Impact of tilting function choice in Scharfstein–Rotnitzky–Robins sensitivity model

Determine how alternative choices of the tilting function s(·) in the Scharfstein, Rotnitzky, and Robins (2021) semiparametric sensitivity model, which links observed and unobserved potential outcome densities, affect the resulting causal effect estimates and uncertainty intervals in analyses such as the maternal smoking on birth weight study, given the same clinical assumptions.

Background

The paper contrasts its sensitivity analysis approach with that of Scharfstein et al. (2021), which uses a sensitivity parameter γ and a user-specified tilting function s(·) to relate observed and unobserved potential outcome densities and requires common support assumptions.

The authors note that Scharfstein et al. also use clinical assumptions both to choose a valid tilting function and to bound sensitivity parameters, whereas the present paper uses such assumptions only to bound sensitivity parameters.

While the two approaches yield different conclusions in the case paper, the authors state that the effect of choosing alternative tilting functions within the Scharfstein et al. framework on the resulting analysis remains unclear.