Setting and Objective
We examined the effect of initiating ART on CD4 and viral response at different time periods during TB therapy (< 14 days; 15–60 days; or ≥60 days) using prospectively collected clinical data from a large HIV clinic in South Africa.
Cohort data analysis for 1499 TB/HIV co-infected patients classified according to timing of ART after the initiation of TB therapy.
In adjusted modified Poisson regression models, CD4 and viral responses showed no significant differences according to timing of ART initiation (failure to increase CD4 by 6 months, <14 days vs. >60 days: RR 1.02 (95% CI 0.85–1.22), 15–60 days vs. >60 days: RR 1.00 (95% CI 0.86–1.15); failure to suppress virus by 6 months, <14 days vs. >60 days: RR 0.98 (95% CI 0.59–1.63), 15–60 days vs. >60 days: RR 0.96 (95% CI 0.66–1.41) and viral rebound at 12 months, 14 days vs. >60 days: RR 1.43 (95% CI 0.50–4.12), 15–60 days vs. >60 days: RR 1.14 (95% CI 0.39–3.34). Similar estimates were found in analysis restricted to patients with severe immunosuppression.
Concerns over the overlapping impact of TB treatment with ART on ART response should not be a reason to delay ART in patients with HIV-associated TB.
Timing of ART; CD4 response; Viral response; TB–HIV co-infection
Motivated by a previously published study of HIV treatment, we simulated data subject to time-varying confounding affected by prior treatment to examine some finite-sample properties of marginal structural Cox proportional hazards models. We compared (a) unadjusted, (b) regression-adjusted, (c) unstabilized and (d) stabilized marginal structural (inverse probability-of-treatment [IPT] weighted) model estimators of effect in terms of bias, standard error, root mean squared error (MSE) and 95% confidence limit coverage over a range of research scenarios, including relatively small sample sizes and ten study assessments. In the base-case scenario resembling the motivating example, where the true hazard ratio was 0.5, both IPT-weighted analyses were unbiased while crude and adjusted analyses showed substantial bias towards and across the null. Stabilized IPT-weighted analyses remained unbiased across a range of scenarios, including relatively small sample size; however, the standard error was generally smaller in crude and adjusted models. In many cases, unstabilized weighted analysis showed a substantial increase in standard error compared to other approaches. Root MSE was smallest in the IPT-weighted analyses for the base-case scenario. In situations where time-varying confounding affected by prior treatment was absent, IPT-weighted analyses were less precise and therefore had greater root MSE compared with adjusted analyses. The 95% confidence limit coverage was close to nominal for all stabilized IPT-weighted but poor in crude, adjusted, and unstabilized IPT-weighted analysis. Under realistic scenarios, marginal structural Cox proportional hazards models performed according to expectations based on large-sample theory and provided accurate estimates of the hazard ratio.
Bias; Causal inference; Marginal structural models; Monte Carlo study
HIV-related outcomes may be affected by biological sex and by pregnancy. Including women in general and pregnant women in particular in HIV-related research is important for generalizability of findings.
To characterize representation of pregnant and non-pregnant women in HIV-related research conducted in general populations.
All HIV-related articles published in fifteen journals from January to March of 2011. We selected the top five journals by 2010 impact factor, in internal medicine, infectious diseases, and HIV/AIDS.
Study Eligibility Criteria
HIV-related studies reporting original research on questions applicable to both men and women of reproductive age were considered; studies were excluded if they did not include individual-level patient data.
Study appraisal and synthesis methods.
Articles were doubly reviewed and abstracted; discrepancies were resolved through consensus. We recorded proportion of female study participants, whether pregnant women were included or excluded, and other key factors.
In total, 2014 articles were published during this period. After screening, 259 articles were included as original HIV-related research reporting individual-level data; of these, 226 were determined to be articles relevant to both men and women of reproductive age. In these articles, women were adequately represented within geographic region. The vast majority of published articles, 183/226 (81%), did not mention pregnancy (or related issues); still fewer included pregnant women (n=33), reported numbers of pregnant women (n=19), or analyzed using pregnancy status (n=9).
Data were missing for some key variables, including pregnancy. The time period over which published works were evaluated was relatively short.
Conclusions and implications of key findings.
