Assessing the effect of hormonal contraception on HIV acquisition in observational data: challenges and recommended analytic approaches
Polis, Chelsea B.a,*; Westreich, Danielb,c,*; Balkus, Jennifer E.d,e,*; Heffron, Reneee,*; participants of the 2013 HC-HIV Observational Analysis Meeting
aOffice of Population and Reproductive Health, United States Agency for International Development (USAID), Washington, DC
bDepartment of Epidemiology, University of North Carolina, Chapel Hill
cDepartment of Obstetrics & Gynecology and Global Health Institute, Duke University, Durham, North Carolina
dVaccine and Infectious Disease Division, Fred Hutchinson Cancer Research Center
eDepartment of Global Health, University of Washington, Seattle, Washington, USA.
*Chelsea B. Polis, Daniel Westreich, Jennifer E. Balkus and Renee Heffron contributed equally to the writing of the article.
Correspondence to Chelsea B. Polis, Research, Technology, and Utilization Division, Office of Population and Reproductive Health, Bureau for Global Health, USAID, 1201 Pennsylvania Avenue, NW, Suite 315, Washington, DC 20004, USA. Tel: +1 202 808 3800; e-mail: firstname.lastname@example.org
Accepted 21 August, 2013
Introduction: Determining whether hormonal contraception, particularly the injectable contraceptive depot-medroxyprogesterone acetate (DMPA), increases a woman's risk of HIV acquisition is a priority question for public health. However, assessing the relationship between various hormonal contraceptive methods and HIV acquisition with observational data involves substantial analytic design issues and challenges. Studies to date have used inconsistent approaches and generated a body of evidence that is complex and challenging to interpret.
Methods: In January 2013, the United States Agency for International Development and FHI 360 supported a meeting of epidemiologists, statisticians, and content experts to develop recommendations for future observational analyses of hormonal contraception and HIV acquisition.
Results: Meeting participants generated recommendations regarding careful definition of exposure groups; handling potential confounders, mediators, and effect modifiers; estimating and addressing the magnitude of measurement error; using multiple methods to account for pregnancy; and exploring the potential for differential exposure to HIV-infected partners. Advantages and disadvantages of various statistical approaches to account for time-varying confounding and estimating total and direct effects were also discussed.
Conclusion: Implementing these recommendations in future observational hormonal contraception-HIV acquisition analyses will enhance interpretation of existing studies and strengthen the overall evidence base for this complex and important area.
Determining whether use of various hormonal contraceptive methods increase a woman's risk of HIV acquisition is a priority research question for women's health [1,2]. Hormonal contraception prevents unintended pregnancy and contributes to reductions in maternal and infant morbidity and mortality . Globally, over 150 million women use hormonal contraception, including oral contraceptive pills, injectable contraceptives [depot-medroxyprogesterone acetate (DMPA), norethisterone enanthate (NET-EN), or combined injectables], contraceptive implants, rings, patches, or levonorgestrel-releasing intrauterine devices (IUDs) . In sub-Saharan Africa, nearly 60% of hormonal contraception users rely on injectable contraception , a highly effective, long-lasting, reversible method that can be used discreetly and provided by community health workers . Some observational studies have raised concerns of a potentially increased risk of HIV acquisition among users of hormonal contraception, primarily DMPA, but results overall are inconsistent and study quality varies greatly . The widespread use of injectables in sub-Saharan Africa, an area of high HIV prevalence and incidence, heightens these concerns. During a 2012 WHO technical consultation, 75 experts reviewed all available biological, epidemiological, and modeling data, and recommended that WHO continue to suggest no restriction on the use of any hormonal contraceptive method; however, they noted that condom use and other HIV preventive measures should be strongly emphasized for women at high risk of HIV who choose progestogen-only injectable contraception .
Twenty observational cohort studies published from 1991 to 2012, and conducted among a range of populations (for example, family planning clinic attendees, commercial sex workers, women with HIV-1-infected partners, etc.), have used varied methodological approaches and generated heterogeneous results . At the 2012 WHO consultation, experts gave the collective body of epidemiological evidence on hormonal contraception and HIV acquisition a GRADE rating of ‘low’ [7–10], due in part to inconsistencies between study results. Greater consistency and rigor in analytic approaches may allow for clearer interpretation of individual study results and comparability across studies, strengthening the overall evidence base and improving the GRADE rating. The complete body of evidence, including studies published since the 2012 WHO consultation [11,12] will be reviewed at the next WHO technical consultation, currently planned for 2014.
