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Abstract:
Three studies of causal inference are presented here. In the first, established statistical methods for drawing causal inferences from observational studies are adapted to estimate psychotherapeutic efficacy from data obtained in psychotherapy outcome studies (POSs). Efficacy is concerned with the outcomes that obtain when the full intended treatment dose is jointly selected by patient and therapist, who instead may respectively drop out of treatment or deviate from the treatment protocol. We argue that the scientifically most interesting definition of efficacy differs from the definition implicitly used by psychotherapy researchers, and show that, under reasonable assumptions, standard statistical methods for analyzing POSs yield optimistically-biased estimates of efficacy as we define it. We show that, under suitable conditions, standard causal inference methods can be readily adapted to give consistent estimates of efficacy from multilevel (patients clustered within therapists) POS data. We assess these methods via simulation studies based on the National Institute of Mental Health Treatment of Depression Collaborative Research Program (TDCRP; Elkin et al., 1989), and reanalyze the TDCRP with these methods. The second study compares different approaches for combining instrumental variable (IV) and biased estimators of causal parameters in order to improve small-sample performance. IV estimation is a standard technique in econometrics, and in recent years has been adapted for the estimation of causal parameters. While these estimators are consistent, they often have large variances, and we examine whether suitably-chosen linear combinations of IV estimators and estimators that are biased but have small variances exhibit smaller mean squared errors than the IV estimators. Via simulation studies, we compare approaches to creating such linear combinations inspired by Greenland (1991) to another approach that uses a new method of crossvalidation, estimating function based cross-validation (EFCV; van der Laan & Rubin, 2005). The third study compares two methods of cross-validation for selecting regression models for use in G-computation, an established method for making causal inferences from observational data. The two methods, EFCV and the Cross-Validated Delete/Substitute/Add Algorithm (CVDSA; Sinisi & van der Laan, 2004), are compared via simulation studies.
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