I have been asked to provide a rather complicated sample size calculation
for a study comparing positive predictive values (PPV) of HIV testing
algorithms.
Basically plasma samples will be taken from individuals appearing at
voluntary HIV counselling and testing (VCT) sites. Each sample will be
tested using Algorithm A (test positive in 2/3 rapid diagnostic tests) and
Algorithm B (test positive in 2/2 rapid diagnostic tests and confirmed by
a 3rd test). The investigators would like to see whether the PPV for
Algorithm B is significantly higher than that for Algorithm A. HIV
prevalence in VCT populations is approximately 10%.
All algorithm A-positive samples and 10% of Algorithm A-negative samples will
be tested with Algorithm B. Sensitivity and specificity of Algorithm A will be
deduced using Western Blot (Gold Standard). The sensitivity of Algorithm A is
expected to be 100% and specificity approx. 96%. As Algorithm B is only being
tested on all Algorithm A-positives and a sample of Algorithm A-negatives, will
this introduce bias? Also the relative PPV, rather than the true PPV, for
Algorithm B will be calculated.
How should I calculate sample size and how should I analyse such a study? Or
is this study design too flawed?
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