DiagTest3Grp (version 1.6)

SampleSize.Youden3Grp: Sample size for the extended Youden index for three ordinal groups

Description

Calculates the sample size required to estimate the extended Youden index within a given margin of error when the diagnostic marker follows normal distributions in each diagnosis group.

Usage

SampleSize.Youden3Grp(mu.minus, mu0, mu.plus, s.minus, s0, s.plus,
t.minus, t.plus, lam.minus, lam0, lam.plus, typeIerror = 0.05, margin=0.05)

Arguments

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 $D+$.

t.minus

A numeric value, the optimal lower cut point to attain the optimal extended Youden index under normal assumptions.

t.plus

A numeric value, the optimal upper cut point to attain the optimal extended Youden index under normal assumptions.

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) based on which the length of CI for sample size calculation will be obtained. Default typeIerror=0.05, i.e., calculate 95% CI.

margin

A numeric value, the margin of error on the extended Youden index estimates in sample size calculation. Default, margin=0.05.

Value

Returns a numeric value indicating required sample size.

Details

The (1-typeIerror)% CI on the Youden index (J) estimate under normality is $(J-Z_a*SE(J),J+Z_a*SE(J))$, then margin= $Z_a*SE(J)$ or half of the CI's length, where $Z_a$ is the normal quantile, $Z_a=1.95$ given default typeIerror $a=0.05$.

References

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.

See Also

Youden3Grp

Examples

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


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

 t.minus <- 7.02
 t.plus <- 10.52

 n <- SampleSize.Youden3Grp(mu.minus, mu0, mu.plus, s.minus, s0, s.plus,
t.minus, t.plus)