# True or False? A clinical trial is conducted to compare an experimental medication to placebo to reduce the symptoms of asthma. Two hundred participants were recruited into the study and randomized to receive an experimental drug or a placebo. The primary outcome is a reduction in self-reported symptoms. Among 50 participants who receive the experimental medication, 30 report a reduction of symptoms as compared to 15 participants of 50 assigned to the placebo. The 95% CI for the relative risk of participants reporting a reduction of symptoms between the experimental and placebo groups is between 1.529 and 8.012.

Question
Confidence intervals
True or False? A clinical trial is conducted to compare an experimental medication to placebo to reduce the symptoms of asthma. Two hundred participants were recruited into the study and randomized to receive an experimental drug or a placebo. The primary outcome is a reduction in self-reported symptoms. Among 50 participants who receive the experimental medication, 30 report a reduction of symptoms as compared to 15 participants of 50 assigned to the placebo. The $$95\%$$ CI for the relative risk of participants reporting a reduction of symptoms between the experimental and placebo groups is between 1.529 and 8.012.

2021-02-01
Step 1
Medication:
Reduction $$\displaystyle={30},\text{no reduction}={20},\text{total}={50}$$
Placebo:
Reduction $$\displaystyle={15},\text{no reduction}={35},\text{total}={50}$$
RR: Relative Risk $$\displaystyle=\frac{{\frac{30}{{50}}}}{{\frac{15}{{50}}}}={2}$$ (Assuming the reduction of of symptoms as incidence in each of the medication and placebo groups)
Step 2
The $$95\%$$ confidence interval for ln(RR) is given by :
ln $$\displaystyle{\left({2}\right)}\pm{1.96}{\left(\sqrt{{{\left[{\left(\frac{{\frac{20}{{30}}}}{{50}}\right)}+{\left(\frac{{\frac{35}{{15}}}}{{50}}\right)}\right]}}}\right)}$$
$$\displaystyle= \ln{{\left({2}\right)}}\pm{0.48}$$
$$\displaystyle={0.693}\pm{0.480}$$
$$\displaystyle={\left({0.693}-{0.480},{0.693}+{0.480}\right)}$$
$$\displaystyle={\left({0.213},{1.173}\right)}$$
Thus, the confidence interval for RR is antilog of the above values $$\displaystyle={\left({1.237},{3.232}\right)}$$
Hence the statement mentioned is false as the values don't match

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