Formal discussion on how to improve the observational hormonal contraception-HIV acquisition evidence base has been limited. In response to the need to strengthen and harmonize hormonal contraception-HIV acquisition analytic approaches for observational data, the United States Agency for International Development (USAID) and FHI 360 supported a meeting entitled ’Best practices in analytic approaches to assess the effect of hormonal contraception on HIV acquisition with observational data,’ in Seattle, WA on 24–25 January 2013. Epidemiologists, biostatisticians, and content experts discussed recommendations on best analytic practices for future observational analyses; this report summarizes those discussions and presents recommendations for future analyses.
Observational analyses to assess the hormonal contraception-HIV acquisition relationship present multiple challenges in analytic design. Below, we highlight several key challenges of conducting these analyses and offer recommendations (summarized in Table 1) that should be considered prior to the initiation of a primary or secondary observational analysis of hormonal contraception and HIV acquisition.
Defining hormonal contraception exposure and HIV outcome
In hormonal contraception-HIV acquisition analyses, the outcome of interest is HIV acquisition, the detection of which requires repeated HIV testing. Defining hormonal contraception exposure is more complex. Each hormonal contraceptive method induces different biological effects; therefore, it is critical to disaggregate by hormonal contraceptive method type (e.g., pills vs. injectables vs. implants vs. IUDs), and when possible, by formulation (e.g., DMPA vs. NET-EN; estrogen; and progestin combined methods vs. progestin-only methods, etc.) and dosage (e.g., intramuscular DMPA vs. lower-dose subcutaneous DMPA, etc.). Some studies to date have disaggregated by hormonal contraceptive type, and a few have disaggregated by formulation . High rates of contraceptive discontinuation and switching  and imperfect adherence  lead to complex exposure patterns, necessitating frequently updated, prospectively collected hormonal contraception exposure data. Sensitivity analyses can explore the impact of censoring follow-up time when women first switch their contraceptive method. Any induced informative censoring would have to be addressed using additional analytic approaches, such as inverse probability weighting. An additional question is whether the exposure of interest is current exposure to hormonal contraception (which most studies have addressed) or some summary of cumulative hormonal contraception exposure .
Defining the ‘no hormonal contraception exposure’ comparison group
To date, most studies have assessed whether a particular hormonal contraceptive method increases HIV risk relative to using no hormonal contraception, but the composition of the ‘no hormonal contraception’ (unexposed) comparison group has varied. Women not using hormonal contraception may be using condoms, copper IUDs, withdrawal, spermicides, diaphragms, sterilization, hysterectomy, traditional methods, or nothing to prevent pregnancy (some of these women may be actively trying to become pregnant). Thus, women not using hormonal contraception may be heterogeneous with respect to any contraceptive use or nonuse, with accompanying differences in other important factors, such as coital frequency, exposure to sexually transmitted infections (STIs), and pregnancy intention, factors that have not always been measured in previous studies. Further, some of these methods (or lack thereof) may magnify or dilute HIV incidence in the comparison group. For example, women using condoms for pregnancy prevention without a hormonal contraceptive method (who would thus be in the ‘no hormonal contraception’ group) typically report more consistent use of condoms than women using condoms for HIV/STI prevention (who could be in either group) [16–21]. This could induce bias in the effect estimate if consistency of condom use over time, a challenging variable to assess, is not adequately measured and controlled. Some studies have contained comparison groups composed largely of women using condoms , whereas others have had few or no condom users in the comparison group . Differences in comparison groups between studies could lead to substantial differences in effect estimates. Thus, clear descriptions of the composition of the comparison group, with these parameters in mind, are necessary for cross-study comparisons.
Alternate comparison groups
In addition to comparisons of hormonal contraception users vs. women who do not use hormonal contraception, future observational analyses could compare HIV acquisition rates among women choosing various effective contraceptive methods, (e.g., DMPA vs. IUD, DMPA vs. NET-EN, etc.). Such comparisons have not been made to date, but would reframe the research question to identifying the safest method of hormonal contraception (with respect to HIV acquisition) among contracepting women at risk of HIV infection. Many recent HIV prevention trials emphasized counseling and on-site provision of effective contraceptive methods for participants; in these trials, most women used hormonal contraception. Thus, future analyses using these datasets may be best suited to answering questions that compare different hormonal contraceptive methods against each other. An advantage to this comparison is that underlying HIV risk (as measured, for example, by report of sexual behaviors and condom use consistency) may be similar among groups of women choosing highly effective contraceptive methods, which would reduce potential confounding by these factors. However, without an established understanding of baseline HIV-related risk of the comparison for each method, interpreting risk estimates may be challenging. For example, a null effect may indicate that neither method impacts risk, or that both methods increase or decrease risk equally.
