As you have phrased your problem, the scalar valued X-variable is "a" propensity-like-score. But why estimate propensity when you can simply
observe it by forming (many) patient subgroups ...each indexed by its range of X-values? Within each subgroup, you can estimate the "local" ATE for (HIV+) minus (HIV-) on any outcome of interest (Y1, Y2, ...) as well as the "local" observed fraction of HIV+ patients. The resulting
distribution of effect-size estimates across subgroups will be of great interest in itself. This is part of the analysis strategy known as
Local Control in which all causal credit for differences in outcome is
initially assigned to HIV status (treatment.) However, in the final phase of LC analysis, you should be able to use SEM to partially "give back" causal credit to X as a mediator. For details and references see
http:/localcontrolstatistics.org------------------------------
Robert L. (Bob) Obenchain
Principal Consultant
------------------------------
Original Message:
Sent: 08-19-2017 08:51
From: Abdus Sattar
Subject: Does SEM remove selection bias in the observational studies?
Hello,
I am working on a cross-sectional two-group observational study (not RCT): HIV+ subjects and HIV- healthy controls. No intervention or treatment in this study. For estimating the effects of HIV status (+ve vs. –ve) on a single outcome or response variable Y1, I am using propensity score matching (PSM) method. I have a continuous covariate or explanatory variable X in the study. Given the HIV status, I am interested in estimating the effect of X on Y1, effect of X and Y1 on Y2, effect of X, Y1, and Y2 on Y3. For this series of effects measure or path analysis, I am hoping to use SEM (structural equation modeling). Is there any way SEM can remove selection bias due to the HIV status (binary variable)? Any peer reviewed article and/or software for the implementation? Note that the Y1, Y2, and Y3 are continuous variables. Further note, I am NOT looking for mediation effect in this analysis (although will be looking into this later). Thanks in advance for any references and helpful information.
Best regards,
Abdus Sattar, Ph.D
Tel. 1.216.368.1501
Email:sattar@case.edu
http://sattar.case.edu