How to solve (ii)? 2. [140 total points/ (medicine) Hypertension is a medical co

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How to solve (ii)?

2. [140 total points/ (medicine) Hypertension is a medical condition in which the blood pressure is chronically elevated. Persistent hypertension is one of the risk factors for strokes, heart attacks, heart failure and arterial aneurysm, was estimated that 29% of American adults were hypertensive, and a U.S. public health goal in and is a leading cause of chronic renal failure; as of 1999, it Subject | 1 23 4 5 6 78910 11 12Mean SD Before200 174 198 170 179 182 193 209 185 155 169 210185.3 17.1 After 191 170 177 167 159 151 176 183 159 145 146 177166.8 14.9 Difference9 +4 21 +3 +20 +31 +17 +26 +26 +10 +23 +33 18.6 10.1 Table 1: Before and after results for n = 12 hypertensive patients treated with Captopril. 2000 was to lower this rate to 16% by 2010 (this goal has not yet been met: the current percentage is still about 28%). Diet and exercise can go a long way to lower blood pressure, but drugs are also sometimes needed (particularly given how hard it is to get Americans to exercise and eat in a healthier way The online reference Wikipedia notes that "Captopril is an angiotensin-converting enzyme (ACE) inhibitor used for the treatment of hypertension and some types of congestive heart failure. Cap- topril was the first ACE inhibitor developed and was considered a breakthrough both because of its novel mechanism of action and also because of the revolutionary development process. The development of Captopril was among the earliest successes of the revolutionary concept of structure- based drug design. The renin-angiotensin-aldosterone system (a hormone system that helps regulate long-term blood pressure and blood volume in the body) had been extensively studied in the mid- 20th century, and it had been decided that this system presented several opportune targets in the development of novel treatments for hypertension." Captopril was developed in the mid 1970s; MacGregor et al. (1979, British Medical Journal) pub- lished the results of a clinical trial on its effects. Systolic blood pressures (in mmHg) were measured for n = 12 representatively-chosen hypertensive patients, before and after taking Captopril for a long enough time period for the drug to work. Before any data had been gathered, let (B, A,) be a pair of random variables signifying the before and after blood pressure readings for person i in the study (as i runs from 1 to n), and define D, = (B,-A) and Dn-1 -1 D,; the realized values of these random variables are given in Table 1

Explanation / Answer

The correlation between diff and before is, r = 0.5001.
So, there is a moderate positive correlation between diff and before.
This shows that the difference in blood pressure before and after treatment increases with the blood pressure of the patient before treatment.
So, the effect of drug is not constant across the 12 patients and there is a tendency for the drug to have a larger effect for people whose initial blood pressure was high than those whose initial reading was lower.

Other cases -
If the correlation between diff and before is near 0, then the the effect of drug is constant.
If the correlation between diff and before is negative, then the the effect of drug is not constant across the 12 patients and there is a tendency for the drug to have a smaller effect for people whose initial blood pressure was high than those whose initial reading was lower.

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