Observational Studies. Based on Rosenbaum (2002) David Madigan. Rosenbaum, P.R. (2002). Observational Studies (2 nd edition) . Springer. Introduction. A empirical study in which: Examples: smoking and heart disease vitamin C and cancer survival DES and vaginal cancer.
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Based on Rosenbaum (2002)
Rosenbaum, P.R. (2002). Observational Studies (2nd edition). Springer
“The objective is to elucidate cause-and-effect relationships in which it is not feasible to use controlled experimentation”
LESSONS: - observational studies are tricky
- randomized study is the gold standard
“An observational study is biased if treatment and control groups differ prior to treatment in ways that matter for the outcome under study”
Overt bias: a bias that can be seen in the data
Hidden bias: involves factors not in the data
Can adjust for overt bias…
treatment (assume binary 0 or 1). pj =Pr(Zj=1)
M units, j=1,…,M
An OS is free of hidden bias if the j’s are known to depend only on the ’s (i.e., )
(so two units with same x have same prob of getting the treatment)
Using a model with 29 covariates to predict VHA use, we wereable to obtain an accuracy of 88 percent (receiver-operating-characteristiccurve, 0.88) and to match 2265 (91.1 percent) of the VHA patientsto Medicare patients. Before matching, 16 of the 29 covariateshad a standardized difference larger than 10 percent, whereasafter matching, all standardized differences were less than5 percent
Conclusions VHA patients had more coexisting conditions thanMedicare patients. Nevertheless, we found no significant differencein mortality between VHA and Medicare patients, a result thatsuggests a similar quality of care for acute myocardial infarction.
for two units j and k with the samex:
between –1 and 1
so the model implies the previous inequality with
(implication goes the other way too)
rank sum test
sum of the ranks for pairs in which treated unit > control unit
and zero with prob 1-ps