lrm {Design}R Documentation

Logistic Regression Model

Description

Fit binary and proportional odds ordinal logistic regression models using maximum likelihood estimation or penalized maximum likelihood estimation. See cr.setup for how to fit forward continuation ratio models with lrm.

Usage

lrm(formula, data, subset, na.action=na.delete, method="lrm.fit",
    model=FALSE, x=FALSE, y=FALSE, linear.predictors=TRUE, se.fit=FALSE, 
    penalty=0, penalty.matrix, tol=1e-7, 
    strata.penalty=0, var.penalty=c('simple','sandwich'),
    weights, normwt, ...)

Arguments

formula a formula object. An offset term can be included. The offset causes fitting of a model such as logit(Y=1) = Xβ + W, where W is the offset variable having no estimated coefficient. The response variable can be any data type; lrm converts it in alphabetic or numeric order to an S factor variable and recodes it 0,1,2,... internally.
data data frame to use. Default is the current frame.
subset logical expression or vector of subscripts defining a subset of observations to analyze
na.action function to handle NAs in the data. Default is na.delete, which deletes any observation having response or predictor missing, while preserving the attributes of the predictors and maintaining frequencies of deletions due to each variable in the model. This is usually specified using options(na.action="na.delete").
method name of fitting function. Only allowable choice at present is lrm.fit.
model causes the model frame to be returned in the fit object
x causes the expanded design matrix (with missings excluded) to be returned under the name x.
y causes the response variable (with missings excluded) to be returned under the name y.
linear.predictors causes the predicted X beta (with missings excluded) to be returned under the name linear.predictors. When the response variable has > in case of non-convergence. This is especially useful in simulation work.

Value

psm returns a fit object with all the information survreg would store as well as what Design stores and units and time.inc. Hazard, Survival, and Quantile return S-functions. residuals.psm with type="censored.normalized" returns a Surv object which has a special attribute "theoretical" which is used by the lines routine. This is the assumed standardized survival function as a function of time or transformed time.

Author(s)

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

See Also

Design, survreg, survReg, residuals.survreg, survreg.object, survreg.distributions, pphsm, survplot, survest, Surv, na.delete, na.detail.response, datadist, latex.psm

Examples

n <- 400
set.seed(1)
age <- rnorm(n, 50, 12)
sex <- factor(sample(c('Female','Male'),n,TRUE))
dd <- datadist(age,sex)
options(datadist='dd')
# Population hazard function:
h <- .02*exp(.06*(age-50)+.8*(sex=='Female'))
d.time <- -log(runif(n))/h
cens <- 15*runif(n)
death <- ifelse(d.time <= cens,1,0)
d.time <- pmin(d.time, cens)

f <- psm(Surv(d.time,death) ~ sex*pol(age,2), 
         dist=if(.R.)'lognormal' else 'gaussian')
# Log-normal model is a bad fit for proportional hazards data

anova(f)
fastbw(f)  # if deletes sex while keeping age*sex ignore the result
f <- update(f, x=TRUE,y=TRUE)       # so can validate, compute certain resids
validate(f, dxy=TRUE, B=10)      # ordinarily use B=150 or more
plot(f, age=NA, sex=NA)       # needs datadist since no explicit age, hosp.
survplot(f, age=c(20,60))     # needs datadist since hospital not set here
# latex(f)

S <- Survival(f)
plot(f$linear.predictors, S(6, f$linear.predictors),
     xlab=if(.R.)expression(X*hat(beta)) else 'X*Beta',
     ylab=if(.R.)expression(S(6,X*hat(beta))) else 'S(6|X*Beta)')
# plots 6-month survival as a function of linear predictor (X*Beta hat)

times <- seq(0,24,by=.25)
plot(times, S(times,0), type='l')   # plots survival curve at X*Beta hat=0
lam <- Hazard(f)
plot(times, lam(times,0), type='l') # similarly for hazard function

med <- Quantile(f)        # new function defaults to computing median only
lp <- seq(-3, 5, by=.1)
plot(lp, med(lp=lp), ylab="Median Survival Time")
med(c(.25,.5), f$linear.predictors)
                          # prints matrix with 2 columns

# fit a model with no predictors
f <- psm(Surv(d.time,death) ~ 1, dist=if(.R.)"weibull" else "extreme")
f
pphsm(f)          # print proportional hazards form
g <- survest(f)
plot(g$time, g$surv, xlab='Time', type='l',
     ylab=if(.R.)expression(S(t)) else 'S(t)')

f <- psm(Surv(d.time,death) ~ age, 
         dist=if(.R.)"loglogistic" else "logistic", y=TRUE)
r <- resid(f, 'cens') # note abbreviation
survplot(survfit(r), conf='none') 
                      # plot Kaplan-Meier estimate of 
                      # survival function of standardized residuals
survplot(survfit(r ~ cut2(age, g=2)), conf='none')  
                      # both strata should be n(0,1)
lines(r)              # add theoretical survival function
#More simply:
survplot(r, age, g=2)

options(datadist=NULL)
[Package Design version 2.1-1 Index]
./usr/lib/R/site-library/Design/html/lrm.html0000644000000000000000000005501110763104675017747 0ustar rootroot R: Logistic Regression Model
lrm {Design}R Documentation

Logistic Regression Model

Description

Fit binary and proportional odds ordinal logistic regression models using maximum likelihood estimation or penalized maximum likelihood estimation. See cr.setup for how to fit forward continuation ratio models with lrm.

