Multiple outbreaks and flu containment plans.
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Animals↗
Biomedical subjects
James M Robins
Publications and source records attributed to James M Robins.
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.
Bias↗
Comparison of dynamic treatment regimes via inverse probability weighting.
Appropriate analysis of observational data is our best chance to obtain answers to many questions that involve dynamic treatment regimes. This paper describes a simple method to compare dynamic treatment regimes by artificially censoring subjects and then using inverse probability weighting (IPW) to adjust for any selection bias introduced by the artificial censoring. The basic strategy can be summarized in four steps: 1) define two regimes of interest, 2) artificially censor individuals when they stop following one of the regimes of interest, 3) estimate inverse probability weights to adjust for the potential selection bias introduced by censoring in the previous step, 4) compare the survival of the uncensored individuals under each regime of interest by fitting an inverse probability weighted Cox proportional hazards model with the dichotomous regime indicator and the baseline confounders as covariates. In the absence of model misspecification, the method is valid provided data are available on all time-varying and baseline joint predictors of survival and regime discontinuation. We present an application of the method to compare the AIDS-free survival under two dynamic treatment regimes in a large prospective study of HIV-infected patients. The paper concludes by discussing the relative advantages and disadvantages of censoring/IPW versus g-estimation of nested structural models to compare dynamic regimes.
Acquired Immunodeficiency Syndrome↗
Estimating causal effects from epidemiological data.
In ideal randomised experiments, association is causation: association measures can be interpreted as effect measures because randomisation ensures that the exposed and the unexposed are exchangeable. On the other hand, in observational studies, association is not generally causation: association measures cannot be interpreted as effect measures because the exposed and the unexposed are not generally exchangeable. However, observational research is often the only alternative for causal inference. This article reviews a condition that permits the estimation of causal effects from observational data, and two methods -- standardisation and inverse probability weighting -- to estimate population causal effects under that condition. For simplicity, the main description is restricted to dichotomous variables and assumes that no random error attributable to sampling variability exists. The appendix provides a generalisation of inverse probability weighting.
Causality↗
Pandemic influenza: risk of multiple introductions and the need to prepare for them.
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Animals↗
Results of multivariable logistic regression, propensity matching, propensity adjustment, and propensity-based weighting under conditions of nonuniform effect.
Observational studies often provide the only available information about treatment effects. Control of confounding, however, remains challenging. The authors compared five methods for evaluating the effect of tissue plasminogen activator on death among 6,269 ischemic stroke patients registered in a German stroke registry: multivariable logistic regression, propensity score-matched analysis, regression adjustment with the propensity score, and two propensity score-based weighted methods-one estimating the treatment effect in the entire study population (inverse-probability-of-treatment weights), another in the treated population (standardized-mortality-ratio weights). Between 2000 and 2001, 212 patients received tissue plasminogen activator. The crude odds ratio between tissue plasminogen activator and death was 3.35 (95% confidence interval: 2.28, 4.91). The adjusted odds ratio depended strongly on the adjustment method, ranging from 1.11 (95% confidence interval: 0.67, 1.84) for the standardized-mortality-ratio weighted to 10.77 (95% confidence interval: 2.47, 47.04) for the inverse-probability-of-treatment-weighted analysis. For treated patients with a low propensity score, risks of dying were high. Exclusion of patients with a propensity score of <5% yielded comparable odds ratios of approximately 1 for all methods. High levels of nonuniform treatment effect render summary estimates very sensitive to the weighting system explicit or implicit in an adjustment technique. Researchers need to be clear about the population for which an overall treatment estimate is most suitable.
Aged↗
Marginal structural models for estimating the effect of highly active antiretroviral therapy initiation on CD4 cell count.
