DA2y {MethComp}

Convert DA to (classical) regression

Description

The functions DA2y and y2DA are convenience functions that convert the estimates of intercept, slope and sd from the regression of D=y_1-y_2 on A=(y_1+y_2)/2, back and forth to the resulting intercept, slope and sd in the relationship between y_1 and y_2, cf. Carstensen (2010), equation 6.

Usage

DA2y(a = 0, b = 0, s = NA)

Arguments

a

Intercept in the linear relation of the differences y1-y2 to the averages (y1+y2)/2. If a vector of length>1, this is used instead of a, b and s, and b and s are ignored.

b

Slope in the linear relstion of the differences to the averages.

s

SD from the regression of the differences in the averages. Can be NA.

Details

DA2y takes the intercept(a), slope(b) and sd(s) from the relationship (y1-y2)=a+b((y1+y2)/2)+e with sd(e)=s, and returns a two by 3 matrix with columns "int","slope","sd" and rows "y1|2","y2|1".

Value

DA2y returns a 2 by 3 matrix with rownames c("y1|2","y2|1") and columnnames c("int","slope","sd"), calculated under the assumption that the differences were formed as D <- y1 - y2.

Author(s)

Bendix Carstensen, Steno Diabetes Center, [e-mail], http://BendixCarstensen.com/MethComp

References

B. Carstensen: Comparing methods of measurement: Extending the LoA by regression. Stat Med, 29:401-410, 2010.

Examples

data( milk )
DA.reg( milk )
data( sbp )
print( DA.reg(sbp), digits=3 )
# Slope, intercept : y1 = 0.7 + 1.2*y2 (0.4)
A <- c(0.7,1.2,0.4)
( y2DA( A ) )
( DA2y( y2DA( A ) ) )