# Clinical Trials

## 7. Statistics

Let us assume that four randomized, double-blind, placebo-controlled trials are conducted to establish the efficacy of two weight-loss drugs (A and B) against placebo, with all subjects, whether on a drug or placebo, receiving similar instructions as to diet, exercise, behavior modification, and other lifestyle changes. The primary endpoint is the weight change (kg) at 2 months from baseline.

The difference in the mean weight change between an active drug and placebo groups can be considered as weight reduction for the active drug against placebo. Table 2 presents the results of hypothesis tests and CIs for the four hypothetical trials. The null hypothesis for each trial is that there is no difference between the active drug treatment and placebo in mean weight change.
In trial 1 of drug A, the reduction of drug A over placebo was 6 kg with only 40 subjects in each group. The P-value of 0.074 suggests that there is no evidence against the null hypothesis of no effect of drug A at the 5% significance level. The 95% CI shows that the results of the trial are consistent with a difference ranging from a large reduction of 12.6 kg in favor of drug A to a reduction of 0.6 kg in favor of placebo.

### Table 2

Point estimate and 95% confidence interval (CI) for the difference in mean weight change from baseline between the active drug and placebo groups in four hypothetical trials of two weight reduction drugs.

Click on the table preview below to see the full table:

D Wang & A Bakhai, (Ed.s). (2006) Clinical Trials: A practical guide to design, analysis and reporting. London: Remedica.

The results for trial 2 among 400 patients, again for drug A, suggest that mean weight was again reduced by 6 kg. This trial was much larger, and the P-value (P < 0.001) shows strong evidence against the null hypothesis of no drug effect. The 95% CI suggests that the effect of drug A is a greater reduction in mean weight over placebo of between 3.9 and 8.1 kg. Because this trial was large, the 95% CI was narrow and the treatment effect was therefore measured more precisely.
In trial 3, for drug B, the reduction in weight was 4 kg. Since the P-value was 0.233, there was no evidence against the null hypothesis that drug B has no statistically significant benefit effect over placebo. Again this was a small trial with a wide 95% CI, ranging from a reduction of 10.6 kg to an increase of 2.6 kg for the drug B against the placebo.

The fourth trial on drug B was a large trial in which a relatively small, 2-kg reduction in mean weight was observed in the active treatment group compared with the placebo group. The P-value (0.008) suggests that there is strong evidence against the null hypothesis of no drug effect. However, the 95% CI shows that the reduction is as little as 0.5 kg and as high as 3.5 kg. Even though this is convincing statistically, any recommendation for its use should consider the small reduction achieved alongside other benefits, disadvantages, and cost of this treatment.

### Table 2

 Point estimate and 95% confidence interval (CI) for the difference in mean weight change from baseline between the active drug and placebo groups in four hypothetical trials of two weight reduction drugs.
 Trial Drug No. of patients per group Difference in mean weight change from baseline (kg) between the active drug and placebo groups Standard deviation of difference Standard error of difference 95% CI for difference P-value 1 A 40 -6 15 3.4 -12.6 0.6 0.074 2 A 400 -6 15 1.1 -8.1 -3.9 0.001 3 B 40 -4 15 3.4 -10.6 2.6 0.233 4 B 800 -2 15 0.8 -3.5 -0.5 0.008