The effect of highly active antiretroviral therapy (HAART) on the evolution of CD4-positive T-lymphocyte (CD4 cell) count among human immunodeficiency virus (HIV)-positive participants was estimated using inverse probability-of-treatment-and-censoring (IPTC)-weighted estimation of a marginal structural model. Of 1,763 eligible participants from two US cohort studies followed between 1996 and 2002, 60 percent initiated HAART. The IPTC-weighted estimate of the difference in mean CD4 cell count at 1 year among participants continuously treated versus those never treated was 71 cells/mm3 (95% confidence interval: 47.5, 94.6), which agrees with the reported results of randomized experiments. The corresponding estimate from a standard generalized estimating equations regression model that included baseline and most recent CD4 cell count and HIV type 1 RNA viral load as regressors was 26 cells/mm3 (95% confidence interval: 17.7, 34.3). These results indicate that nonrandomized studies of HIV treatment need to be analyzed with methods (e.g., IPTC-weighted estimation) that, in contrast to standard methods, appropriately adjust for time-varying covariates that are simultaneously confounders and intermediate variables. The 1-year estimate of 71 cells/mm3 was followed by an estimated continued increase of 29 cells/mm3 per year (estimated effect at 6 years: 216 cells/mm3), providing evidence that the large short-term effect found in randomized experiments persists and continues to improve over 6 years.
Acquired Immunodeficiency Syndrome↗
When is baseline adjustment useful in analyses of change? An example with education and cognitive change.
In research on the determinants of change in health status, a crucial analytic decision is whether to adjust for baseline health status. In this paper, the authors examine the consequences of baseline adjustment, using for illustration the question of the effect of educational attainment on change in cognitive function in old age. With data from the US-based Assets and Health Dynamics Among the Oldest Old survey (n = 5,726; born before 1924), they show that adjustment for baseline cognitive test score substantially inflates regression coefficient estimates for the effect of schooling on change in cognitive test scores compared with models without baseline adjustment. To explain this finding, they consider various plausible assumptions about relations among variables. Each set of assumptions is represented by a causal diagram. The authors apply simple rules for assessing causal diagrams to demonstrate that, in many plausible situations, baseline adjustment induces a spurious statistical association between education and change in cognitive score. More generally, when exposures are associated with baseline health status, this bias can arise if change in health status preceded baseline assessment or if the dependent variable measurement is unreliable or unstable. In some cases, change-score analyses without baseline adjustment provide unbiased causal effect estimates when baseline-adjusted estimates are biased.
Age Factors↗
Structural accelerated failure time models for survival analysis in studies with time-varying treatments.
BACKGROUND: In the absence of unmeasured confounding factors and model misspecification, standard methods for estimating the causal effect of time-varying treatments on survival are biased when (i) there exists a time-dependent risk factor for survival that also predicts subsequent treatment and (ii) past treatment history predicts subsequent risk factor level. In contrast, structural models provide consistent estimates of causal effects when unmeasured confounding and model misspecification are absent. The parameters of nested structural models are estimated by g-estimation and those of marginal structural models by inverse probability weighting. METHODS: We describe a nested structural accelerated failure time model and use it to estimate the total causal effect of highly active antiretroviral therapy (HAART) on the time to AIDS or death among human immunodeficiency virus (HIV)-infected participants of the Multicenter AIDS Cohort and Women's Interagency HIV Studies. The Appendix describes g-estimation and methods to deal with censoring. RESULTS: Comparing the regime 'always treated' to 'never treated,' the AIDS-free survival time ratio was 2.5 (95% confidence interval [CI]: 1.7, 3.3). CONCLUSIONS: Our finding of a strongly beneficial effect is consistent with results from randomized trials and from a previous analysis of the same data using a marginal structural Cox model. In contrast, a previous analysis using a standard (non-structural) model did not find an effect of treatment on survival.
Antiretroviral Therapy, Highly Active↗
Doubly robust estimation in missing data and causal inference models.
