Consider a placebo-controlled trial of a nitroglycerin patch to increase bone mineral density (BMD) in women with osteoporosis. The outcome is change in BMD from randomization to 12 months. Numbers of...

Consider a placebo-controlled trial of a nitroglycerin patch to increase bone mineral density (BMD) in women with osteoporosis. The outcome is change in BMD from randomization to 12 months. Numbers of patches used is available for the duration of the trial, in both groups, providing estimates of percent compliance to treatment. Clearly, percent compliance is a postrandomization variable potentially confounded by other behaviors that may be associated with changes in BMD, including smoking, exercise, and calcium supplement use. Consider how percent compliance could be used to estimate the causal effect of treatment received. How can percent compliance in the placebo group be used to remove confounding? What could invalidate this analysis?