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Sensitivity analysis for unmeasured confounding in a marginal structural Cox proportional hazards model

Abstract

Sensitivity analysis for unmeasured confounding should be reported more often, especially in observational studies. In the standard Cox proportional hazards model, this requires substantial assumptions and can be computationally difficult. The marginal structural Cox proportional hazards model (Cox proportional hazards MSM) with inverse probability weighting has several advantages compared to the standard Cox model, including situations with only one assessment of exposure (point exposure) and time-independent confounders. We describe how simple computations provide sensitivity for unmeasured confounding in a Cox proportional hazards MSM with point exposure. This is achieved by translating the general framework for sensitivity analysis for MSMs by Robins and colleagues to survival time data. Instead of bias-corrected observations, we correct the hazard rate to adjust for a specified amount of unmeasured confounding. As an additional bonus, the Cox proportional hazards MSM is robust against bias from differential loss to follow-up. As an illustration, the Cox proportional hazards MSM was applied in a reanalysis of the association between smoking and depression in a population-based cohort of Norwegian adults. The association was moderately sensitive for unmeasured confounding.

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References

  • Avison WR, Turner RJ (1988) Stressful life events and depressive symptoms: disaggregating the effects of acute stressors and chronic strains. J Health Soc Behav 29: 253–264

    Article  Google Scholar 

  • Brumback BA, Hernan MA, Haneuse SJ, Robins JM (2004) Sensitivity analyses for unmeasured confounding assuming a marginal structural model for repeated measures. Stat Med 23: 749–767

    Article  Google Scholar 

  • Derogatis LR, Lipman RS, Rickels K, Uhlenhuth EH, Covi L (1974) The Hopkins Symptom Checklist (HSCL): a self-report symptom inventory. Behav Sci 19: 1–15

    Article  Google Scholar 

  • Greenland S (1996) Basic methods for sensitivity analysis of biases. Int J Epidemiol 25: 1107–1116

    Article  Google Scholar 

  • Greenland S (2003) Quantifying biases in causal models: classical confounding vs collider-stratification bias. Epidemiology 14: 300–306

    Article  Google Scholar 

  • Hernan MA, Robins JM (1999) Method for conducting sensitivity analysis. Biometrics 55: 1316–1317

    Google Scholar 

  • Hernan MA, Brumback B, Robins JM (2000) Marginal structural models to estimate the causal effect of Zidovudine on the survival of HIV-positive men. Epidemiology 11: 561–570

    Article  Google Scholar 

  • Hernan MA, Brumback B, Robins JM (2001) Marginal structural models to estimate the joint causal effect of nonrandomized treatments. J Am Stat Assoc 96: 440–448

    MATH  Article  MathSciNet  Google Scholar 

  • Hernan MA, Hernandez-Diaz S, Werler MM, Mitchell AA (2002) Causal knowledge as a prerequisite for confounding evaluation: an application to birth defects epidemiology. Am J Epidemiol 155: 176–184

    Article  Google Scholar 

  • Hernan MA, Hernandez-Diaz S, Robins JM (2004) A structural approach to selection bias. Epidemiology 15: 615–625

    Article  Google Scholar 

  • Holland P (1986) Statistics and causal inference. J Am Stat Assoc 81: 945–961

    MATH  Article  MathSciNet  Google Scholar 

  • Kendler KS, Neale MC, MacLean CJ, Heath AC, Eaves LJ, Kessler RC (1993) Smoking and major depression. A causal analysis. Arch Gen Psychiatry 50: 36–43

    Google Scholar 

  • Klungsoyr O, Nygard JF, Sorensen T, Sandanger I. (2006) Cigarette smoking and incidence of first depressive episode. An 11-year, population-based follow-up study. Am J Epidemiol 163: 421–432

    Article  Google Scholar 

  • Korhonen T, Broms U, Varjonen J, Romanov K, Koskenvuo M, Kinnunen T, Kaprio J (2007) Smoking behaviour as a predictor of depression among Finnish men and women: a prospective cohort study of adult twins. Psychol Med 37: 705–715

    Article  Google Scholar 

  • Lin DY, Psaty BM, Kronmal RA (1998) Assessing the sensitivity of regression results to unmeasured confounders in observational studies. Biometrics 54: 948–963

