VAJointSurv (version 0.1.1)

surv_term: Creates Data for One Type of Survival Outcome

Description

Creates Data for One Type of Survival Outcome

Usage

surv_term(formula, id, data, time_fixef, with_frailty = FALSE, delayed = NULL)

Value

An object of class surv_term with data required for survival outcome.

Arguments

formula

a two-sided formula with the survival outcome on the left-hand side and fixed effect covariates on the right-hand side. The left-hand side needs to be a Surv object and can be either right-censored and left-truncated.

id

the variable for the id of each individual.

data

data.frame with at least the time variable.

time_fixef

the time-varying fixed effects. See .e.g. poly_term. This is for the baseline hazard. Note that many basis expansions have boundary knots. It is important that these are set to cover the full range of survival times including time zero for some expansions.

with_frailty

TRUE if there should be a frailty term.

delayed

a vector with an entry which is TRUE if the left-truncation time from the survival outcome is from a delayed entry.

Details

The time_fixef should likely not include an intercept as this is often included in formula.

The delayed argument is to account for delayed entry with terminal events when observations are sampled in a way such that they must not have had the event prior to their left-truncation time. In this case, the proper complete data likelihood is

$$\frac{a(u)h(t_{ij}\mid u)^{d_{ij}}S(t_{ij} \mid u)g(u)}{\int a(u) S(v_{ij} \mid u) du}$$

and not

$$a(u)h(t_{ij} \mid u)^{d_{ij}}\frac{S(t_{ij} \mid u)}{S(v_{ij} \mid u)}g(u)$$

where \(h\) is conditional hazard, \(S\) is the conditional survival function, \(g\) is additional conditional likelihood factors from other outcomes, \(a\) is the random effect distribution, \(t_{ij}\) is the observed time, \(d_{ij}\) is an event indicator, and \(v_{ij}\) is the left truncation time.

The denominator in the proper complete likelihood becomes the expectation over all delayed entries when a cluster has more than one delayed entry. See van den Berg and Drepper (2016) and Crowther et al. (2016) for further details.

References

Crowther MJ, Andersson TM, Lambert PC, Abrams KR & Humphreys K (2016). Joint modelling of longitudinal and survival data: incorporating delayed entry and an assessment of model misspecification. Stat Med, 35(7):1193-1209. doi:10.1002/sim.6779

van den Berg GJ & Drepper B (2016). Inference for Shared-Frailty Survival Models with Left-Truncated Data. Econometric Reviews, 35:6, 1075-1098, doi: 10.1080/07474938.2014.975640

Examples

# load in the data
library(survival)
data(pbc, package = "survival")

# re-scale by year
pbcseq <- transform(pbcseq, day_use = day / 365.25)
pbc <- transform(pbc, time_use = time / 365.25)

# base knots on observed event times
bs_term_knots <-
  with(pbc, quantile(time_use[status == 2], probs = seq(0, 1, by = .2)))

boundary <- c(bs_term_knots[ c(1, length(bs_term_knots))])
interior <- c(bs_term_knots[-c(1, length(bs_term_knots))])

# create the survival term
s_term <- surv_term(
  Surv(time_use, status == 2) ~ 1, id = id, data = pbc,
  time_fixef = bs_term(time_use, Boundary.knots = boundary, knots = interior))