R: Plot Survival Curves and Hazard Functions

survplot {rms} | R Documentation

## Plot Survival Curves and Hazard Functions

### Description

Plot estimated survival curves, and for parametric survival models, plot hazard functions. There is an option to print the number of subjects at risk at the start of each time interval. Curves are automatically labeled at the points of maximum separation (using the `labcurve` function), and there are many other options for labeling that can be specified with the `label.curves` parameter. For example, different plotting symbols can be placed at constant x-increments and a legend linking the symbols with category labels can automatically positioned on the most empty portion of the plot.

For the case of a two stratum analysis by `npsurv`, `survdiffplot` plots the difference in two Kaplan-Meier estimates along with approximate confidence bands for the differences, with a reference line at zero. The number of subjects at risk is optionally plotted. This number is taken as the minimum of the number of subjects at risk over the two strata. When `conf='diffbands'`, `survdiffplot` instead does not make a new plot but adds a shaded polygon to an existing plot, showing the midpoint of two survival estimates plus or minus 1/2 the width of the confidence interval for the difference of two Kaplan-Meier estimates.

`survplotp` creates an interactive `plotly` graphic with shaded confidence bands. In the two strata case, it draws the 1/2 confidence bands for the difference in two probabilities centered at the midpoint of the probability estimates, so that where the two curves touch this band there is no significant difference (no multiplicity adjustment is made). For the two strata case, the two individual confidence bands have entries in the legend but are not displayed until the user clicks on the legend.

When `code` was from running `npsurv` on a multi-state/competing risk `Surv` object, `survplot` plots cumulative incidence curves properly accounting for competing risks. You must specify exactly one state/event cause to plot using the `state` argument. `survplot` will not plot multiple states on one graph. This can be accomplished using multiple calls with different values of `state` and specifying `add=TRUE` for all but the first call.

### Usage

    survplot(fit, ...)
    survplotp(fit, ...)
    ## S3 method for class 'rms'
    survplot(fit, ..., xlim,
             ylim=if(loglog) c(-5, 1.5) else if
                     (what == "survival" & missing(fun)) c(0, 1),
             xlab, ylab, time.inc,
             what=c("survival","hazard"),
             type=c("tsiatis","kaplan-meier"),
             conf.type=c("log","log-log","plain","none"),
             conf.int=FALSE, conf=c("bands","bars"), mylim=NULL,
             add=FALSE, label.curves=TRUE,
             abbrev.label=FALSE, levels.only=FALSE,
             lty, lwd=par("lwd"),
             col=1, col.fill=gray(seq(.95, .75, length=5)),
             adj.subtitle=TRUE, loglog=FALSE, fun,
             n.risk=FALSE, logt=FALSE, dots=FALSE, dotsize=.003,
             grid=NULL, srt.n.risk=0, sep.n.risk=0.056, adj.n.risk=1,
             y.n.risk, cex.n.risk=.6, cex.xlab=par('cex.lab'),
             cex.ylab=cex.xlab, pr=FALSE)
    ## S3 method for class 'npsurv'
    survplot(fit, xlim,
             ylim, xlab, ylab, time.inc, state=NULL,
             conf=c("bands","bars","diffbands","none"), mylim=NULL,
             add=FALSE, label.curves=TRUE, abbrev.label=FALSE,
             levels.only=FALSE, lty,lwd=par('lwd'),
             col=1, col.fill=gray(seq(.95, .75, length=5)),
             loglog=FALSE, fun, n.risk=FALSE, aehaz=FALSE, times=NULL,
             logt=FALSE, dots=FALSE, dotsize=.003, grid=NULL,
             srt.n.risk=0, sep.n.risk=.056, adj.n.risk=1,
             y.n.risk, cex.n.risk=.6, cex.xlab=par('cex.lab'), cex.ylab=cex.xlab,
             pr=FALSE, ...)
    ## S3 method for class 'npsurv'
    survplotp(fit, xlim, ylim, xlab, ylab, time.inc, state=NULL,
             conf=c("bands", "none"), mylim=NULL, abbrev.label=FALSE,
             col=colorspace::rainbow_hcl,  levels.only=TRUE,
             loglog=FALSE, fun=function(y) y, aehaz=FALSE, times=NULL,
             logt=FALSE, pr=FALSE, ...)
    survdiffplot(fit, order=1:2, fun=function(y) y,
               xlim, ylim, xlab, ylab="Difference in Survival Probability",
               time.inc, conf.int, conf=c("shaded", "bands","diffbands","none"),
               add=FALSE, lty=1, lwd=par('lwd'), col=1,
               n.risk=FALSE, grid=NULL,
               srt.n.risk=0, adj.n.risk=1,
               y.n.risk, cex.n.risk=.6, cex.xlab=par('cex.lab'),
               cex.ylab=cex.xlab, convert=function(f) f)

