Miguel A. Hernán

Marginal structural models and causal inference in epidemiology

In observational studies with exposures or treatments that vary over time, standard approaches for adjustment of confounding are biased when there exist time-dependent confounders that are also affected by previous treatment. This paper introduces marginal structural models, a new class of causal models that allow for improved adjustment of confounding in those situations. The parameters of a marginal structural model can be consistently estimated using a new class of estimators, the inverse-probability-of-treatment weighted estimators.

A Structural Approach to Selection Bias

The term “selection bias” encompasses various biases in epidemiology. We describe examples of selection bias in case-control studies (eg, inappropriate selection of controls) and cohort studies (eg, informative censoring). We argue that the causal structure underlying the bias in each example is essentially the same: conditioning on a common effect of 2 variables, one of which is either exposure or a cause of exposure and the other is either the outcome or a cause of the outcome. This structure is shared by other biases (eg, adjustment for variables affected by prior exposure). A structural classification of bias distinguishes between biases resulting from conditioning on common effects (“selection bias”) and those resulting from the existence of common causes of exposure and outcome (“confounding”). This classification also leads to a unified approach to adjust for selection bias.

Marginal structural models to estimate the causal effect of zidovudine on the survival of HIV-positive men.

Standard methods for survival analysis, such as the time-dependent Cox model, may produce biased effect estimates when there exist time-dependent confounders that are themselves affected by previous treatment or exposure. Marginal structural models are a new class of causal models the parameters of which are estimated through inverse-probability-of-treatment weighting; these models allow for appropriate adjustment for confounding. We describe the marginal structural Cox proportional hazards model and use it to estimate the causal effect of zidovudine on the survival of human immunodeficiency virus-positive men participating in the Multicenter AIDS Cohort Study. In this study, CD4 lymphocyte count is both a time-dependent confounder of the causal effect of zidovudine on survival and is affected by past zidovudine treatment. The crude mortality rate ratio (95% confidence interval) for zidovudine was 3.6 (3.0-4.3), which reflects the presence of confounding. After controlling for baseline CD4 count and other baseline covariates using standard methods, the mortality rate ratio decreased to 2.3 (1.9-2.8). Using a marginal structural Cox model to control further for time-dependent confounding due to CD4 count and other time-dependent covariates, the mortality rate ratio was 0.7 (95% conservative confidence interval = 0.6-1.0). We compare marginal structural models with previously proposed causal methods.

Constructing Inverse Probability Weights for Marginal Structural Models

The method of inverse probability weighting (henceforth, weighting) can be used to adjust for measured confounding and selection bias under the four assumptions of consistency, exchangeability, positivity, and no misspecification of the model used to estimate weights. In recent years, several published estimates of the effect of time-varying exposures have been based on weighted estimation of the parameters of marginal structural models because, unlike standard statistical methods, weighting can appropriately adjust for measured time-varying confounders affected by prior exposure. As an example, the authors describe the last three assumptions using the change in viral load due to initiation of antiretroviral therapy among 918 human immunodeficiency virus-infected US men and women followed for a median of 5.8 years between 1996 and 2005. The authors describe possible tradeoffs that an epidemiologist may encounter when attempting to make inferences. For instance, a tradeoff between bias and precision is illustrated as a function of the extent to which confounding is controlled. Weight truncation is presented as an informal and easily implemented method to deal with these tradeoffs. Inverse probability weighting provides a powerful methodological tool that may uncover causal effects of exposures that are otherwise obscured. However, as with all methods, diagnostics and sensitivity analyses are essential for proper use.

Activated Injectable Vitamin D and Hemodialysis Survival: A Historical Cohort Study

Patients with ESRD commonly experience secondary hyperparathyroidism, a condition primarily managed with activated injectable vitamin D. The biologic effects of vitamin D, however, are widespread, and it is possible that activated injectable vitamin D alters survival in ESRD. This hypothesis was tested in a historical cohort study of incident hemodialysis patients who lived throughout the United States between January 1996 and December 1999. The primary outcome was 2-yr survival among those who survived for at least 90 d after initiation of chronic hemodialysis. During this period, 51,037 chronic hemodialysis patients survived for at least 90 d from the initiation of hemodialysis, and in the ensuing 2 yr, 37,173 received activated injectable vitamin D and 13,864 did not. At 2 yr, mortality rates were 13.8/100 person-years in the group that received injectable vitamin D compared with 28.6/100 person-years in the group that did not (P < 0.001). Cox proportional hazards analyses adjusting for several potential confounders and examining injectable vitamin D therapy as a time-dependent exposure suggested that compared with patients who did not receive injectable vitamin D, the 2-yr survival advantage associated with the group that did receive injectable vitamin D was 20% (hazard ratio, 0.80; 95% confidence interval, 0.76 to 0.83). The incidence of cardiovascular-related mortality was 7.6/100 person-years in the injectable vitamin D group, compared with 14.6/100 person-years in the non-vitamin D group (P < 0.001). The benefit of injectable vitamin D was evident in 48 of 49 strata examined, including those with low serum levels of intact parathyroid hormone and elevated levels of serum calcium and phosphorus, situations in which injectable vitamin D is often withheld. Repeating the entire analysis using marginal structural models to adjust for time-dependent confounding by indication yielded a survival advantage of 26% (hazard ratio, 0.74; 95% confidence interval, 0.71 to 0.79) associated with the injectable vitamin D group. In this historical cohort study, chronic hemodialysis patients in the group that received injectable vitamin D had a significant survival advantage over patients who did not. Randomized clinical trials would permit definitive conclusions.

A meta-analysis of coffee drinking, cigarette smoking, and the risk of Parkinson's disease.

