est.CIF: Cumulative incidence function.
In CompetingRisk: The Semi-Parametric Cumulative Incidence Function

Description Usage Arguments Details Value References Examples

This is the main function to obtain the point estimator and pointwise confidence interval for the cumulative incidence function.

1 2	est.CIF(formulas, data, group, group.in.train, newdata, compute.CI, alpha = 0.05, transform = "log-log", save)

`formulas`	A list of length K contains formula objects, where K is the number of failures. Each element is a formula object, with the response on the left of a ~ operator, and the predictors on the right. The response must be a survival object as returned by the `Surv` function.
`data`	A data frame with n observations and p number of covariates.
`group`	The name of the group covariates (if any). If specified, the cumulative incidence function will be estimated for each group separately. Default is `group=NULL`.
`group.in.train`	This argument is valid only when the group argument is specified. If group is presented in both data and newdata, use `group.in.train=T`; If group is presented in only newdata but not data, use `group.in.train=F`.
`newdata`	A data frame or a matrix used for prediction. If not specified, the original data will be used instead.
`compute.CI`	A logic operator for whether to compute the pointwise confidence interval. The default is `compute.CI=FALSE`.
`alpha`	The significance level. The default is 0.05, which computes the `95%` pointwise confidence interval.
`transform`	An indicator if transformation is used for the confidence interval. Only log-log transformation is implemented currently.
`save`	An option to save the computed S0 and S1. It is highly recommended for large-scale dataset to improve the computational efficiency. Default is `save=FALSE`.

This is the main function to compute the point estimator and pointwise confidence interval for the cumulative incidence function. We implemented a flexible function to allow prediction of cumulative incidence function under the cause-specific proportion hazards model in scenarios: 1) when group segmentation is not specified in training and test data; 2) when group segmentation is specified in both training and test data; 3) group segmentation is presented in the test data only; 4) the type of failure is associated with a different setts of covariates. To predict, user can input the new values of all covariates as a vector. If the newdata is specified, the mean of all observations with corresponding covariates will be used in the prediction. In addition, the generic functions such as plot(), summary() are available for the newly defined CIF class.

When group=NULL, est.CIF returns a list of length K. For each sublist, it contains:

`model.fit`	Details of model fit, such as parameter estimates, standard error, etc.
`call`	The survival object used for a the k^th type of failure.
`Estimate`	A data frame contains events.time, overall survival, cumulative incidence, upper and lower bounds (if `compute.CI = TRUE`).

When group is specified, est.CIF returns a list of length that equals to the number of levels in group . For each sublist, it contains a list of length K.

Cheng, S. C., Jason P. Fine, and L. J. Wei. "Prediction of cumulative incidence function under the proportional hazards model." Biometrics (1998): 219-228.

## Not run: 
data("train.data")
data("test.data2")

#1.Example: no group in training and test #
formulas <- list(as.formula("Surv(dtime, prostate) ~ AG + WT + PF + HX +HG + SZ + SG + RX"),
                 as.formula("Surv(dtime, cardio) ~ AG + WT + PF + HX +HG + SZ + SG + RX"),
                 as.formula("Surv(dtime, Other_causes) ~ AG + WT + PF + HX +HG + SZ + SG + RX"))
CIF.output <- est.CIF(formulas, data = train.data, newdata = test.data2,
                  group=NULL, compute.CI=T,save=F)
plot(CIF.output)

#2. Example: group in training data and test data #
formulas <- list(as.formula("Surv(dtime, prostate) ~ AG + WT + PF + HX +HG + SZ + SG + RX"),
                 as.formula("Surv(dtime, cardio) ~ AG + WT + PF + HX +HG + SZ + SG + RX"),
                 as.formula("Surv(dtime, Other_causes) ~ AG + WT + PF + HX +HG + SZ + SG + RX"))
CIF.output <- est.CIF(formulas, data=train.data, group="RX", group.in.train=T,
                      newdata=test.data2, compute.CI=T, alpha=0.05, transform="log-log", save=F)
plot(CIF.output, group="RX")

#3. Example: group not in training data and but in test data #
formulas <- list(as.formula("Surv(dtime, prostate) ~ AG + WT + PF + HX +HG + SZ + SG"),
                 as.formula("Surv(dtime, cardio) ~ AG + WT + PF + HX +HG + SZ + SG "),
                 as.formula("Surv(dtime, Other_causes) ~ AG + WT + PF + HX +HG + SZ + SG"))
CIF.output <- est.CIF(formulas, data=train.data, group="RX", group.in.train=F, newdata=test.data2,
                      compute.CI=T, alpha=0.05, transform="log-log", save=F)
plot(CIF.output, group="RX")


#4. Example: 1)group not in training data and but in test data
#            2)different risk factors associated with cause of failure #
formulas <- list(as.formula("Surv(dtime, prostate) ~ AG + WT + PF + HX +HG"),
                 as.formula("Surv(dtime, cardio) ~  PF + HX +HG "),
                 as.formula("Surv(dtime, Other_causes) ~ AG + WT + PF + HX +HG + SZ"))
CIF.output <- est.CIF(formulas, data=train.data, group="RX", group.in.train=F,
                      newdata=test.data2,compute.CI=T, alpha=0.05, transform="log-log", save=T)
plot(CIF.output, group="RX")

#5. Example: different risk factors associated with cause of failure #
formulas <- list(as.formula("Surv(dtime, prostate) ~ AG + WT + PF + HX +HG"),
                 as.formula("Surv(dtime, cardio) ~  PF + HX +HG + SZ"),
                 as.formula("Surv(dtime, Other_causes) ~ AG + WT + PF + HX +HG + SZ + SG"))
CIF.output <- est.CIF(formulas, data=train.data, group=NULL, group.in.train=F, newdata=test.data2,
                      compute.CI=T, alpha=0.05, transform="log-log", save=F)
plot(CIF.output)

## End(Not run)