### Arguments

`fit` | result of fit (`cph`, `psm`, `npsurv`, `survest.psm`). For `survdiffplot`, `fit` must be the result of `npsurv`.
`...` | list of factors with names used in model. For fits from `npsurv` these arguments do not appear - all strata are plotted. Otherwise the first factor listed is the factor used to determine different survival curves. Any other factors are used to specify single constants to be adjusted to, when defaults given to fitting routine (through `limits`) are not used. The value given to factors is the original coding of data given to fit, except that for categorical or strata factors the text string levels may be specified. The form of values given to the first factor are none (omit the equal sign to use default range or list of all values if variable is discrete), `"text"` if factor is categorical, `c(value1, value2, ...)`, or a function which returns a vector, such as `seq(low,high,by=increment)`. Only the first factor may have the values omitted. In this case the `Low effect`, `Adjust to`, and `High effect` values will be used from `datadist` if the variable is continuous. For variables not defined to `datadist`, you must specify non-missing constant settings (or a vector of settings for the one displayed variable). Note that since `npsurv` objects do not use the variable list in `...`, you can specify any extra arguments to `labcurve` by adding them at the end of the list of arguments. For `survplotp` ... (e.g., `height`, `width`) is passed to `plotly::plot_ly`.
`xlim` | a vector of two numbers specifiying the x-axis range for follow-up time. Default is `(0,maxtime)` where `maxtime` was the `pretty()`d version of the maximum follow-up time in any stratum, stored in `fit$maxtime`. If `logt=TRUE`, default is `(1, log(maxtime))`.
`ylim` | y-axis limits. Default is `c(0,1)` for survival, and `c(-5,1.5)` if `loglog=TRUE`. If `fun` or `loglog=TRUE` are given and `ylim` is not, the limits will be computed from the data. For `what="hazard"`, default limits are computed from the first hazard function plotted.
`xlab` | x-axis label. Default is `units` attribute of failure time variable given to `Surv`.
`ylab` | y-axis label. Default is `"Survival Probability"` or `"log(-log Survival Probability)"`. If `fun` is given, the default is `""`. For `what="hazard"`, the default is `"Hazard Function"`. For a multi-state/competing risk application the default is `"Cumulative Incidence"`.
`time.inc` | time increment for labeling the x-axis and printing numbers at risk. If not specified, the value of `time.inc` stored with the model fit will be used.
`state` | the state/event cause to use in plotting if the fit was for a multi-state/competing risk `Surv` object
`type` | specifies type of estimates, `"tsiatis"` (the default) or `"kaplan-meier"`. `"tsiatis"` here corresponds to the Breslow estimator. This is ignored if survival estimates stored with `surv=TRUE` are being used. For fits from `npsurv`, this argument is also ignored, since it is specified as an argument to `npsurv`.
`conf.type` | specifies the basis for confidence limits. This argument is ignored for fits from `npsurv`.
