Inference for IDI, continuous NRI, and median improvement

Description

This function performs inference for IDI, continuous NRI, and median improvement. Censoring is adjusted by the inverse probability censoring weight. Proportinal hazards models are used as working models.

Usage

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IDI.INF(indata, covs0, covs1, t0, npert = 300, npert.rand = NULL, seed1 = NULL, alpha = 0.05)

Arguments

indata

Time-to-event data. The number of columns should be 2. The 1st column should be time-to-event, and the 2nd column is event indicator (1=event, 0=censor).

covs0

Covariates/predictors data for a base model (Model 0). Factor variables or character variables are not allowed. If any factor variable is involved in the set of predictors, use model.matrix() for dummy coding. covs0 need to be a design matrix. Also missing value should not be included here.

covs1

Covariates/predictors data for a new model (Model 0). Factor variables or character variables are not allowed. If any factor variable is involved in the set of predictors, use model.matrix() for dummy coding. covs1 need to be a design matrix. Also missing value should not be included here.

t0

A timepoint to define event=yes/no (case/control). Risk score is calculated as the event probability at t0 for each model.

npert

The number of iterations for the perturbation-resampling. Default is 300.

npert.rand

If NULL (default), fresh random numbers will be generated in this routine. If a (n x m) matrix is given as npert.rand, those numbers are used in the pertubation instead, where n is the number of subjects and m is the number of iterations of the resampling. The random numbers should be generated from a distribution with mean 1 and variance 1 independently.

seed1

A seed for generating random numbers for the perturbation-resampling. Default is NULL.

alpha

(1-alpha/2) confidence interval will be calcualted. A 0.95 confidence interval will be provided as a default.

Value

m1

Result of IDI. Point and corresponding (1-alpha/2) confidence interval are given

m2

Result of continuous-NRI. Point and corresponding (1-alpha/2) confidence interval are given. Note that m2 corresponds to the quantity defined as “1/2 NRI(>0)” in Pencina et al.(2011)

m3

Result of median improvement in risk score. Point and corresponding (1-alpha/2) confidence interval are given

m1.est

A vector with 3 elements. The 1st element is the point estimate of the IDI and the 2nd element is the average of risk score in “event” group, and the 3rd element is the average of risk score in “non-event” group. The 1st element is equal to the 2nd element minus the 3rd element.

m2.est

A vector with 3 elements. The 1st element is the point estimate of the continous-NRI. The 2nd element is the proportion of patients in whom the risk scores with the new model were higher than the risk scores with the old model, among “event” group. The 3rd element is the same proportion but among “non-event” group. The 1st element is equal to the 2nd element minus the 3rd element.

m3.est

A vector with 3 elements. The 1st element is the point estimate of the median improvement and the 2nd element is the median of risk score in “event” group, and the 3rd element is the median of risk score in “non-event” group. The 1st element is equal to the 2nd element minus the 3rd element.

m3.est

A vector with 3 elements. The 1st element is the point estimate of the median improvement and the 2nd element is the median of risk score in “event” group, and the 3rd element is the median of risk score in “non-event” group. The 1st element is equal to the 2nd element minus the 3rd element.

point

An object used in IDI.INF.GRAPH()

Note

m2 corresponds to the quantity defined as “1/2 NRI(>0)” in Pencina et al.(2011)

When the base model and the new model are nested, make sure that regression coefficients for the added predictors are significantly different from 0 in the new model, before using this function.

References

Pencina MJ, D'Agostino RB, Steyerberg EW. Extensions of net reclassification improvement calculations to measure usefulness of new biomarkers. Statistics in Medicine 2011. doi:10.1002/sim.5647

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. doi:10.1002/sim.5647

See Also

Papers regarding the issue on evaluating nested models:

Kerr KF, McClelladm RL, Brown ER, Lumley T. Evaluating the Incremental Value of New Biomarkers With Integrated Discrimination Improvement American journal of epidemiology 2011, 174(3):364-74.

Demler OV, Pencina MJ, D'Agostino RB. Misuse of DeLong test to compare AUCs for nested models. Statistics in Medicine 2012; online ahead of print.

Examples

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  #--- sample data (pbc in survival package) ---
  D=subset(pbc, select=c("time","status","age","albumin","edema","protime","bili"))
  D$status=as.numeric(D$status==2)
  D=D[!is.na(apply(D,1,mean)),] ; dim(D)  
  mydata=D[1:100,]

  t0=365*5
  indata1=mydata; 
  indata0=mydata[,-7] ; n=nrow(D) ;
  covs1<-as.matrix(indata1[,c(-1,-2)])
  covs0<-as.matrix(indata0[,c(-1,-2)])

  #--- inference ---
  x<-IDI.INF(mydata[,1:2], covs0, covs1, t0, npert=200) ; 

  #--- results ---
  IDI.INF.OUT(x) ;

  #--- Graphical presentaion of the estimates ---
  # IDI.INF.GRAPH(x) ;