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Causal Inference in Hybrid Intervention Trials Involving Treatment Choice


  • Qi Long

    (University of Michigan)

  • Rod Little

    (University of Michigan)

  • Xihong Lin

    (University of Michigan)


Randomized allocation of treatments is a cornerstone of experimental design, but has drawbacks when a limited set of individuals are willing to be randomized, or the act of randomization undermines the success of the treatment. Choice-based experimental designs allow a subset of the participants to choose their treatments. We discuss here causal inferences for experimental designs where some participants are randomly allocated to treatments and others receive their treatment preference. This paper was motivated by the "Women Take Pride" (WTP) study (Janevic et al., 2001), a doubly randomized preference trail (DRPT) to assess behavioral interventions for women with heart disease. We propose a model that allows us to estimate the causal effects in the subpopulations defined by treatment preferences and the preference effects for a DRPT, and develop an EM Algorithm to compute maximum likelihood estimates of the model parameters. The method is illustrated by analyzing treatment compliance of the WTP data. Our results show that there were strong preference effects in the WTP study, that is, women assigned to their preferred treatment were more likely to comply. We also expand these methods to handle a broader class of designs, and discuss alternative designs from the perspective of the strength of assumptions required to make causal inferences.

Suggested Citation

  • Qi Long & Rod Little & Xihong Lin, 2004. "Causal Inference in Hybrid Intervention Trials Involving Treatment Choice," The University of Michigan Department of Biostatistics Working Paper Series 1033, Berkeley Electronic Press.
  • Handle: RePEc:bep:mchbio:1033

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    References listed on IDEAS

    1. Janevic, Mary R. & Janz, Nancy K. & Dodge, Julia A. & Lin, Xihong & Pan, Wenqin & Sinco, Brandy R. & Clark, Noreen M., 2003. "The role of choice in health education intervention trials: a review and case study," Social Science & Medicine, Elsevier, vol. 56(7), pages 1581-1594, April.
    2. J.D. Angrist & Guido W. Imbens & D.B. Rubin, 1993. "Identification of Causal Effects Using Instrumental Variables," NBER Technical Working Papers 0136, National Bureau of Economic Research, Inc.
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    Cited by:

    1. Strobl, Renate & Wunsch, Conny, 2018. "Identification of causal mechanisms based on between-subject double randomization designs," CEPR Discussion Papers 13028, C.E.P.R. Discussion Papers.
    2. Strobl, Renate & Wunsch, Conny, 2018. "Risky Choices and Solidarity: Why Experimental Design Matters," Working papers 2018/17, Faculty of Business and Economics - University of Basel.
    3. Qi Long & Roderick J. A. Little & Xihong Lin, 2010. "Estimating causal effects in trials involving multitreatment arms subject to nonā€compliance: a Bayesian framework," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(3), pages 513-531, May.
    4. Onur Altindag & Theodore J. Joyce & Julie A. Reeder, 2019. "Can Nonexperimental Methods Provide Unbiased Estimates of a Breastfeeding Intervention? A Within-Study Comparison of Peer Counseling in Oregon," Evaluation Review, , vol. 43(3-4), pages 152-188, June.


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