For each pair of methods in data, a regression of the differences on
the averages between methods is made and a linear relationship between
methods with prediction standard deviations is derived.
DA.reg(
data,
Transform = NULL,
trans.tol = 1e-06,
print = TRUE,
random.raters = FALSE,
DA.slope = TRUE
)DA.reg returns a MethComp object, i.e. a list
with three components, Conv, VarComp, and data.
Conv is a three-dimensional array, with dimensions To,
From (both with levels equal to the methods in data) and an
unnamed dimension with levels "alpha", "beta",
"sd.pred", "beta=1", referring to the linear relationship of
To to From, "int(t-f)", "slope(t-f)",
"sd(t-f)", referring to the regression of the differences on the
averages, and "int(sd)", "slope(sd)", and "s.d.=K",
referring to the regression of the absoulte residuals on the averages, and
LoA-lo, LoA-hi, the limits of agreement.
Converting from method \(l\) to method \(k\) using
$$y_{k|l}=\alpha+\beta y_l$$ with prediction standard deviation
\(\sigma\), just requires the entries
[k,l,c("alpha","beta","sd.pred")], if we assume the s.d. is constant.
The next entry is the p-values for the hypothesis \(\beta=1\), intercept
and slope of the SD of the differences as a linear function of the average
and finally p-value of the hypothesis that standard errors are constant over
the range. The latter three are derived by regressing the absolute values of
the residuals on the averages, and can be used to produce LoA where the s.d.
increases (or decreases) by the mean, using the function DA2y.
The VarComp element of the list is NULL, and only present for
compatibility with the print method for MethComp objects.
The data element is the input dataframe. The measurements in y
are left un-transformed, even if data are transformed (i.e. if the
Transform attribute of the object is non-null).
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.
y2DA returns a 3-component vector with names
c("DA-int","DA-slope","DA-sd"), referring to differences
D=y1-y2 as a linear function of A=(y1+y2)/2.
A Meth object. May also be a data frame with
columns meth, item and y.
A character string, or a list of two functions, each
other's inverse. The measurements are transformed by this before analysis.
Possibilities are: "exp", "log", "logit", "pctlogit" (transforms percentages
by the logit), "sqrt", "sq" (square), "cll" (complementary log-minus-log),
"ll" (log-minus-log). For further details see choose.trans.
The tolerance used to check whether the supplied
transformation and its inverse combine to the identity. Only used if
Transform is a list of two functions.
Should the results be printed?
If methods really are a random selection of raters,
neither intercept nor slope different from 0 are sensible, so if this is
TRUE, intercept and slope in the regression of difference on averages
are fixed to 0. Meaning that we are essentially looking at the raw
differences as residuals.
If this is TRUE, a slope of the differences in the verages is estimated, otherwise the relationship is assumed constant.
Bendix Carstensen, Steno Diabetes Center, bendix.carstensen@regionh.dk, https://BendixCarstensen.com/MethComp/
If the input object contains replicate measurements these are taken as separate items in the order they appear in the dataset.
B. Carstensen: Comparing methods of measurement: Extending the LoA by regression. Stat Med, 29:401-410, 2010.
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 ) ) )
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