`conf.int` | Default is `FALSE`. Specify e.g. `.95` to plot 0.95 confidence bands. For fits from parametric survival models, or Cox models with `x=TRUE` and `y=TRUE` specified to the fit, the exact asymptotic formulas will be used to compute standard errors, and confidence limits are based on `log(-log S(t))` if `loglog=TRUE`. If `x=TRUE` and `y=TRUE` were not specified to `cph` but `surv=TRUE` was, the standard errors stored for the underlying survival curve(s) will be used. These agree with the former if predictions are requested at the mean value of X beta or if there are only stratification factors in the model. This argument is ignored for fits from `npsurv`, which must have previously specified confidence interval specifications. For `survdiffplot` if `conf.int` is not specified, the level used in the call to `npsurv` will be used.
`conf` | `"bars"` for confidence bars at each `time.inc` time point. If the fit was from `cph(..., surv=TRUE)`, the `time.inc` used will be that stored with the fit. Use `conf="bands"` (the default) for bands using standard errors at each failure time. For `npsurv` objects only, `conf` may also be `"none"`, indicating that confidence interval information stored with the `npsurv` result should be ignored. For `npsurv` and `survdiffplot`, `conf` may be `"diffbands"` whereby a shaded region is drawn for comparing two curves. The polygon is centered at the midpoint of the two survival estimates and the height of the polygon is 1/2 the width of the approximate `conf.int` pointwise confidence region. Survival curves not overlapping the shaded area are approximately significantly different at the `1 - conf.int` level.
`mylim` | used to curtail computed `ylim`. When `ylim` is not given by the user, the computed limits are expanded to force inclusion of the values specified in `mylim`.
`what` | defaults to `"survival"` to plot survival estimates. Set to `"hazard"` or an abbreviation to plot the hazard function (for `psm` fits only). Confidence intervals are not available for `what="hazard"`.
`add` | set to `TRUE` to add curves to an existing plot.
`label.curves` | default is `TRUE` to use `labcurve` to label curves where they are farthest apart. Set `label.curves` to a `list` to specify options to `labcurve`, e.g., `label.curves=list(method="arrow", cex=.8)`. These option names may be abbreviated in the usual way arguments are abbreviated. Use for example `label.curves=list(keys=1:5)` to draw symbols (as in `pch=1:5` - see `points`) on the curves and automatically position a legend in the most empty part of the plot. Set `label.curves=FALSE` to suppress drawing curve labels. The `col`, `lty`, `lwd`, and `type` parameters are automatically passed to `labcurve`, although you can override them here. To distinguish curves by line types and still have `labcurve` construct a legend, use for example `label.curves=list(keys="lines")`. The negative value for the plotting symbol will suppress a plotting symbol from being drawn either on the curves or in the legend.
`abbrev.label` | set to `TRUE` to `abbreviate()` curve labels that are plotted
`levels.only` | set to `TRUE` to remove `variablename=` from the start of curve labels.
`lty` | vector of line types to use for different factor levels. Default is `c(1,3,4,5,6,7,...)`.
`lwd` | vector of line widths to use for different factor levels. Default is current `par` setting for `lwd`.
