Amplification of Sensitivity Analysis in Matched Observational Studies

Abstract

A sensitivity analysis displays the increase in uncertainty that attends an inference when a key assumption is relaxed. In matched observational studies of treatment effects, a key assumption in some analyses is that subjects matched for observed covariates are comparable, and this assumption is relaxed by positing a relevant covariate that was not observed and not controlled by matching. What properties would such an unobserved covariate need to have to materially alter the inference about treatment effects? For ease of calculation and reporting, it is convenient that the sensitivity analysis be of low dimension, perhaps indexed by a scalar sensitivity parameter, but for interpretation in specific contexts, a higher dimensional analysis may be of greater relevance. An amplification of a sensitivity analysis is defined as a map from each point in a low dimensional sensitivity analysis to a set of points, perhaps a ‘curve,’ in a higher dimensional sensitivity analysis such that the possible inferences are the same for all points in the set. Possessing an amplification, an investigator may calculate and report the low dimensional analysis, yet have available the interpretations of the higher dimensional analysis.

Discovering Effect Modification in an Observational Study of Surgical Mortality at Hospitals with Superior Nursing

“…That is, stated technically, Γ = 1.17 amplifies to (Λ, ∆) = (2.0, 1.61); see Rosenbaum and Silber (2009). McNemar's test applied to all 23,715 pairs yields a P -value bound of 0.063 at Γ = 1.15, so this overall test is slightly more sensitive to unmeasured biases and provides no information about subgroups.…”

“…Using the method in Rosenbaum and Silber (2009), a bias of Γ = 1.5 corresponds with an unobserved covariate that increases the odds of surgery at a control hospital by a factor of 4 and increases the odds of going to the ICU by a factor of 2. Closed testing rejects no effect only in group 2 for 1.6 ≤ Γ ≤ 1.8, and cannot reject even Fisher's H 0 for Γ = 1.9.…”

Assessing Sensitivity to Unmeasured Confounding Using a Simulated Potential Confounder

“…This simplification is overly conservative and may lead researchers to be more concerned with violations of ignorability than is merited. In more recent work, Rosenbaum and Silber (2009) have extended this paradigm to decompose the G parameter into a constrained set of corresponding parameters that reflect both the association between the unobserved confounder and the treatment as well as the association between the unobserved confounder and the sign of the difference in outcomes across members of the matched pairs. This extension has the merit of allowing the researcher to consider a wider range of potential unobserved confounders.…”

Constructed Second Control Groups and Attenuation of Unmeasured Biases

“…The one parameter Γ may be interpreted or amplified into an equivalent formulation in terms of two parameters, Λ and Δ, where Λ controls the relationship between treatment assignment Z and u, Δ controls the relationship between response under control r C and u, and one sensitivity analysis at Γ is exactly equivalent to an infinite curve of sensitivity analyses with Γ = (ΛΔ + 1) / (Λ + Δ); see Rosenbaum and Silber (2009) for a precise statement using the semiparametric model introduced by Wolfe (1974). For instance, as 1.25 = (2 × 2 + 1) / (2 + 2), it follows that Γ = 1.25 is equivalent to an unobserved covariate that doubles the odds of treatment (Λ = 2) and doubles the odds of a positive treatedminus-control response difference (Δ = 2).…”

“…in the senmw function of the sensitivitymw package in R. Rosenbaum and Silber (2009) and the amplify function in the sensitivitymv package in R.…”