The under-reporting and inattention to pregnancy in the HIV literature may reduce policy-makers’ ability to set evidence-based policy around HIV/AIDS care for pregnant women and women of child-bearing age.
Pregnancy is a common indication for initiation of highly active antiretroviral therapy (HAART) in sub-Saharan Africa. Our objective was to evaluate how pregnancy at treatment initiation predicts virologic response to HAART.
We evaluated an open cohort of 9,173 patients who initiated HAART between April 2004 and September 2009 in the Themba Lethu Clinic in Johannesburg, South Africa. Risk ratios were estimated using log-binomial regression; hazard ratios were estimated using Cox proportional hazards models; time ratios were estimated using accelerated failure time models. We controlled for calendar date, age, ethnicity, employment status, history of smoking, tuberculosis, WHO stage, weight, body mass index, hemoglobin, CD4 count and CD4 percent, and whether clinical care was free. Extensive sensitivity and secondary analyses were performed.
During follow-up, 822 non-pregnant women and 70 pregnant women experienced virologic failure. In adjusted analyses, pregnancy at baseline was associated with reduced risk of virologic failure by six months (risk ratio 0.66, 95% confidence limits [CL] 0.35, 1.22) and with reduced hazard of virologic failure over follow-up (hazard ratio 0.69, 95% CL 0.50, 0.95). The adjusted time ratio for failure was 1.44 (95% CL 1.13, 1.84), indicating 44% longer time to event among women pregnant at baseline. Sensitivity analyses generally confirmed main findings.
Pregnancy at HAART initiation is not associated with increased risk of virologic failure at six months or during longer follow-up.
Pregnancy; HIV; highly active antiretroviral therapy (HAART); South Africa
The parametric g-formula can be used to contrast the distribution of potential outcomes under arbitrary treatment regimes. Like g-estimation of structural nested models and inverse probability weighting of marginal structural models, the parametric g-formula can appropriately adjust for measured time-varying confounders that are affected by prior treatment. However, there have been few implementations of the parametric g-formula to date. Here, we apply the parametric g-formula to assess the impact of highly active antiretroviral therapy on time to AIDS or death in two US-based HIV cohorts including 1,498 participants. These participants contributed approximately 7,300 person-years of follow-up of which 49% was exposed to HAART and 382 events occurred; 259 participants were censored due to drop out. Using the parametric g-formula, we estimated that antiretroviral therapy substantially reduces the hazard of AIDS or death (HR=0.55; 95% confidence limits [CL]: 0.42, 0.71). This estimate was similar to one previously reported using a marginal structural model 0.54 (95% CL: 0.38, 0.78). The 6.5-year difference in risk of AIDS or death was 13% (95% CL: 8%, 18%). Results were robust to assumptions about temporal ordering, and extent of history modeled, for time-varying covariates. The parametric g-formula is a viable alternative to inverse probability weighting of marginal structural models and g-estimation of structural nested models for the analysis of complex longitudinal data.
Cohort study; Confounding; g-formula; HIV/AIDS; Monte Carlo methods
The effect of tuberculosis on mortality in people initiating highly active antiretroviral treatment (HAART) remains unclear; here, we strengthened a previous cohort analysis. Multivariate Cox proportional hazards models were used to assess the association of baseline tuberculosis and time to all-cause mortality among HAART initiators. In reanalysis, treatment for tuberculosis at time of HAART initiation remained unassociated with increased risks of all-cause mortality, with adjusted hazard ratios ranging from 1.00 to 1.09.
Little is known about the impact of pregnancy on response to highly active antiretroviral therapy (HAART) in sub-Saharan Africa. We examined the effect of incident pregnancy after HAART initiation on clinical response to HAART.
We evaluated a prospective clinical cohort of adult women initiating HAART in Johannesburg, South Africa between 1 April 2004 and 31 March 2011, and followed up until an event, transfer, drop-out, or administrative end of follow-up on 30 September 2011. Women over age 45 and women who were pregnant at HAART initiation were excluded from the study. Main exposure was having experienced pregnancy after HAART initiation; main outcome was death and (separately) death or new AIDS event. We calculated adjusted hazard ratios (HRs) and 95% confidence limits (CL) using marginal structural Cox proportional hazards models.
