CSC: Cause-specific Cox proportional hazard regression

Description

Interface for fitting cause-specific Cox proportional hazard regression models in competing risk.

Usage

CSC(formula, data, cause, surv.type = "hazard", fitter = "coxph", ...)

Value

models: a list with the fitted (cause-specific) Cox regression objects
response: the event history response
eventTimes: the sorted (unique) event times
surv.type: the value of surv.type
theCause: the cause of interest. see cause
causes: the other causes

Arguments

formula: Either a single Hist formula or a list of formulas. If it is a list it must contain as many Hist formulas as there are causes when surv.type="hazard" and exactly two formulas when surv.type="survival". If it is a list the first formula is used for the cause of interest specific Cox regression and the other formula(s) either for the other cause specific Cox regression(s) or for the Cox regression of the combined event where each cause counts as event. Note that when only one formula is given the covariates enter in exactly the same way into all Cox regression analyses.
data: A data in which to fit the models.
cause: The cause of interest. Defaults to the first cause (see Details).
surv.type: Either "hazard" (the default) or "survival". If "hazard" fit cause-specific Cox regression models for all causes. If "survival" fit one cause-specific Cox regression model for the cause of interest and also a Cox regression model for event-free survival.
fitter: Routine to fit the Cox regression models. If coxph use survival::coxph else use rms::cph.
...: Arguments given to fitter, e.g., coxph.

Author

Thomas A. Gerds tag@biostat.ku.dk and Ulla B. Mogensen

Details

The causes and their order are determined by prodlim::getStates() applied to the Hist object.

References

B. Ozenne, A. L. Soerensen, T.H. Scheike, C.T. Torp-Pedersen, and T.A. Gerds. riskregression: Predicting the risk of an event using Cox regression models. R Journal, 9(2):440--460, 2017.

J Benichou and Mitchell H Gail. Estimates of absolute cause-specific risk in cohort studies. Biometrics, pages 813--826, 1990.

T.A. Gerds, T.H. Scheike, and P.K. Andersen. Absolute risk regression for competing risks: Interpretation, link functions, and prediction. Statistics in Medicine, 31(29):3921--3930, 2012.

Examples

Run this code


library(prodlim)
library(survival)
data(Melanoma)
## fit two cause-specific Cox models
## different formula for the two causes
fit1 <- CSC(list(Hist(time,status)~sex+age,Hist(time,status)~invasion+epicel+log(thick)),
            data=Melanoma)
print(fit1)
if (FALSE) {
library(Publish)
publish(fit1)
}

## model hazard of all cause mortality instead of hazard of type 2
fit1a <- CSC(list(Hist(time,status)~sex+age,Hist(time,status)~invasion+epicel+log(thick)),
             data=Melanoma,
             surv.type="surv")

## the predicted probabilities are similar
plot(predictRisk(fit1,times=500,cause=1,newdata=Melanoma),
     predictRisk(fit1a,times=500,cause=1,newdata=Melanoma))

## special case where cause 2 has no covariates
fit1b <- CSC(list(Hist(time,status)~sex+age,Hist(time,status)~1),
             data=Melanoma)
print(fit1b)
predict(fit1b,cause=1,times=100,newdata=Melanoma)


## same formula for both causes
fit2 <- CSC(Hist(time,status)~invasion+epicel+age,
            data=Melanoma)
print(fit2)

## combine a cause-specific Cox regression model for cause 2
## and a Cox regression model for the event-free survival:
## different formula for cause 2 and event-free survival
fit3 <- CSC(list(Hist(time,status)~sex+invasion+epicel+age,
                 Hist(time,status)~invasion+epicel+age),
            surv.type="surv",
            data=Melanoma)
print(fit3)

## same formula for both causes
fit4 <- CSC(Hist(time,status)~invasion+epicel+age,
            data=Melanoma,
            surv.type="surv")
print(fit4)

## strata
fit5 <- CSC(Hist(time,status)~invasion+epicel+age+strata(sex),
            data=Melanoma,
            surv.type="surv")
print(fit5)

## sanity checks

cox1 <- coxph(Surv(time,status==1)~invasion+epicel+age+strata(sex),data=Melanoma)
cox2 <- coxph(Surv(time,status!=0)~invasion+epicel+age+strata(sex),data=Melanoma)
all.equal(coef(cox1),coef(fit5$models[[1]]))
all.equal(coef(cox2),coef(fit5$models[[2]]))

## predictions
##
## surv.type = "hazard": predictions for both causes can be extracted
## from the same fit
fit2 <- CSC(Hist(time,status)~invasion+epicel+age, data=Melanoma)
predict(fit2,cause=1,newdata=Melanoma[c(17,99,108),],times=c(100,1000,10000))
predictRisk(fit2,cause=1,newdata=Melanoma[c(17,99,108),],times=c(100,1000,10000))
predictRisk(fit2,cause=2,newdata=Melanoma[c(17,99,108),],times=c(100,1000,10000))
predict(fit2,cause=1,newdata=Melanoma[c(17,99,108),],times=c(100,1000,10000))
predict(fit2,cause=2,newdata=Melanoma[c(17,99,108),],times=c(100,1000,10000))

## surv.type = "surv" we need to change the cause of interest
library(survival)
fit5.2 <- CSC(Hist(time,status)~invasion+epicel+age+strata(sex),
            data=Melanoma,
            surv.type="surv",cause=2)
## now this does not work
try(predictRisk(fit5.2,cause=1,newdata=Melanoma,times=4))

## but this does
predictRisk(fit5.2,cause=2,newdata=Melanoma,times=100)
predict(fit5.2,cause=2,newdata=Melanoma,times=100)
predict(fit5.2,cause=2,newdata=Melanoma[4,],times=100)

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