sirspline {popEpi}

Estimate splines for SIR or SMR

Description

Splines for standardised incidence or mortality ratio. A useful tool to e.g. check whether a constant SIR can be assumed for all calendar periods, age groups or follow-up intervals. Splines can be fitted for these time dimensions separately or in the same model.

Usage

sirspline(
  coh.data,
  coh.obs,
  coh.pyrs,
  ref.data = NULL,
  ref.obs = NULL,
  ref.pyrs = NULL,
  ref.rate = NULL,
  subset = NULL,
  print = NULL,
  adjust = NULL,
  mstate = NULL,
  spline,
  knots = NULL,
  reference.points = NULL,
  dependent.splines = TRUE
)

Arguments

coh.data

cohort data with observations and at risk time variables

coh.obs

variable name for observed cases

coh.pyrs

variable name for person-years in cohort data

ref.data

aggregated population data

ref.obs

variable name for observed cases

ref.pyrs

variable name for person-years in population data

ref.rate

population rate observed/expected. This overwrites the parameters ref.pyrs and ref.obs.

subset

logical condition to subset coh.data before any computations

print

variable names for which to estimate SIRs/SMRs and associated splines separately

adjust

variable names for adjusting the expected cases

mstate

set column names for cause specific observations. Relevant only when coh.obs length is two or more. See help for sir.

spline

variable name(s) for the splines

knots

number knots (vector), pre-defined knots (list of vectors) or for optimal number of knots left NULL

reference.points

fixed reference values for rate ratios. If left NULL the smallest value is the reference point (where SIR = 1). Ignored if dependent.splines = FALSE

dependent.splines

logical; if TRUE, all splines are fitted in same model.

Details

See sir for help on SIR/SMR estimation in general; usage of splines is discussed below.

The spline variables

The model can include one, two or three splines variables. Variables can be included in the same model selecting dependent.splines = TRUE and SIR ratios are calculated (first one is the SIR, others SIR ratios). Reference points vector can be set via reference.points where first element of the vector is the reference point for first ratio.

Variable(s) to fit splines are given as a vector in argument spline. Order will affect the results.

dependent.splines

By default dependent.splines is FALSE and all splines are fitted in separate models. If TRUE, the first variable in spline is a function of a SIR and other(s) are ratios.

knots

There are three options to set knots to splines:

Set the number of knots for each spline variable with a vector. The knots are automatically placed to the quantiles of observed cases in cohort data. The first and last knots are always the maximum and minimum values, so knot value needs to be at least two.

Predefined knot places can be set with a list of vectors. The vector for each spline in the list specifies the knot places. The lowest and the largest values are the boundary knots and these should be checked beforehand.

If knots is left NULL, the model searches the optimal number of knots by model AIC by fitting models iteratively from 2 to 15 knots and the one with smallest AIC is selected. If dependent.splines = TRUE, the number of knots is searched by fitting each spline variable separately.

print

Splines can be stratified by the levels of variable given in print. If print is a vector, only the first variable is accounted for. The knots are placed globally for all levels of print. This also ensures that the likelihood ratio test is valid. Splines are also fitted independently for each level of print. This allows for searching interactions, e.g. by fitting spline for period (splines='period') for each age group (print = 'agegroup').

p-values

The output p-value is a test of whether the splines are equal (homogenous) at different levels of print. The test is based on the likelihood ratio test, where the full model includes print and is compared to a null model without it. When (dependent.splines = TRUE) the p-value returned is a global p-value. Otherwise the p-value is spline-specific.

Value

A list of data.frames and vectors. Three spline estimates are named as spline.est.A/B/C and the corresponding values in spline.seq.A/B/C for manual plotting

Author(s)

Matti Rantanen, Joonas Miettinen

See Also

splitMulti A SIR calculation vignette

Other sir functions: lines.sirspline(), plot.sirspline(), sir(), sir_exp(), sir_ratio()

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

Examples

## for examples see: vignette('sir')