Usage

lrm(formula, data, subset, na.action=na.delete, method="lrm.fit",
    model=FALSE, x=FALSE, y=FALSE, linear.predictors=TRUE, se.fit=FALSE, 
    penalty=0, penalty.matrix, tol=1e-7, 
    strata.penalty=0, var.penalty=c('simple','sandwich'),
    weights, normwt, ...)

Arguments

formula a formula object. An offset term can be included. The offset causes fitting of a model such as logit(Y=1) = Xβ + W, where W is the offset variable having no estimated coefficient. The response variable can be any data type; lrm converts it in alphabetic or numeric order to an S factor variable and recodes it 0,1,2,... internally.
data data frame to use. Default is the current frame.
subset logical expression or vector of subscripts defining a subset of observations to analyze
na.action function to handle NAs in the data. Default is na.delete, which deletes any observation having response or predictor missing, while preserving the attributes of the predictors and maintaining frequencies of deletions due to each variable in the model. This is usually specified using options(na.action="na.delete").
method name of fitting function. Only allowable choice at present is lrm.fit.
model causes the model frame to be returned in the fit object
x causes the expanded design matrix (with missings excluded) to be returned under the name x.
y causes the response variable (with missings excluded) to be returned under the name y.
linear.predictors causes the predicted X beta (with missings excluded) to be returned under the name linear.predictors. When the response variable has > in case of non-convergence. This is especially useful in simulation work.

Value

psm returns a fit object with all the information survreg would store as well as what Design stores and units and time.inc. Hazard, Survival, and Quantile return S-functions. residuals.psm with type="censored.normalized" returns a Surv object which has a special attribute "theoretical" which is used by the lines routine. This is the assumed standardized survival function as a function of time or transformed time.

Author(s)

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

See Also

Design, survreg, survReg, residuals.survreg, survreg.object, survreg.distributions, pphsm, survplot, survest, Surv, na.delete, na.detail.response, datadist, latex.psm

Examples

n <- 400
set.seed(1)
age <- rnorm(n, 50, 12)
sex <- factor(sample(c('Female','Male'),n,TRUE))
dd <- datadist(age,sex)
options(datadist='dd')
# Population hazard function:
h <- .02*exp(.06*(age-50)+.8*(sex=='Female'))
d.time <- -log(runif(n))/h
cens <- 15*runif(n)
death <- ifelse(d.time <= cens,1,0)
d.time <- pmin(d.time, cens)

f <- psm(Surv(d.time,death) ~ sex*pol(age,2), 
         dist=if(.R.)'lognormal' else 'gaussian')
# Log-normal model is a bad fit for proportional hazards data

anova(f)
fastbw(f)  # if deletes sex while keeping age*sex ignore the result
f <- update(f, x=TRUE,y=TRUE)       # so can validate, compute certain resids
validate(f, dxy=TRUE, B=10)      # ordinarily use B=150 or more
plot(f, age=NA, sex=NA)       # needs datadist since no explicit age, hosp.
survplot(f, age=c(20,60))     # needs datadist since hospital not set here
# latex(f)

S <- Survival(f)
plot(f$linear.predictors, S(6, f$linear.predictors),
     xlab=if(.R.)expression(X*hat(beta)) else 'X*Beta',
     ylab=if(.R.)expression(S(6,X*hat(beta))) else 'S(6|X*Beta)')
# plots 6-month survival as a function of linear predictor (X*Beta hat)

times <- seq(0,24,by=.25)
plot(times, S(times,0), type='l')   # plots survival curve at X*Beta hat=0
lam <- Hazard(f)
plot(times, lam(times,0), type='l') # similarly for hazard function

med <- Quantile(f)        # new function defaults to computing median only
lp <- seq(-3, 5, by=.1)
plot(lp, med(lp=lp), ylab="Median Survival Time")
med(c(.25,.5), f$linear.predictors)
                          # prints matrix with 2 columns

# fit a model with no predictors
f <- psm(Surv(d.time,death) ~ 1, dist=if(.R.)"weibull" else "extreme")
f
pphsm(f)          # print proportional hazards form
g <- survest(f)
plot(g$time, g$surv, xlab='Time', type='l',
     ylab=if(.R.)expression(S(t)) else 'S(t)')

f <- psm(Surv(d.time,death) ~ age, 
         dist=if(.R.)"loglogistic" else "logistic", y=TRUE)
r <- resid(f, 'cens') # note abbreviation
survplot(survfit(r), conf='none') 
                      # plot Kaplan-Meier estimate of 
                      # survival function of standardized residuals
survplot(survfit(r ~ cut2(age, g=2)), conf='none')  
                      # both strata should be n(0,1)
lines(r)              # add theoretical survival function
#More simply:
survplot(r, age, g=2)

options(datadist=NULL)
[Package Design version 2.1-1 Index]
./usr/lib/R/site-library/Design/html/lrm.html0000644000000000000000000005501110763104675017747 0ustar rootroot R: Logistic Regression Model
lrm {Design}R Documentation

