R Functions to calculate NRI for comparing time to event and binary response models.

Description

This package provides the functions to estimate the net reclassification improvement (NRI) for competing risk prediction models with time to event and binary response data. The NRI for binary response models can be calculated by nribin, and that for time to event models can be calculated by nricens. The risk category based NRI and the risk difference based NRI are provided by these functions. Users can use several estimators for comparing time to event models. Confidence intervals are calculated by the percentile bootstrap method. In this version, several types of input data are allowed to improve user-friendliness and convenience.

Details

Author(s)

Eisuke Inoue <eisuke.inoue@marianna-u.ac.jp>

References

Pencina MJ, D'Agostino RB, Steyerberg EW. Extensions of net reclassification improvement calculations to measure usefulness of new biomarkers. Statistics in Medicine 2011.

Uno H, Tian L, Cai T, Kohane IS, Wei LJ. A unified inference procedure for a class of measures to assess improvement in risk prediction systems with survival data, Statistics in Medicine 2012.

Hsu CH, Taylor JMG. A robust weighted Kaplan-Meier approach for data with dependent censoring using linear combinations of prognostic covariates, Statistics in Medicine 2010.

Examples

## consider pbc dataset in survival package as an example
library(survival)
dat = pbc[1:312,]
dat$sex = ifelse(dat$sex=='f', 1, 0)

## predciting the event of 'death'
time  = dat$time
event = ifelse(dat$status==2, 1, 0)

## standard prediction model: age, bilirubin, and albumin
z.std = as.matrix(subset(dat, select = c(age, bili, albumin)))

## new prediction model: age, bilirubin, albumin, and protime
z.new = as.matrix(subset(dat, select = c(age, bili, albumin, protime)))

## fitting cox models
mstd = coxph(Surv(time, event) ~ ., data.frame(time, event, z.std), x=TRUE)
mnew = coxph(Surv(time, event) ~ ., data.frame(time, event, z.new), x=TRUE)

## Calculation of the risk category NRI at 2000 days
nricens(mdl.std = mstd, mdl.new = mnew, t0 = 2000, cut = c(0.2, 0.4),
        niter = 10)


## Next, consider binary prediction models
library(survival)
dat = pbc[1:312,]
dat$sex = ifelse(dat$sex=='f', 1, 0)

## subjects censored before 2000 days are excluded
dat = dat[ dat$time > 2000 | (dat$time < 2000 & dat$status == 2), ]

## predciting the event of 'death' before 2000 days
event = ifelse(dat$time < 2000 & dat$status == 2, 1, 0)

## standard prediction model: age, bilirubin, and albumin
z.std = as.matrix(subset(dat, select = c(age, bili, albumin)))

## new prediction model: age, bilirubin, albumin, and protime
z.new = as.matrix(subset(dat, select = c(age, bili, albumin, protime)))

## glm fit (logistic model)
mstd = glm(event ~ ., binomial(logit), data.frame(event, z.std), x=TRUE)
mnew = glm(event ~ ., binomial(logit), data.frame(event, z.new), x=TRUE)

## Calculation of risk difference NRI
nribin(mdl.std = mstd, mdl.new = mnew, cut = 0.02, niter = 0,
       updown = 'diff')

Categorization of a continuous variable.

Description

Internaly used function to categorize a continuous variable.

Usage

categorize(dat, threshold)

Arguments

Calculate individual risks based on the Cox regression model.

Description

This function estimates Pr\{T < t_0\} given covariates under the Cox model.

Usage

get.risk.coxph(mdl, t0)

Arguments

Calculate individual risks based on the parametric survival regression model.

Description

This function estimates Pr\{T < t_0\} given covariates under the parametric survival model.

Usage

get.risk.survreg(mdl, t0)

Arguments

Calculate a survival probability at a given time by the standard Kaplan-Meier estimator.

Description

This function estimates Pr\{T > t_0\} by the Kaplan-Meier estimator. t_0 should be given.

Usage

get.surv.km(time, event, t0, subs = NULL)

Arguments

Determine UP and DOWN for the NRI calculation

Description

Internaly used function to detemine subjects who belong to UP and DOWN.

Usage

get.uppdwn(time, event, objs, flag.mdl, flag.prd, flag.rsk, t0, updown,
           cut, get.risk, msg = FALSE)

Arguments

Determine UP and DOWN for the NRI calculation

Description

Internaly used function to detemine subjects who belong to UP and DOWN.

Usage

get.uppdwn.bin(event, objs, flag.mdl, flag.prd, flag.rsk, updown, cut,
               link, msg = FALSE)

Arguments

NRI for binary models

Description

This function estimates the NRI for competing risk prediction models with binary response variable. glm objects, predictors, and predicted risks can be used as input data for the calculation. The risk category based NRI and the risk difference based NRI can be calculated. The percentile bootstrap method is used for an interval estimation.

