R: Fit semiparametric additive hazards model

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.

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])

# Fit additive hazards model
fit1 <- ahaz(surv, X)
summary(fit1)

# Univariate models
X <- as.matrix(sorlie[,3:ncol(sorlie)])
fit2 <- ahaz(surv, X, univariate = TRUE)
# Equivalent to the following (slower) solution
beta <- apply(X,2,function(x){coef(ahaz(surv,x))})
plot(beta,coef(fit2))

[Package ahaz version 1.15 Index]