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.

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Marginal Structural Models and Causal Inference in Epidemiology

BACKGROUND: The efficacy of the ALK inhibitor crizotinib as compared with standard chemotherapy as first-line treatment for advanced ALK-positive non-small-cell lung cancer (NSCLC) is unknown. METHODS: We conducted an open-label, phase 3 trial comparing crizotinib with chemotherapy in 343 patients with advanced ALK-positive nonsquamous NSCLC who had received no previous systemic treatment for advanced disease. Patients were randomly assigned to receive oral crizotinib at a dose of 250 mg twice daily or to receive intravenous chemotherapy (pemetrexed, 500 mg per square meter of body-surface area, plus either cisplatin, 75 mg per square meter, or carboplatin, target area under the curve of 5 to 6 mg per milliliter per minute) every 3 weeks for up to six cycles. Crossover to crizotinib treatment after disease progression was permitted for patients receiving chemotherapy. The primary end point was progression-free survival as assessed by independent radiologic review. RESULTS: Progression-free survival was significantly longer with crizotinib than with chemotherapy (median, 10.9 months vs. 7.0 months; hazard ratio for progression or death with crizotinib, 0.45; 95% confidence interval [CI], 0.35 to 0.60; P<0.001). Objective response rates were 74% and 45%, respectively (P<0.001). Median overall survival was not reached in either group (hazard ratio for death with crizotinib, 0.82; 95% CI, 0.54 to 1.26; P=0.36); the probability of 1-year survival was 84% with crizotinib and 79% with chemotherapy. The most common adverse events with crizotinib were vision disorders, diarrhea, nausea, and edema, and the most common events with chemotherapy were nausea, fatigue, vomiting, and decreased appetite. As compared with chemotherapy, crizotinib was associated with greater reduction in lung cancer symptoms and greater improvement in quality of life. CONCLUSIONS: Crizotinib was superior to standard first-line pemetrexed-plus-platinum chemotherapy in patients with previously untreated advanced ALK-positive NSCLC. (Funded by Pfizer; PROFILE 1014 ClinicalTrials.gov number, NCT01154140.).

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First-line crizotinib versus chemotherapy in ALK-positive lung cancer

In applied problems it is common to specify a model for the conditional mean of a response given a set of regressors. A subset of the regressors may be missing for some study subjects either by design or happenstance. In this article we propose a new class of semiparametric estimators, based on inverse probability weighted estimating equations, that are consistent for parameter vector α0 of the conditional mean model when the data are missing at random in the sense of Rubin and the missingness probabilities are either known or can be parametrically modeled. We show that the asymptotic variance of the optimal estimator in our class attains the semiparametric variance bound for the model by first showing that our estimation problem is a special case of the general problem of parameter estimation in an arbitrary semiparametric model in which the data are missing at random and the probability of observing complete data is bounded away from 0, and then deriving a representation for the efficient score...

https://www.jstor.org/stable/pdfplus/2290910.pdf

Estimation of Regression Coefficients When Some Regressors are not Always Observed

SUMMARY The primary aim of this paper is to show how graphical models can be used as a mathematical language for integrating statistical and subject-matter information. In particular, the paper develops a principled, nonparametric framework for causal inference, in which diagrams are queried to determine if the assumptions available are sufficient for identifying causal effects from nonexperimental data. If so the diagrams can be queried to produce mathematical expressions for causal effects in terms of observed distributions; otherwise, the diagrams can be queried to suggest additional observations or auxiliary experiments from which the desired inferences can be obtained.

https://escholarship.org/content/qt6gv9n38c/qt6gv9n38c.pdf

Causal diagrams for empirical research

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.

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

AIDS Clinical Trial Group Randomized Trial 002 compared the effect of high-dose with low-dose 3-azido-3-deoxythymidine (AZT) on the survival of AIDS patients. Embedded within the trial was an essentially uncontrolled observational study of the effect of prophylaxis therapy for pneumocystis carinii pneumonia on survival. In this paper, we estimate the causal effect of prophylaxis therapy on survival by using the method of G-estimation to estimate the parameters of a structural nested failure time model (SNFTM). Our SNFTM relates a subject's observed time of death and observed prophylaxis history to the time the subject would have died if, possibly contrary to fact, prophylaxis therapy had been withheld. We find that, under our assumptions, the data are consistent with prophylaxis therapy increasing survival by 16% or decreasing survival by 18% at the alpha = 0.05 level. The analytic approach proposed in this paper will be necessary to control bias in any epidemiologic study in which there exists a time-dependent risk factor for death, such as pneumocystis carinii pneumonia history, that (A1) influences subsequent exposure to the agent under study, for example, prophylaxis therapy, and (A2) is itself influenced by past exposure to the study agent. Conditions A1 and A2 will be true whenever there exists a time-dependent risk factor that is simultaneously a confounder and an intermediate variable.

Michael Wulfsohn

Papers

G-estimation of the effect of prophylaxis therapy for Pneumocystis carinii pneumonia on the survival of AIDS patients.