Biostatistics (2004), 5, 2, pp. 207-222
Biostatistics Vol. 5 No. 2 © Oxford University Press 2004; all rights reserved.
Analyzing a randomized trial on breast self-examination with noncompliance and missing outcomes
Dipartimento di Statistica ‘G. Parenti’, Università di Firenze, Italy
University of California at Berkeley, Department of Economics and Department of Agricultural and Resource Economics, Berkeley, CA 94720-3880, USA
imbens{at}econ.berkeley.edu
Istituto Oncologico Romagnolo, Faenza, Italy
Dipartimento di Statistica ‘G. Parenti’, Università di Firenze, Italy
Currently at Ospedale S. Orsola-Malpighi, Bologna.
Recently, instrumental variables methods have been used to address non-compliance in randomized experiments. Complicating such analyses is often the presence of missing data. The standard model for missing data, missing at random (MAR), has some unattractive features in this context. In this paper we compare MAR-based estimates of the complier average causal effect (CACE) with an estimator based on an alternative, nonignorable model for the missing data process, developed by Frangakis and Rubin (1999, Biometrika, 86, 365–379). We also introduce a new missing data model that, like the Frangakis–Rubin model, is specially suited for models with instrumental variables, but makes different substantive assumptions. We analyze these issues in the context of a randomized trial of breast self-examination (BSE). In the study two methods of teaching BSE, consisting of either mailed information about BSE (the standard treatment) or the attendance of a course involving theoretical and practical sessions (the new treatment), were compared with the aim of assessing whether teaching programs could increase BSE practice and improve examination skills. The study was affected by the two sources of bias mentioned above: only 55% of women assigned to receive the new treatment complied with their assignment and 35% of the women did not respond to the post-test questionnaire. Comparing the causal estimand of the new treatment using the MAR, Frangakis–Rubin, and our new approach, the results suggest that for these data the MAR assumption appears least plausible, and that the new model appears most plausible among the three choices.
Keywords: Complier average causal effect; Instrumental variables; Intention–to–treat effect; Missing at random; Non-compliance; Non-ignorable missing data; Randomized experiments
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