We wish to compare a new rapid test to gold standard PCR for a disease with a population prevalence of 1-. 2 %. Samples will be tested by both methods concurrently (paired analysis). We will be testing symptomatic people (not the general population) and will want a sample size which will enable detection of approx 5-15% sensitivity difference with 80% power - if you can tell me how to do this in STATA (14) I'd be grateful.
Sensitivity and specificity are calculated on separate populations : those with and without the health state of interest. In each case, the appropriate sample size is for a single proportion. In Stata, this is power oneproportion. Your null proportion is the sensitivity/specificity of PCR, and your alternative proportion is the proportion that would represent a clinically significant difference. For example, calculation for 90% power to detect a test that's 92.5% sensitive or worse compared with PCR which is 97.5% sensitive.
. power oneproportion .975 .925, power(.9)
Performing iteration ...
Estimated sample size for a one-sample proportion test
Score z test
Ho: p = p0 versus Ha: p != p0
Study parameters:
alpha = 0.0500
power = 0.9000
delta = -0.0500
p0 = 0.9750
pa = 0.9250
Estimated sample size:
N = 166
Note that 80% power is not acceptable in real life settings. It guarantees a 20% chance of failure to detect! For real health research, 90% or 95% power is required – someone could die if you come to the wrong conclusion!
If you take a general population sample, a relatively small percentage will be true cases, so in order to get an adequate sample size for sensitivity you will have a sample that is far bigger than you need for specificity.
The solution is to sample for sensitivity separately, and to use identified cases to build up your sample quicker than you would with a general sample.
OMG! Ronán Michael Conroy(Prof) answers mine too. Thank you sir!
I am trying to account for population prevalence of the disease to calculate sample size in Stata but I did not manage. The calculations provided by Ronan are perfect but I dont find how they take into account the proposed population prevalence of 1-.2%
Dear Juan Ignacio Garcia , it seems that you are going conduct a research on a rare disease and you really want a huge sample size. Since it is a prevalence study, are you going to use a single of two population sampling?
-Sample size for risk factor and
-Sample size for prevalence.
Hence, use two population formula if your study also involves risk factors assessment.
Anyways, if I have understood you, please use a lower value of margin of error , for example, 2. So that your sample size might be higher.
Thanks!
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