The study included 7,534 women, and 20,813 person-years of follow-up; 918 women had at least one recognized pregnancy during follow-up. For death alone, the weighted (adjusted) HR was 0.84 (95% CL 0.44, 1.60). Sensitivity analyses confirmed main results, and results were similar for analysis of death or new AIDS event. Incident pregnancy was associated with a substantially reduced hazard of drop-out (HR = 0.62, 95% CL 0.51, 0.75).
Recognized incident pregnancy after HAART initiation was not associated with increases in hazard of clinical events, but was associated with a decreased hazard of drop-out. High rates of pregnancy after initiation of HAART may point to a need to better integrate family planning services into clinical care for HIV-infected women.
This study examines the timing of menarche in relation to infant feeding methods, specifically addressing the potential effects of soy isoflavone exposure through soy-based infant feeding. Subjects were participants in the Avon Longitudinal Study of Parents and Children (ALSPAC). Mothers were enrolled during pregnancy and their children have been followed prospectively. Early life feeding regimes, categorized as primarily breast, early formula, early soy, and late soy were defined using infant feeding questionnaires administered during infancy. For this analysis, age at menarche was assessed through questionnaires administered approximately annually between ages 8 and 14.5. Eligible subjects were limited to term, singleton, white females. We used Kaplan-Meier survival curves and Cox proportional hazards models to assess age at menarche and risk of menarche over the study period.
The present analysis included 2,920 girls. Approximately 2% of mothers reported that soy products were introduced into the infant diet at or before 4 months of age (early soy). The median age at menarche [interquartile range (IQR)] in the study sample was 153 months [144–163], approximately 12.8 years. The median age at menarche among early soy fed girls was 149 months (12.4 years) [IQR, 140–159]. Compared to girls fed non-soy based infant formula or milk (early formula), early soy fed girls were at 25% higher risk of menarche throughout the course of follow up (Hazard Ratio 1.25 [95% confidence interval, 0.92, 1.71]). Our results also suggest that girls fed soy products in early infancy may have an increased risk of menarche specifically in early adolescence. These findings may be the observable manifestation of mild endocrine disrupting effects of soy isoflavone exposure. However, our study is limited by few soy-exposed subjects and is not designed to assess biological mechanisms. Because soy formula use is common in some populations, this subtle association with menarche warrants more indepth evaluation in future studies.
While Berkson’s bias is widely recognized in the epidemiologic literature, it remains underappreciated as a model of both selection bias and bias due to missing data. Simple causal diagrams and 2×2 tables illustrate how Berkson’s bias connects to collider bias and selection bias more generally, and show the strong analogies between Berksonian selection bias and bias due to missing data. In some situations, considerations of whether data are missing at random or missing not at random is less important than the causal structure of the missing-data process. While dealing with missing data always relies on strong assumptions about unobserved variables, the intuitions built with simple examples can provide a better understanding of approaches to missing data in real-world situations.
In occupational epidemiologic studies, the healthy-worker survivor effect refers to a process that leads to bias in the estimates of an association between cumulative exposure and a health outcome. In these settings, work status acts both as an intermediate and confounding variable, and may violate the positivity assumption (the presence of exposed and unexposed observations in all strata of the confounder). Using Monte Carlo simulation, we assess the degree to which crude, work-status adjusted, and weighted (marginal structural) Cox proportional hazards models are biased in the presence of time-varying confounding and nonpositivity. We simulate data representing time-varying occupational exposure, work status, and mortality. Bias, coverage, and root mean squared error (MSE) were calculated relative to the true marginal exposure effect in a range of scenarios. For a base-case scenario, using crude, adjusted, and weighted Cox models, respectively, the hazard ratio was biased downward 19%, 9%, and 6%; 95% confidence interval coverage was 48%, 85%, and 91%; and root MSE was 0.20, 0.13, and 0.11. Although marginal structural models were less biased in most scenarios studied, neither standard nor marginal structural Cox proportional hazards models fully resolve the bias encountered under conditions of time-varying confounding and nonpositivity.
Background. Little is known about rates of incident pregnancy among HIV-positive women initiating highly active antiretroviral therapy (HAART).
Methods. We conducted a retrospective clinical cohort study among therapy-naïve women ages 18–45 initiating HAART between 1 April 2004 and 30 September 2009 at an adult HAART clinic in Johannesburg, South Africa. We used Poisson regression to characterize rates and rate ratios of pregnancy.
