smcfcs (version 1.9.2)

smcfcs.flexsurv: Substantive model compatible fully conditional specification imputation of covariates and event times using flexible parametric survival models

Description

Multiply imputes missing covariate values and event times using substantive model compatible fully conditional specification with a Royston-Parmar flexible parametric survival model.

Usage

smcfcs.flexsurv(
  originaldata,
  smformula,
  k = 2,
  imputeTimes = FALSE,
  censtime = NULL,
  originalKnots = TRUE,
  method,
  predictorMatrix = NULL,
  m = 5,
  numit = 10,
  rjlimit = 1000,
  noisy = FALSE,
  errorProneMatrix = NULL
)

Arguments

originaldata

The original data frame with missing values.

smformula

A formula of the form "Surv(t,d)~x+z"

k

Number of knots to use in the flexible parametric survival model

imputeTimes

If set to TRUE, smcfcs.flexsurv will impute censored survival times, as well as any missing covariates

censtime

Value(s) to use for censoring of imputed event times. If a vector, it should be of length equal to the number of original censored individuals

originalKnots

If imputing censored event times, setting originalKnots=TRUE means the automatically chosen knot locations from the model fitted to the observed times are used throughout. If FALSE, knots are chosen automatically at each iteration by flexsurvspline based on the current observed+imputed event times, according to the chosen value of k.

method

A required vector of strings specifying for each variable either that it does not need to be imputed (""), the type of regression model to be be used to impute. Possible values are "norm" (normal linear regression), "logreg" (logistic regression), "brlogreg" (bias reduced logistic regression), "poisson" (Poisson regression), "podds" (proportional odds regression for ordered categorical variables), "mlogit" (multinomial logistic regression for unordered categorical variables), or a custom expression which defines a passively imputed variable, e.g. "x^2" or "x1*x2". "latnorm" indicates the variable is a latent normal variable which is measured with error. If this is specified for a variable, the "errorProneMatrix" argument should also be used.

predictorMatrix

An optional predictor matrix. If specified, the matrix defines which covariates will be used as predictors in the imputation models (the outcome must not be included). The i'th row of the matrix should consist of 0s and 1s, with a 1 in the j'th column indicating the j'th variable be used as a covariate when imputing the i'th variable. If not specified, when imputing a given variable, the imputation model covariates are the other covariates of the substantive model which are partially observed (but which are not passively imputed) and any fully observed covariates (if present) in the substantive model. Note that the outcome variable is implicitly conditioned on by the rejection sampling scheme used by smcfcs, and should not be specified as a predictor in the predictor matrix.

m

The number of imputed datasets to generate. The default is 5.

numit

The number of iterations to run when generating each imputation. In a (limited) range of simulations good performance was obtained with the default of 10 iterations. However, particularly when the proportion of missingness is large, more iterations may be required for convergence to stationarity.

rjlimit

Specifies the maximum number of attempts which should be made when using rejection sampling to draw from imputation models. If the limit is reached when running a warning will be issued. In this case it is probably advisable to increase the rjlimit until the warning does not appear.

noisy

logical value (default FALSE) indicating whether output should be noisy, which can be useful for debugging or checking that models being used are as desired.

errorProneMatrix

An optional matrix which if specified indicates that some variables are measured with classical measurement error. If the i'th variable is measured with error by variables j and k, then the (i,j) and (i,k) entries of this matrix should be 1, with the remainder of entries 0. The i'th element of the method argument should then be specified as "latnorm". See the measurement error vignette for more details.

Author

Jonathan Bartlett

Details

This version of smcfcs is for time-to-event outcomes which are modelled using a flexible parametric proportional hazards survival model, as proposed by Royston and Parmar (2002). The model is fitted using the flexsurvspline function in the flexsurv package. Specifically it fits models using the hazard scale. The flexibility of the model can be changed by modifying the k argument, which specifies the number of knots.

If desired, smcfcs.flexsurv can be used to impute event times for individuals who are originally censored, by specifying imputeTimes=TRUE. In the resulting imputed datasets every individual will have an event time and the event indicator will be one for all. Alternatively, you can impute censored times, but setting a larger potential censoring time, which is either a common value used for all or a vector of times, by using the censtime argument. If some individuals have their time-to-event outcome completely missing and you want to impute this, they should have a time of zero and the event indicator set to zero.

flexsurvspline sometimes fails during model fitting. If/when this occurs, smcfcs.flexsurv takes a posterior draw based on the model fit from the preceding iteration, and a warning is printed at the end of the smcfcs.flexsurv run detailing how many times it occurred.

References

Royston P, Parmar MKB. Flexible parametric proportional-hazards and proportional-odds models for censored survival data, with application to prognostic modelling and estimation of treatment effects. Statistics in Medicine 2002; 21(15): 2175-2197. tools:::Rd_expr_doi("doi:10.1002/sim.1203")

Examples

#the following example is not run when the package is compiled on CRAN
#(to keep computation time down), but it can be run by package users
if (FALSE) {

  set.seed(63213)
  imps <- smcfcs.flexsurv(ex_flexsurv,
                          k=2,
                          smformula="Surv(t,d)~x+z",
                          method=c("","","logreg",""))
  library(mitools)
  impobj <- imputationList(imps$impDatasets)
  models <- with(impobj, flexsurvspline(Surv(t,d)~x+z, k=2))
  summary(MIcombine(models))

  # now impute event times as well as missing covariates
  imps <- smcfcs.flexsurv(ex_flexsurv,
                          k=2,
                          smformula="Surv(t,d)~x+z",
                          method=c("","","logreg",""),
                          imputeTimes=TRUE)

  # now impute event times as well as missing covariates,
  # but setting max observed event time to 2
  imps <- smcfcs.flexsurv(ex_flexsurv,
                          k=2,
                          smformula="Surv(t,d)~x+z",
                          method=c("","","logreg",""),
                          imputeTimes=TRUE,
                          censtime=2)

}