Hodges-Lehmann Point Estimates of Treatment Effect in Observational Studies

Abstract

A Hodges-Lehmann point estimate of an additive treatment effect is a robust estimate derived from the randomization distribution of a rank test. This article shows how to cany out a sensitivity analysis for such an estimate in an observational study where treatments are not randomly assigned. Two cases are discussed in detail: matched pairs and the comparison of two unmatched groups. The method uses a model for the distribution of treatment assignments when hidden biases may be present. This model has previously been used for sensitivity analysis of significance levels and confidence intervals.

Do Chief Executives’ Traits Affect the Financial Performance of Risk‐trading Firms? Evidence from the UK Insurance Industry

“…We perform Rosenbaum's () bounds tests (using the rbounds module in Stata, set α to 0.95) to assess the sensitivity of differences in each performance measure between the treatment and control groups based upon the bounds for the Hodges−Lehmann (HL) point estimate of the average treatment effect (Rosenbaum, ). The HL estimate of the average treatment effect is a single point when Г is equal to 1.…”

Does team-based primary health care improve patients’ perception of outcomes? Evidence from the 2007–08 Canadian Survey of Experiences with Primary Health

“…If the outcome variable is continuous, bounds can be constructed using the distribution of Hodges-Lehmann (1963) point estimate under the null hypothesis of zero ATT at different values of e y [47,[57][58][59]. The sensitivity analysis was conducted using the STATA command "psmatch2" written by Leuven and Sianesi [47].…”

Amplification of Sensitivity Analysis in Matched Observational Studies

“…To test H τ 0 : r Tij − r Cij = τ 0 ij , ∀ ij , where τ 0 = (τ 011 ,…, τ 0 I 2 ) T is specified, apply Proposition 1 to the adjusted responses, r Cij = R ij − Z ij − τ 0 ij . This test may be inverted to obtain confidence statements and point estimates (Rosenbaum 1993), for instance for an constant effect, τ 0 = θ 0 (1,…, 1) T , or for an attributable effect summarizing nonconstant effects (Rosenbaum 2003, 2007a). …”