predict.ahaz {ahaz} R Documentation

## Prediction methods for ahaz

### Description

Compute regression coefficients, linear predictor, cumulative hazard function, or integrated martingale residuals for a fitted semiparametric additive hazards model.

### Usage

```## 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, ...)
```

### Arguments

 `object` The result of an `ahaz` fit. `newX` Optional new matrix of covariates at which to do predictions. Currently only supported for `type="lp"`. `type` Type of prediction. Options are the regression coefficients ("`coef`"), the linear predictor ("`lp`"), the martingale residuals ("`residuals`"), or the cumulative hazard ("`cumhaz`"). See the details. `beta` Optional vector of regression coefficients. If unspecified, the regression coefficients derived from `object` are used. `...` For future methods.

### Details

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.

### Value

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).

### References

Martinussen, T. & Scheike, T. H. & (2006). Dynamic Regression Models for Survival Data. Springer.

`ahaz`, `summary.ahaz`, `plot.cumahaz`.

### Examples

```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))
```

[Package ahaz version 1.14 Index]