Identification and estimation of survivor average causal effects

Assessing the Potential for Bias From Nonresponse to a Study Follow-up Interview: An Example From the Agricultural Health Study

Prospective cohort studies are important tools for identifying causes of disease. However, these studies are susceptible to attrition. When information collected after enrollment is through interview or exam, attrition leads to missing information for nonrespondents. The Agricultural Health Study enrolled 52,394 farmers in 1993-1997 and collected additional information during subsequent interviews. Forty-six percent of enrolled farmers responded to the 2005-2010 interview; 7% of farmers died prior to the interview. We examined whether response was related to attributes measured at enrollment. To characterize potential bias from attrition, we evaluated differences in associations between smoking and incidence of 3 cancer types between the enrolled cohort and the subcohort of 2005-2010 respondents, using cancer registry information. In the subcohort we evaluated the ability of inverse probability weighting (IPW) to reduce bias. Response was related to age, state, race/ethnicity, education, marital status, smoking, and alcohol consumption. When exposure and outcome were associated and case response was differential by exposure, some bias was observed; IPW conditional on exposure and covariates failed to correct estimates. When response was nondifferential, subcohort and full-cohort estimates were similar, making IPW unnecessary. This example provides a demonstration of investigating the influence of attrition in cohort studies using information that has been self-reported after enrollment.

Identification and estimation of causal effects with outcomes truncated by death

It is common in medical studies that the outcome of interest is truncated by death, meaning that a subject has died before the outcome could be measured. In this case, restricted analysis among survivors may be subject to selection bias. Hence, it is of interest to estimate the survivor average causal effect, defined as the average causal effect among the subgroup consisting of subjects who would survive under either exposure. In this paper, we consider the identification and estimation problems of the survivor average causal effect. We propose to use a substitution variable in place of the latent membership in the always-survivor group. The identification conditions required for a substitution variable are conceptually similar to conditions for a conditional instrumental variable, and may apply to both randomized and observational studies. We show that the survivor average causal effect is identifiable with use of such a substitution variable, and propose novel model parameterizations for estimation of the survivor average causal effect under our identification assumptions. Our approaches are illustrated via simulation studies and a data analysis.

Statistics, Adjusted Statistics, and Maladjusted Statistics

Statistical adjustment is a ubiquitous practice in all quantitative fields that is meant to correct for improprieties or limitations in observed data, to remove the influence of nuisance variables or to turn observed correlations into causal inferences. These adjustments proceed by reporting not what was observed in the real world, but instead modeling what would have been observed in an imaginary world in which specific nuisances and improprieties are absent. These techniques are powerful and useful inferential tools, but their application can be hazardous or deleterious if consumers of the adjusted results mistake the imaginary world of models for the real world of data. Adjustments require decisions about which factors are of primary interest and which are imagined away, and yet many adjusted results are presented without any explanation or justification for these decisions. Adjustments can be harmful if poorly motivated, and are frequently misinterpreted in the media's reporting of scientific studies. Adjustment procedures have become so routinized that many scientists and readers lose the habit of relating the reported findings back to the real world in which we live.

Post-traumatic stress disorder and cardiometabolic disease: improving causal inference to inform practice

Post-traumatic stress disorder (PTSD) has been declared 'a life sentence' based on evidence that the disorder leads to a host of physical health problems. Some of the strongest empirical research - in terms of methodology and findings - has shown that PTSD predicts higher risk of cardiometabolic diseases, specifically cardiovascular disease (CVD) and type 2 diabetes (T2D). Despite mounting evidence, PTSD is not currently acknowledged as a risk factor by cardiovascular or endocrinological medicine. This view is unlikely to change absent compelling evidence that PTSD causally contributes to cardiometabolic disease. This review suggests that with developments in methods for epidemiological research and the rapidly expanding knowledge of the behavioral and biological effects of PTSD the field is poised to provide more definitive answers to questions of causality. First, we discuss methods to improve causal inference using the observational data most often used in studies of PTSD and health, with particular reference to issues of temporality and confounding. Second, we consider recent work linking PTSD with specific behaviors and biological processes, and evaluate whether these may plausibly serve as mechanisms by which PTSD leads to cardiometabolic disease. Third, we evaluate how looking more comprehensively into the PTSD phenotype provides insight into whether specific aspects of PTSD phenomenology are particularly relevant to cardiometabolic disease. Finally, we discuss new areas of research that are feasible and could enhance understanding of the PTSD-cardiometabolic relationship, such as testing whether treatment of PTSD can halt or even reverse the cardiometabolic risk factors causally related to CVD and T2D.

Beyond Composite Endpoints Analysis: Semicompeting Risks as an Underutilized Framework for Cancer Research

BACKGROUND

Composite endpoints (CEP), such as progression-free survival, are commonly used in cancer research. Notwithstanding their popularity, however, CEP analyses suffer from a number of drawbacks, especially when death is combined with a nonterminal event (ie, progression or recurrence), exemplifying the semicompeting risks setting. We investigated the semicompeting risks framework as a complementary analysis strategy that avoids certain drawbacks of CEPs.

