Prognostic Scores Sample Clauses

Prognostic Scores. ^ The propensity score described in section 1.3 can be thought of as a summary of the associ- ation between treatment assignment and a collection of covariates. Similarly, the prognostic score can be thought of as a summary of the association between a potential outcome and a collection of covariates [Xxxxxx, 2008]. By conditioning on the regression of Yc on x (where Yc is the outcome under control and x is a vector of covariates), essentially identifying those covariates associated with outcome among the control group, one can achieve a type of balance like that obtained by conditioning on the propensity score. This idea has its roots in work by Xxxxxx [1941], Xxxxxx [1956], Xxxxxxx [1969], Xxxxx [1984], and Xxxxxxxxx and Greenhouse [1995] who all suggested “. . . estimating the treatment effect as the treatment group mean of yi − E(Yci|X = x) [Xxxxxx, 2008].” In other words, the observed outcome minus the predicted outcome based on parameters estimated from a regression model us- ing only the control patients. Xxxxxx [2008] defines these predictived outcome values as prognostic scores Ψ(X). Just as Xxxxxx compares achieving propensity balance to identifying the randomized ex- periment hidden in an observational study [2008], he likewise compares the application of prognostic scores to scientific experimentation: In a second experimental ideal, it is the process by which outcomes are gener- ated that is repeatable, understood, and carefully controlled, not the process of assigning units to treatment. Studies approaching this idea use experimental control in the interest of removing associations between covariates and potential outcomes, not treatment assignment. If in advance of studying a new experimen- tal manipulation, an investigator conducts tests absent the new manipulation in order to better understand accompanying conditions and their influence on the outcome, then it is this second ideal that her procedure seeks to attain. Xxxxxx states that “[p]rinciples of sufficiency and of conditional independence support a theory of prognostic balance that parallels Xxxxxxxxx and Xxxxx’x [1983a] account of propensity balance, with a few important differences [2008].” In general, if Yc⊥X|Ψ(X), XsA (1.10) for any measurable set A, then Ψ(X) is a prognostic score, and achieves ‘prognostic balance’ along the outcome measure for given X in the same sense that a propensity score achieves balance along the treatment assignment for given X. Unfortunately, this progn...