`col` | color for curve, default is `1`. Specify a vector to assign different colors to different curves. For `survplotp`, `col` is a vector of colors corresponding to strata, or a function that will be called to generate such colors.
`col.fill` | a vector of colors to used in filling confidence bands
`adj.subtitle` | set to `FALSE` to suppress plotting subtitle with levels of adjustment factors not plotted. Defaults to `TRUE`. This argument is ignored for `npsurv`.
`loglog` | set to `TRUE` to plot `log(-log Survival)` instead of `Survival`
`fun` | specifies any function to translate estimates and confidence limits before plotting. If the fit is a multi-state object the default for `fun` is `function(y) 1 - y` to draw cumulative incidence curves.
`logt` | set to `TRUE` to plot `log(t)` instead of `t` on the x-axis
`n.risk` | set to `TRUE` to add number of subjects at risk for each curve, using the `surv.summary` created by `cph` or using the failure times used in fitting the model if `y=TRUE` was specified to the fit or if the fit was from `npsurv`. The numbers are placed at the bottom of the graph unless `y.n.risk` is given. If the fit is from `survest.psm`, `n.risk` does not apply.
`srt.n.risk` | angle of rotation for leftmost number of subjects at risk (since this number may run into the second or into the y-axis). Default is `0`.
`adj.n.risk` | justification for leftmost number at risk. Default is `1` for right justification. Use `0` for left justification, `.5` for centered.
`sep.n.risk` | multiple of upper y limit - lower y limit for separating lines of text containing number of subjects at risk. Default is `.056*(ylim[2]-ylim[1])`.
`y.n.risk` | When `n.risk=TRUE`, the default is to place numbers of patients at risk above the x-axis. You can specify a y-coordinate for the bottom line of the numbers using `y.n.risk`. Specify `y.n.risk='auto'` to place the numbers below the x-axis at a distance of 1/3 of the range of `ylim`.
`cex.n.risk` | character size for number of subjects at risk (when `n.risk` is `TRUE`)
`cex.xlab` | `cex` for x-axis label
`cex.ylab` | `cex` for y-axis label
`dots` | set to `TRUE` to plot a grid of dots. Will be plotted at every `time.inc` (see `cph`) and at survival increments of .1 (if `d>.4`), .05 (if `.2 < d <= .4`), or .025 (if `d <= .2`), where `d` is the range of survival displayed.
`dotsize` | size of dots in inches
`grid` | defaults to `NULL` (not drawing grid lines). Set to `TRUE` to plot `gray(.8)` grid lines, or specify any color.
`pr` | set to `TRUE` to print survival curve coordinates used in the plots
`aehaz` | set to `TRUE` to add number of events and exponential distribution hazard rate estimates in curve labels. For competing risk data the number of events is for the cause of interest, and the hazard rate is the number of events divided by the sum of all failure and censoring times.
`times` | a numeric vector of times at which to compute cumulative incidence probability estimates to add to curve labels
`order` | an integer vector of length two specifying the order of groups when computing survival differences. The default of `1:2` indicates that the second group is subtracted from the first. Specify `order=2:1` to instead subtract the first from the second. A subtitle indicates what was done.
`convert` | a function to convert the output of `summary.survfitms` to pick off the data needed for a single state

