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Propensity Scoring and Beyond: Why? and How?. Midwest Biopharmaceutical Statistics Workshop, 2009. Notation for Variables. y = observed outcome variable(s) x = observed baseline covariate(s) t = observed treatment assignment (usually non-random) z = unobserved explanatory variable(s).

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Propensity Scoring and Beyond:


Midwest Biopharmaceutical Statistics Workshop, 2009

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Notation for Variables

y= observed outcome variable(s)

x= observed baseline covariate(s)

t= observed treatment assignment (usually non-random)

z= unobserved explanatory variable(s)

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A fundamental difficulty in observational research is that the probability of treatment assignment, t, is NOT independent of the observed baseline x-covariates. Moreover, these baseline x-covariates are often not ignorable/ancillary. They may of themselves be predictive of y-outcome.

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Propensity Score “Factoring”

Joint distribution ofxandtgivenp:

Pr( x, t | p ) = Pr( x | p ) Pr( t | p )

i.e. xandtareconditionally independent

given the

propensity for “new” treatment,

p= Pr(t= 1| x ).

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Why Go Beyond PS Methods?

  • True PS frequently UNKNOWN.

  • Estimated PS can easily fail to function the same as true PS.

  • Validating PS Estimates can be Tedious and Frustrating.

  • Alternatives are worth exploring!

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Numerical Example for this Session.

The data in the freely distributed “analytical files,” Lsim10K and Lsim5K, used in this session were simulated to be “like” that in an actual OS with only ~1K patients (Lindner Center: Kereiakes et al. Amer Heart J. 2000.)

Unfortunately, many authors and study sponsors do not recognize that sharing their data enhances the credibility of both their study and their analyzes!

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The “LSIM10K” dataset contains 10 simulated measurements on 10,325 hypothetical patients.

[1] mort6mo : Binary 6-month mortality indicator.

[2] cardcost : Cumulative 6-month cardiac related charges.

[3] trtm : Binary indicator (1 => treated, 0 => untreated).

[4] stent : Binary indicator (1 => coronary stent deployment.)

[5] height : Patient height rounded to the nearest centimeter.

[6] female : Binary sex indicator (1 => yes, 0 => male.)

[7] diabetic : Binary indicator (1 => diabetes mellitus, 0 => no.)

[8] acutemi : Binary indicator (1 => acute myocardial infarction

within the previous 7 days, 0 => no.)

[9] ejecfrac : Left ejection fraction % rounded to integer.

[10] ves1proc : Number of vessels involved in initial PCI.

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Confounding adjustment: concepts and heuristic ideas. on 10,325 hypothetical patients. Lingling Li, Harvard Medical School and Harvard Pilgrim Health Care

Confounding adjustment: ideas in action – a case study. Xiaochun Li, Div. Biostatistics, IU School of Medicine


The “Local Control” Approach. Bob Obenchain, Risk Benefit Statistics LLC


Gerhardt Pohl, Research Advisor, Lilly USA