Confounding, time-varying confounding, mediation, and effect modification
Women who choose to use hormonal contraception are different from women who do not, and these differences may also be related to underlying risks for HIV infection. Such differences will result in confounded estimates of the hormonal contraception-HIV relationship if not appropriately controlled. In addition, mediating factors that result from the exposure (hormonal contraception) and that cause the outcome (HIV acquisition) can also complicate analyses and the interpretation of results. Some confounders may simultaneously act as mediators. For example, DMPA use may be influenced by recent coital frequency, and DMPA use may also affect subsequent coital frequency. Such variables, known as time-varying confounders, must be addressed using appropriate analytic techniques, for example, marginal structural models (MSMs), which have been used in some studies [11,24–26]. Several early hormonal contraception-HIV studies did not adjust for important confounders , and to date, no published observational studies have assessed potential mediation.
As it is not always clear whether certain variables (for example, coital frequency or condom use) should be assessed as confounders, mediators, or both, it is important to consider how each variable is included in a statistical model. Conceptual models can be used to help specify a priori which factors are assumed to operate as potential confounders, mediators, or both. Meeting participants drafted a simplified conceptual model (Fig. 1) to illustrate theoretical relationships between use of a hormonal contraceptive method (exposure) and HIV acquisition (outcome), listing multiple important potential confounders and/or mediators [27–31]. Uncertainty on how best to incorporate the large number of potential variables made it infeasible to specify a single model. However, participants agreed which key factors to consider, and that several time-varying factors have been demonstrated in previous studies to act simultaneously as confounders and mediators, including condom use, participant behavioral risk, and primary partner risk . Future analyses should consider factors shown in Fig. 1, and provide a rationale if they are not included in statistical models.
Previous studies have assessed whether various factors such as age, country, or infection with herpes simplex virus type-2 (HSV-2), could potentially act as effect modifiers of the hormonal contraception-HIV acquisition relationship, but results have been mixed. Future investigations should explain biologically plausible mechanisms for apparent effect modification, and also consider the potential for differential confounding across strata, which could generate spurious effect modification .
Total and direct effects
The terms ‘total effects’ and ‘direct effects’ are used to describe relationships between an exposure, an outcome, and other factors in the causal pathway [33,34]. Figure 2 displays a simplified causal diagram for one hypothesized hormonal contraception-HIV relationship, suggesting condom use as one potential mediator. In Fig. 2, the ‘direct effect’ of hormonal contraception on HIV risk is not mediated through condom use, whereas the ‘indirect effect’ of hormonal contraception on HIV is the mediated pathway through condom use. In this simplified example, the ‘total effect’ is the overall effect of hormonal contraceptive use on HIV acquisition (after controlling for confounding factors) of the direct and indirect effects combined (i.e., through both pathways). All three types of effects – direct, indirect, and total – are assumed to be free of confounding.
At the meeting, opinions differed as to whether estimating a total effect or a direct effect of hormonal contraception not mediated by behavioral factors (informally referred to as a ‘biological’ effect) would be more relevant to the policy agenda. Total effects are useful when the interest is in the overall effect of a hormonal contraceptive method (including consequent effects of hormonal contraceptive on mediators) on HIV risk, whereas the direct effect attempts to isolate the effect of a hormonal contraception method on HIV risk not mediated by other factors. The direct effect may be more generalizable if the biological response to hormonal contraception differs less than socially, culturally, and behaviorally mediated responses. Although direct effects may be valuable, they may be difficult to obtain, given challenges in accurately measuring confounding and mediating factors, the requisite additional assumptions required for their estimation, and potential loss of statistical precision [34,35].
Regardless of the effect estimated, it will continue to be important to prioritize novel programs to increase condom use alongside highly effective contraceptive methods, develop multipurpose prevention technologies [36,37], and expand contraceptive method options. However, if DMPA is found to increase risk of HIV, and a large portion of that effect is ‘biological’ (and of substantial magnitude) , then it would be particularly crucial to enhance access to alternative safe, acceptable highly effective contraceptive methods, particularly in areas where both DMPA use and HIV prevalence is high. Such an effort might be lower priority if the total effect of hormonal contraception on HIV were due to behavioral factors rather than (for example) physiological changes caused in the body by hormonal contraception. Future studies should be clear about the effect being estimated (total or direct; and if direct, with respect to what factors), and consider estimating both, wherever possible.