Results. We evaluated 5,996 women who experienced 727 pregnancies during 14,095 person-years at risk. The overall rate of pregnancy was 5.2 per 100 person-years (95% confidence limits [CL] 4.8, 5.5). By six years, cumulative incidence of first pregnancy was 22.9% (95% CL 20.6%, 25.4%); among women ages 18–25 at HAART initiation, cumulative incidence was 52.2% (95% CL 35.0%, 71.8%). The strongest predictor of incidence of pregnancy was age, with women 18–25 having 13.2 times the rate of pregnancy of women ages 40–45 in adjusted analysis. CD4 counts below 100 and worse adherence to HAART were associated with lower rates of incident pregnancy.
Conclusions. Women experience high rates of incident pregnancy after HAART initiation. Understanding which women are most likely to experience pregnancy will help planning and future efforts to understand the implications of pregnancy for response to HAART.
The risk of squamous intra-epithelial lesions (SIL) is higher in HIV-positive women. As these women begin to live longer due to highly active antiretroviral therapy (HAART), their risk of cervical cancer may increase. Few data exist regarding the effect of HAART on the incidence and progression of SIL in HIV-positive African women. The aim of this study was to evaluate the effect of HAART on the incidence and progression of SIL in HIV-positive women in South Africa.
A prospective observational study of HIV-seropositive women was conducted over 5 years in an HIV treatment clinic in Johannesburg, South Africa. The participants consisted of 601 women on and off HAART who had repeat Pap smears greater than 6 months apart. The effect of HAART use on incidence and progression rates of SIL was determined using multivariate Poisson regression to obtain incidence rate ratios (IRRs), adjusted for age, CD4 count and other potential confounders.
Median follow-up time was 445 days (inter-quartile range 383, 671). The crude rate of incidence of any SIL was 15.9 episodes (95% confidence limit (CL) 12.7, 19.9) per 100 person-years; the crude rate of all progression of cervical dysplasia among women was 13.5 episodes (95% CL 11.3, 16.1) per 100 person-years. HAART use was associated with a robust reduction in the rate of incidence and progression of cervical lesions, adjusted IRR=0.55 (95% CL 0.37, 0.80). Sensitivity analyses confirmed this main association held for incidence and progression when they were considered separately, and that the result was not dependent on the length of HAART exposure.
HAART use was associated with a reduction in the rate of both incidence and progression of cervical lesions among HIV-positive women.
HAART effect; cervical dysplasia; HIV-positive women; South Africa
To determine tuberculosis (TB) incidence rates and risk factors among individuals receiving antiretroviral treatment (ART).
Observational cohort in Johannesburg, South Africa.
Incident TB was classified as early (<6 months of ART) or late (>6 months of ART) incident TB. CD4 cell counts, viral load (VL), body mass index (BMI) and hemoglobin were measured 6-monthly. Hazard ratios for factors associated with early and late incident TB were assessed using Cox proportional hazards regression.
During 13,416 person-years (py) follow-up, 501 TB cases occurred among 7,536 individuals, corresponding to a 10% risk in the first four years of ART, and an overall incidence rate of 4.2 cases/100 py. The highest incidence rate (21.7 /100 py) was observed in the first 3 months of ART among people with CD4 count below 50 cells/mm3. Low baseline CD4 count, anemia, and low BMI were the strongest risk factor for early incident TB. Low updated CD4 count, low updated BMI, anemia, and high VL on ART were strong risk factors for late incident TB.
Severity of HIV disease and unfavorable response to ART are associated with early and late incident TB, respectively. Early ART initiation and intensified TB screening at ART initiation are crucial to reduce incident TB.
tuberculosis; TB; antiretroviral treatment; incidence; risk factors; South Africa
Doubly robust estimation combines a form of outcome regression with a model for the exposure (i.e., the propensity score) to estimate the causal effect of an exposure on an outcome. When used individually to estimate a causal effect, both outcome regression and propensity score methods are unbiased only if the statistical model is correctly specified. The doubly robust estimator combines these 2 approaches such that only 1 of the 2 models need be correctly specified to obtain an unbiased effect estimator. In this introduction to doubly robust estimators, the authors present a conceptual overview of doubly robust estimation, a simple worked example, results from a simulation study examining performance of estimated and bootstrapped standard errors, and a discussion of the potential advantages and limitations of this method. The supplementary material for this paper, which is posted on the Journal's Web site (http://aje.oupjournals.org/), includes a demonstration of the doubly robust property (Web Appendix 1) and a description of a SAS macro (SAS Institute, Inc., Cary, North Carolina) for doubly robust estimation, available for download at http://www.unc.edu/∼mfunk/dr/.
