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Bayesian inference for causal mechanisms with application to a randomized study for postoperative pain control

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Abstract

Principal stratification and mediation analysis are two ways to conceptualize the mediating role of an intermediate variable in the causal pathways by which a treatment affects an outcome. They are often viewed as competing frameworks, and their role in dealing with issues concerning causal mechanisms has often fired up glowing discussions. However a thoughtful comparative analysis, highlighting the substantive differences between the two frameworks is still lacking. We aim at filling this gap conducting both principal stratification and mediation analysis using, as a motivating example, a prospective, randomized, double-blind study to investigate to which extent the positive overall effect of treatment on postoperative pain control is mediated by postoperative self administration of intra-venous analgesia by patients. Using the Bayesian approach for inference, we estimate both associative and dissociative principal strata effects arising in principal stratification analysis, as well as natural effects and controlled direct effects from mediation analysis. We highlight that principal stratification and mediation analysis focus on different causal estimands, answer different causal questions and involve different sets of identifying assumptions. We discuss these aspects along the results arising from our analyses.

Suggested Citation

  • Michela Baccini & Alessandra Mattei & Fabrizia Mealli, 2015. "Bayesian inference for causal mechanisms with application to a randomized study for postoperative pain control," Econometrics Working Papers Archive 2015_06, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
    • Handle: RePEc:fir:econom:wp2015_06
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    1. Mealli Fabrizia & Mattei Alessandra, 2012. "A Refreshing Account of Principal Stratification," The International Journal of Biostatistics, De Gruyter, vol. 8(1), pages 1-19, April.
    2. Kosuke Imai & Dustin Tingley & Teppei Yamamoto, 2013. "Experimental designs for identifying causal mechanisms," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 176(1), pages 5-51, January.
    3. Constantine E. Frangakis & Donald B. Rubin, 2002. "Principal Stratification in Causal Inference," Biometrics, The International Biometric Society, vol. 58(1), pages 21-29, March.
    4. VanderWeele, Tyler J., 2008. "Simple relations between principal stratification and direct and indirect effects," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2957-2962, December.
    5. Mealli, Fabrizia & Rubin, Donald B., 2003. "Assumptions allowing the estimation of direct causal effects," Journal of Econometrics, Elsevier, vol. 112(1), pages 79-87, January.
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