Predict {rms}R Documentation

Compute Predicted Values and Confidence Limits

Description

Predict allows the user to easily specify which predictors are to vary. When the vector of values over which a predictor should vary is a single value that is NA (usually specified as a single dot), the range will be all levels of a categorical predictor or equally-spaced points between the datadist "Low:prediction" and "High:prediction" values for the variable (datadist by default uses the 10th smallest and 10th largest predictor values in the dataset). Predicted values are the linear predictor (X beta), a user-specified transformation of that scale, or estimated probability of surviving past a fixed single time point given the linear predictor. Predict is usually used for plotting predicted values but there is also a print method.

There is a plot method for Predict objects that makes it easy to show predicted values and confidence bands.

The rbind method for Predict objects allows you to create separate sets of predictions under different situations and to combine them into one set for feeding to plot.Predict. For example you might want to plot confidence intervals for means and for individuals using ols, and have the two types of confidence bands be superposed onto one plot or placed into two panels. Another use for rbind is to combine predictions from quantile regression models that predicted three different quantiles.

Usage

Predict(x, ..., fun,
        type = c("predictions", "model.frame", "x"),
        np = 200, conf.int = 0.95,
        conf.type = c("mean", "individual"),
        adj.zero = FALSE, ref.zero = FALSE,
        non.slopes, time = NULL, loglog = FALSE, digits=4, name)

## S3 method for class 'Predict':
print(x, ...)

## S3 method for class 'Predict':
rbind(..., rename)

Arguments

x an rms fit object, or for print the result of Predict. options(datadist="d") must have been specified (where d was created by datadist), or it must have been in effect when the the model was fitted.
... One or more variables to vary, or single-valued adjustment values. Specify x=. to use the default display range, or any range you choose (e.g. seq(0,100,by=2),c(2,3,7,14)). The default list of values for which predictions are made is taken as the list of unique values of the variable if they number fewer than 11. For variables with >10 unique values, np equally spaced values in the range are used for plotting if the range is not specified. Variables not specified are set to the default adjustment value limits[2], i.e. the median for continuous variables and a reference category for non-continuous ones. Later variables define adjustment settings. For categorical variables, specify the class labels in quotes when specifying variable values. If the levels of a categorical variable are numeric, you may omit the quotes. For variables not described using datadist, you must specify explicit ranges and adjustment settings for predictors that were in the model. If no variables are specified in ..., predictions will be made by separately varying all predictors in the model over their default range, holding the other predictors at their adjustment values. This has the same effect as specifying name as a vector containing all the predictors. For rbind, ... represents a series of results from Predict. If you name the results, these names will be taken as the values of the new .set. variable added to the concatenated data frames. See an example below.
fun an optional transformation of the linear predictor
type defaults to providing predictions. Set to "model.frame" to return a data frame of predictor settings used. Set to "x" to return the corresponding design matrix constructed from the predictor settings.
np the number of equally-spaced points computed for continuous predictors that vary, i.e., when the specified value is . or NA
conf.int confidence level. Default is 0.95. Specify FALSE to suppress.
conf.type type of confidence interval. Default is "mean" which applies to all models. For models containing a residual variance (e.g, ols), you can specify conf.type="individual" instead, to obtain limits on the predicted value for an individual subject.
adj.zero Set to TRUE to adjust all non-plotted variables to 0 (or reference cell for categorical variables) and to omit intercept(s) from consideration. Default is FALSE.
ref.zero Set to TRUE to subtract a constant from X beta before plotting so that the reference value of the x-variable yields y=0. This is done before applying function fun.
non.slopes This is only useful in a multiple intercept model such as the ordinal logistic model. There to use to second of three intercepts, for example, specify non.slopes=c(0,1,0). The default is non.slopes=rep(0,k) if adj.zero=TRUE, where k is the number of intercepts in the model. If adj.zero=FALSE, the default is (1,0,0,...,0).
time Specify a single time u to cause function survest to be invoked to plot the probability of surviving until time u when the fit is from cph or psm.
loglog Specify loglog=TRUE to plot log[-log(survival)] instead of survival, when time is given.
digits Controls how ``adjust-to'' values are plotted. The default is 4 significant digits.
name Instead of specifying the variables to vary in the variables (...) list, you can specify one or more variables by specifying a vector of character string variable names in the name argument. Using this mode you cannot specify a list of variable values to use; prediction is done as if you had said e.g. age=.. Also, interacting factors can only be set to their reference values using this notation.
rename If you are concatenating predictor sets using rbind and one or more of the variables were renamed for one or more of the sets, but these new names represent different versions of the same predictors (e.g., using or not using imputation), you can specify a named character vector to rename predictors to a central name. For example, specify rename=c(age.imputed='age', corrected.bp='bp') to rename from old names age.imputed, corrected.bp to age, bp. This happens before concatenation of rows.

Details

When there are no intercepts in the fitted model, plot subtracts adjustment values from each factor while computing variances for confidence limits.

