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

[David Winsemius]

> On Jun 15, 2016, at 6:44 PM, Marie-Pierre Sylvestre <mp.sylvestre at gmail.com> wrote:
> 
> 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.

Your output appears to imply that the `auc` function is ignoring the weights, whereas the lrm function is honoring them. The `lrm` documentation implies these are handled as possibly fractional case weights.

-- 
David.
> 
> Best regards,
> MP
> 
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> 
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David Winsemius
Alameda, CA, USA