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The effect of misclassification on sample size: one-sample proportion test
  • PharmD Péter Hársfalvi,
  • Jenő Reiczigel
PharmD Péter Hársfalvi
University of Veterinary Medicine Budapest

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Jenő Reiczigel
University of Veterinary Medicine Budapest
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Abstract

Potential misclassification of a binary outcome measure is often ignored in study design, causing considerable loss of power, and threatening the quality of research. Although there exist studies taking misclassification into account in data analysis, we argue that it should be accounted for already in sample size calculation. We illustrate this by comparing sample sizes needed with and without misclassification in case of the binomial test. Our sample size procedure, implemented as an R function, calculates exact power, and accounts for non-monotonicity of power as a function of sample size, and for potential drop-out or lack of data in the study. The necessary sample size is computed from the null proportion p 0, the assumed true proportion pa, and the probabilities of correct classification, sensitivity ( Se) and specificity ( Sp). Our results show that misclassification may drastically affect the necessary sample size. For p 0<0.5, the effect of specificity is stronger than that of sensitivity, whereas for p 0>.5 it is the other way round. Effects are strongest when p 0 is near 0 or 1, especially for one-sided tests with pa located farther from 0.5 than the null value p 0. For example, even with Se = Sp = 99%, p 0 = 0.01, and left-sided alternative, sample size is more than fourfold of that without misclassification (3-fold if p 0=0.02; 1.4-fold if p 0=0.05).