# Prediction methods for ahaz Compute regression coefficients, linear predictor, cumulative hazard function, or integrated martingale residuals for a fitted semiparametric additive hazards model. ```r ## 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 $$ D(\hat{\beta}-\beta_0) -d \approx \epsilon_1+\cdots+\epsilon_nD*(beta-beta_0) - d~ epsilon_1 + ... + epsilon_n $$ 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. ## Returns 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. ## See Also `ahaz`, `summary.ahaz`, `plot.cumahaz`. ## Examples ```r 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)) ```

predict.ahaz function