(medicine) 140 total points) Hypertension is a medical condition in which the bl
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(medicine) 140 total points) Hypertension is a medical condition in which the blood pressure is s onically eevated. Persistent hypertension is one of the risk factors for strokes, heart attacks leart failure and arterial aneurysm, and is a leading cause of chronic renal failure: as of 1999, it was estimated that 29% of American adults were hypertensive, and a US public health goal in 2000 was to lower this rate to 16% by 2010 (this goal has not yet been met) Det 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. Capto- pril 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 de- velopment of Captopril was among the earliest successes of the revolutionary concept of structu based drug design. The renin-angiotensin-aldosterone system (a hormone system that helps regu- late long-term blood pressure and blood volume in the body) had been extensively stud mid-20th century, and it had been decided that this system presented several oppor in the development of novel treatments for hypertension. tune targets 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 m for n = 12 representatively chosen hypertensive patients before and after taking Captopril for a long enough time period for the drug to work; the results are given in Table 1. (Note: I've used a bit of different notation below than what we used in class; this is to give you practice in the skill of reading statistical discussions in sources other than the classes and textbooks in which you originally learned the concepts.) mHg) were measured Subject A B C D E F G H I J K L?Mean SD Before 200 174 198 170 179 182 193 209 185 155 169 210 185.3 17.1 After 191 170 177 167 159 151 176 183 159 145 146 177 166.8 14.9 Difference +9 +4 +21 +3 +20+31 +17+26 +26 +10 +23 +33 18.6 101 Table 1: Before and after results for 12 hypertensive patients treated with Captopril. (a) Estimate the average effect A of Captopril in the population to which you believe it's ap- propriate to generalize here, and explicitly identify that population. Is this estimated effect large in clinical terms? Attach a standard error to your estimated effect, and construct a 95% confidence interval for ?. Is the estimated effect statistically significant? What do youExplanation / Answer
Sol:
(a)
The average effect (reduction in Systolic blood pressure) of Captopril is 18.6 mmHg
The population is American hypertensive adults.
The estimated effect of 18.6 mmHg is large in clinical terms.
The standard deviation of difference is 10.1
Standard error of the mean difference = 10.1 / sqrt(12) = 2.9156
Degree of freedom = n-1 = 12 - 1 = 11
Critical value of t at 95% confidence level and df = 11 is 2.2
95% confidence interval is,
(18.6 - 2.2 * 2.9156, 18.6 + 2.2 * 2.9156)
(12.18568, 25.01432)
As, 95% confidence interval does not contains 0, the estimated effect is statistically significant.
As, the estimated effect is statistically significant, Captopril is useful in treating hypertension with mean effect of 18.6 mmHg and between 12.18568 and 25.01432) with 95% confidence.
(b)
(i)
Variance(diff) = Variance(After - Before) = Variance(After) + Variance(Before) - 2 Covariance(Before, After)
As, before and after Systolic blood pressure have high positive correlation, Covariance(Before, After) is high.
High Covariance(Before, After) leads to low Variance(diff) and consequently low SD of the differences.
It is difficult to find homogeneous hypertensive patients in all respects and hence completely randomized design is less accurate than the paired design given in the problem where the same subjects were involved in before and after treatments.
(ii)
The diff is positive correlated with before. This means as Systolic blood pressure before treatment increases, the difference of before and after increases.
So, there seems to have a larger effect for people with high initial blood pressure than low initial blood pressure.
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