The goal of this article is to construct doubly robust (DR) estimators in ignorable missing data and causal inference models. In a missing data model, an estimator is DR if it remains consistent when either (but not necessarily both) a model for the missingness mechanism or a model for the distribution of the complete data is correctly specified. Because with observational data one can never be sure that either a missingness model or a complete data model is correct, perhaps the best that can be hoped for is to find a DR estimator. DR estimators, in contrast to standard likelihood-based or (nonaugmented) inverse probability-weighted estimators, give the analyst two chances, instead of only one, to make a valid inference. In a causal inference model, an estimator is DR if it remains consistent when either a model for the treatment assignment mechanism or a model for the distribution of the counterfactual data is correctly specified. Because with observational data one can never be sure that a model for the treatment assignment mechanism or a model for the counterfactual data is correct, inference based on DR estimators should improve upon previous approaches. Indeed, we present the results of simulation studies which demonstrate that the finite sample performance of DR estimators is as impressive as theory would predict. The proposed method is applied to a cardiovascular clinical trial.
Antidepressive Agents↗
Transmissibility of 1918 pandemic influenza.
The 1918 influenza pandemic killed 20-40 million people worldwide, and is seen as a worst-case scenario for pandemic planning. Like other pandemic influenza strains, the 1918 A/H1N1 strain spread extremely rapidly. A measure of transmissibility and of the stringency of control measures required to stop an epidemic is the reproductive number, which is the number of secondary cases produced by each primary case. Here we obtained an estimate of the reproductive number for 1918 influenza by fitting a deterministic SEIR (susceptible-exposed-infectious-recovered) model to pneumonia and influenza death epidemic curves from 45 US cities: the median value is less than three. The estimated proportion of the population with A/H1N1 immunity before September 1918 implies a median basic reproductive number of less than four. These results strongly suggest that the reproductive number for 1918 pandemic influenza is not large relative to many other infectious diseases. In theory, a similar novel influenza subtype could be controlled. But because influenza is frequently transmitted before a specific diagnosis is possible and there is a dearth of global antiviral and vaccine stores, aggressive transmission reducing measures will probably be required.
Cities↗
Sensitivity analyses for unmeasured confounding assuming a marginal structural model for repeated measures.
Robins introduced marginal structural models (MSMs) and inverse probability of treatment weighted (IPTW) estimators for the causal effect of a time-varying treatment on the mean of repeated measures. We investigate the sensitivity of IPTW estimators to unmeasured confounding. We examine a new framework for sensitivity analyses based on a nonidentifiable model that quantifies unmeasured confounding in terms of a sensitivity parameter and a user-specified function. We present augmented IPTW estimators of MSM parameters and prove their consistency for the causal effect of an MSM, assuming a correct confounding bias function for unmeasured confounding. We apply the methods to assess sensitivity of the analysis of Hernán et al., who used an MSM to estimate the causal effect of zidovudine therapy on repeated CD4 counts among HIV-infected men in the Multicenter AIDS Cohort Study. Under the assumption of no unmeasured confounders, a 95 per cent confidence interval for the treatment effect includes zero. We show that under the assumption of a moderate amount of unmeasured confounding, a 95 per cent confidence interval for the treatment effect no longer includes zero. Thus, the analysis of Hernán et al. is somewhat sensitive to unmeasured confounding. We hope that our research will encourage and facilitate analyses of sensitivity to unmeasured confounding in other applications.
CD4 Lymphocyte Count↗
On the efficacy of screening for breast cancer.
BACKGROUND: 'Mammography' (screening for breast cancer by X-ray examination) came to be widely-although not universally-accepted in the 1980s when a number of clinical trials demonstrated a substantial reduction in risk. Early detection, before the disease spread, permitted therapy that was simultaneously less invasive and more effective. Questions that remained were largely about efficacy for younger women and optimal frequency for older women. The consensus was challenged in a series of papers by two researchers at the Nordic branch of the Cochrane collaboration, Gøtzsche and Olsen, who concluded that mammography does not save lives: instead, it exposes women to unnecessary surgical procedures. METHODS: Qualitative review. RESULTS: The basis for the Gøtzsche-Olsen critique turns out to be simple. Studies that found a benefit from mammography were discounted as being of poor quality; remaining negative studies were combined by meta-analysis. The critique therefore rests on judgements of study quality, but these judgements are based on misreadings of the data and the literature. CONCLUSION: The prior consensus on mammography was correct.
