[R] Package rms: c-statistic from lrm function with weights

[Marie-Pierre Sylvestre]

Dear list,

I am using the lrm function from the rms package to estimate a logistic
model with weights. The c-statistic (or area under the curve) is part of
the lrm output.

To understand how the weights enter the computation of the c-statistics, I
looked at the script of lrm and lrm.fit but I am out of luck because it is
making a call to a Fortran routine and I don't know Fortran.

    z <- .Fortran("lrmfit", coef = initial, nx, 1:nx, x,
            y, offset, u = double(nvi), double(nvi * (nvi + 1)),
            double(1), n, nx, sumw, nvi, v = double(nvi * nvi),
            double(nvi), double(2 * nvi), double(nvi), integer(nvi),
            opts = opts, ftable, penmat, weights, PACKAGE = "rms")


Can somebody help me figure out how the weights from the regression are
used in the computation of the c-statistic? Here is a small example that
shows that the c-statistic computed from the rms package and using the pROC
packages are not the same (not even close) when calculated from a weighted
logistic regression.

set.seed(1233)
x <- rnorm(100)
w <- runif(100)
y <- rbinom(100, 1, .5)
require(rms)
# unweighted model
umod <- lrm(y~x)
umod$stat # c-statistic is   0.5776796
# weighted model
wmod <- lrm(y~x, weight = w)
wmod$stat # c-statistic is  0.65625
# using pROC
require(pROC)
umod2 <- glm(y~x, family = binomial)
auc(y, predict(umod2)) # 0.5769
wmod2 <- glm(y~x, weights = w, family = binomial)
auc(y, predict(wmod2)) # 0.5769

BTW results from umod and umod2 and from wmod and wmod2 are identical so
the discrepancy in c-statistics in not due to using lrm vs. glm.

Best regards,
MP

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