    MATH  Article  Google Scholar 

  • Neyman J (1990) (1923) On the application of probability theory to agricultural experiments: essay on principles. Section 9, translated. Stat Sci 5: 465–480

    MATH  MathSciNet  Google Scholar 

  • Paykel ES (1997) The interview for recent life events. Psychol Med 27: 301–310

    Article  Google Scholar 

  • Pearl J (2000) Causality. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • R-Development-Core-Team (2006) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna

  • Rickels K, Garcia CR, Lipman RS, Derogatis LR, Fisher EL (1976) The Hopkins Symptom Checklist. Assessing emotional distress in obstetric-gynecologic practice. Prim Care 3: 751–764

    Google Scholar 

  • Robins JM (1986) A new approach to causal inference in mortality studies with sustained exposure periods—application to control of the healthy worker survivor effect. Math Model 7: 1393–1512

    MATH  Article  MathSciNet  Google Scholar 

  • Robins JM (1987) Addendum to A new approach to causal inference in mortality studies with sustained exposure periods—application to control of the healthy worker survivor effect. Comput Math Appl 14: 923–945

    MATH  Article  MathSciNet  Google Scholar 

  • Robins JM (1998) Marginal structural models. Proceedings of the American Statistical Association, Section on Bayesian Statistical Science, pp 1–10

  • Robins JM (1999) Association, causation, and marginal structural models. Synthese 121: 151–179

    MATH  Article  MathSciNet  Google Scholar 

  • Robins JM, Greenland S (1992) Identifiability and exchangeability for direct and indirect effects. Epidemiology 3: 143–155

    Article  Google Scholar 

  • Robins JM, Greenland S, Hu FC (1999a) Rejoinder to Estimation of the Causal Effect of a Time-varying Exposure on the Marginal Mean of a Repeated Binary Outcome. J Am Stat Assoc 94: 708–712

    Article  MathSciNet  Google Scholar 

  • Robins JM, Rotnitzky A, Scharfstein DO (1999b) Sensitivity analysis for selection bias and unmeasured confounding in missing data and causal inference models in Statistical Models in Epidemiology: The Environment and Clinical Trials. Springer, New York

    Google Scholar 

  • Robins JM, Hernan MA, Brumback B (2000) Marginal structural models and causal inference in epidemiology. Epidemiology 11: 550–560

    Article  Google Scholar 

  • Rubin DB (1978) Bayesian inference for causal effects: the role of randomization. Ann Stat 6: 34–58

    MATH  Article  Google Scholar 

  • Sandanger I, Nygard JF, Ingebrigtsen G, Sorensen T, Dalgard OS (1999) Prevalence, incidence and age at onset of psychiatric disorders in Norway. Soc Psychiatry Psychiatr Epidemiol 34: 570–579

    Article  Google Scholar 

  • Sandanger I, Nygard JF, Sorensen T, Moum T (2004) Is women’s mental health more susceptible than men’s to the influence of surrounding stress?. Soc Psychiatry Psychiatr Epidemiol 39: 177–184

    Article  Google Scholar 

  • Sato T, Matsuyama Y (2003) Marginal structural models as a tool for standardization. Epidemiology 14: 680–686

    Article  Google Scholar 

  • Saunders JB, Aasland OG (1987) WHO collaborative on identification and treatment of persons with harmful alcohol consumption. World Health Organization, Oslo, p 97

  • Silberg J, Rutter M, D’Onofrio B, Eaves L (2003) Genetic and environmental risk factors in adolescent substance use. J Child Psychol Psychiatry 44: 664–676

    Article  Google Scholar 

  • Winokur A, Winokur DF, Rickels K, Cox DS (1984) Symptoms of emotional distress in a family planning service: stability over a four-week period. Br J Psychiatry 144: 395–399

    Article  Google Scholar 

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Correspondence to Ole Klungsøyr.

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Klungsøyr, O., Sexton, J., Sandanger, I. et al. Sensitivity analysis for unmeasured confounding in a marginal structural Cox proportional hazards model. Lifetime Data Anal 15, 278–294 (2009). https://doi.org/10.1007/s10985-008-9109-x

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  • DOI: https://doi.org/10.1007/s10985-008-9109-x

Keywords

  • Sensitivity analysis
  • Selection bias
  • Unmeasured confounding