relpois {popEpi}

Excess hazard Poisson model

Description

Estimate a Poisson piecewise constant excess hazards model

Usage

relpois(data, formula, fot.breaks = NULL, subset = NULL, check = TRUE, ...)

Arguments

data

a dataset split with e.g. lexpand; must have expected hazard merged within

formula

a formula which is passed on to glm; see Details

fot.breaks

optional; a numeric vector of [a,b) breaks to specify survival intervals over the follow-up time; if NULL, the existing breaks along the mandatory fot time scale in data are used (e.g. the breaks for fot supplied to lexpand)

subset

a logical vector or condition; e.g. subset = sex == 1; limits the data before estimation

check

logical; if TRUE, tabulates excess cases by all factor variables in the formula to check for negative / NA excess cases before fitting the GLM

...

any argument passed on to glm

Details

Basics

relpois employs a custom link function of the Poisson variety to estimate piecewise constant parametric excess hazards. The pieces are determined by fot.breaks. A log(person-years) offset is passed automatically to the glm call.

Formula usage

The formula can be used like any ordinary glm formula. The user must define the outcome in some manner, which is usually lex.Xst after splitting with e.g. lexpand. The exception is the possibility of including the baseline excess hazard terms by including the reserved term FOT in the formula.

For example, lex.Xst != 0 ~ FOT + agegr estimates a model with constant excess hazards at the follow-up intervals as specified by the pertinent breaks used in splitting data, as well as for the different age groups. FOT is created ad hoc if it is used in the formula. If you leave out FOT, the hazard is effectively assumed to be constant across the whole follow-up time.

You can also simply use your own follow-up time interval variable that you have created before calling relpois. However, when using FOT, relpois automatically checks for e.g. negative excess cases in follow-up intervals, allowing for quickly finding splitting breaks where model estimation is possible. It also drops any data outside the follow-up time window.

Splitting and merging population hazard

The easiest way to both split and to include population hazard information is by using lexpand. You may also fairly easily do it by hand by splitting first and then merging in your population hazard information.

Data requirements

The population hazard information must be available for each record and named pop.haz. The follow-up time variable must be named "fot" e.g. as a result of using lexpand. The lex.dur variable must also be present, containing person-year information.

Value

A glm object created using a custom Poisson family construct. Some glm methods are applicable.

Author(s)

Joonas Miettinen, Karri Seppa

References

Paul W Dickman, Andy Sloggett, Michael Hills, and Timo Hakulinen. Regression models for relative survival. Stat Med. 2004 Jan 15;23(1):51-64. doi:10.1002/sim.1597

See Also

lexpand, poisson, glm

Other main functions: Surv(), rate(), relpois_ag(), sir(), sirspline(), survmean(), survtab(), survtab_ag()

Other relpois functions: RPL, relpois_ag(), rpcurve()

Examples

## use the simulated rectal cancer cohort
data("sire", package = "popEpi")
sire$agegr <- cut(sire$dg_age, c(0,45,60,Inf), right=FALSE)

## usable straight away after splitting
fb <- c(0,3/12,6/12,1,2,3,4,5)
x <- lexpand(sire, birth = bi_date, entry = dg_date,
             exit = ex_date, status=status,
             breaks = list(fot=fb), pophaz=popmort)
rpm <- relpois(x, formula = lex.Xst %in% 1:2 ~ FOT + agegr)
 
## some methods for glm work. e.g. test for interaction

rpm2 <- relpois(x, formula = lex.Xst %in% 1:2 ~ FOT*agegr)
anova(rpm, rpm2, test="LRT")
AIC(rpm, rpm2)
## update() won't work currently