Logistic Regression Model

Description

Fit binary and proportional odds ordinal logistic regression models using maximum likelihood estimation or penalized maximum likelihood estimation. See cr.setup for how to fit forward continuation ratio models with lrm.

Usage

lrm(formula, data, subset, na.action=na.delete, method="lrm.fit",
    model=FALSE, x=FALSE, y=FALSE, linear.predictors=TRUE, se.fit=FALSE, 
    penalty=0, penalty.matrix, tol=1e-7, 
    strata.penalty=0, var.penalty=c('simple','sandwich'),
    weights, normwt, ...)

Arguments

formula a formula object. An offset term can be included. The offset causes fitting of a model such as logit(Y=1) = Xβ + W, where W is the offset variable having no estimated coefficient. The response variable can be any data type; lrm converts it in alphabetic or numeric order to an S factor variable and recodes it 0,1,2,... internally.
data data frame to use. Default is the current frame.
subset logical expression or vector of subscripts defining a subset of observations to analyze
na.action function to handle NAs in the data. Default is na.delete, which deletes any observation having response or predictor missing, while preserving the attributes of the predictors and maintaining frequencies of deletions due to each variable in the model. This is usually specified using options(na.action="na.delete").
method name of fitting function. Only allowable choice at present is lrm.fit.
model causes the model frame to be returned in the fit object
x causes the expanded design matrix (with missings excluded) to be returned under the name x.
y causes the response variable (with missings excluded) to be returned under the name y.
linear.predictors causes the predicted X beta (with missings excluded) to be returned under the name linear.predictors. When the response variable has > in case of non-convergence. This is especially useful in simulation work.

Value

psm returns a fit object with all the information survreg would store as well as what Design stores and units and time.inc. Hazard, Survival, and Quantile return S-functions. residuals.psm with type="censored.normalized" returns a Surv object which has a special attribute "theoretical" which is used by the lines routine. This is the assumed standardized survival function as a function of time or transformed time.

Author(s)

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

See Also

Design, survreg, survReg, residuals.survreg, survreg.object, survreg.distributions, pphsm, survplot, survest, Surv, na.delete, na.detail.response, datadist, latex.psm

Examples

n <- 400
set.seed(1)
age <- rnorm(n, 50, 12)
sex <- factor(sample(c('Female','Male'),n,TRUE))
dd <- datadist(age,sex)
options(datadist='dd')
# Population hazard function:
h <- .02*exp(.06*(age-50)+.8*(sex=='Female'))
d.time <- -log(runif(n))/h
cens <- 15*runif(n)
death <- ifelse(d.time <= cens,1,0)
d.time <- pmin(d.time, cens)

f <- psm(Surv(d.time,death) ~ sex*pol(age,2), 
         dist=if(.R.)'lognormal' else 'gaussian')
# Log-normal model is a bad fit for proportional hazards data

anova(f)
fastbw(f)  # if deletes sex while keeping age*sex ignore the result
f <- update(f, x=TRUE,y=TRUE)       # so can validate, compute certain resids
validate(f, dxy=TRUE, B=10)      # ordinarily use B=150 or more
plot(f, age=NA, sex=NA)       # needs datadist since no explicit age, hosp.
survplot(f, age=c(20,60))     # needs datadist since hospital not set here
# latex(f)

S <- Survival(f)
plot(f$linear.predictors, S(6, f$linear.predictors),
     xlab=if(.R.)expression(X*hat(beta)) else 'X*Beta',
     ylab=if(.R.)expression(S(6,X*hat(beta))) else 'S(6|X*Beta)')
# plots 6-month survival as a function of linear predictor (X*Beta hat)

times <- seq(0,24,by=.25)
plot(times, S(times,0), type='l')   # plots survival curve at X*Beta hat=0
lam <- Hazard(f)
plot(times, lam(times,0), type='l') # similarly for hazard function

med <- Quantile(f)        # new function defaults to computing median only
lp <- seq(-3, 5, by=.1)
plot(lp, med(lp=lp), ylab="Median Survival Time")
med(c(.25,.5), f$linear.predictors)
                          # prints matrix with 2 columns

# fit a model with no predictors
f <- psm(Surv(d.time,death) ~ 1, dist=if(.R.)"weibull" else "extreme")
f
pphsm(f)          # print proportional hazards form
g <- survest(f)
plot(g$time, g$surv, xlab='Time', type='l',
     ylab=if(.R.)expression(S(t)) else