poisreg: Family Object for Poisson Regression

In Epi: Statistical Analysis in Epidemiology

Family Object for Poisson Regression

Description

The poisreg family allows Poisson regression models to be fitted using the glm function.

In a Poisson regression model, we assume that the data arise from a Poisson process. We observe D disease events in follow up time Y and wish to estimate the incidence rate, which is assumed to be constant during the follow-up period for any individual. The incidence rate varies between individuals according to the predictor variables and the link function in the model specification.

When using the poisreg family in the glm function, the response should be specified as a two-column matrix with the first column giving the number of events (D) and the second column giving the observation time (Y). This is similar to the binomial family for which a two-column outcome can be used representing the number of successes and the number of failures.

Usage

poisreg(link = "log")

Arguments

link	a specification for the model link function. The poisreg family accepts the links identity, log and inverse.

Value

An object of class "family". See family for details.

The family name, represented by the element "family" in the returned object, is "poisson" and not "poisreg". This is necessary to prevent the summary.glm function from estimating an overdispersion parameter (which should be fixed at 1) and therefore giving incorrect standard errors for the estimates.

Note

When using the log link, Poisson regression can also be carried out using the poisson family by including the log follow-up time log(Y) as an offset. However this approach does not generalize to other link functions. The poisreg family allows more general link functions including additive risk models with poisreg(link = "identity").

See Also

glm, family.

Examples

  ## Estimate incidence rate of diabetes in Denmark (1996-2015) by
  ## age and sex
  data(DMepi)
  DMepi$agegrp <- cut(DMepi$A, seq(from=0, to=100, by=5))
  inc.diab <- glm(cbind(X, Y.nD) ~ -1 + agegrp + sex, family=poisreg,
                  data=DMepi)
  ## The coefficients for agegrp are log incidence rates for men in each
  ## age group. The coefficient for sex is the log of the female:male
  ## incidence rate ratio.
  summary(inc.diab)

  ## Smooth function with non-constant M/F RR:
  requireNamespace("mgcv")
  library( mgcv )
  gam.diab <- gam( cbind(X, Y.nD) ~ s(A,by=sex) + sex,
                   family=poisreg,
                   data=DMepi)

  ## There is no need/use for Y.nD in prediction data frames:
  nM <- data.frame( A=20:90, sex="M" )
  nF <- data.frame( A=20:90, sex="F" )

  ## Rates are returned in units of (1 year)^-1, so we must scale the
  ## rates by hand: 
  matshade( nM$A, cbind( ci.pred(gam.diab,     nM    )*1000,
                         ci.pred(gam.diab,        nF )*1000,
                         ci.exp( gam.diab,list(nM,nF)) ),
            plot=TRUE, col=c("blue","red","black"),
            log="y", xlab="Age", ylab="DM incidence rates per 1000     /     M vs. F RR" )
  abline(h=1)

Epi documentation built on March 19, 2024, 3:07 a.m.