intccr (version 1.0.0)

ciregic: Competing Risks Regression with Interval-Censored Data

Description

The function ciregic performs semiparametric regression on cumulative incidence function with interval-censored competing risks data. It fits the proportional subdistribution hazards model (Fine-Gray model), the proportional odds model, and other models that belong to the class of semiparametric generalized odds rate transformation models.

Usage

ciregic(formula, data, alpha, do.par, nboot)

Arguments

formula

a formula object relating the survival object Surv2(v, u, event) to a set of covariates.

data

a data frame to be used.

alpha

\(\alpha = (\alpha1, \alpha2)\) contains parameters that define the link functions from class of generalized odds-rate transformation models. The components \(\alpha1\) and \(\alpha2\) should both be \(\ge 0\). If \(\alpha1 = 0\) the user assumes a proportional subdistribution hazards or Fine-Gray model for cause of failure 1. If \(\alpha2 = 1\) the user assumes a proportional odds model for cause of failure 2.

do.par

an option to use parallel computing for bootstrap. If TRUE, parallel computing will be used during the bootstrap estimation of the variance-covariance matrix for the regression parameter estimates.

nboot

a number of bootstrap samples for estimating variances and covariances of the estimated regression coefficients. If nboot = 0, ciregic does not perform bootstrap estimation of the variance-covariance matrix of the regression parameter estimates and returns NA in the place of the estimated variance-covariance matrix of the regression parameter estimates.

Value

The function ciregic provides an object of class ciregic with components:

varnames

a vector containing variable names

coefficients

a vector of the regression coefficient estimates

gamma

a vector of the estimated coefficients for the B-splines

vcov

a variance-covariance matrix of the estimated regression coefficients

alpha

a vector of the link function parameters

loglikelihood

a loglikelihood of the fitted model

convergence

an indicator of convegence

tms

a vector of the minimum and maximum observation times

Bv

a list containing the B-splines basis functions evaluated at v

numboot

a number of converged bootstrap

call

a matched call

Details

The formula for the model has the form response ~ predictors. The response is a Surv2(v, u, event) object where v is the last observation time prior to the failure, u is the first observation time after the failure, and event is the event or censoring indicator. event should include 0, 1 or 2, denoting right-censoring, failure from cause 1 and failure from cause 2, respectively. If event=0 (i.e. right-censored observation) then u is not included in any calculation as it corresponds to \(\infty\). The user can provide any value in u for the right-censored cases, even NA. The function fits models that belong to the class of generalized odds rate transformation models which includes the proportional subdistribution hazards or the Fine-Gray model and the proportional odds model. The parameter \(\alpha=(\alpha1, \alpha2)\) defines the link function/model to be fitted for cause of failure 1 and 2, respectively. A value of 0 corresponds to the Fine-Gray model and a value of 1 corresponds to the proportional odds model. For example, if \(\alpha=(0,1)\) then the function ciregic fits the Fine-Gray model for cause 1 and the proportional odds model for cause 2.

References

Bakoyannis, G., Yu, M., and Yiannoutsos C. T. (2017). Semiparametric regression on cumulative incidence function with interval-censored competing risks data. Statistics in Medicine, 36:3683-3707.

Fine, J. P. and Gray, R. J. (1999). A proportional hazards model for the subdistribution of a competing risk. Journal of the American Statistical Association, 94:496-509.

See Also

summary.ciregic for the summarized results and predict.ciregic for value of the predicted cumulative incidence functions. coef and vcov are the generic functions. dataprep for reshaping data from a long format to a suitable format to be used in the function ciregic.

Examples

# NOT RUN {
## Set seed in order to have reproducibility of the bootstrap standard error estimate
set.seed(1234)

## Reshaping data from a long format to a suitable format
newdat <- dataprep(data = longdat, ID = "id", time = "t", event = "c", Z = c("z1", "z2"))
## Estimation of regression parameters only. No bootstrap variance estimation.
fit <- ciregic(Surv2(v, u, c) ~ z1 + z2, data = newdat,
               alpha = c(1, 1), nboot = 0, do.par = FALSE)
fit

# }
# NOT RUN {
## Bootstrap variance estimation based on 50 replications
fit <- ciregic(Surv2(v, u, c) ~ z1 + z2, data = simdat,
               alpha = c(1, 1), nboot = 50, do.par = FALSE)
# }
# NOT RUN {
## Note that the user can use parallel computing to decrease
## the computation time of the bootstrap variance-covariance
## estimation (e.g. nboot = 50)

## Summarize semiparametric regression model
summary(fit)

## Predict and draw plot the cumulative incidence function evaluated at z1=1 and z2=0.5
t <- seq(from = 0, to = 2.8, by = 2.8/99)
pred <- predict(object = fit, covp = c(1, 0.5), times = t)
pred
plot(pred$t, pred$cif1, type = "l", ylim=c(0, 1))
points(pred$t, pred$cif2, type = "l", col = 2)

# }