SampleSize.VUS: Sample size for volume under surface (VUS)
In DiagTest3Grp: Diagnostic test summary measures for three ordinal groups

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Calculates the sample size required to estimate volume under surface (VUS) within a given margin of error when the diagnostic marker follows normal distributions in each diagnosis group.

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SampleSize.VUS(mu.minus, mu0, mu.plus, s.minus, s0, s.plus, p = 0, q =
0, lam.minus = 1/3, lam0 = 1/3, lam.plus = 1/3, typeIerror = 0.05,
 margin = 0.05,subdivisions = 50000, ...)

`mu.minus`	A numeric value, the sample mean estimate for the mean parameter of normal distribution in D-.
`mu0`	A numeric value, the sample mean estimate for the mean parameter of normal distribution in D0.
`mu.plus`	A numeric value, the sample mean estimate for the mean parameter of normal distribution in D+.
`s.minus`	A numeric value, the sample standard deviation (SD) estimate for the SD parameter of normal distribution in D-.
`s0`	A numeric value, the sample SD estimate for the SD parameter of normal distribution in D0.
`s.plus`	A numeric value, the sample SD estimate for the SD parameter of normal distribution in D+.
`p`	A numeric value, the minimum required specificity, 0<=p<1, for calculation partial volume under ROC surface. Default, p=0.
`q`	A numeric value, the minimum desired sensitivity,0<=q<1, for calculation partial volume under ROC surface. Default, q=0. p=q=0 will give the complete VUS estimate, otherwise give the partial VUS estimate satisfying specificity no less than p and sensitivity no less than q.
`lam.minus`	A numeric value, the expected population proportion of the D_- group, used for sample size calculation. Default, lam.minus=1/3. The proportions of the three ordinal groups (lam.minus, lam0, lam.plus) should sum to 1.
`lam0`	A numeric value, the expected population proportion of the D_0 group, used for sample size calculation. Default, lam0=1/3. The proportions of the three ordinal groups (lam.minus, lam0, lam.plus) should sum to 1.
`lam.plus`	A numeric value, the expected population proportion of the D_+ group, used for sample size calculation. Default, lam.plus=1/3.The proportions of the three ordinal groups (lam.minus, lam0, lam.plus) should sum to 1.
`typeIerror`	A numeric value, (1-typeIerror)*100% confidence interval (CI) in sample size calculation. Default typeIerror=0.05, i.e., calculate 95% CI.
`margin`	A numeric value, the margin of error on the VUS estimates in sample size calculation. Default, margin=0.05.
`subdivisions`	A numeric value, the number of subintervals for integration using adaptive quadrature in the R function `integrate`. Default, subdivisions=50000.
`...`	Other arguments that can be passed to the R function `integrate`, e.g., abs.tol, rel.tol, stop.on.error etc.

The (1-typeIerror)% CI on VUS estimate under normality is (VUS-Z_a*SE(VUS),VUS+Z_a*SE(VUS)), then the sample size will be calculated such that : margin= Z_a*SE(VUS) or half of the CI's length, where Z_a is the normal quantile, Z_a=1.95 given default typeIerror a=0.05.

Returns a numeric value indicating required sample size.

Bug reports, malfunctioning, or suggestions for further improvements or contributions can be sent to Jingqin Luo <rosy@wubios.wustl.edu>.

Jingqin Luo

Xiong, C. and van Belle, G. and Miller, J.P. and Morris, J.C. (2006) Measuring and Estimating Diagnostic Accuracy When There Are Three Ordinal Diagnostic Groups. Statistics In Medicine 25 7 1251–1273.

Normal.VUS

 mu.minus <- 6
 mu0 <- 8
 mu.plus <- 13.36


 s.minus <- 1
 s0 <- 1.2
 s.plus <- 1.4

 n <- SampleSize.VUS(mu.minus,mu0,mu.plus,s.minus,s0,s.plus,p=0,q=0,typeIerror=0.05)