validate.lrm {rms} R Documentation

## Resampling Validation of a Logistic or Ordinal Regression Model

### Description

The `validate` function when used on an object created by `lrm` or `orm` does resampling validation of a logistic regression model, with or without backward step-down variable deletion. It provides bias-corrected Somers' D_{xy} rank correlation, R-squared index, the intercept and slope of an overall logistic calibration equation, the maximum absolute difference in predicted and calibrated probabilities E_{max}, the discrimination index D (model L.R. (chi-square - 1)/n), the unreliability index U = difference in -2 log likelihood between un-calibrated X beta and X beta with overall intercept and slope calibrated to test sample / n, the overall quality index (logarithmic probability score) Q = D - U, and the Brier or quadratic probability score, B (the last 3 are not computed for ordinal models), the g-index, and `gp`, the g-index on the probability scale. The corrected slope can be thought of as shrinkage factor that takes into account overfitting. For `orm` fits, a subset of the above indexes is provided, Spearman's ρ is substituted for D_{xy}, and a new index is reported: `pdm`, the mean absolute difference between 0.5 and the predicted probability that Y≥q the marginal median of Y.

### Usage

```# fit <- lrm(formula=response ~ terms, x=TRUE, y=TRUE) or orm
## S3 method for class 'lrm'
validate(fit, method="boot", B=40,
bw=FALSE, rule="aic", type="residual", sls=0.05, aics=0,
force=NULL, estimates=TRUE,
pr=FALSE,  kint, Dxy.method=if(k==1) 'somers2' else 'lrm',
emax.lim=c(0,1), ...)
## S3 method for class 'orm'
validate(fit, method="boot", B=40, bw=FALSE, rule="aic",
type="residual",	sls=.05, aics=0, force=NULL, estimates=TRUE,
pr=FALSE,  ...)
```

### Arguments

 `fit` a fit derived by `lrm` or `orm`. The options `x=TRUE` and `y=TRUE` must have been specified. `method,B,bw,rule,type,sls,aics,force,estimates,pr` see `predab.resample` `kint` In the case of an ordinal model, specify which intercept to validate. Default is the middle intercept. For `validate.orm`, intercept-specific quantities are not validated so this does not matter. `Dxy.method` `"lrm"` to use `lrm`s computation of D_{xy} correlation, which rounds predicted probabilities to nearest .002. Use `Dxy.method="somers2"` (the default) to instead use the more accurate but slower `somers2` function. This will matter most when the model is extremely predictive. The default is `"lrm"` for ordinal models, since `somers2` only handles binary response variables. `emax.lim` range of predicted probabilities over which to compute the maximum error. Default is entire range. `...` other arguments to pass to `lrm.fit` (now only `maxit` and `tol` are allowed) and to `predab.resample` (note especially the `group`, `cluster`, and `subset` parameters)

### Details

If the original fit was created using penalized maximum likelihood estimation, the same `penalty.matrix` used with the original fit are used during validation.

### Value

a matrix with rows corresponding to D_{xy}, R^2, `Intercept`, `Slope`, E_{max}, D, U, Q, B, g, gp, and columns for the original index, resample estimates, indexes applied to the whole or omitted sample using the model derived from the resample, average optimism, corrected index, and number of successful re-samples. For `validate.orm` not all columns are provided, Spearman's rho is returned instead of D_{xy}, and `pdm` is reported.

### Side Effects

prints a summary, and optionally statistics for each re-fit

### Author(s)

Frank Harrell
Department of Biostatistics, Vanderbilt University
f.harrell@vanderbilt.edu

### References

Miller ME, Hui SL, Tierney WM (1991): Validation techniques for logistic regression models. Stat in Med 10:1213–1226.

Harrell FE, Lee KL (1985): A comparison of the discrimination of discriminant analysis and logistic regression under multivariate normality. In Biostatistics: Statistics in Biomedical, Public Health, and Environmental Sciences. The Bernard G. Greenberg Volume, ed. PK Sen. New York: North-Holland, p. 333–343.

`lrm`, `calibrate`, `cr.setup`, `orm`

### Examples

```n <- 1000    # define sample size
age            <- rnorm(n, 50, 10)
blood.pressure <- rnorm(n, 120, 15)
cholesterol    <- rnorm(n, 200, 25)
sex            <- factor(sample(c('female','male'), n,TRUE))

# Specify population model for log odds that Y=1
L <- .4*(sex=='male') + .045*(age-50) +
(log(cholesterol - 10)-5.2)*(-2*(sex=='female') + 2*(sex=='male'))
# Simulate binary y to have Prob(y=1) = 1/[1+exp(-L)]
y <- ifelse(runif(n) < plogis(L), 1, 0)

f <- lrm(y ~ sex*rcs(cholesterol)+pol(age,2)+blood.pressure, x=TRUE, y=TRUE)
#Validate full model fit
validate(f, B=10)              # normally B=300
validate(f, B=10, group=y)
# two-sample validation: make resamples have same numbers of
# successes and failures as original sample

#Validate stepwise model with typical (not so good) stopping rule
validate(f, B=10, bw=TRUE, rule="p", sls=.1, type="individual")

## Not run:
#Fit a continuation ratio model and validate it for the predicted
#probability that y=0
u <- cr.setup(y)
Y <- u\$y
cohort <- u\$cohort
attach(mydataframe[u\$subs,])
f <- lrm(Y ~ cohort+rcs(age,4)*sex, penalty=list(interaction=2))
validate(f, cluster=u\$subs, subset=cohort=='all')
#see predab.resample for cluster and subset

## End(Not run)
```

[Package rms version 4.1-0 Index]