R: Compute Predicted Values and Confidence Limits

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 not specified, 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.

When the first argument to `Predict` is a fit object created by `bootcov` with `coef.reps=TRUE`, confidence limits come from the stored matrix of bootstrap repetitions of coefficients, using bootstrap percentile nonparametric confidence limits, basic bootstrap, or BCa limits. Such confidence intervals do not make distributional assumptions. You can force `Predict` to instead use the bootstrap covariance matrix by setting `usebootcoef=FALSE`. If `coef.reps` was `FALSE`, `usebootcoef=FALSE` is the default.

There are `ggplot`, `plotp`, and `plot` methods 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`, `ggplot.Predict`, or `plotp.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.

If `conf.type="simultaneous"`, simultaneous (over all requested predictions) confidence limits are computed. See the `predictrms` function for details.

### Usage

    Predict(x, ..., fun,
            type = c("predictions", "model.frame", "x"),
            np = 200, conf.int = 0.95,
            conf.type = c("mean", "individual","simultaneous"),
            usebootcoef=TRUE, boot.type=c("percentile","bca","basic"),
            adj.zero = FALSE, ref.zero = FALSE,
            kint=NULL, time = NULL, loglog = FALSE, digits=4, name,
            factors=NULL, offset=NULL)

    ## 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 a variable name without an equal sign 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. Specify `fun='mean'` if the fit is a proportional odds model fit and you ran `bootcov` with `coef.reps=TRUE`. This will let the mean function be re-estimated for each bootstrap rep to properly account for all sources of uncertainty in estimating the mean response.
`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. Specify `conf.type="simultaneous"` to obtain simultaneous confidence bands for mean predictions with family-wise coverage of `conf.int`.
`usebootcoef` | set to `FALSE` to force the use of the bootstrap covariance matrix estimator even when bootstrap coefficient reps are present
`boot.type` | set to `'bca'` to compute BCa confidence limits or `'basic'` to use the basic bootstrap. The default is to compute percentile intervals
`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`. This is especially useful for Cox models to make the hazard ratio be 1.0 at reference values, and the confidence interval have width zero.
`kint` | 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 `kint=2`. The default is 1 for `lrm` and the middle intercept corresponding to the median `y` for `orm`.
`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` without the equal sign. Also, interacting factors can only be set to their reference values using this notation.
`factors` | an alternate way of specifying ..., mainly for use by `survplot` or `gendata`. This must be a list with one or more values for each variable listed, with `NA` values for default ranges.
`offset` | a list containing one value for one variable, which is mandatory if the model included an offset term. The variable name must match the innermost variable name in the offset term. The single offset is added to all predicted values.
`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

`plot.Predict`, `ggplot.Predict`, `plotp.Predict`, `datadist`, `predictrms`, `contrast.rms`, `summary.rms`, `rms`, `rms.trans`, `survest`, `survplot`, `rmsMisc`, `transace`, `rbind`, `bootcov`, `bootBCa`, `boot.ci`

### 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
    # Get simultaneous confidence limits accounting for making 7 estimates
    # Predict(fit, age=seq(20,80,by=10), sex='male', conf.type='simult')
    # (this needs the multcomp package)

    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, ggplot.Predict, plotp.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(Srv ~ rcs(age), dist='lognormal')
    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),
    # and for the latter, also show bootstrap percentile nonparametric
    # pointwise confidence limits
    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, x=TRUE, y=TRUE)  # x y for bootcov
    fb <- bootcov(f, B=100)
    pb <- Predict(fb, x1, x2=c(.25,.75))
    p1 <- Predict(f,  x1, x2=c(.25,.75))
    p <- rbind(normal=p1, boot=pb)
    plot(p)

    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)

    ## Example using offset
    g <- Glm(Y ~ offset(log(N)) + x1 + x2, family=poisson)
    Predict(g, offset=list(N=100))

    ## End(Not run)
    options(datadist=NULL)

[Package rms version 5.1-1 Index]