Sample Size/Power Calculation

Herein, we are setting a sensitivity threshold equal to p>0.8 for the bio marker. The aim is therefore to calculate a sample size (n) to have a 95% of possibility to detect a sensitivity of 0.9. The significance level is set at α=0.05

## 
##      proportion power calculation for binomial distribution (arcsine transformation) 
## 
##               h = 0.2837941
##               n = 106.3315
##       sig.level = 0.05
##           power = 0.9
##     alternative = greater

A sample size of ca. 106 patients with the disease is required to detect a sensitivity of 0.90, with power 0.90, given a significance level is 0.05.

A binomial test is used to estimate the sensitivity and the confidence interval.

## 
##  Exact binomial test
## 
## data:  sum(x) and n
## number of successes = 97, number of trials = 106, p-value < 2.2e-16
## alternative hypothesis: true probability of success is greater than 0.5
## 95 percent confidence interval:
##  0.8565164 1.0000000
## sample estimates:
## probability of success 
##              0.9150943

Sensitivity: 0.86 Confidence Interval: 0.79, 1