causal inference; epidemiologic methods; propensity score
The applied literature on propensity scores has often cited the c-statistic as a measure of the ability of the propensity score to control confounding. However, a high c-statistic in the propensity model is neither necessary nor sufficient for control of confounding. Moreover, use of the c-statistic as a guide in constructing propensity scores may result in less overlap in propensity scores between treated and untreated subjects; this may require the analyst to restrict populations for inference. Such restrictions may reduce precision of estimates and change the population to which the estimate applies. Variable selection based on prior subject matter knowledge, empirical observation, and sensitivity analysis is preferable and avoids many of these problems.
Propensity scores; c-statistic; variable selection; confounding
As stavudine remains an important and widely prescribed drug in resource-limited settings, the effect of a reduced dose of stavudine (from 40 mg to 30 mg) on outcomes of highly active antiretroviral therapy (HAART) remains an important public health question.
We analyzed prospectively collected data from the Themba Lethu Clinic in Johannesburg, South Africa. We assessed the relationship between stavudine dose and six- and/or 12-month outcomes of stavudine substitution, failure to suppress viral load to below 400 copies/ml, development of peripheral neuropathy, lipoatrophy and hyperlactatemia/lactic acidosis. Since individuals with a baseline weight of less than 60 kg were expected to have received the same dose of stavudine throughout the study period, analysis was restricted to individuals who weighed 60 kg or more at baseline. Data were analyzed using logistic regression.
Between 1 April 2004 and 30 September 2009, 3910 patients were initiated on antiretroviral therapy (ART) with a recorded stavudine dose and were included in the analysis. Of these, 2445 (62.5%) received a 40 mg stavudine dose while 1565 (37.5%) received 30 mg. In multivariate analysis, patients receiving a 40 mg dose were more likely to discontinue stavudine use (adjusted odds ratio, OR 1.71; 95% confidence limits, CI 1.13-2.57) than those receiving 30 mg by 12 months on ART. Additionally, patients receiving 40 mg doses of stavudine were more likely to report peripheral neuropathy (OR 3.12; 95% CI 1.86-5.25), lipoatrophy (OR 11.8; 95% CI 3.2-43.8) and hyperlactatemia/lactic acidosis (OR 8.37; 95% CI 3.83-18.29) in the same time period. Failure to suppress HIV viral load within 12 months of HAART initiation was somewhat more common among those given 40 mg doses (OR 1.62; 95% CI 0.88, 2.97) although this result lacked precision. Sensitivity analyses accounting for death and loss to follow up generally supported these estimates.
Lower stavudine dosage is associated with fewer reports of several stavudine-associated adverse events and also a lower risk of stavudine discontinuation within the first year on ART.
Antiretroviral toxicity; Stavudine; Resource-limited setting; Cohort study; Virologic failure
Although women of reproductive age are the largest group of HIV-infected individuals in sub-Saharan Africa, little is known about the impact of pregnancy on response to highly active antiretroviral therapy (HAART) in that setting. We examined the effect of incident pregnancy after HAART initiation on virologic response to HAART.
Methods and Findings
We evaluated a prospective clinical cohort of adult women who initiated HAART in Johannesburg, South Africa between 1 April 2004 and 30 September 2009, and followed up until an event, death, transfer, drop-out, or administrative end of follow-up on 31 March 2010. Women over age 45 and women who were pregnant at HAART initiation were excluded from the study; final sample size for analysis was 5,494 women. Main exposure was incident pregnancy, experienced by 541 women; main outcome was virologic failure, defined as a failure to suppress virus to ≤400 copies/ml by six months or virologic rebound >400 copies/ml thereafter. We calculated adjusted hazard ratios using marginal structural Cox proportional hazards models and weighted lifetable analysis to calculate adjusted five-year risk differences. The weighted hazard ratio for the effect of pregnancy on time to virologic failure was 1.34 (95% confidence limit [CL] 1.02, 1.78). Sensitivity analyses generally confirmed these main results.
