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).