addhazard (version 1.0.0)

ah.2ph: Fit Additive Hazards Regression Models to Two-phase Sampling

Description

The function fits a semiparametric additive hazards model $$\lambda(t|Z=z) = \lambda_0(t) + \beta'z.$$ to two-phase sampling data. The estimating procedures follow Hu (2014).

Usage

ah.2ph(formula, data, R, Pi, robust = FALSE, calibration.variables = NULL)

Arguments

formula

a formula object for the regression model of the form response ~ predictors. The outcome is a survival object created by Surv.

data

a data frame. Input dataset.

R

a phase II membership indicator. A vector of values of 0 and 1. The subject is selected to phase II if R = 1.

Pi

the probability of a subject to be selected to the phase II subsample.

robust

a logical variable. Robust standard errors are provided if robust = TRUE.

calibration.variables

a vector of some column names of the data. These are the variables available for every observation. They are used to calibrate the weight assigned to each subject in order to improve estimation efficiency.

Value

• An object of class "ah.2h" representing the fit.

References

Jie Hu (2014) A Z-estimation System for Two-phase Sampling with Applications to Additive Hazards Models and Epidemiologic Studies. Dissertation, University of Washington.

See Also

predict.ah.2ph for prediction based on fitted additive hazards model with two-phase sampling and nwtsco for the description of nwtsco dataset.

Examples

library(survival)
### load data
nwts <- nwtsco[1:100,]

### create strata based on institutional histology and disease status
nwts$strt <- 1+nwts$instit
### add a stratum containing all (relapsed) cases
nwts$strt[nwts$relaps==1] <- 3

### assign phase II subsampling probabilities
### oversample unfavorable histology (instit =1) and cases
### Pi = 0.5 for instit =0, Pi =1 for instit =1 and relaps =1
nwts$Pi<-  0.5 * (nwts$strt == 1) + 1 * (nwts$strt == 2) + 1 * (nwts$strt == 3)

### generate phase II sampling indicators
N <- dim(nwts)[1]
nwts$in.ph2 <-  rbinom(N, 1, nwts$Pi)

### fit an additive hazards model to two-phase sampling data without calibration
fit1 <- ah.2ph(Surv(trel,relaps) ~ age + histol, data = nwts, R = in.ph2, Pi = Pi,
                                 robust = FALSE,  calibration.variables = NULL)
summary(fit1)


### fit an additve hazards model with calibration on age
fit2 <- ah.2ph(Surv(trel,relaps) ~ age + histol, data = nwts, R = in.ph2, Pi = Pi,
                                   robust = FALSE, calibration.variables = age)
summary(fit2)

### calibrate on age square
### note if users create a  calibration variable, then
### the new variable should be added to the original data frame
nwts$age2 <- nwts$age^2
fit3 <- ah.2ph(Surv(trel,relaps) ~ age + histol, data = nwts, R = in.ph2, Pi = Pi,
                                   robust = FALSE, calibration.variables = age2)
summary(fit3)