viral load and the increase in CD4 cell count prior to time t. Moreover, the standard approach may additionally induce selection bias, because CD4 cell count is affected by previous HAART use (8
10
).
However, the above difficulties can be surmounted. Robins (1113
) has developed methods based on marginal and nested structural models to adjust for variables, such as viral load, that are time-varying confounders affected by prior treatment. In a previous report (14
), we estimated the total effect of HAART initiation on time to acquired immunodeficiency syndrome (AIDS) or death using a marginal structural Cox model based on observational data from the Multicenter AIDS Cohort Study and the Women's Interagency HIV Study. Here, we use a marginal structural mean model to estimate the effect of HAART on the evolution of CD4 cell counts from 1996 to 2002 in these two ongoing cohort studies.
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MATERIALS AND METHODS |
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Each participant contributed a maximum of 12 person-visits beginning with the first semiannual study visit after April 1996 (the baseline visit) and ending with 1) the last visit at which he or she was seen alive, 2) the last visit before the first missing CD4 cell count, or 3) April 2002, whichever came first. For participants who were missing baseline data on any time-varying covariate, baseline was redefined to be the first visit with complete data.
The outcome variable was the number of CD4 cells per cubic millimeter of blood. T-lymphocyte subsets were determined by immunofluorescence using flow cytometry in laboratories participating in the National Institute of Allergy and Infectious Diseases Quality Assurance Program. Specifically, T-cell subsets were measured in purified peripheral blood mononuclear cells or ethylenediaminetetraacetic acid-anticoagulated whole blood by staining with fluorescent dye-conjugated monoclonal antibodies that were specific for CD4 lymphocytes (Becton Dickinson, Mountain View, California) (17).
The effect of exposure to HAART on CD4 cell count was of primary interest. The definition of HAART was based on the US Department of Health and Human Services panel guidelines (4) and has been previously published (14
). Typical HAART regimens consisted of two or more nucleoside or nucleotide reverse transcriptase inhibitors in combination with at least one protease inhibitor or one nonnucleotide reverse transcriptase inhibitor. Therapy regimens not classified as HAART were categorized as either monotherapy or combination antiretroviral therapy.
Data on a number of time-fixed and time-varying (i.e., visit-specific) covariates were recorded, including CD4 cell count (in cells/mm3), viral load (in copies/ml), and indicators of monotherapy and combination antiretroviral therapy use. Viral load was quantified using a reverse transcription polymerase chain reaction amplification technique (Roche Molecular Systems, Branchburg, New Jersey), which had a lower limit of detection of 400 copies/ml. When there was missing information on time-varying covariates, information was carried forward from the most recent prior observed value.
Statistical model
Let Xij be a time-varying indicator of HAART initiation for participant i on or before the jth semiannual visit from the start of follow-up (i.e., visit j = 0). Let Lij be the vector of time-varying covariates measured at visit j 1, ensuring that Lij is temporally prior to Xij, with Li0 being the vector of covariates (time-fixed and time-varying) measured at the visit before baseline. For any time-varying variable, overbars are used to denote the history of that variable up to and including j; for instance, is the covariate process for participant i up to visit j. The CD4 cell count Yij is a component of Lij. The subscript i, denoting the participant, ranges from 1 to 1,763, while the subscript j, denoting the semiannual study visit, ranges from 0 to a maximum of 11.
Consider the piecewise linear spline regression model with a knot at cumulative treatment of 1 year:
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For participants who remained alive and under follow-up at visit j, the above model was fitted using standard generalized estimating equations (GEE) repeated-measures software with an identity working covariance matrix, except that the model was weighted by inverse probability-of-treatment-and-censoring (IPTC) weights. If confounding by unmeasured factors is absent and censoring is ignorable, the IPTC-weighted GEE estimate the parameters of a marginal structural model (MSM) (18). To describe this MSM, let the potential outcome
be a random variable representing participant i's CD4 cell count at visit j had he or she followed a given therapy history
rather than his or her observed therapy history
An average causal effect on a difference scale is the mean of the potential outcomes under the HAART regimen
minus the mean of the potential outcomes under an alternate HAART regimen
The aforementioned IPTC-weighted estimates of model 1 are consistent estimates of the parameters of the marginal structural piecewise linear spline regression model with a knot at cumulative treatment of 1 year:
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Fitting model 1 with IPTC weights gives asymptotically unbiased estimates of the parameters of model 2 under the assumptions of 1) no model misspecification, 2) ignorable censoring, and 3) no unmeasured confounding. This last assumption states that conditional on past measured HAART and covariate histories, current therapy is independent of future potential outcomes (19).
