# baseHaz: The baseline hazard estimate of an 'mjoint' object In joineRML: Joint Modelling of Multivariate Longitudinal Data and Time-to-Event Outcomes

## Description

This function returns the (baseline) hazard increment from a fitted mjoint object. In addition, it can report either the uncentered or the more ubiquitous centered version.

## Usage

 1 baseHaz(object, centered = TRUE, se = FALSE) 

## Arguments

 object an object inheriting from class mjoint for a joint model of time-to-event and multivariate longitudinal data. centered logical: should the baseline hazard be for the mean-centered covariates model or not? Default is centered=TRUE. See Details. se logical: should standard errors be approximated for the hazard increments? Default is se=FALSE.

## Details

When covariates are included in the time-to-event sub-model, mjoint automatically centers them about their respective means. This also applies to non-continuous covariates, which are first coded using a dummy-transformation for the design matrix and subsequently centered. The reason for the mean-centering is to improve numerical stability, as the survival function involves exponential terms. Extracting the baseline hazard increments from mjoint.object returns the Breslow hazard estimate (Lin, 2007) that corresponds to this mean-centered model. This is the same as is done in the R survival package when using coxph.detail (Therneau and Grambsch, 2000). If the user wants to access the baseline hazard estimate for the model in which no mean-centering is applied, then they can use this function, which scales the mean-centered baseline hazard by

\exp\{-\bar{w}^\top γ_v\},

where \bar{w} is a vector of the means from the time-to-event sub-model design matrix.

## Value

A data.frame with two columns: the unique failure times and the estimate baseline hazard. If se=TRUE, then a third column is appended with the corresponding standard errors (for the centred case).

## Author(s)

Graeme L. Hickey (graemeleehickey@gmail.com)

## References

Therneau TM, Grambsch PM. Modeling Survival Data: Extending the Cox Model. New Jersey: Springer-Verlag; 2000.

Lin DY. On the Breslow estimator. Lifetime Data Anal. 2007; 13(4): 471-480.

mjoint and coef.
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ## Not run: # Fit a joint model with bivariate longitudinal outcomes data(heart.valve) hvd <- heart.valve[!is.na(heart.valve$log.grad) & !is.na(heart.valve$log.lvmi), ] fit2 <- mjoint( formLongFixed = list("grad" = log.grad ~ time + sex + hs, "lvmi" = log.lvmi ~ time + sex), formLongRandom = list("grad" = ~ 1 | num, "lvmi" = ~ time | num), formSurv = Surv(fuyrs, status) ~ age, data = list(hvd, hvd), inits = list("gamma" = c(0.11, 1.51, 0.80)), timeVar = "time", verbose = TRUE) baseHaz(fit2, centered = FALSE) ## End(Not run)