# Re: [R] Extracting P-values from the lrm function in the rms library

From: David Winsemius <dwinsemius_at_comcast.net>
Date: Sat, 19 Jun 2010 11:30:38 -0400

>
> Hi,
>
> mod.poly3\$coef/sqrt(diag(mod.poly3\$var))
>
> will give you the Wald stat values, so
>
> pnorm(abs(mod.poly3\$coef/sqrt(diag(mod.poly3\$var))),lower.tail=F)*2
>
> will yield the corresponding p-vals

It will, although it may appear as magic to those untutored in examining R model objects. Josh B should also consider looking at the output of str(mod.poly3) and then tracing through the logic used in the rms/Design function, print.lrm(). It's not a hidden function, so simply tyoing its name at the console will let him see what steps Harrell uses. They are a bit different, but are mathematically equivalent. Stripped of quite a bit of code that is not essential in this case:

print.lrm.simple <- function (x, digits = 4) {
# first a couple of utility formatting functions: sg <- function(x, d) {

```         oldopt <- options(digits = d)
on.exit(options(oldopt))
format(x)
```

rn <- function(x, d) format(round(as.single(x), d)) # Then the extraction of compoents from the model, "x" cof <- x\$coef # using name completion, since the full name is x \$coefficients
vv <- diag(x\$var) # the diagonal of the variance-covariance matrix z <- cof/sqrt(vv) # the Wald Z value
stats <- cbind(sg(cof, digits),
```                sg(sqrt(vv), digits),
rn(cof/sqrt(vv),
2))
stats <- cbind(stats,
# This is the step that calculates the p-values
rn(1 - pchisq(z^2, 1), 4))
```
#
dimnames(stats) <- list(names(cof), c("Coef", "S.E.", "Wald Z",

"P"))
print(stats, quote = FALSE)

cat("\n")
# the regular print.lrm does not return anything, ... it just prints, # but if you add this line you will be able to access the components of:
invisible(stats)
}

> print.lrm.simple(mod.poly3)[ , 4] # still prints first

Coef S.E. Wald Z P

```Intercept -5.68583 5.23295 -1.09  0.2772
x1         1.87020 2.14635  0.87  0.3836
x1^2      -0.42494 0.48286 -0.88  0.3788
x1^3       0.02845 0.03120  0.91  0.3618
x2         3.49560 3.54796  0.99  0.3245
x2^2      -0.94888 0.82067 -1.16  0.2476
x2^3       0.06362 0.05098  1.25  0.2121

# the 4th column are the p-values:
Intercept        x1      x1^2      x1^3        x2      x2^2      x2^3
```
"0.2772" "0.3836" "0.3788" "0.3618" "0.3245" "0.2476" "0.2121"
```--

David Winsemius, MD
West Hartford, CT

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