Specifying time will not work for Cox models with time-dependent covariables. Use survest or survfit for that purpose.

Value

a data frame containing all model predictors and the computed values yhat, lower, upper, the latter two if confidence intervals were requested. The data frame has an additional class "Predict". If name is specified or no predictors are specified in ..., the resulting data frame has an additional variable called .predictor. specifying which predictor is currently being varied. .predictor. is handy for use as a paneling variable in lattice or ggplot2 graphics.

Author(s)

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

See Also

datadist, predictrms, contrast.rms, summary.rms, rms, rms.trans, survest, survplot, rmsMisc, transace, rbind

Examples

n <- 1000    # define sample size
set.seed(17) # so can reproduce the results
age            <- rnorm(n, 50, 10)
blood.pressure <- rnorm(n, 120, 15)
cholesterol    <- rnorm(n, 200, 25)
sex            <- factor(sample(c('female','male'), n,TRUE))
label(age)            <- 'Age'      # label is in Hmisc
label(cholesterol)    <- 'Total Cholesterol'
label(blood.pressure) <- 'Systolic Blood Pressure'
label(sex)            <- 'Sex'
units(cholesterol)    <- 'mg/dl'   # uses units.default in Hmisc
units(blood.pressure) <- 'mmHg'

# 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)

ddist <- datadist(age, blood.pressure, cholesterol, sex)
options(datadist='ddist')

fit <- lrm(y ~ blood.pressure + sex * (age + rcs(cholesterol,4)))
Predict(fit, age=., cholesterol=., np=4)
Predict(fit, age=seq(20,80,by=10), sex=., conf.int=FALSE)
Predict(fit, age=seq(20,80,by=10), sex='male')  # works if datadist not used

ddist$limits$age[2] <- 30    # make 30 the reference value for age
# Could also do: ddist$limits["Adjust to","age"] <- 30
fit <- update(fit)   # make new reference value take effect
Predict(fit, age=., ref.zero=TRUE, fun=exp)

# Make two curves, and plot the predicted curves as two trellis panels
w <- Predict(fit, age=., sex=.)
require(lattice)
xyplot(yhat ~ age | sex, data=w, type='l')
# To add confidence bands we need to use the Hmisc xYplot function in
# place of xyplot
xYplot(Cbind(yhat,lower,upper) ~ age | sex, data=w, 
       method='filled bands', type='l', col.fill=gray(.95))
# If non-displayed variables were in the model, add a subtitle to show
# their settings using title(sub=paste('Adjusted to',attr(w,'info')$adjust),adj=0)
# Easier: feed w into plot.Predict
## Not run: 
# Predictions form a parametric survival model
n <- 1000
set.seed(731)
age <- 50 + 12*rnorm(n)
label(age) <- "Age"
sex <- factor(sample(c('Male','Female'), n, 
              rep=TRUE, prob=c(.6, .4)))
cens <- 15*runif(n)
h <- .02*exp(.04*(age-50)+.8*(sex=='Female'))
t <- -log(runif(n))/h
label(t) <- 'Follow-up Time'
e <- ifelse(t<=cens,1,0)
t <- pmin(t, cens)
units(t) <- "Year"
ddist <- datadist(age, sex)
Srv <- Surv(t,e)

# Fit log-normal survival model and plot median survival time vs. age
f <- psm(Surv(t, e) ~ rcs(age), dist=if(.R.)'lognormal' else 'gaussian')
med <- Quantile(f)       # Creates function to compute quantiles
                         # (median by default)
Predict(f, age=., fun=function(x)med(lp=x))
# Note: This works because med() expects the linear predictor (X*beta)
#       as an argument.  Would not work if use 
#       ref.zero=TRUE or adj.zero=TRUE.
# Also, confidence intervals from this method are approximate since
# they don't take into account estimation of scale parameter

# Fit an ols model to log(y) and plot the relationship between x1
# and the predicted mean(y) on the original scale without assuming
# normality of residuals; use the smearing estimator.  Before doing
# that, show confidence intervals for mean and individual log(y)
set.seed(1)
x1 <- runif(300)
x2 <- runif(300)
ddist <- datadist(x1,x2); options(datadist='ddist')
y  <- exp(x1+ x2 - 1 + rnorm(300))
f  <- ols(log(y) ~ pol(x1,2) + x2)
p1 <- Predict(f, x1=., conf.type='mean')
p2 <- Predict(f, x1=., conf.type='individual')
p  <- rbind(mean=p1, individual=p2)
plot(p, label.curve=FALSE)   # uses superposition
plot(p, ~x1 | .set.)         # 2 panels

r <- resid(f)
smean <- function(yhat)smearingEst(yhat, exp, res, statistic='mean')
formals(smean) <- list(yhat=numeric(0), res=r[!is.na(r)])
#smean$res <- r[!is.na(r)]   # define default res argument to function
Predict(f, x1=., fun=smean)
## End(Not run)
options(datadist=NULL)

[Package rms version 2.1-0 Index]