MIICD (version 2.1)

MIICD.crreg: Fine & Gray regression for interval censored competing risks data using data augmentation and multiple imputation

Description

Uses data augmentation and multiple imputation approach to compute regression coefficient and its associated variance-covariance matrix, and baseline cumulative incidence estimates for competing risks interval censorded competing risks data

Usage

MIICD.crreg(formula, k, m, status, trans, cens.code, data, method = c("PMDA",
  "ANDA"), verbose = FALSE)

Arguments

formula

A formula. The right hand side indicates names of covariables to be found in data

k

An integer, indicates the number of iteration to perform

m

An integer, indicates the number of imputation to perform at each iteration

status

The name of the column where status are to be found

trans

Denomination of the event of interest in the status column

cens.code

Censor indicator in the status column of the data

data

The input data (see details)

method

Which data augmentation scheme shall be used ? Two algorithms are implemented : The Poor man's Data Augmentation scheme and the Asymptotic Normal Data Augmentation scheme (the later may be preferred).

verbose

Logical, display the results ?

Value

• Coef. Final estimate of the coefficient

  vcov Final estimate of the variance-covariance matrix

  Coef_seq Sequence of the coefficient estimate over iterations

  Sigma_seq Sequence of the coefficient standard deviation over iterations

  df data frame containing the main results

  ... Other returned values

Details

This function uses data augmentation and multiple imputation aproach to estimate regression coefficient, variance-covariance matrix and baseline cumulative incidence estimates in a competing risks proportional hazards regression model for interval censorded competing risks data.

Estimates are computed using Rubin's rules (Rubin (1987)). Estimate of coefficient is computed as the mean of estimates over imputation. The variance-covariance matrix is computed as the within imputation variance and the between imputation variance augmented byan inflation factor to take into account the finite number of imputation. At each iteration, the baseline cumulative incidence function is updated and multiple imputation is performed using the updated estimates. Print and plot methods are available to handle results.

Print and plot methods are available to handle results.

The data must contain at last four columns. One named left, one named right, the name of the 3^{rd} is indicated by the status parameter and one for the covariate to be tested. For interval censored data, the left and right columns indicates the lower and the upper bounds of the intervals respectively. Inf in the right column stands for right censored observations. When an observation is right censored, the status column must contain the censor indicator specified by cens.code. The transition of interest must be precised by the trans parameter.

References

Fine JP and Gray RJ (1999) A proportional hazards model for the subdistribution of a competing risk. JASA 94:496-509.

PAN, Wei. A Multiple Imputation Approach to Cox Regression with Interval-Censored Data. Biometrics, 2000, vol. 56, no 1, p. 199-203.

Rubin, D. B. (1987). Multiple imputation for nonresponse in surveys.

Schenker, N. and Welsh, A. (1988). Asymptotic results for multiple imputation. The Annals of Statistics pages 1550-1566.

Tanner, M. A. and Wong, W. H. (1987). An application of imputation to an estimation problem in grouped lifetime analysis. Technometrics 29, 23-32.

Wei, G. C., & Tanner, M. A. (1991). Applications of multiple imputation to the analysis of censored regression data. Biometrics, 47(4), 1297-1309.

See Also

Surv, survfit, FGR, mvrnorm

Examples

#res <- MIICD.crreg(formula = ~ treatment, k = 10, m = 10, status = 'status',
 #trans = 1, data = ICCRD,  cens.code = 0, method = 'ANDA', verbose = FALSE )
 #res
 #plot(res)
 #diagnostic plot for coefficients end associated standard error
 #plot(res , type = 'coef' , coef = 1)
 #plot(res , type = 'sigma' , coef = 1)