The contribution of participant i to the calculation at visit j for model 1 is weighted by an estimate of the IPTC weight Wij, which is the product of the estimated stabilized inverse probability-of-treatment and inverse probability-of-censoring weights. The stabilized inverse probability-of-treatment weights are
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We estimated the denominator of the using a pooled logistic model (20
) for the probability of initiating HAART at each visit given baseline and time-varying covariates (18
). Specifically, for estimation of the denominator of
the model for the logit of the probability that participant i, uncensored at visit k, initiated treatment between visits k 1 and k (i.e., Xik) included the baseline regressors Li0 and the subset of the time-varying covariates Li1, ..., Lik. This subset consisted of 1) indicator variables for detectable HIV-1 RNA and 2) non-HAART retroviral therapy at k 1, 3) CD4 cell count, and 4) detectable log10 HIV-1 viral load measured at time k 1, modeled as restricted cubic splines with four knots located at the 5th, 35th, 65th, and 95th percentiles. For estimation of the denominator
the model for the logit of the probability that participant i was first censored between k and k + 1 included the above covariates plus treatment Xik at k. The same logit models were used to estimate the numerators of
and
except that terms depending on the time-varying covariates Lik, k > 0, were eliminated.
Numerous additional functional forms for the above pooled logistic models were explored (e.g., including covariates measured at times j 2 and j 3), as well as a broader set of covariates (e.g., age, race, clinical AIDS, body mass index, HIV-related symptoms, receipt of Pneumocystis carinii pneumonia prophylaxis, and red blood, platelet, CD3, and CD8 cell counts), but such alternative model specifications did not appreciably alter the results.
The piecewise linear spline form for model 2 was chosen on the basis of an exploratory analysis in which each subsequent year of cumulative exposure was allowed to have its own linear effect. This exploratory analysis clearly showed that the slope of the treatment effect changed at approximately 1 year of cumulative exposure. This would be expected on biologic grounds, since, after sufficient improvement in CD4 cell counts, one would expect homeostatic mechanisms to slow the rate of further increase. In secondary analyses, interactions between HAART and sex and between HAART and baseline CD4 cell count categories, which were suggested by prior research (14), were allowed. In further secondary analyses, the weights were trimmed at the first and 99th percentiles, which is an imperfect method of exploring the impact of influential observations. Trimming weights is not an ideal model-checking procedure, because the extreme weights encode the greatest amount of confounding. Therefore, trimming the weights will typically result in a shift of the estimated effect towards the (biased) unweighted value. Analyses using the natural logarithm of CD4 cell count as the outcome variable provided similar inferences.
All analyses were conducted using the Statistical Analysis System, version 8 (SAS Institute, Inc., Cary, North Carolina). Confidence intervals were based on robust variance estimates (21). For comparison, results from a standard repeated-measures linear model fitted using GEE are presented (22
).
Sensitivity analysis
To explore the possible impact of unmeasured confounding, we performed a sensitivity analysis in which a parameter that encodes the degree of confounding by unmeasured factors was varied but not estimated. To do so, we implemented the augmented IPTC-weighted estimators of Robins (23
) in a similar fashion as Brumback et al. (24
) and Ko et al. (25
). Briefly, the observed outcome Yij+1 is replaced with a bias-adjusted outcome Yij+1(
), defined as
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RESULTS |
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The corresponding estimates from the standard (unweighted) GEE regression model that included baseline and time-varying CD4 cell count and HIV-1 viral load as regressors were 26 cells/mm3 (95 percent CI: 17.7, 34.3) for the first year and 0.6 cells/mm3 per year after the first year, which results in an estimated mean CD4 increase at 6 years of 23 cells/mm3.