### Details

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

There is a set a system option `mgp.axis.labels` to allow x and y-axes to have differing `mgp` graphical parameters (see `par`). This is important when labels for y-axis tick marks are to be written horizontally (`par(las=1)`), as a larger gap between the labels and the tick marks are needed. You can set the axis-specific 2nd component of `mgp` using `mgp.axis.labels(c(xvalue,yvalue))`.

### Value

list with components adjust (text string specifying adjustment levels) and `curve.labels` (vector of text strings corresponding to levels of factor used to distinguish curves). For `npsurv`, the returned value is the vector of strata labels, or NULL if there are no strata.

### Side Effects

plots. If `par()$mar[4] < 4`, issues `par(mar=)` to increment `mar[4]` by 2 if `n.risk=TRUE` and `add=FALSE`. The user may want to reset `par(mar)` in this case to not leave such a wide right margin for plots. You usually would issue `par(mar=c(5,4,4,2)+.1)`.

### See Also

`datadist`, `rms`, `cph`, `psm`, `survest`, `predictrms`, `plot.Predict`, `ggplot.Predict`, `units`, `errbar`, `survfit`, `survreg.distributions`, `labcurve`, `mgp.axis`, `par`,

### Examples

    # Simulate data from a population model in which the log hazard
    # function is linear in age and there is no age x sex interaction
    n <- 1000
    set.seed(731)
    age <- 50 + 12*rnorm(n)
    label(age) <- "Age"
    sex <- factor(sample(c('male','female'), n, TRUE))
    cens <- 15*runif(n)
    h <- .02*exp(.04*(age-50)+.8*(sex=='female'))
    dt <- -log(runif(n))/h
    label(dt) <- 'Follow-up Time'
    e <- ifelse(dt <= cens,1,0)
    dt <- pmin(dt, cens)
    units(dt) <- "Year"
    dd <- datadist(age, sex)
    options(datadist='dd')
    S <- Surv(dt,e)

    # When age is in the model by itself and we predict at the mean age,
    # approximate confidence intervals are ok

    f <- cph(S ~ age, surv=TRUE)
    survplot(f, age=mean(age), conf.int=.95)
    g <- cph(S ~ age, x=TRUE, y=TRUE)
    survplot(g, age=mean(age), conf.int=.95, add=TRUE, col='red', conf='bars')

    # Repeat for an age far from the mean; not ok
    survplot(f, age=75, conf.int=.95)
    survplot(g, age=75, conf.int=.95, add=TRUE, col='red', conf='bars')

    #Plot stratified survival curves by sex, adj for quadratic age effect
    # with age x sex interaction (2 d.f. interaction)

    f <- cph(S ~ pol(age,2)*strat(sex), x=TRUE, y=TRUE)
    #or f <- psm(S ~ pol(age,2)*sex)
    Predict(f, sex, age=c(30,50,70))
    survplot(f, sex, n.risk=TRUE, levels.only=TRUE)   #Adjust age to median
    survplot(f, sex, logt=TRUE, loglog=TRUE)   #Check for Weibull-ness (linearity)
    survplot(f, sex=c("male","female"), age=50)
                                            #Would have worked without datadist
                                            #or with an incomplete datadist
    survplot(f, sex, label.curves=list(keys=c(2,0), point.inc=2))
                                            #Identify curves with symbols

    survplot(f, sex, label.curves=list(keys=c('m','f')))
                                            #Identify curves with single letters

    #Plots by quintiles of age, adjusting sex to male
    options(digits=3)
    survplot(f, age=quantile(age,(1:4)/5), sex="male")

    #Plot survival Kaplan-Meier survival estimates for males
    f <- npsurv(S ~ 1, subset=sex=="male")
    survplot(f)

    #Plot survival for both sexes and show exponential hazard estimates
    f <- npsurv(S ~ sex)
    survplot(f, aehaz=TRUE)
    #Check for log-normal and log-logistic fits
    survplot(f, fun=qnorm, ylab="Inverse Normal Transform")
    survplot(f, fun=function(y)log(y/(1-y)), ylab="Logit S(t)")

    #Plot the difference between sexes
    survdiffplot(f)

    #Similar but show half-width of confidence intervals centered
    #at average of two survival estimates
    survplot(f, conf='diffbands')

    options(datadist=NULL)
    ## Not run:
    #
    # Time to progression/death for patients with monoclonal gammopathy
    # Competing risk curves (cumulative incidence)
    # status variable must be a factor with first level denoting right censoring
    m <- upData(mgus1, stop = stop / 365.25, units=c(stop='years'),
                labels=c(stop='Follow-up Time'), subset=start == 0)
    f <- npsurv(Surv(stop, event) ~ 1, data=m)

    # Use survplot for enhanced displays of cumulative incidence curves for
    # competing risks

    survplot(f, state='pcm', n.risk=TRUE, xlim=c(0, 20), ylim=c(0, .5), col=2)
    survplot(f, state='death', aehaz=TRUE, col=3,
             label.curves=list(keys='lines'))
    f <- npsurv(Surv(stop, event) ~ sex, data=m)
    survplot(f, state='death', aehaz=TRUE, n.risk=TRUE, conf='diffbands',
             label.curves=list(keys='lines'))

    ## End(Not run)

[Package rms version 5.1-1 Index]