Sample Size Considerations for Diagnostic Tests

Abstract

Innovations in diagnostic techniques are increasing worldwide. Sensitivity and specificity are used to measure the accuracy of new dichotomous outcome diagnostic tests in the presence of an existing gold standard. The first question to be dealt is what number of subjects is sufficient to attain adequate power in the case of hypothesis testing. This chapter explains sample size issues for estimating the sensitivity and specificity and compares sensitivity and specificity under different goals for two commonly used study designs, case–control and prospective designs in paired and unpaired subjects. The chapter also explains and compares the three methods to control uncertainty under the prospective design.

Appendix: How to Use the Goal Seek Command Available in the What if Analysis Tool in the Data Menu for Solving Equations Using MS Excel 2007

To solve the equation:

• 1. Open an Excel spreadsheet and write the value for case–control sample size obtained (cell B1)

• 2. Write the value of the sample size obtained using the naive approach in cell B2

• 3. Write the anticipated prevalence of disease in cell B3

• 4. Calculate the value of the standard normal distribution using the function NORMSINV for the desired probability; for example, the upper tail for probability 0.95 under the standard normal distribution is −1.645

• 5. Put the equation $\frac{{B1-B3\times B2}}{{\sqrt{{B3\times (1-B3)\times B2}}}}$ in cell B5

From the Excel menu bar, click Data, locate the Data tool panel and then What if analysis item; from What if analysis select Goal Seek. The Goal Seek dialogue box appears

• 1. Set cell: insert B5 (the equation as described above)

• 2. To value: write the value of the standard normal of the preselected probability using the NORMSINV function

• 3. By changing cell: insert B2

Goal Seek changes the value of cell B2 until the desired solution of the equation is obtained, i.e. −1.64485. The final value of n appears in cell B2.

How to Use the Goal Seek Command to Solve the Exact Binomial Using MS Excel 2007

• 1. Open an Excel spreadsheet and write the value of the sample size obtained using the naive approach in cell B1 (to avoid convergence problem)

• 2. Write the value for the case–control sample size obtained (cell B2)

• 3. Write the anticipated prevalence of disease in cell B3

• 4. Write the function = 1 – BINOMDIST (x, n, prev, 1) where x is number of successes, n = sample size, Prev is the probability, 1 is the cumulative probability

From the Excel menu bar, click Data, locate the Data tool panel and then the What if analysis item; from what if analysis, select Goal Seek. The Goal Seek dialogue box appears

• 1. Set cell: insert B4, the expression as described above

• 2. To value: insert the value of the preselected probability = 0.95

• 3. By changing cell: insert B1

Goal Seek changes the value of cell B1 until 1 – BINOMSDIT is 0.95 and the final value of n appears in cell B1. Sometimes you may not find the exact solution; the user may try other adjacent values of sample size based on the naive approach.

Table 7.3 Number of subjects with disease (or without disease) for estimation of the expected sensitivity (or specificity) ranging from 0.50 to 0.99

Table 7.4 Study sample size for estimating the sensitivity in prospective design using the naive method, normal approximation, and exact binomial

Table 7.5 Number of subjects required using the mid-point level for one-sided equivalence for various sensitivities with 80 % and 90 % power and 95 % confidence level