A puzzle for the intellectually curious

Novel Drug A for treating hypertension was just released on the market after a well-publicized clinical trial showed it to be superior to Standard Drug B in lowering systolic blood pressure. Specifically, the study showed that a larger percentage of patients (65%) had a greater than 10 point drop in systolic blood pressure after just 1 month compared with patients on Drug B (50%). The results are summarized in the Table below:

Table 1. Results show that Drug A superior to Drug B

 

Drug A

Drug B

Total

Achieved > 10 mmHg drop in SBP

65

50

115

Failed to achieve drop

35

50

85

 

100

100

200

Chi-squared test: p = 0.03.

The chief investigator saw his first hypertensive patient (a woman) just days after the study results were announced. He remembered that women responded differently to hypertensive medication, so he asked his research assistant to confirm that women had a better response under Drug A. The research assistant did the subset analysis (chi-squared test using only women) and reported that women had better outcomes on Drug B.

"Interesting, " thought the chief investigator. "I guess this is really a man's drug."

So when his next patient came (a man), he immediately prescribed Drug A. But after the patient left, he asked his research assistant to send him the subset analysis for male patients. The researcher came back with the report: men had better outcomes also on Drug B!

"Impossible!" explained the chief investigator. But is he right? Can you construct  two 2x2 tables, one for males (n=100) and one for females (n=100)  that:

  1. add up to the numbers in Table 1 (n=200), and
  2. show that both males and females have significantly better outcomes under Drug B?

Blank tables are provided below.

Males only

 

Drug A

Drug B

Total

Achieved > 10 mmHg drop in SBP

 

 

 

Failed to achieve drop

 

 

 

 

 

 

100

 

+

Females only

 

Drug A

Drug B

Total

Achieved > 10 mmHg drop in SBP

 

 

 

Failed to achieve drop

 

 

 

 

 

 

100

= Table 1?