Summaries of fitted flexible survival models

Return fitted survival, cumulative hazard or hazard at a series of times from a fitted flexsurvreg or flexsurvspline model.

Usage

# S3 method for flexsurvreg
summary(
  object,
  newdata = NULL,
  X = NULL,
  type = "survival",
  fn = NULL,
  t = NULL,
  quantiles = 0.5,
  start = 0,
  cross = TRUE,
  ci = TRUE,
  se = FALSE,
  B = 1000,
  cl = 0.95,
  tidy = FALSE,
  na.action = na.pass,
  ...
)

Arguments

object

Output from flexsurvreg or flexsurvspline, representing a fitted survival model object.

newdata

Data frame containing covariate values to produce fitted values for. Or a list that can be coerced to such a data frame. There must be a column for every covariate in the model formula, and one row for every combination of covariates the fitted values are wanted for. These are in the same format as the original data, with factors as a single variable, not 0/1 contrasts.

If this is omitted, if there are any continuous covariates, then a single summary is provided with all covariates set to their mean values in the data - for categorical covariates, the means of the 0/1 indicator variables are taken. If there are only factor covariates in the model, then all distinct groups are used by default.

X

Alternative way of defining covariate values to produce fitted values for. Since version 0.4, newdata is an easier way that doesn't require the user to create factor contrasts, but X has been kept for backwards compatibility.

Columns of X represent different covariates, and rows represent multiple combinations of covariate values. For example matrix(c(1,2),nrow=2) if there is only one covariate in the model, and we want survival for covariate values of 1 and 2. A vector can also be supplied if just one combination of covariates is needed.

For ``factor'' (categorical) covariates, the values of the contrasts representing factor levels (as returned by the contrasts function) should be used. For example, for a covariate agegroup specified as an unordered factor with levels 20-29, 30-39, 40-49, 50-59, and baseline level 20-29, there are three contrasts. To return summaries for groups 20-29 and 40-49, supply X = rbind(c(0,0,0), c(0,1,0)), since all contrasts are zero for the baseline level, and the second contrast is ``turned on'' for the third level 40-49.

type

"survival" for survival probabilities.

"cumhaz" for cumulative hazards.

"hazard" for hazards.

"rmst" for restricted mean survival.

"mean" for mean survival.

"median" for median survival (alternative to type="quantile" with quantiles=0.5).

"quantile" for quantiles of the survival time distribution.

"link" for the fitted value of the location parameter (i.e. the "linear predictor" but on the natural scale of the parameter, not on the log scale)

Ignored if "fn" is specified.

fn

Custom function of the parameters to summarise against time. This has optional first two arguments t representing time, and start representing left-truncation points, and any remaining arguments must be parameters of the distribution. It should be vectorised, and return a vector corresponding to the vectors given by t, start and the parameter vectors.

t

Times to calculate fitted values for. By default, these are the sorted unique observation (including censoring) times in the data - for left-truncated datasets these are the "stop" times.

quantiles

If type="quantile", this specifies the quantiles of the survival time distribution to return estimates for.

start

Optional left-truncation time or times. The returned survival, hazard or cumulative hazard will be conditioned on survival up to this time. Predicted times returned with "rmst", "mean", "median" or "quantile" will be times since time zero, not times since the start time.

A vector of the same length as t can be supplied to allow different truncation times for each prediction time, though this doesn't make sense in the usual case where this function is used to calculate a predicted trajectory for a single individual. This is why the default start time was changed for version 0.4 of flexsurv - this was previously a vector of the start times observed in the data.

cross

If TRUE (the default) then summaries are calculated for all combinations of times specified in t and covariate vectors specifed in newdata.

If FALSE, then the times t should be of length equal to the number of rows in newdata, and one summary is produced for each row of newdata paired with the corresponding element of t. This is used, e.g. when determining Cox-Snell residuals.

ci

Set to FALSE to omit confidence intervals.

se

Set to TRUE to include standard errors.

B

Number of simulations from the normal asymptotic distribution of the estimates used to calculate confidence intervals or standard errors. Decrease for greater speed at the expense of accuracy, or set B=0 to turn off calculation of CIs and SEs.

cl

Width of symmetric confidence intervals, relative to 1.

tidy

If TRUE, then the results are returned as a tidy data frame instead of a list. This can help with using the ggplot2 package to compare summaries for different covariate values.

na.action

Function determining what should be done with missing values in newdata. If na.pass (the default) then summaries of NA are produced for missing covariate values. If na.omit, then missing values are dropped, the behaviour of summary.flexsurvreg before flexsurv version 1.2.

...

Further arguments passed to or from other methods. Currently unused.

Value

If tidy=FALSE, a list with one component for each unique covariate value (if there are only categorical covariates) or one component (if there are no covariates or any continuous covariates). Each of these components is a matrix with one row for each time in t, giving the estimated survival (or cumulative hazard, or hazard) and 95% confidence limits. These list components are named with the covariate names and values which define them.

If tidy=TRUE, a data frame is returned instead. This is formed by stacking the above list components, with additional columns to identify the covariate values that each block corresponds to.

If there are multiple summaries, an additional list component named X contains a matrix with the exact values of contrasts (dummy covariates) defining each summary.

The plot.flexsurvreg function can be used to quickly plot these model-based summaries against empirical summaries such as Kaplan-Meier curves, to diagnose model fit.

Confidence intervals are obtained by sampling randomly from the asymptotic normal distribution of the maximum likelihood estimates and then taking quantiles (see, e.g. Mandel (2013)).

Details

Time-dependent covariates are not currently supported. The covariate values are assumed to be constant through time for each fitted curve.

References

Mandel, M. (2013). "Simulation based confidence intervals for functions with complicated derivatives." The American Statistician (in press).

Author

C. H. Jackson chris.jackson@mrc-bsu.cam.ac.uk