Statistical Discrimination in Health Care 

 This blog has frequently written about testing for discrimination (see for example  here ,  here , and  here ).  This is also a hot issue in health care.  In health care there is a case for 'rational' discrimination' where physicians respond to clinical uncertainty by relying on priors about the prevalence of diseases across racial groups (for example).   

 A  paper by Balsa, McGuire and Meredith  in 2005 lays out a very nice application of Bayes Rule to look into this question.  The Institute of Medicine suggests that there are three types of discrimination: simple prejudice, stereotyping, and statistical discrimination where docs use probability theory to overcome uncertainty.  The latter occurs when the uncertainty of a patients condition leads the physician to treat her differently from similar people of different race.   


 The paper uses Bayes Rule to conceptualize the decision a doctor has to make when hearing symptom reports from a patient and has to decide whether the patient really has the disease: 

 Pr(Disease | Symptom) = Pr(Symptom | Disease) * Pr(Disease) / Pr(Symptom) 

 A doc would decide differently if she believed that disease prevalence differs across racial groups (which affects Pr(Disease)), or if diagnostic signals are more noisy from some groups (which changes Pr(symptom)), maybe because the quality of doctor-patient communication differs across races. 

 The authors test their model on diagnosis data from family physicians and internists, and find that sensible priors about disease prevalance could explain racial differences in the diagnosis of hypertension and diabetes.  For the diagnosis of depression there is evidence that differences in doctors' decisions may be driven by different communication patterns between white docs and their white vs. minority patients. 

 Obviously prejudice and stereotyping are different from statistical discriminiation, and have quite different policy implicatons.  This is a really nice paper that makes these distinctions clear as well as nicely using Bayes Rule to conceptualize the issues.  The general idea might also apply to other issues of policy including police stop and search.