Analytic challenges and considerations
Measurement error and missing data
Self-reported data about sexual behavior and hormonal contraceptive use are subject to biases, including misreporting, recall, and social desirability. In addition, data on these important factors may be intermittently missing as a result of unattended follow-up visits. Methods to address measurement error and missing data, minimize bias and estimate its magnitude and direction, or examine the robustness of primary analytic results may help to interpret findings from observational analyses. For example, to examine the accuracy of self-reported condom use, investigators can compare HIV (or other STI) acquisition rates or pregnancy rates between women who report consistently using condoms and those who do not. HIV incidence rates among consistent condom users are expected to be lower than women who never use condoms. If female genital specimens are available, biologic markers of unprotected intercourse [for example, prostate specific antigen (PSA) or Y-chromosome testing] could provide a biomarker of this behavior to help to estimate overreporting of condom use among women who report recent sex . Investigators can also conduct sensitivity analyses among individuals who report no condom use (by censoring at initiation of condom use, though this may be informative), as these individuals may theoretically be less vulnerable to social desirability bias [40,41]; similarly, studies that include a small proportion of condom users may be less impacted by condom overreporting. To examine the accuracy of self-reported hormonal contraceptive use, pregnancy rates among women reporting different types of contraceptive methods can be compared. Pregnancy rates would be expected to be higher among women using more user-dependent methods (condoms, oral contraceptives) compared with user-independent methods (injections, implants, IUDs). If these trends hold, they are an indication that self-reported data are accurate on an aggregate level. Other sensitivity analyses may be possible to examine the extent of inaccuracy in other potentially confounding factors.
If confounding (including residual confounding due to misreporting) is suspected to impact the effect estimates, it is important to provide information on the likely magnitude and direction of bias. One recent mathematical modeling example assessed the magnitude of differential misreporting required to generate a spurious doubling of HIV risk with injectable hormonal contraceptive use in a recent hormonal contraception-HIV acquisition study , and suggested that underreporting of condom use would need to be unrealistically large to have generated the reported effect estimate if condom use were the only confounder .
Accounting for pregnancy
Previous studies have addressed pregnancy in several ways: no reported adjustment for incident pregnancy, censoring at pregnancy, and treatment of pregnancy as a time-varying confounder. Hormonal contraception prevents pregnancy, and pregnancy has been associated with an increased risk of HIV acquisition in some, but not all, observational studies [22,23,43,44]. Yet even if pregnancy acts as a confounder of the hormonal contraception-HIV relationship, adjusting for pregnancy may be problematic, as becoming pregnant makes a woman ‘ineligible’ for hormonal contraceptive use, thereby violating the positivity assumption, which requires that there are both exposed and unexposed participants at all values of the confounder(s) . The meeting's participants concluded that the most appropriate method to address pregnancy should depend on the question being asked. If analytic interest is in direct effects not influenced by pregnancy, then censoring at pregnancy may be appropriate, although such censoring may be informative. If interest is in the total effect, then pregnancy (as part of that total effect) should not be ‘controlled away’ (although confounding by pregnancy status may still be an issue). The optimal approaches to address pregnancy in hormonal contraception-HIV analyses require further study. At present, implementation of various approaches for pregnancy is recommended in order to gauge the range of results when different approaches are employed.
Accounting for HIV exposure and partner risk
A substantial proportion of women participating in HIV prevention studies may never be exposed to HIV [6,46]. Heterogeneity in HIV exposure risk may introduce bias if HIV exposure is linked to decisions regarding contraceptive method choice. If HIV exposure differs by hormonal contraceptive method, this could impact results. Characterization of the level of HIV exposure could be achieved by assessing serodiscordant couples (ideally with information on male partner HIV viral load), by testing of female genital samples for viral HIV-1 DNA from male partners, or by testing partners for HIV. In the absence of data on partner risk, composite variables of sociodemographic factors related to partner risk could be considered, but proxy measures of partner risk may have limited utility  and should be validated. Further research would be useful for improving our understanding of HIV exposure in different populations, and whether hormonal contraceptive use is associated with the likelihood of HIV exposure.