There appeared to be a larger effect of HAART on CD4 cell count within 1 year of initiation among men (92.9 cells/mm3, 95 percent CI: 53.9, 131.8) than among women (62.1 cells/mm3, 95 percent CI: 36.0, 81.3) (interaction p < 0.001), but there was a similar effect of HAART on CD4 cell count by cohort beyond 1 year after initiation (interaction p = 0.341). There also appeared to be a larger effect of HAART on CD4 cell count within 1 year of initiation among persons with a lower baseline CD4 cell count (interaction p = 0.047). Specifically, among those with a baseline CD4 count below 200 cells/mm3, the difference was 105.7 cells/mm3 (95 percent CI: 80.7, 130.6), while among those with a baseline CD4 count of 350 cells/mm3, the difference was 54.1 cells/mm3 (95 percent CI: 17.8, 90.3). There was no strong evidence for heterogeneity in the effect of HAART on differences in CD4 count beyond 1 year after initiation (interaction p = 0.194).
Figure 1 illustrates the sensitivity of the average difference in CD4 cell count due to unmeasured confounding. When the bias parameter was 30 cells/mm3, reflecting moderately strong residual confounding, the difference in CD4 count within 1 year of HAART initiation increased from 71 cells/mm3 to 109.6 cells/mm3, while the difference in CD4 count beyond 1 year after HAART initiation increased from 29 cells/mm3 to 38.5 cells/mm3. A
of 30 represents unmeasured confounding of nearly two thirds the amount of the measured confounding (i.e., 30/(71 21.5)).
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DISCUSSION |
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In a randomized trial, AIDS Clinical Trials Group 320 (2) previously reported an 82-cell/mm3 (95 percent CI: 46, 118) difference in CD4 cell count after 40 weeks of HAART treatment as compared with a less potent treatment among participants with prior antiretroviral therapy and CD4 cell counts below 201 cells/mm3. In the subgroup with a CD4 cell count less than 200 cells/mm3 at baseline, a similar estimated 81-cell/mm3 (105.7 x 40/52 = 81.3) difference at 40 weeks was found using the marginal structural linear spline model.
The present work extends the findings of randomized trials (2, 3
) by including participants with baseline CD4 cell counts above 200 cells/mm3 and extending follow-up to 6 years. In a recent report using an MSM and 2 years of prospective data from the HIV Epidemiology Research Study, Ko et al. (25
) reported a 64-cell/mm3 difference in CD4 count for persons on HAART as compared with those not on HAART in the stratum where baseline CD4 count was below 200 cells/mm3. While the effect estimates of Ko et al. appear somewhat muted, the inferential pattern of 1) smaller effects in standard unweighted analyses and 2) a stronger effect at lower baseline CD4 cell counts remains consistent.
These results should be taken in concert with the following limitations. First, the estimates have a causal interpretation only under the assumption of no unmeasured confounding. This assumption probably holds (approximately) here, because the most important clinical and laboratory information used by physicians as indications for HAART was collected and used in the models for the estimation of the weights (26). If the assumption of no unmeasured confounders is correct and the model used to create the treatment weights is correct, then weighting creates a pseudopopulation in which 1) the probability of HAART initiation is not a function of the time-varying covariates (i.e., no confounding exists) but 2) the effect of HAART initiation on CD4 cell count is the same as in the actual study population.
Second, the results are based on the assumption that dropout is ignorable, conditional on measured covariates. Neither the present analyses nor past analyses (14, 27
) suggested that there is notable measured informative censoring in these data. However, a majority of participants were censored at their first missing CD4 cell count. A secondary analysis censoring participants at dropout rather than at first missing CD4 cell count provided a similar estimate but did not significantly improve precision (data not shown). Note that death was treated as a censoring event in the analysis, which may not always be appropriate. Robins and Greenland (28
) discuss the pros and cons of this choice.
Third, these results may be sensitive to the relative infrequency of data collection (i.e., 6-month intervals). Misclassification due to this coarse measurement (with respect to time) could have reintroduced some confounding, which could have biased the estimated difference in either direction (29).
