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1、Propensity Score MethodsSession I: Introduction and overview of the problemSession II: Allowing for observed confoundersUse of propensity scoresSession III: Allowing for unobserved confoundersInstrumental variable modelsMendelian randomisationSession IV: Principal stratificationSession 2: OutlineA q
2、uick look at the chocolate and depression data again.Use of propensity scores through- matching- stratification- regression- the use of inverse probability of treatment weights- Introduction to the pscore and atts commands. Illustration using LaLondes earnings data.Typical Questions - 7Are occupatio
3、nal differences in coronary heart disease the result of differences in diet?How do we allow for potential confounding or selection effects?How do we allow for the measurement errors in our dietary assessments?Typical Questions - 8We have carried out a questionnaire survey of drinking habits in a gro
4、up of hypertensive men. As well as giving us information on their current alcohol consumption, the men are asked to tell us whether they have, in the past, ever received advice from their doctor to cut down or quit drinking. Does advice from a doctor have an effect on drinking? What is the effect of
5、 the advice on the amount consumed?Treatment Assignment MechanismsIf we have measurements on covariates, X, treatment assignment is said to be ignorable if (Y(0),Y(1) D | X where “” means “statistically independent of”. In words, treatment assignment (receipt) is ignorable if the two potential outco
6、mes are jointly independent of D given X.If we allow for the covariates, X, in an appropriate way then we can obtain unbiased (unconfounded) estimates of the treatment effects.Alternative descriptions: “Ignorable treatment assignment”,“Selection on observables” and “Exogeneity” If a treatment assign
7、ment is not ignorable then it is confounded. treatment is said to be endogenous.A Hypothetical Observational StudyA simple hypothetical example with no unmeasured confounders:Depression (outcome) and Chocolate Consumption (treatment orexposure) (Dunn and Everitt, 1995) The marginal two-way table:Dep
8、ressed Not DepressedYes 65 500Chocolate EaterNo 25 650There is an association between the two.But the subjects sex is a measured confounder.The Path Diagram (DAG) Women are more likely to eat chocolate Women are more likely to be depressed Does chocolate eating lead to depression?ChocolateEater Depr
9、essionSex?Assumption: No hidden confoundersConditional on the sex of the respondentMen:Depressed Not DepressedYes 5 200Chocolate EaterNo 15 600Odds-ratio: 1.00Women:Depressed Not DepressedYes 60 300Chocolate EaterNo 10 50Odds-ratio: 1.00Mantel-Haenszel estimate of an odds-ratioEstimate the odds-rati
10、o for each stratum.Estimate the variance of the natural logarithm of the stratum-specific odds-ratios.Calculate a weighted average of the stratum-specific odds-ratios, using weights that are inversely proportional to the above variance estimates.Calculate standard errors, test statistics and confide
11、nce following standard methods.The Propensity Score(assuming ignorable treatment assignment)With a binary treatment assignment, the propensity score is the Probability of receiving treatment given the covariates, X, that isPr(D = 1 | X).Treatment effects are only identifiable for a given subject if
12、there is the possibility that he or she could receive either treatment allocation. That is 0 chi2 = 1.0000Test that combined OR = 1:Mantel-Haenszel chi2(1) = 0.00Prchi2 = 1.0000Logistic regression modelsUncorrected: logistic dep choc-dep | Odds Ratio Std. Err. z P|z| 95% Conf. Interval-+-choc | 3.38
13、 .8204638 5.02 0.000 2.100368 5.439237-Conditioning on sex: logistic dep choc sex-dep | Odds Ratio Std. Err. z P|z| 95% Conf. Interval-+-choc | 1 .3042707 -0.00 1.000 .5508132 1.815498sex | 7.999999 2.561501 6.49 0.000 4.271159 14.98422-Conditioning on propensity score: logistic dep choc ps-dep | Odds Ratio Std. Err. z P|z| 95% Conf. Interval-+-choc | 1 .3042707 0.00 1.000 .5508132 1.815498ps | 30.72149 16.20153 6.49 0.000 10.92813 86.36518-Using IPTW Marginal ModelMarginal model (i.e. ignoring sex) with probability weights:l