Statistical model considerations in the presence of time-dependent confounding
The majority of prospective hormonal contraception-HIV studies have used Cox proportional hazards regression models, which can induce bias in the presence of time-varying confounders that are also mediating factors [48–50]. For example, if coital frequency (which changes over time) affects both use of DMPA and HIV acquisition risk (and so is a confounder), but is also affected by DMPA use (and so is also a mediator), then traditional regression approaches such as Cox models can give a biased effect estimate. This may happen even if there is no uncontrolled confounding (see also previous section entitled Confounding, time-varying confounding, mediation, and effect modification). Several alternative methods can estimate unbiased effects in such data (subject to assumptions including no uncontrolled confounding): the parametric g-formula [51–53], g-estimation of structural nested models [54,55], and MSMs [48,49] fit with inverse probability weights (IPWs) . Collectively, these are referred to as ‘the g-methods.’ These methods can also estimate either total or direct effects in specific situations in which traditional regression approaches cannot .
Of these methods, MSMs fit with IPWs are technically easiest to implement, and several recent hormonal contraception-HIV analyses have used this approach [11,24–26,57]. In contrast to MSMs, neither g-estimation nor the parametric g-formula has been widely implemented. The parametric g-formula is technically and computationally intensive, and has the disadvantage of requiring numerous parametric assumptions. A notable advantage of this approach, however, is that the assumptions of the parametric g-formula complement those of IPW MSMs : the sets of relations modeled are complementary between the two methods. As such, the g-formula may make a good sensitivity analysis for hormonal contraception-HIV acquisition analyses. More statistical details regarding MSM [48,49,58] and the g-formula [51,53] can be found elsewhere.
Despite theoretical advantages of g-methods (including MSMs), over traditional regression approaches, if strong time-dependent confounding is absent from a dataset being used to estimate a hormonal contraception-HIV acquisition relationship, then g-methods are unlikely to provide markedly different results from traditional methods . The absence of strong time-dependent confounding could occur because current hormonal contraceptive use has little or no effect on the mediator/confounder or because the mediator/confounder has little effect on the probability of future exposure to hormonal contraceptive use; such assumptions could be tested prior to employing g-methods .
Theory shows that g-methods are the more statistically appropriate methods for longitudinal hormonal contraception-HIV acquisition analyses. However, it is critical to note that their use does not guarantee an unbiased answer. The g-methods, like all statistical approaches, require a number of assumptions to be met. The aforementioned measurement issues, such as the failure to measure all relevant confounders or to appropriately account for measurement error, are likely to yield biased estimates from any analytic approach, including the g-methods. In addition, there are numerous practical and technical issues with the implementation of g-methods, and MSMs specifically, that are not currently addressed in the epidemiologic or biostatistical literature. Descriptions of these challenges and suggested solutions would be helpful in framing future hormonal contraception-HIV acquisition analyses (as well as other subjects).
Despite the challenges described here, future secondary analyses using existing high-quality datasets could inform our understanding of the hormonal contraception-HIV acquisition relationship. Several analyses are on the horizon, including those from both individual and combined datasets. Furthermore, new HIV prevention studies that will collect information on contraceptive use will provide additional relevant data (including trials of tenofovir gel and a dapivirine-containing vaginal ring). Future studies that do not address the issues listed in Table 1 are less likely to meaningfully contribute to the existing evidence base.
This study aims to contribute to an evolving discussion on observational hormonal contraception-HIV acquisition evidence. We hope to spur conversations that build upon the recommendations in this study. Methodological progress on addressing pregnancy in hormonal contraception-HIV acquisition analyses is needed, as is dialogue with investigators conducting longitudinal cohort studies in areas of high HIV incidence, to ensure inclusion of relevant data collection tools into ongoing trials. Additionally, in light of a growing evidence base, discussions on how best to systematically assess this complex body of literature should also continue. We hope our recommendations might assist in interpreting existing studies; by outlining major challenges of observational hormonal contraception-HIV analyses, systematic assessment across studies is more straightforward. A recent hormonal contraception-HIV acquisition systematic review specified minimum quality criteria for more in-depth analysis of higher quality studies . As the evidence base continues to change and improve, these criteria should be continually refined. Finally, given the interdisciplinary nature of hormonal contraception-HIV acquisition analyses, collaborative efforts between specialists of various disciplines are urgently needed.
