2) A clinical trial is run of hypertension (high blood pressure) are recruited t

Question

2) A clinical trial is run of hypertension (high blood pressure) are recruited to participate in the t receive either the new drug or placebo. Participants take the assigned drug for 12 blood pressure hypertension or not. The data are shown here: to look at the efficacy of a new blood pressure drug. Patients with a diagnosis weeks and their status is recorded. At the end of the trial, participants are classified as still having Number with Hypertension at Number Free of Hypertension at 12 Group Placebo New Drug 12 weeks Weeks 36 14 a) What was the prevalence of hypertension at the start of the trial? b) What was the prevalence of hypertension at the end of the trial? c) What was the incidence of recovery over the course of the trial? d) Compute the relative risk of hypertension, comparing the new drug and the placebo. e) Based on the results above, what can you conclude about the efficacy of the new drug?

Explanation / Answer

Preparatory work

The question says that all the participants were patients with a diagnosis of hypertension….. (1)

Part (a)

By (1) above, prevalence of hypertension at the start of the trial = 100% ANSWER

Part (b)

Out of 100 participants as at the start of the trial, 20 (6 under placebo and 14 under new drug) were found to be free from hypertension. So, the prevalence of hypertension at the end of the trial = 100 – 20 = 80% ANSWER

Part (c)

The answers to above two parts imply that the incidence of recovery during the course of the trial = 20% ANSWER

Part (d)

Out of 50 who were administered placebo, 44 were found to be with hypertension at 12 weeks of trial. This implies that the risk of hypertension for ‘placebo’ group is 88% ANSWER 1

Out of 50 who were administered the new drug, only 36 were found to be with hypertension at 12 weeks of trial. This implies that the risk of hypertension for ‘new drug’ group is only 72% ANSWER 1

Part (e)

In this part, we will statistically test if the above difference in risk suggest the new drug is effective.

Let X = Number of ‘placebo’ participants who were free of hypertension after the trial

and Y = Number of ‘new drug’ participants who were free of hypertension after the trial

Then, X ~ B(n1, p1), and Y ~ B(n2, p2) where n1 and n2 are sample sizes and p1 = probability that a ‘placebo’ participant is free of hypertension after the trial and p2 = probability that a ‘new drug’ participant is free of hypertension after the trial, which are also equal to the respective proportions in the population.

Claim :

New drug is effective in freeing participants of hypertension. i.e., p1 < p2

Hypotheses:

Null H0 : p1 = p2   Vs HA : p1 < p2

Test Statistic:

Z = (p2cap – p1cap)/[pcap(1 - pcap){(1/n1) + (1/n2)} where p1cap and p2cap are sample proportions, n1, n2 are sample sizes and pcap = {(n1 x p1cap) + (n2 x p2cap)}/(n1 + n2).

Calculations:

Given, n1 = n2 = 50, X= 6. Y = 14, p2cap = 14/50 = 0.28, p1cap = 6/50 = 0.12 and

Pcap = (14 + 6)/(50 + 50) = 0.2.

Z= 0.16/(0.2 x 0.8 x 0.04)

= 0.16/0.08

= 2

Distribution, Critical Value and p-value:

Under H0, distribution of Z can be approximated by Standard Normal Distribution

So, given a level of significance of %, Critical Value = upper % of N(0, 1), and

p-value = P(Z > Zcal)

Using Excel Functions of N(0, 1), for % = 5% (assumed since it is most popular level of significance), Critical Value = 1.645 and p-value = P(Z > 2) = 0.0228.

Decision Criterion (Rejection Region):

Reject H0, if Zcal > Zcrit or if p-value < .

Decision:

Since Zcal (2) > Zcrit (1.645), H0 is rejected. This is also confirmed by the p-value of 0.0228 being less than 0.05.

Conclusion

There is sufficient evidence to suggest that the claim that the new drug is effective in freeing patients of hypertension is valid.

DONE

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