ahaz {ahaz} R Documentation

## Fit semiparametric additive hazards model

### Description

Fit a semiparametric additive hazards regression model. Right-censored and left-truncated survival data are supported.

### Usage

ahaz(surv, X, weights, univariate=FALSE, robust=FALSE)  

### Arguments

 surv Response in the form of a survival object, as returned by the function Surv() in the package survival. Right-censoring and left-truncation is supported. Tied survival times are not supported. X Design matrix. Missing values are not supported. weights Optional vector of observation weights. Default is 1 for each observation. univariate Fit all univariate models instead of the joint model. Default is univar = FALSE. robust Robust calculation of variance. Default is robust = FALSE.

### Details

The semiparametric additive hazards model specifies a hazard function of the form:

h(t) = h_0(t) + \beta' Z_i

for i=1,\ldots,n where Z_i is the vector of covariates, \beta the vector of regression coefficients and h_0 is an unspecified baseline hazard. The semiparametric additive hazards model can be viewed as an additive analogue of the well-known Cox proportional hazards regression model.

Estimation is based on the estimating equations of Lin & Ying (1994).

The option univariate is intended for screening purposes in data sets with a large number of covariates. It is substantially faster than the standard approach of combining ahaz with apply, see the examples.

### Value

An object with S3 class "ahaz".

 call The call that produced this object. nobs Number of observations. nvars Number of covariates. D A nvars x nvars matrix (or vector of length nvars if univar = TRUE). d A vector of length nvars; the regression coefficients equal solve(D,d). B An nvars x nvars matrix such that D^{-1} B D^{-1} estimates the covariance matrix of the regression coefficients. If robust=FALSE then B is estimated using an asymptotic approximation; if robust=TRUE then B is estimated from residuals, see residuals. univariate Is univariate=TRUE? data Formatted version of original data (for internal use). robust Is robust=TRUE?

### References

Lin, D.Y. & Ying, Z. (1994). Semiparametric analysis of the additive risk model. Biometrika; 81:61-71.

summary.ahaz, predict.ahaz, plot.ahaz. The functions coef, vcov, residuals.

### Examples

data(sorlie)

# Break ties
set.seed(10101)
time <- sorlie$time+runif(nrow(sorlie))*1e-2 # Survival data + covariates surv <- Surv(time,sorlie$status)
X <- as.matrix(sorlie[,15:24])