smcfcs.dtsam {smcfcs}

Substantive model compatible fully conditional specification imputation of covariates for discrete time survival analysis

Description

Multiply imputes missing covariate values using substantive model compatible fully conditional specification for discrete time survival analysis.

Usage

smcfcs.dtsam(
  originaldata,
  smformula,
  timeEffects = "factor",
  method,
  predictorMatrix = NULL,
  m = 5,
  numit = 10,
  rjlimit = 1000,
  noisy = FALSE,
  errorProneMatrix = NULL
)

Arguments

originaldata

The data in wide form (i.e. one row per subject)

smformula

A formula of the form "Surv(t,d)~x1+x2+x3", where t is the discrete time variable, d is the binary event indicator, and the covariates should not include time. The time variable should be an integer coded numeric variable taking values from 1 up to the final time period.

timeEffects

Specifies how the effect of time is modelled. timeEffects="factor" (the default) models time as a factor variable. timeEffects="linear" and timeEffects="quad" specify that time be modelled as a continuous linear or quadratic effect on the log odds scale respectively.

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.

Details

For this substantive model type, like for the other substantive model types, smcfcs expects the originaldata to have one row per subject. Variables indicating the discrete time of failure/censoring and the event indicator should be passed in smformula, as described.

The default is to model the effect of time as a factor. This will not work in datasets where there is not at least one observed event in each time period. In such cases you must specify a simpler parametric model for the effect of time. At the moment you can specify either a linear or quadratic effect of time (on the log odds scale).

Author(s)

Jonathan Bartlett [e-mail]

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
## Not run: 
  #discrete time survival analysis example
  M <- 5
  imps <- smcfcs.dtsam(ex_dtsam, "Surv(failtime,d)~x1+x2",
                 method=c("logreg","", "", ""),m=M)
  #fit dtsam model to each dataset manually, since we need
  #to expand to person-period data form first
  ests <- vector(mode = "list", length = M)
  vars <- vector(mode = "list", length = M)
  for (i in 1:M) {
    longData <- survSplit(Surv(failtime,d)~x1+x2, data=imps$impDatasets[[i]],
                          cut=unique(ex_dtsam$failtime[ex_dtsam$d==1]))
    mod <- glm(d~-1+factor(tstart)+x1+x2, family="binomial", data=longData)
    ests[[i]] <- coef(mod)
    vars[[i]] <- diag(vcov(mod))
  }
  library(mitools)
  summary(MIcombine(ests,vars))

## End(Not run)