Fourth, in these analyses, we assumed that participants remained on HAART after initiation. This assumption was correct for 86 percent of 6,516 post-HAART-initiation person-visits. However, because 14 percent of the visits occurred among persons who had stopped using HAART, the IPTC-weighted analysis did not estimate the effect of continuing HAART therapy versus no HAART therapy. Formally, the IPTC-weighted analysis estimated the "intention-to-treat effect" of HAART therapy versus no HAART therapy in a hypothetical randomized clinical trial in which 1) participants were randomly assigned to begin continuous HAART at different visits, 2) all participants initially complied and began HAART at their assigned visit, and 3) 14 percent later discontinued HAART. If many of the patients in the study discontinued HAART because of toxicity (rather than for nonmedical reasons), it is this intention-to-treat effect, not the effect of continuous HAART usage, that would be the parameter of public health interest. This is because, had we estimated the effect of continuous HAART, we would have been estimating the effect of forcing people to continue therapy even in the presence of toxicity. In fact, detailed information on reasons for discontinuation was not contained in the database. However, on the basis of anecdotal discussions with clinicians, we believe that many participants discontinued therapy because of toxicity, and therefore the analysis presented is the most appropriate. Note that the above discussion implies that the results reported in this paper do not address the effect of discontinuing HAART on CD4 cell count.
Without data from randomized trials that follow patients with widely varying risk profiles for prolonged periods, ongoing prospective observational studies with repeated assessments of exposure and detailed collection of clinical and laboratory information provide the best evidence available for the estimation of risk group-specific, long-term therapeutic effects. These results show, however, that one must be careful to correctly analyze such data. We found that the estimated effect of HAART on CD4 cell count at 6 years based on IPTC-weighted estimation of an MSM was strikingly larger than estimates based on standard GEE analyses. We believe the MSM estimate to be closer to the true effect, both on theoretical grounds (11, 19
) and because the MSM analysis, in contrast to standard GEE analyses, successfully reproduced the limited results from a previous randomized trial.
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ACKNOWLEDGMENTS |
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Data for this article were collected through the Multicenter AIDS Cohort Study, with centers (Principal Investigators) at the Johns Hopkins Bloomberg School of Public Health (Drs. Joseph B. Margolick and Alvaro Muñoz), the Howard Brown Health Center and Northwestern University Medical School (Dr. John Phair), the University of California, Los Angeles (Drs. Roger Detels and Beth Jamieson), and the University of Pittsburgh (Dr. Charles Rinaldo), and the Women's Interagency HIV Study, with the following centers/consortia (Principal Investigators): the New York City/Bronx Consortium (Dr. Kathryn Anastos), Brooklyn, New York (Dr. Howard Minkoff), the Washington, DC, Metropolitan Consortium (Dr. Mary Young), the Connie Wofsy Study Consortium of Northern California (Dr. Ruth Greenblatt), the Los Angeles County/Southern California Consortium (Dr. Alexandra Levine), the Chicago Consortium (Dr. Mardge Cohen), and the Data Coordinating Center (Dr. Alvaro Muñoz). World Wide Web links for both studies are located at http://www.statepi.jhsph.edu.
The Multicenter AIDS Cohort Study is funded by the National Institute of Allergy and Infectious Diseases, with additional supplemental funding from the National Cancer Institute (grants UO1-AI-35042, 5-MO1-RR-00722 (General Clinical Research Center), UO1-AI-35043, UO1-AI-37984, UO1-AI-35039, UO1-AI-35040, UO1-AI-37613, and UO1-AI-35041). The Women's Interagency HIV Study is also funded by the National Institute of Allergy and Infectious Diseases, with supplemental funding from the National Cancer Institute, the National Institute of Child Health and Human Development, the National Institute on Drug Abuse, and the National Institute of Craniofacial and Dental Research (grants U01-AI-35004, U01-AI-31834, U01-AI-34994, AI-34989, U01-HD-32632 (National Institute of Child Health and Human Development), U01-AI-34993, and U01-AI-42590).
Conflict of interest: none declared.
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References |
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