We conducted a systematic review to summarize the epidemiological evidence on the association between cigarette smoking, coffee drinking, and the risk of Parkinsons disease. Case–control and cohort studies that reported the relative risk of physician‐confirmed Parkinsons disease by cigarette smoking or coffee drinking status were included. Study‐specific log relative risks were weighted by the inverse of their variances to obtain a pooled relative risk and its 95% confidence interval (CI). Results for smoking were based on 44 case–control and 4 cohort studies, and for coffee 8 case–control and 5 cohort studies. Compared with never smokers, the relative risk of Parkinsons disease was 0.59 (95% CI, 0.54–0.63) for ever smokers, 0.80 (95% CI, 0.69–0.93) for past smokers, and 0.39 (95% CI, 0.32–0.47) for current smokers. The relative risk per 10 additional pack‐years was 0.84 (95% CI, 0.81–0.88) in case–control studies and 0.78 (95% CI, 0.73–0.84) in cohort studies. Compared with non–coffee drinkers, relative risk of Parkinsons disease was 0.69 (95% CI, 0.59–0.80) for coffee drinkers. The relative risk per three additional cups of coffee per day was 0.75 (95% CI, 0.64–0.86) in case–control studies and 0.68 (95% CI, 0.46–1.00) in cohort studies. This meta‐analysis shows that there is strong epidemiological evidence that smokers and coffee drinkers have a lower risk of Parkinsons disease. Further research is required on the biological mechanisms underlying this potentially protective effect.

Instruments for causal inference: an epidemiologist's dream?

The use of instrumental variable (IV) methods is attractive because, even in the presence of unmeasured confounding, such methods may consistently estimate the average causal effect of an exposure on an outcome. However, for this consistent estimation to be achieved, several strong conditions must hold. We review the definition of an instrumental variable, describe the conditions required to obtain consistent estimates of causal effects, and explore their implications in the context of a recent application of the instrumental variables approach. We also present (1) a description of the connection between 4 causal models—counterfactuals, causal directed acyclic graphs, nonparametric structural equation models, and linear structural equation models—that have been used to describe instrumental variables methods; (2) a unified presentation of IV methods for the average causal effect in the study population through structural mean models; and (3) a discussion and new extensions of instrumental variables methods based on assumptions of monotonicity.

Long-term effectiveness of potent antiretroviral therapy in preventing AIDS and death: a prospective cohort study

BACKGROUND Evidence on the effectiveness of highly active antiretroviral therapy (HAART) for HIV-infected individuals is limited. Most clinical trials examined surrogate endpoints over short periods of follow-up and there has been no placebo-controlled randomised trial of HAART. Estimation of treatment effects in observational studies is problematic, because of confounding by indication. We aimed to use novel methodology to overcome this problem in the Swiss HIV Cohort Study. METHODS Patients were included if they had been examined after January 1996, when HAART became available in Switzerland, were not on HAART, and were free of AIDS at baseline. Cox regression models were weighted to create a statistical population in which the probability of being treated at each time point was unrelated to prognostic factors. RESULTS Low CD4 counts and increasing HIV-1 viral load were associated with increased probability of starting HAART. Overall hazard ratios were 0.14 (95% CI 0.07-0.29) for HAART compared with no treatment, and 0.49 (0.31-0.79) compared with dual therapy. Compared with no treatment, HAART became more beneficial with increasing time since initiation but was less beneficial for patients whose presumed mode of transmission was via intravenous drug use (hazard ratio 0.27, 0.12-0.61) than for other patients (0.08, 0.03-0.19). INTERPRETATION Our results, which are appropriately controlled for confounding by indication, are consistent with reported declines in rates of AIDS and death in developed countries, and provide a context in which to consider adverse effects of HAART.

Temporal trends in the incidence of multiple sclerosis A systematic review

Background: Multiple sclerosis (MS) has been traditionally considered to be more frequent in women and in regions more distant from the equator. However, recent reports suggest that the latitude gradient could be disappearing and that the female-to-male ratio among patients with MS has increased in the last decades. We have conducted a systematic review of incidence studies of MS to assess the overall incidence of MS and explore possible changes in the latitude gradient and the female-to-male ratio over time. Methods: Systematic review of incidence studies of MS published in Medline between 1966 and February 2007. Age- and sex-specific incidence rates were collected from eligible publications. We computed age-adjusted rates using the world population as standard, and assessed differences in rates according to latitude and period of case ascertainment. Additionally, we evaluated the association between period of case ascertainment and the female-to-male ratio. Results: The overall incidence rate of MS was 3.6 cases per 100,000 person-years (95% CI 3.0, 4.2) in women and 2.0 (95% CI 1.5, 2.4) in men. Higher latitude was associated with higher MS incidence, though this latitude gradient was attenuated after 1980, apparently due to increased incidence of MS in lower latitudes. The female-to-male ratio in MS incidence increased over time, from an estimated 1.4 in 1955 to 2.3 in 2000. Conclusion: The latitude gradient present in older incidence studies of multiple sclerosis (MS) is decreasing. The female-to-male MS ratio has increased in the last five decades.

ROBINS-I: a tool for assessing risk of bias in non-randomised studies of interventions

Non-randomised studies of the effects of interventions are critical to many areas of healthcare evaluation, but their results may be biased. It is therefore important to understand and appraise their strengths and weaknesses. We developed ROBINS-I (“Risk Of Bias In Non-randomised Studies - of Interventions”), a new tool for evaluating risk of bias in estimates of the comparative effectiveness (harm or benefit) of interventions from studies that did not use randomisation to allocate units (individuals or clusters of individuals) to comparison groups. The tool will be particularly useful to those undertaking systematic reviews that include non-randomised studies.