Usage

nribin(event = NULL, mdl.std = NULL, mdl.new = NULL, z.std = NULL, z.new = NULL,
       p.std = NULL, p.new = NULL, updown = "category", cut = NULL,
       link = "logit", niter = 1000, alpha = 0.05, msg = TRUE)
       

Arguments

Details

Either one set of the following arguments should be specified for the NRI calculation: (mdl.std, mdl.new); (event, z.std, z.new); and (event, p.std, p.new).

In the first set of the argument, (mdl.std, mdl.new), fitted results are used for the NRI calculation. event, z.std, and z.new are extracted from fitted result objects. The variance of model parameters are accounted for an interval estimation of the NRI. When event is specified in arguments, those specified is used without extracting from glm object.

In the second set of the argument, (event, z.std, z.new), a standard and a new prediction models are fitted inside this function with specified link. The variance of model parameters are also accounted for an interval estimation of the NRI.

In the third set of the argument, (event, p.std, p.new), predicted risks are used. Since fit of prediction models are not conducted while in a bootstrap, this can be used for a validation study by an external data source or by a cross-validation.

For the risk category based NRI calculation, cutoff values of risk category can be specified by cut, which is a scalar for the case of two risk categories and is a vector for the case of more than two risk categories. UP and DOWN are determined by the movement in risk categories.

For the risk difference based NRI calculation, cutoff values of risk difference can also be specified by cut, where UP and DOWN are defiend as p_{new} - p_{standard} > \delta and p_{standard} - p_{new} > \delta, respectively. p_{standard} and p_{new} are predicted individual risks from a standard and a new prediction model, respectively, and \delta corresponds to cut. The continuous NRI, which is the special version of the risk difference based NRI, can be calculated by specifying both updown = "diff" and cut = 0.

Interval estimation is based on the percentile bootstrap method.

Value

Returns a list of the following items:

Examples

## here consider pbc dataset in survival package as an example
library(survival)
dat = pbc[1:312,]
dat$sex = ifelse(dat$sex=='f', 1, 0)

## subjects censored before 2000 days are excluded
dat = dat[ dat$time > 2000 | (dat$time < 2000 & dat$status == 2), ]

## predciting the event of 'death' before 2000 days
event = ifelse(dat$time < 2000 & dat$status == 2, 1, 0)

## standard prediction model: age, bilirubin, and albumin
z.std = as.matrix(subset(dat, select = c(age, bili, albumin)))

## new prediction model: age, bilirubin, albumin, and protime
z.new = as.matrix(subset(dat, select = c(age, bili, albumin, protime)))

## glm fit (logistic model)
mstd = glm(event ~ ., binomial(logit), data.frame(event, z.std), x=TRUE)
mnew = glm(event ~ ., binomial(logit), data.frame(event, z.new), x=TRUE)

## predicted risk
p.std = mstd$fitted.values
p.new = mnew$fitted.values

## Calculation of risk difference NRI using ('mdl.std', 'mdl.std').
nribin(mdl.std = mstd, mdl.new = mnew, cut = 0.02, niter = 0,
       updown = 'diff')

## Calculation of risk difference NRI using ('event', 'z.std', 'z.std').
nribin(event = event, z.std = z.std, z.new = z.new, cut = 0.02,
       niter = 0, updown = 'diff')

## Calculation of risk difference NRI using ('event', 'p.std', 'p.std').
nribin(event = event, p.std = p.std, p.new = p.new, cut = 0.02,
       niter = 0, updown = 'diff')

## Calculation of risk category NRI using ('mdl.std', 'mdl.std').
nribin(mdl.std = mstd, mdl.new = mnew, cut = c(0.2, 0.4),
       niter = 0, updown = 'category')

Estimate NRI by the counting method.

Description

Internaly used function by nribin. In the comparison for binary models, it is possible to use directly when UP and DOWN subjects are known.

Usage

nribin.count.main(event, upp, dwn)

Arguments

NRI for time to event models

Description

This function estimates the NRI for competing risk prediction models with time to event variable. coxph object, survreg object, predictors, and predicted risks can be used as input data for the calculation. The risk category based NRI and the risk difference based NRI can be calculated. Users can use several types of estimators to obtain point estimates of the NRI and its components. The percentile bootstrap method is used for an interval estimation.

Usage

nricens(time = NULL, event = NULL, mdl.std = NULL, mdl.new = NULL,
        z.std = NULL, z.new = NULL, p.std = NULL, p.new = NULL, t0 = NULL,
        updown = "category", cut = NULL, point.method = "km",
        niter = 1000, alpha = 0.05, msg = TRUE)

Arguments

Details

Either one set of the following arguments should be specified for the NRI calculation: (mdl.std, mdl.new); (time, event, z.std, z.new); and (time, event, p.std, p.new).

