rms (version 6.2-0)

# validate.lrm: 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. $$(\chi^2 - 1)/n$$), 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 $$\rho$$ is substituted for $$D_{xy}$$, and a new index is reported: pdm, the mean absolute difference between 0.5 and the predicted probability that $$Y\geq$$ the marginal median of $$Y$$.

## Usage

# fit <- lrm(formula=response ~ terms, x=TRUE, y=TRUE) or orm
# S3 method for 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 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 validate and 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 lrms 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)

## 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

## 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.

## 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.

predab.resample, fastbw, lrm, rms, rms.trans, calibrate, somers2, cr.setup, gIndex, orm

## Examples

# NOT RUN {
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
# }