PAM 4380 february 14

# PAM 4380 february 14 - Outline: 2/14/2011 2.2 Empirical...

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Outline: 2/14/2011 2.2 Empirical methods Selection bias in public health research OLS versus logistic regression The ‘estrogen debacle’ Observational data in epidemiology Healthy user bias Compliance bias Recommendations Reading: Taubes article Homework #2 due Friday, 2/18

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OLS versus Logistic Regression Standard approach in health policy economics – Y i = α + ρ D i + β X i + η i – X i is a vector of control variables, i.e. observable characteristics of individual i that might be important to outcome Y i Want to estimate ρ = treatment effect – Main problem is selection bias: D i is endogenous, i.e. correlated with η i – Typically, Y i is a continuous variable, so use OLS In epidemiology, outcome is often a 0-1 indicator – Y i = 1 if dead, = 0 if alive – Y i = 1 if cancer, = 0 if no cancer Logistic regression: model the probability of the 0-1 event as the “odds ratio”
Odds Ratio If p = probability event occurs, so 1 – p = probability event doesn’t occur Odds ratio = p/ (1 – p) Example: on Titanic, of 462 female passengers: 308 survived and 154 died Probability of death = p = 154/ 462 = 0.33 Probability of survival = 1- p = 0.67 Odds ratio = 0.33/0.67 = 0.5 709 of the 851 male passengers died, so p = 0.83; odds ratio = 4.99

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Different ways to describe risks Levels: Probability of female passengers dying = 0.33 Probability of male passengers dying = 0.83 Odds ratios Odds ratio is 10 times higher for males (4.99/0.5) ≈ 10 Relative risk = risk exposed/ risk unexposed Here, “exposure” is being male Relative risk of death for males = 0.83/0.33 = 2.5 Have to remember when look at either odds ratio or relative risk, that the absolute levels of many health risks are very low Source of Titanic example: http://www.childrens- mercy.org/stats/journal/oddsratio.asp
Logistic regression Log (p/ 1-p) = α + ρ D i + β X i + η i Now ρ gives the relative odds for someone in the treatment

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## This note was uploaded on 04/28/2011 for the course PAM 4380 taught by Professor Kenkel during the Spring '08 term at Cornell University (Engineering School).

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PAM 4380 february 14 - Outline: 2/14/2011 2.2 Empirical...

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