Aim: To Calculate Sample Size to estimate Sensitivity and Specificity of a diagnostic test with specified precision
Formula Used for absolute precision
If precision for sensitivity is relative, then εSn^2 is to be replaced by to Sn * εSn^2
If precision for specificity is relative, then εSp^2 is to be replaced by to Sp * εSp^2
Larger of N1 and N2 is the required sample size in your setting.
Sn= Expected Sensitivity of the test
Z 1-αSn/2 = the standard normal deviate corresponding the confidence level for Sensitivity
εSn = Absolute Precision for Sensitivity. (< 1) (e.g. 10% = 0.1)
Prv = Prevalence in the given setting
Sp = Expected Specificity of the test
Z 1-αSp/2 = the standard normal deviate corresponding the confidence level for Specificity
εSp = Absolute Precision for Specificity (< 1) (e.g. 10% = 0.1)
Example:
You want to estimate Sensitivity and Specificity of a new diagnostic test, with an absolute precision of 5% and 10% respectively and confidence level of 95% for both. The prevalence of the condition to be tested is 20% in your setting. Pilot study has shown that the Sensitivity and Specificity of the test is approximately 80% and 85% respectively. How much sample size is required?
Solution:
Here
Sn = 80%, Sp=90%, εSn= 5%, εSp=10%, Prv = 20%, CL for Sn = 95%, CL for Sp = 95%
After putting these values, we get required sample size = 1230.
With this sample size, there will be approximately 246 persons with the condition (20% Prevalence) and 984 persons without the condition.
What are expected results, with given sample size, sensitivity, secificity and prevalence? (Though practically impossible, fraction are kept unchanged to maintain proportions.)
|
Gold Standard |
Total |
| Diseased |
Not Diseased |
| Test under evaluation |
Positive |
196.8 |
147.6 |
344.4 |
| Negative |
49.2 |
836.4 |
885.6 |
| Total |
246 |
984 |
1230 |
SE for Sensitivity = SQRT (0.8 * 0.2 / 246) = 0.025
95 % CI for Sensitivity = 0.8 ± 1.96* 0.025 = 0.75 – 0.85 (With allowable error of 5%)
SE for Specificity = SQRT (0.85 * 0.15 / 984) = 0.011
95 % CI for Specificity = 0.85 ± 1.96 * 0.011 = 0.83 – 0.87 (With absolute error of < 10 % : Higher precision)
Please note that, our sample size has yielded more absolute precision for Specificity than intended. With allowable absolute error of 10%, our intended CI was 0.75 - 0.85. Actually our CI for specificity is much narrower than the intended. This has happened because we have to have at least 246 diseased persons in the study to get intended precision of Sensitivity. Then, considering the prevalence of 20%, we have to include more non-diseased person, resulting in increased precision in Specificity.
@ Sachin Mumbare