Adult↗
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.
Case-Control Studies↗
Effect of highly active antiretroviral therapy on time to acquired immunodeficiency syndrome or death using marginal structural models.
To estimate the net (i.e., overall) effect of highly active antiretroviral therapy (HAART) on time to acquired immunodeficiency syndrome (AIDS) or death, the authors used inverse probability-of-treatment weighted estimation of a marginal structural model, which can appropriately adjust for time-varying confounders affected by prior treatment or exposure. Human immunodeficiency virus (HIV)-positive men and women (n = 1,498) were followed in two ongoing cohort studies between 1995 and 2002. Sixty-one percent (n = 918) of the participants initiated HAART during 6,763 person-years of follow-up, and 382 developed AIDS or died. Strong confounding by indication for HAART was apparent; the unadjusted hazard ratio for AIDS or death was 0.98. The hazard ratio from a standard time-dependent Cox model that included time-varying CD4 cell count, HIV RNA level, and other time-varying and fixed covariates as regressors was 0.81 (95% confidence interval: 0.61, 1.07). In contrast, the hazard ratio from a marginal structural survival model was 0.54 (robust 95% confidence interval: 0.38, 0.78), suggesting a clinically meaningful net benefit of HAART. Standard Cox analysis failed to detect a clear net benefit, because it does not appropriately adjust for time-dependent covariates, such as HIV RNA level and CD4 cell count, that are simultaneously confounders and intermediate variables.
Acquired Immunodeficiency Syndrome↗
Transmission dynamics and control of severe acute respiratory syndrome.
Severe acute respiratory syndrome (SARS) is a recently described illness of humans that has spread widely over the past 6 months. With the use of detailed epidemiologic data from Singapore and epidemic curves from other settings, we estimated the reproductive number for SARS in the absence of interventions and in the presence of control efforts. We estimate that a single infectious case of SARS will infect about three secondary cases in a population that has not yet instituted control measures. Public-health efforts to reduce transmission are expected to have a substantial impact on reducing the size of the epidemic.
Contact Tracing↗
Incorporating prior beliefs about selection bias into the analysis of randomized trials with missing outcomes.
In randomized studies with missing outcomes, non-identifiable assumptions are required to hold for valid data analysis. As a result, statisticians have been advocating the use of sensitivity analysis to evaluate the effect of varying assumptions on study conclusions. While this approach may be useful in assessing the sensitivity of treatment comparisons to missing data assumptions, it may be dissatisfying to some researchers/decision makers because a single summary is not provided. In this paper, we present a fully Bayesian methodology that allows the investigator to draw a 'single' conclusion by formally incorporating prior beliefs about non-identifiable, yet interpretable, selection bias parameters. Our Bayesian model provides robustness to prior specification of the distributional form of the continuous outcomes.
Acquired Immunodeficiency Syndrome↗
Estimating the causal effect of zidovudine on CD4 count with a marginal structural model for repeated measures.
Even in the absence of unmeasured confounding factors or model misspecification, standard methods for estimating the causal effect of a time-varying treatment on the mean of a repeated measures outcome (for example, GEE regression) may be biased when there are time-dependent variables that are simultaneously confounders of the effect of interest and are predicted by previous treatment. In contrast, the recently developed marginal structural models (MSMs) can provide consistent estimates of causal effects when unmeasured confounding and model misspecification are absent. We describe an MSM for repeated measures that parameterizes the marginal means of counterfactual outcomes corresponding to prespecified treatment regimes. The parameters of MSMs are estimated using a new class of estimators - inverse-probability of treatment weighted estimators. We used an MSM to estimate the effect of zidovudine therapy on mean CD4 count among HIV-infected men in the Multicenter AIDS Cohort Study. We estimated a potential expected increase of 5.4 (95 per cent confidence interval -1.8,12.7) CD4 lymphocytes/l per additional study visit while on zidovudine therapy. We also explain the theory and implementation of MSMs for repeated measures data and draw upon a simple example to illustrate the basic ideas.
Anti-HIV Agents↗