Incident pregnancy after HAART initiation was associated with modest increases in both relative and absolute risks of virologic failure, although uncontrolled confounding cannot be ruled out. Nonetheless, these results reinforce that family planning is an essential part of care for HIV-positive women in sub-Saharan Africa. More work is needed to confirm these findings and to explore specific etiologic pathways by which such effects may operate.
Propensity scores for the analysis of observational data are typically estimated using logistic regression. Our objective in this Review was to assess machine learning alternatives to logistic regression which may accomplish the same goals but with fewer assumptions or greater accuracy.
Study Design and Setting
We identified alternative methods for propensity score estimation and/or classification from the public health, biostatistics, discrete mathematics, and computer science literature, and evaluated these algorithms for applicability to the problem of propensity score estimation, potential advantages over logistic regression, and ease of use.
We identified four techniques as alternatives to logistic regression: neural networks, support vector machines, decision trees (CART), and meta-classifiers (in particular, boosting).
While the assumptions of logistic regression are well understood, those assumptions are frequently ignored. All four alternatives have advantages and disadvantages compared with logistic regression. Boosting (meta-classifiers) and to a lesser extent decision trees (particularly CART) appear to be most promising for use in the context of propensity score analysis, but extensive simulation studies are needed to establish their utility in practice.
Propensity scores; classification and regression trees (CART); recursive partitioning algorithms; neural networks; logistic regression; review
That conditioning on a common effect of exposure and outcome may cause selection, or collider-stratification, bias is not intuitive. We provide two hypothetical examples to convey concepts underlying bias due to conditioning on a collider. In the first example, fever is a common effect of influenza and consumption of a tainted egg-salad sandwich. In the second example, case-status is a common effect of a genotype and an environmental factor. In both examples, conditioning on the common effect imparts an association between two otherwise independent variables; we call this selection bias.
Bias; selection; methods; epidemiologic
Typical applications of marginal structural time-to-event (e.g., Cox) models have used time on study as the time scale. Here, the authors illustrate use of time on treatment as an alternative time scale. In addition, a method is provided for estimating Kaplan-Meier–type survival curves for marginal structural models. For illustration, the authors estimate the total effect of highly active antiretroviral therapy on time to acquired immunodeficiency syndrome (AIDS) or death in 1,498 US men and women infected with human immunodeficiency virus and followed for 6,556 person-years between 1995 and 2002; 323 incident cases of clinical AIDS and 59 deaths occurred. Of the remaining 1,116 participants, 77% were still under observation at the end of follow-up. By using time on study, the hazard ratio for AIDS or death comparing always with never using highly active antiretroviral therapy from the marginal structural model was 0.52 (95% confidence interval: 0.35, 0.76). By using time on treatment, the analogous hazard ratio was 0.44 (95% confidence interval: 0.32, 0.60). In time-to-event analyses, the choice of time scale may have a meaningful impact on estimates of association and precision. In the present example, use of time on treatment yielded a hazard ratio further from the null and more precise than use of time on study as the time scale.
acquired immunodeficiency syndrome; antiretroviral therapy, highly active; bias (epidemiology); causal inference; confounding factors (epidemiology); proportional hazards model; survival curve; survival time
Positivity, or the experimental treatment assignment assumption, requires that there be both exposed and unexposed participants at every combination of the values of the observed confounders in the population under study. Positivity is essential for inference but is often overlooked in practice by epidemiologists. This issue of the Journal includes 2 articles featuring discussions related to positivity. Here the authors define positivity, distinguish between deterministic and random positivity, and discuss the 2 relevant papers in this issue. In addition, the commentators illustrate positivity in simple 2 × 2 tables, as well as detail some ways in which epidemiologists may examine their data for nonpositivity and deal with violations of positivity in practice.
causality; causal inference; confounding factors (epidemiology); epidemiologic methods; exchangeability; identifiability; multilevel analysis; propensity score
While the Latin phrase in vitro and in vivo are well understood in the medical literature, neither term accurately describes the science performed at the level of the population by epidemiologists and others. In particular, results in a single organism can differ broadly from results in a population, for reasons from random error to herd immunity. We suggest that in populo, meaning literally “in the people”, can fill this gap in the literature, and urge its wide adoption.