Use a logistic regression to model the odds of death with

Question

An example of Simpson's paradox. Here is an example of Simpson's paradox, the reversal of the direction of a comparison or an association when data from several groups are combined to form a single group. The data concern two hospitals, A and B, and whether or not patients undergoing surgery died or survived. Here are the data for all patients:

	Hospital A	Hospital B
Died	63	16
Survived	2037	784
Total	2100	800

And here are the more detailed data where the patients are categorized as being in good condition or poor condition before having the surgery

Good condition
	Hospital A	Hospital B
Died	6	8
Survived	594	592
Total	600	600

Poor condition
	Hospital A	Hospital B
Died	57	8
Survived	1443	192
Total	1500	200

(a) Use a logistic regression to model the odds of death with hospital as the explanatory variable. Summarize the results of your analysis and give a 95% confidence interval for the odds ratio of Hospital A relative to Hospital B.

(b) Rerun your analysis in part (a) using hospital and the condition of the patient as explanatory variables. Summarize the results of your analysis and give a 95% confidence interval for the odds ratio of Hospital A relative to Hospital B.

(c) Explain Simpson's paradox in terms of your results in parts (a) and (b).