In the first set of the argument, (mdl.std, mdl.new), fitted results by coxph or survreg are used for the NRI calculation. time, event, z.std, and z.new are extracted from fitted result objects. The variance of model parameters are accounted for an interval estimation of the NRI. When time and event are specified in arguments, those specified are used without extracting from coxph or survreg objects.

In the second set of the argument, (time, event, z.std, z.new), a standard and a new prediction models are fitted inside this function with time, event, z.std and z.new. The variance of model parameters are also accounted for an interval estimation of the NRI.

In the third set of the argument, (time, event, p.std, p.new), predicted risks are used. Since fit of prediction models are not conducted while in a bootstrap, this can be used for a validation study by an external data source or by a cross-validation.

For the risk category based NRI calculation, cutoff values of risk category can be specified by cut, which is a scalar for the case of two risk categories and is a vector for the case of more than two risk categories. UP and DOWN are determined by the movement in risk categories.

For the risk difference based NRI calculation, cutoff values of risk difference can also be specified by cut, where UP and DOWN are defiend as p_{new} - p_{standard} > \delta and p_{standard} - p_{new} > \delta, respectively. p_{standard} and p_{new} are predicted individual risks from a standard and a new prediction model, respectively, and \delta corresponds to cut. The continuous NRI, which is the special version of the risk difference based NRI, can be calculated by specifying both updown = "diff" and cut = 0.

Interval estimation is based on the percentile bootstrap method.

Value

Returns a list of the following items:

References

Pencina MJ, D'Agostino RB, Steyerberg EW. Extensions of net reclassification improvement calculations to measure usefulness of new biomarkers. Statistics in Medicine 2011.

Uno H, Tian L, Cai T, Kohane IS, Wei LJ. A unified inference procedure for a class of measures to assess improvement in risk prediction systems with survival data, Statistics in Medicine 2012.

Hsu CH, Taylor JMG. A robust weighted Kaplan-Meier approach for data with dependent censoring using linear combinations of prognostic covariates, Statistics in Medicine 2010.

Examples

## here consider pbc dataset in survival package as an example
library(survival)
dat = pbc[1:312,]
dat$sex = ifelse(dat$sex=='f', 1, 0)

## predciting the event of 'death'
time  = dat$time
event = ifelse(dat$status==2, 1, 0)

## standard prediction model: age, bilirubin, and albumin
z.std = as.matrix(subset(dat, select = c(age, bili, albumin)))

## new prediction model: age, bilirubin, albumin, and protime
z.new = as.matrix(subset(dat, select = c(age, bili, albumin, protime)))

## coxph fit
mstd = coxph(Surv(time,event) ~ ., data.frame(time,event,z.std), x=TRUE)
mnew = coxph(Surv(time,event) ~ ., data.frame(time,event,z.new), x=TRUE)

## predicted risk at t0=2000
p.std = get.risk.coxph(mstd, t0=2000)
p.new = get.risk.coxph(mnew, t0=2000)

## Calculation of risk category NRI
##   by the KM estimator using ('mdl.std', 'mdl.std').
nricens(mdl.std = mstd, mdl.new = mnew, t0 = 2000, cut = c(0.2, 0.4),
        niter = 0)

##   by the KM estimator using ('time', 'event', 'z.std', 'z.std').
nricens(time = time, event = event, z.std = z.std, z.new = z.new,
        t0 = 2000, cut = c(0.2, 0.4), niter = 0)

##   by the KM estimator using ('time','event','p.std','p.std').
nricens(time = time, event = event, p.std = p.std, p.new = p.new,
        t0 = 2000, cut = c(0.2, 0.4), niter = 0)

## Calculation of risk difference NRI by the KM estimator
nricens(mdl.std = mstd, mdl.new = mnew, t0 = 2000, updown = 'diff',
        cut = 0.05, niter = 0)

## Calculation of risk difference NRI by the IPW estimator
nricens(mdl.std = mstd, mdl.new = mnew, t0 = 2000, updown = 'diff',
        cut = 0.05, point.method = 'ipw', niter = 0)

Estimate NRI by the inverse probability weighting (IPW) method.

Description

Internaly used function by nricens to provide the NRI estimator by the IPW method. In the comparison for time to event models, it is possible to use directly when UP and DOWN subjects are known.

Usage

nricens.ipw.main(time, event, upp, dwn, t0)

Arguments

Estimate NRI by the standard Kaplan-Meier method.

Description

Internaly used function by nricens to provide the NRI estimator by the Kaplan-Meier(KM) method. In the comparison for time to event models, it is possible to use directly when UP and DOWN subjects are known.

Usage

nricens.km.main(time, event, upp, dwn, t0)

Arguments