METHODS

The illness-death model under the semicompeting risks framework was compared with standard analysis approaches: CEP analyses and (separate) univariate analyses for each component endpoint. Data from a previously published phase III randomized clinical trial in metastatic colon cancer including 1419 participants in the N9741 trial (conducted between 1997 and 2003) were used to determine the impact of the loss of information associated with combining multiple endpoints, as well as of ignoring the potentially informative role of death. A simulation study was conducted to further explore these issues.

RESULTS

Failure to account for critical features of semicompeting risks data can lead to potentially severely misleading conclusions. Advantages of semicompeting risks analyses include a clear delineation of treatment effects on both events, the ability to draw conclusions about a patient's joint risk of the two events, and an assessment of the dependence between the two event types.

CONCLUSIONS

Embedding and analyzing component outcomes in the semicompeting risks framework, either as a supplement or alternative to CEP analyses, represents an important, underutilized, and feasible opportunity for cancer research.

Hierarchical models for semi-competing risks data with application to quality of end-of-life care for pancreatic cancer

Readmission following discharge from an initial hospitalization is a key marker of quality of health care in the United States. For the most part, readmission has been studied among patients with 'acute' health conditions, such as pneumonia and heart failure, with analyses based on a logistic-Normal generalized linear mixed model (Normand et al., 1997). Naïve application of this model to the study of readmission among patients with 'advanced' health conditions such as pancreatic cancer, however, is problematic because it ignores death as a competing risk. A more appropriate analysis is to imbed such a study within the semi-competing risks framework. To our knowledge, however, no comprehensive statistical methods have been developed for cluster-correlated semi-competing risks data. To resolve this gap in the literature we propose a novel hierarchical modeling framework for the analysis of cluster-correlated semi-competing risks data that permits parametric or non-parametric specifications for a range of components giving analysts substantial flexibility as they consider their own analyses. Estimation and inference is performed within the Bayesian paradigm since it facilitates the straightforward characterization of (posterior) uncertainty for all model parameters, including hospital-specific random effects. Model comparison and choice is performed via the deviance information criterion and the log-pseudo marginal likelihood statistic, both of which are based on a partially marginalized likelihood. An efficient computational scheme, based on the Metropolis-Hastings-Green algorithm, is developed and had been implemented in the SemiCompRisks R package. A comprehensive simulation study shows that the proposed framework performs very well in a range of data scenarios, and outperforms competitor analysis strategies. The proposed framework is motivated by and illustrated with an on-going study of the risk of readmission among Medicare beneficiaries diagnosed with pancreatic cancer. Using data on n=5,298 patients at J=112 hospitals in the six New England states between 2000-2009, key scientific questions we consider include the role of patient-level risk factors on the risk of readmission and the extent of variation in risk across hospitals not explained by differences in patient case-mix.

A Simulation Platform for Quantifying Survival Bias: An Application to Research on Determinants of Cognitive Decline

Bias due to selective mortality is a potential concern in many studies and is especially relevant in cognitive aging research because cognitive impairment strongly predicts subsequent mortality. Biased estimation of the effect of an exposure on rate of cognitive decline can occur when mortality is a common effect of exposure and an unmeasured determinant of cognitive decline and in similar settings. This potential is often represented as collider-stratification bias in directed acyclic graphs, but it is difficult to anticipate the magnitude of bias. In this paper, we present a flexible simulation platform with which to quantify the expected bias in longitudinal studies of determinants of cognitive decline. We evaluated potential survival bias in naive analyses under several selective survival scenarios, assuming that exposure had no effect on cognitive decline for anyone in the population. Compared with the situation with no collider bias, the magnitude of bias was higher when exposure and an unmeasured determinant of cognitive decline interacted on the hazard ratio scale to influence mortality or when both exposure and rate of cognitive decline influenced mortality. Bias was, as expected, larger in high-mortality situations. This simulation platform provides a flexible tool for evaluating biases in studies with high mortality, as is common in cognitive aging research.

Semi-Competing Risks Data Analysis: Accounting for Death as a Competing Risk When the Outcome of Interest Is Nonterminal

Hospital readmission is a key marker of quality of health care. Notwithstanding its widespread use, however, it remains controversial in part because statistical methods used to analyze readmission, primarily logistic regression and related models, may not appropriately account for patients who die before experiencing a readmission event within the time frame of interest. Toward resolving this, we describe and illustrate the semi-competing risks framework, which refers to the general setting where scientific interest lies with some nonterminal event (eg, readmission), the occurrence of which is subject to a terminal event (eg, death). Although several statistical analysis methods have been proposed for semi-competing risks data, we describe in detail the use of illness-death models primarily because of their relation to well-known methods for survival analysis and the availability of software. We also describe and consider in detail several existing approaches that could, in principle, be used to analyze semi-competing risks data, including composite end point and competing risks analyses. Throughout we illustrate the ideas and methods using data on N=49 763 Medicare beneficiaries hospitalized between 2011 and 2013 with a principle discharge diagnosis of heart failure.

