Evaluating the impact of treating the optimal subgroup

Abstract

Suppose we have a binary treatment used to influence an outcome. Given data from an observational or controlled study, we wish to determine whether or not there exists some subset of observed covariates in which the treatment is more effective than the standard practice of no treatment. Furthermore, we wish to quantify the improvement in population mean outcome that will be seen if this subgroup receives treatment and the rest of the population remains untreated. We show that this problem is surprisingly challenging given how often it is an (at least implicit) study objective. Blindly applying standard techniques fails to yield any apparent asymptotic results, while using existing techniques to confront the non-regularity does not necessarily help at distributions where there is no treatment effect. Here we describe an approach to estimate the impact of treating the subgroup which benefits from treatment that is valid in a nonparametric model and is able to deal with the case where there is no treatment effect. The approach is a slight modification of an approach that recently appeared in the individualized medicine literature.

Internet interventions for mental health in university students: A systematic review and meta‐analysis

“…Our finding in the subgroup analyses that effects were larger when participants were preselected through symptom cut‐offs or risk factors points at this direction. If so, we hope to develop reliable clinical decision support systems based on artificial intelligence methods (e.g., Luedtke & van der Laan, ) to help match students in need of treatment with optimal Internet interventions and to determine which students need referrals to other types of treatment.…”

Predictive approaches to heterogeneous treatment effects: a scoping review

“…A growing literature exists on estimating the effect of introducing the OTR to the entire population [56][57][58][59]. Luedtke and Van der Laan [56] provide an estimate of the optimal value-the value of the OTR-that is valid even when a subset of covariates exists for which treatment is neither beneficial nor harmful.…”

A Preliminary Precision Treatment Rule for Remission of Suicide Ideation

“…The approach we used to estimate the PTR is based on an extension of the same SL ML method that was used to balance baseline covariates. This approach begins by using SL to estimate the outcome separately in each of the two treatment arms and then generating a preliminary predicted outcome score for each patient under each of the two treatment conditions based on these results (Luedtke & van der Laan, ). A propensity‐weighted difference between the two conditional predicted outcome scores is then used as the outcome in a second SL model, where interactions between treatment and baseline covariates are estimated directly (i.e., the outcome is an estimate of the within‐patient difference in treatment response across treatment arms), avoiding the need to estimate main effects.…”

“…CAMS was estimated to be optimal if the predicted difference score was positive and E‐CAU if the predicted difference score was negative. This approach has advantages over more conventional methods of estimating a PTR, most of which require correct specification of both the (possibly nonlinear) main effects and the (possibly complex nonlinear and higher‐order) interactions to estimate the PTR, as only the interactions need to be specified correctly in the SL approach (Luedtke & van der Laan, ). This SL‐based approach also improves on other approaches that estimate interactions directly by using ensemble ML rather than relying on any single algorithm to specify interactions correctly.…”