ahaz (version 1.14)

ahaz: 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.

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?

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.

References

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

See Also

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

Examples

# NOT RUN {
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))

# }