Augmenting treatment arms with external data through propensity-score weighted power-priors with an application in expanded access 203 9♥ Sensitivity analysis: superfluous covariates In Supplementary Figure 1 in the Supplementary Material, we further examine the effect of including superfluous covariates, i.e. covariates that do not influence the outcome but do influence the allocation. We do this by setting βj = 0, for j = {1},j = {1,2},j = {1,2,3},j = {1,2,3,4}, whilst the overall effect of β remains constant (Σβj = c). We observe that the RMSE is relatively similar or merely increases slightly along with the number of ’superfluous’ covariates included in our model. Without superfluous covariates, the lowest RMSE of the ProPP is 0.02742 and attained when µE = 0. The differences are almost negligible: when one covariate is superfluous, the RMSE increases to 0.02745 (0.1%) and when three covariates are redundant, the RMSE increases to 0.02758 (0.6%). The ProPP method seems to outperform the methods of Wang across the range of our simulation set-up when including redundant covariates, which suggests that the ProPP is relatively robust to misspecification.
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