predict.ahaz | R Documentation |
Compute regression coefficients, linear predictor, cumulative hazard function, or integrated martingale residuals for a fitted semiparametric additive hazards model.
## S3 method for class 'ahaz' predict(object, newX, type=c("coef", "lp", "residuals", "cumhaz"), beta=NULL, ...) ## S3 method for class 'ahaz' coef(object, ...) ## S3 method for class 'ahaz' vcov(object, ...) ## S3 method for class 'ahaz' residuals(object, ...)
object |
The result of an |
newX |
Optional new matrix of covariates at which to do
predictions. Currently only supported for |
type |
Type of prediction. Options are the regression coefficients
(" |
beta |
Optional vector of regression coefficients. If unspecified,
the regression coefficients derived from |
... |
For future methods. |
The Breslow estimator of the baseline cumulative hazard is described in Lin & Ying (1994).
The regression coefficients beta_0 in the semiparametric additive hazards model are obtained as the solution beta to a quadratic system of linear equations D*beta = d. The (integrated) martingale residuals epsilon_i for i=1,...,n are vectors, of length corresponding to the number of covariates, so that
D*(beta-beta_0) - d ~ epsilon_1 + ... + epsilon_n
The residuals estimate integrated
martingales and are
asymptotically distributed as mean-zero IID multivariate Gaussian. They can be used to derive a sandwich-type variance
estimator for regression coefficients (implemented in
summary.ahaz
when robust=TRUE
is specified). They can moreover be used for implementing consistent standard error
estimation under clustering; or for implementing resampling-based
inferential methods.
See Martinussen & Scheike (2006), Chapter 5.4 for details.
For type="coef"
and type="lp"
, a vector of
predictions.
For type="coef"
, a matrix of (integrated) martingale
residuals, with number of columns corresponding to the number of
covariates.
For type="cumhaz"
, an object with S3 class "cumahaz"
consisting of:
time |
Jump times for the cumulative hazard estimate. |
cumhaz |
The cumulative hazard estimate. |
event |
Status at jump times (1 corresponds to death, 0 corresponds to entry/exit). |
Martinussen, T. & Scheike, T. H. & (2006). Dynamic Regression Models for Survival Data. Springer.
ahaz
, summary.ahaz
, plot.cumahaz
.
data(sorlie) set.seed(10101) # Break ties 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 regression model fit <- ahaz(surv, X) # Parameter estimates coef(fit) # Linear predictor, equivalent to X%*%coef(fit) predict(fit,type="lp") # Cumulative baseline hazard cumahaz <- predict(fit, type="cumhaz") # Residuals - model fit resid <- predict(fit, type = "residuals") # Decorrelate, standardize, and check QQ-plots stdres <- apply(princomp(resid)$scores,2,function(x){x/sd(x)}) par(mfrow = c(2,2)) for(i in 1:4){ qqnorm(stdres[,i]) abline(c(0,1)) } # Residuals - alternative variance estimation resid <- residuals(fit) cov1 <- summary(fit)$coef[,2] invD <- solve(fit$D) Best<-t(resid)%*%resid cov2 <- invD %*% Best %*% invD # Compare with (nonrobust) SEs from 'summary.ahaz' plot(cov1, sqrt(diag(cov2)),xlab="Nonrobust",ylab="Robust") abline(c(0,1))
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