Introduction: The double-blinded randomised control trial (RCT) has been developed in order to provide gold standard estimation of causal effects. However, in many circumstances it is impossible to design studies that meet this standard of blinding and hence this potentially introduces a placebo effect. One example of a study where it was impossible to blind the participants was the Heating Housing and Health Study (HHHS); the intervention was the installation of modern, efficient heaters in the participants’ homes. The statistical models used explicitly assume there is no placebo effect.
Method: In order to clarify the meaning of the placebo effect, we defined the contrast between the placebo effects from assignment to the treatment group and the placebo effects of assignment to the control group as the Assignment Effect. Using this definition we developed three approaches, which allow the explicit assumption of such an assignment effect.
Using the HHHS as a worked example, we explored three different approaches;
Dummy outcome variables, where the intervention is assumed to have no effect, but we assume that these variables have similar assignment effects. The observed changes in such variables are estimates of the assignment effect.
Secondly, we attempt to directly measure the susceptibility to this assignment effect by the use of proxy variables of assignment susceptibility.
Intermediate Variables. We measure the assignment effect by looking at the effects that are unexplained by changes in the intermediate variables. (In the HHHS example the direct effect of the intervention should be largely due to a rise in temperature, hence we estimate the assignment effect by health effects unexplained by temperature)
Results: We explore, through both simulated and real data, the implications of these approaches and then give recommendations on what is needed in order to use models with an assumption of an assignment effect. Combining these approaches in a Bayesian framework, we have calculated estimates of the assignment effect and updated the intervention effects in the HHHS. While the assignment effect itself was not significant with an OR (Odds Ratio) of 0.86 (0.63 to 1.20), there was little change in the size of the intervention effect for Dry Cough at night from OR= 0.50 (0.32 to 0.79) to OR= 0.53 (0.28 to 0.98), but a large reduction in the effect of the intervention on self-reported poor health from 0.46 (0.30 to 0.71) to 0.70 (0.30 to 1.63).
Conclusion: We recommend that analyses of single-blinded RCTs include a sensitivity analysis that assumes an assignment effect. We show how, with carefully chosen assumptions, it is possible to use data already collected, and a Bayesian modelling approach, to give informative estimates of the likely size of the assignment effect and hence provide a better estimate of the true effect of the intervention in participant unblinded RCTs.
