Sample Size Estimation For Diagnostic Accuracy Studies
Haldun Akoglu, MD, Prof.
Email: drhaldun@gmail.com | Twitter: @istanbulemdoc
This spreadsheet is online supplement for the review article published on Turkish Journal of Emergency Medicine. Please cite this journal article if you are using this spreadsheet in your articles.
Akoglu, H. "Sample Size Estimation For Diagnostic Accuracy Studies". Turk J Emerg Med. 2022, 22(4):XX-XX. doi: PMID:
When to use
This formula is used to estimate the sample size when the new diagnostic test is compared with the reference standard in a cohort where the true disease status and prevalance is known.
Comments
Sens or Spec: pre-determined value ascertained by previous published data or clinician experience/judgment
Marginal error: maximum error of the estimate with a confidence level of 95%.
Prevalance: disease prevalance in the study population.
Estimated sample sizes will be different for the same sensitivity and specificity if the disease prevalance is not 50%, or when the number subjects with and without the disease are not equal.
Equation
\[n_{se} = {{{Z_{\alpha \over 2}^2} \times Se (1 - Se)} \over d^2}\] \[n_{sp} = {{{Z_{\alpha \over 2}^2} \times Sp (1 - Sp)} \over d^2}\]Adjusting for disease prevalance
\[n_{se} = n \over Prevalance \] \[n_{sp} = n \over (1 - Prevalance) \]When to use
This formula is used to estimate the sample size when the diagnostic test is compared with the reference standard in a cohort where the true disease status and prevalance is unknown.
After the using the Equations, calculated values should be adjusted according to disease prevelance.
Comments
Sens or Spec: pre-determined value ascertained by previous published data or clinician experience/judgment
Marginal error: maximum error of the estimate with a confidence level of 95%.
Prevalance: disease prevalance in the study population.
Estimated sample sizes will be different for the same sensitivity and specificity if the disease prevalance is not 50%, or when the number subjects with and without the disease are not equal.
Equation
\[n = { \left[ {Z_{\alpha \over 2} } \sqrt{{P_0(1-{P_0})}} + {Z_{\beta} \sqrt{{P_1(1-{P_1})}}} \right]^2 \over ({P_1} - {P_0})^2 }\]Adjusting for disease prevalance
\[n_{se} = n \over Prevalance \] \[n_{sp} = n \over (1 - Prevalance) \]Yates’ Continuity Correction
\[= { n \over 4 }{(1 + \sqrt{1 + 4/(n|P_1 - P_2|)} )} ^2 \]When to use
Unpaired (between-subjects) design
"Participants are randomly assigned to either the index or comparator test.
Paired (within-subjects) design
Two comparator tests are applied to all subjects along with the reference standard
Comments
One-sided N is preferred since we want to test if one of the paths are different than the other
Ψ (min) where the disagreement is minimum (P2-P1)
Ψ (max) where the agreement is by chance, or disagreement is maximum
Cont.Correction are the values where the Yates' continuity correction was applied
Equation
Unpaired
\[ n = { \left[ {Z_{\alpha} } \sqrt{2 \times {\overline{P}(1-\overline{P})}} + {Z_{\beta} \sqrt{ {P_1(1-{P_1})} + {P_2(1-{P_2})}}} \right]^2 \over ({P_1} - {P_2})^2 }\]Paired
\[ n = {{\left[Z_{\alpha}\sqrt{\psi} + Z_{\beta}\sqrt{\psi - (P_2-P_1)^2} \right]^2} \over {(P_1 - P_2)^2}} \] \[ \psi_{min} = P_2 - P_1 \] \[ \psi_{max} = P_1 \times (1 - P_2) + P_2 \times (1 - P_1) \]Yates’ Continuity Correction
\[= { n \over 4 }{(1 + \sqrt{1 + 4/(n|P_1 - P_2|)} )} ^2 \]