Straight Metalworking Fluids and All-Cause and Cardiovascular Mortality Analyzed by Using G-Estimation of an Accelerated Failure Time Model With Quantitative Exposure: Methods and Interpretations

Straight metalworking fluids have been linked to cardiovascular mortality in analyses using binary exposure metrics, accounting for healthy worker survivor bias by using g-estimation of accelerated failure time models. A cohort of 38,666 Michigan autoworkers was followed (1941-1994) for mortality from all causes and ischemic heart disease. The structural model chosen here, using continuous exposure, assumes that increasing exposure from 0 to 1 mg/m(3) in any single year would decrease survival time by a fixed amount. Under that assumption, banning the fluids would have saved an estimated total of 8,468 (slope-based 95% confidence interval: 2,262, 28,563) person-years of life in this cohort. On average, 3.04 (slope-based 95% confidence interval: 0.02, 25.98) years of life could have been saved for each exposed worker who died from ischemic heart disease. Estimates were sensitive to both model specification for predicting exposure (multinomial or logistic regression) and characterization of exposure as binary or continuous in the structural model. Our results provide evidence supporting the hypothesis of a detrimental relationship between straight metalworking fluids and mortality, particularly from ischemic heart disease, as well as an instructive example of the challenges in obtaining and interpreting results from accelerated failure time models using a continuous exposure in the presence of competing risks.

Biased Exposure-Health Effect Estimates from Selection in Cohort Studies: Are Environmental Studies at Particular Risk?

BACKGROUND

The process of creating a cohort or cohort substudy may induce misleading exposure-health effect associations through collider stratification bias (i.e., selection bias) or bias due to conditioning on an intermediate. Studies of environmental risk factors may be at particular risk.

OBJECTIVES

We aimed to demonstrate how such biases of the exposure-health effect association arise and how one may mitigate them.

METHODS

We used directed acyclic graphs and the example of bone lead and mortality (all-cause, cardiovascular, and ischemic heart disease) among 835 white men in the Normative Aging Study (NAS) to illustrate potential bias related to recruitment into the NAS and the bone lead substudy. We then applied methods (adjustment, restriction, and inverse probability of attrition weighting) to mitigate these biases in analyses using Cox proportional hazards models to estimate adjusted hazard ratios (HRs) and 95% confidence intervals (CIs).

RESULTS

Analyses adjusted for age at bone lead measurement, smoking, and education among all men found HRs (95% CI) for the highest versus lowest tertile of patella lead of 1.34 (0.90, 2.00), 1.46 (0.86, 2.48), and 2.01 (0.86, 4.68) for all-cause, cardiovascular, and ischemic heart disease mortality, respectively. After applying methods to mitigate the biases, the HR (95% CI) among the 637 men analyzed were 1.86 (1.12, 3.09), 2.47 (1.23, 4.96), and 5.20 (1.61, 16.8), respectively.

CONCLUSIONS

Careful attention to the underlying structure of the observed data is critical to identifying potential biases and methods to mitigate them. Understanding factors that influence initial study participation and study loss to follow-up is critical. Recruitment of population-based samples and enrolling participants at a younger age, before the potential onset of exposure-related health effects, can help reduce these potential pitfalls.

CITATION

Weisskopf MG, Sparrow D, Hu H, Power MC. 2015. Biased exposure-health effect estimates from selection in cohort studies: are environmental studies at particular risk? Environ Health Perspect 123:1113-1122; http://dx.doi.org/10.1289/ehp.1408888.

Invited commentary: Estimating population impact in the presence of competing events

The formal approach in the field of causal inference has enabled epidemiologists to clarify several complications that arise when estimating the effect of an intervention on a health outcome of interest. When the outcome is a failure time or longitudinal process, researchers must often deal with competing events. In this issue of the Journal, Picciotto et al. (Am J Epidemiol. 2015;181(8):563-570) use structural nested failure time models to assess potential population effects of hypothetical interventions and censor competing events. In the present commentary, we discuss 2 interpretations that result from treating competing events as censored observations and how they relate to measures of public health impact. We also comment on 2 alternative approaches for handling competing events: an inverse probability weighting estimator of the survivor average causal effect and the parametric g-formula, which can be used to estimate a functional of the subdistribution of the event of interest. We argue that careful consideration of the tradeoff between the interpretation of the parameters from each approach and the assumptions required to estimate these parameters should guide researchers on the various ways to handle competing events in epidemiologic research.

Doubly robust estimation and causal inference in longitudinal studies with dropout and truncation by death

Motivated by aging research, we propose an estimator of the effect of a time-varying exposure on an outcome in longitudinal studies with dropout and truncation by death. We use an inverse-probability weighted (IPW) estimator to derive a doubly robust augmented inverse-probability weighted (AIPW) estimator. IPW estimation involves weights for the exposure mechanism, dropout, and mortality; AIPW estimation additionally involves estimating data-generating models via regression. We demonstrate that the estimators identify a causal contrast that is a function of principal strata effects under a set of assumptions. Simulations show that AIPW estimation is unbiased when weights or outcome regressions are correct, and that AIPW estimation is more efficient than IPW estimation when all models are correct. We apply the method to a study of vitamin D and gait speed among older adults.