Moving from data to policy regarding hormonal contraception and HIV acquisition requires clearly framing the pertinent question(s) that can be answered with robust methods that assess necessarily imperfect data. Randomized trial data do not currently exist and animal model results have not always had clear implications for human female reproductive biology. Discussions about the feasibility of a randomized trial in this area are ongoing, but results would not be available for at least 5 years. In this vein, observational analyses from ongoing and planned epidemiologic studies, performed with robust analytic techniques and applied to high quality datasets, may be the most efficient and cost-effective means to contribute further understanding of this problem, especially in the near-term. Policy guidelines must consider the important contributions of hormonal contraception to reducing maternal and infant morbidity and mortality and balance this with a robust estimation of the magnitude of how specific hormonal contraceptive methods may or may not increase HIV acquisition risk. Resolution of this question is a high priority on the global health agenda, for women at risk of HIV, their partners, contraceptive and HIV care providers, women's health advocates, and the global health community.
The authors are grateful to the study participants and investigators who have contributed to understanding of this complex subject. The authors are also grateful to USAID and the FHI 360 PTA project for funding this meeting, and to the Bill and Melinda Gates Foundation for hosting.
The meeting was conceived of by C.P. (USAID), D.W. (Duke University), and Stephen Cole (University of North Carolina) with valuable input from multiple partners. The authors thank all meeting participants who are co-authors of this study, including Jared M. Baeten (University of Washington), Jennifer Balkus (Fred Hutchinson Cancer Research Center/University of Washington), Matthew Barnhart (USAID/OHA), Diana Blithe (NIH/NICHD), Elizabeth Brown (Fred Hutchinson Cancer Research Center/University of Washington), Delivette Castor (USAID/OHA), Pai-Lien Chen (FHI360), Michael Chirenje (University of Zimbabwe), Stephen Cole (University of North Carolina, Chapel Hill), Angela Crook (Medical Research Council, Clinical Trials Unit, UK), Deborah Donnell (University of Washington/Fred Hutchinson Cancer Research Center), Geoff Garnett (Bill and Melinda Gates Foundation), Emily Harris (USAID/OHA), Renee Heffron (University of Washington), Benny Kottiri (USAID/OHA), Jeanne Marrazzo (University of Washington), Sandi McCoy (University of California, Berkeley), Erica Moodie (McGill University), Charles Morrison (FHI360), Lisa Noguchi (Johns Hopkins Bloomberg School of Public Health), Sharon Phillips (World Health Organization), Chelsea Polis (USAID/PRH), Lauren Ralph (University of California, Berkeley), Denise Russo (NIH/NICHD/MPID), Jim Shelton (USAID), Tabitha Sripipatana (USAID/PRH), David Stanton (USAID/OHA), James Trussell (Princeton University), and Daniel Westreich (Duke University). They also thank meeting participants who are not authors of this article, including Kathryn Curtis (CDC/NCCDPHP/DRH). Finally, they thank Jared Baeten, Stephen Cole, Sandra McCoy, and Charles Morrison for their comments on an early draft of this article.
Conflicts of interest
James Trussell's participation in this work was supported in part by the Eunice Kennedy Shriver National Institute of Child Health and Human Development grant for Infrastructure for Population Research at Princeton University, Grant R24HD047879.
The findings and conclusions in this article are those of the authors and do not necessarily represent the official position of the United States Agency for International Development.
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52. Westreich D, Cole SR, Young JG, Palella F, Tien PC, Kingsley L, et al. The parametric g-formula to estimate the effect of highly active antiretroviral therapy on incident AIDS or death
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53. Taubman SL, Robins JM, Mittleman MA, Hernan MA. Intervening on risk factors for coronary heart disease: an application of the parametric g-formula
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54. Hernan MA, Cole SR, Margolick J, Cohen M, Robins JM. Structural accelerated failure time models for survival analysis in studies with time-varying treatments
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55. Robins JM, Blevins D, Ritter G, Wulfsohn M. G-estimation of the effect of prophylaxis therapy for Pneumocystis carinii pneumonia on the survival of AIDS patients
56. Cole SR, Hernan MA. Constructing inverse probability weights for marginal structural models
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57. Chen PL, Cole SR, Morrison CS. Hormonal contraception and HIV risk: evaluating marginal-structural-model assumptions
58. Cole SR, Hernan MA, Robins JM, Anastos K, Chmiel J, Detels R, et al. Effect of highly active antiretroviral therapy on time to acquired immunodeficiency syndrome or death using marginal structural models
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59. Westreich D, Cole SR, Schisterman EF, Platt RW. A simulation study of finite-sample properties of marginal structural Cox proportional hazards models
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contraception; depot-medroxyprogesterone acetate; HIV acquisition; injectable; observational epidemiology
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