In a comparative doubleblind randomized study of single dose

In a comparative double-blind randomized study of single dose fosfomycin trometamol with trimethoprim in the treatment of uncomplicated urinary infections, 26 of 34 were cured with fosfomycin trometamol and 19 of 37 were cured with the reference drug trimethoprim. Denote the eradication rates for fosfomycin trometamol and the reference drug trimethoprim by p1 and P2 respectively. (a) Evaluate the test statistic (b) Use the R function pnorm() and the value of the test statistic from (a) to find the p-value for the test H0 : p = P2 versus HA: p1 is not equal to p2. (c) Calculate a 94% two-sided confidence interval for the difference p1 - p2 using the formula and the critical value z* = 1.8808. The interval ranges from to . (d) Find the p-value for the test H0 : p1 = p2 versus HA : p1 is not equal to p2 using the R function prop.test(). (e) Are the eradication rates for the two drugs significantly different? Use the result of (d) and significance level a = 0.06 to answer this question. (f) Calculate a 94% two-sided confidence interval for the difference p1 - p2 using the R function prop. Test(). The interval ranges from to

Solution

a) estimates of p1 = 0.765 , p2 = 0.514 and p = 0.6338

Test statistics = (0.765 - 0.514) / 0.11445 = 0.248/ 0.11445 = 2.1668

b) using pnorm() function we get value 0.9848749 but normal reads from left to write so we 1 - 0.9848749 = 0.015

And as we perform two tailed so p-value = 2 * 0.015 = 0.03

c) 94% CI for the difference p1 - p2 is ((0.765 - 0.514) - (1.8808 * 0.1097) , (0.765 - 0.514) + (1.8808 * 0.1097))

= (0.0446 , 0.457)

d) Ouptput using prop.test is

        2-sample test for equality of proportions with continuity correction

data: c(26, 19) out of c(34, 37)
X-squared = 3.7954, df = 1, p-value = 0.05139
alternative hypothesis: two.sided
95 percent confidence interval:
0.007877275 0.494507462
sample estimates:
   prop 1    prop 2
0.7647059 0.5135135

e) since p-value = 0.05139 < 0.06 we will reject the null hypothesis and conclude that eradication rates for the two drugs differs significantly.

f) 94% CI using prop.test is (0.01656581 ,0.48581893)

p-value =