intccr (version 3.0.4)

ciregic_lt: Competing Risks Regression with Left-truncated and Interval-Censored Data

Description

The function ciregic_lt performs semiparametric regression on cumulative incidence function with left-truncated and 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. The least-square method is implemented to estimate the standard error of the regression coefficients.

Usage

ciregic_lt(formula, data, alpha, k = 1, do.par, nboot, ...)

Arguments

formula

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

data

a data frame that includes the variables named in the formula argument

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 the proportional subdistribution hazards model or the Fine-Gray model for the cause of failure 1. If \(\alpha2 = 1\), the user assumes the proportional odds model for the cause of failure 2.

k

a parameter that controls the number of knots in the B-spline with \(0.5 \le \)k\( \le 1\)

do.par

an option to use parallel computing for bootstrap. If do.par = 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, the function ciregic_lt returns a closed-form variance estimator using the least-squares method and does not perform bootstrap estimation of the variance-covariance matrix of the regression parameter estimates. For nboot \(\ge 1\), the function ciregic_lt returns the boostrap variance estimator of the regression parameter estimates.

...

further arguments

Value

The function ciregic_lt provides an object of class ciregic_lt 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

notconverged

a list of number of bootstrap samples that did not converge

call

a matched call

Details

The function ciregic_lt is capable of analyzing left-truncated and interval-censored competing risks data. A triplet of time points (w, v, u) is required if an observation is left-truncated and interval-censored. A part of left-truncation is also allowed by defining w = 0 for interval-censored only observation. The formula for the model has the form of response ~ predictors. The response in the formula is a Surv2(v, u, w, event) object where w is a left-truncation time, 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 ciregic_lt 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_lt 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_lt for the summarized results and predict.ciregic_lt 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_lt.

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
newdata <- dataprep_lt(data = longdata_lt, ID = id, time = t, W = w,
                       event = c, Z = c(z1, z2))
## Estimation of regression parameters only. No bootstrap variance estimation.
## with 'newdata'
fit_lt <- ciregic_lt(formula = Surv2(v = v, u = u, w = w, event = c) ~ z1 + z2, data = newdata,
                    alpha = c(1, 1), nboot = 0, do.par = FALSE)
fit_lt

## Bootstrap variance estimation based on 50 replications
fit_lt <- ciregic_lt(formula = Surv2(v = v, u = u, w = w, event = c) ~ z1 + z2, data = newdata,
                    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_lt)

## Predict and draw plot the cumulative incidence function evaluated at z1 = 1 and z2 = 0.5
mint <- fit_lt$tms[1]
maxt <- fit_lt$tms[2]
pred <- predict(object = fit_lt, covp = c(1, 0.5),
                times = seq(mint, maxt, by = (maxt - mint) / 99))
pred
plot(pred$t, pred$cif1, type = "l", ylim = c(0, 1))
points(pred$t, pred$cif2, type = "l", col = 2)
# }