R: Tests and Confidence Intervals on Directly Standardized Rates

dsrTest {dsrTest}

R Documentation

Tests and Confidence Intervals on Directly Standardized Rates

Description

A number of methods have been proposed for calculating confidence intervals for directly standardized rates. Ng et al (2008), compare a number of methods, some of which are implemented here. The default uses the Gamma method by Fay and Feuer (1997) and implemented in wspoissonTest.

Usage

dsrTest(
  x,
  n,
  w,
  null.value = NULL,
  alternative = c("two.sided", "less", "greater"),
  conf.level = 0.95,
  mult = 1,
  method = c("gamma", "asymptotic", "dobson", "beta", "bootstrap"),
  control = list()
)

Arguments

`x`	a vector of strata-specific counts.
`n`	a vector of strata-specific time bases for counts.
`w`	a vector of strata-specific weights (or standard populations).
`null.value`	a null hypothesis value of the directly rate, if NULL no test is done. If not NULL, provide in rate per mult.
`alternative`	type of alternative hypothesis.
`conf.level`	confidence level for the returned confidence interval.
`mult`	a factor to multiply the estimate and confidence intervals by, to give rates per mult.
`method`	Method used to perform the test and construct the confidence interval. See details.
`control`	list of arguments / type of modification used for each method. See details and relevant `"xxxxControl"` documentation

Details

Five classes of method have been implemented here:

"gamma": Calls wspoissonTest. By default uses the Gamma Method proposed by Fay and Feuer (1997). Modifications proposed by Tiwari et al (2006) and Fay and Kim (2017) also implemented - see gammaControl.
"asymptotic": Using the normal approximation of the MLE or transformed MLE distribution - see asymptoticControl
"dobson": Uses the method proposed by Dobson et al (1991). Estimating the confidence interval on the unweighted sum is done by calling poisson.exact - both the exact method and a mid-p method are possible - see dobsonControl.
"beta": Methods based on the beta distribution by Tiwari et al (2006) - see betaControl.
"bootstrap": Approximate Bootstrap method by Swift (1995). P-values are estimated by solving for p.

For each method there is a control function that will return a list of parameters that can be used to define sub-types of each of the broad groups

Value

a list with class "htest" containing the following components:

`statistic`	number of strata or summands: `k = length(x)`
`parameter`	mult
`p.value`	p-value, set to `NA` if `null.value = NULL`
`conf.int`	confidence interval on the true directly standardized rate
`estimate`	directly standardized rate
`null.value`	null hypothesis value for the DSR
`alternative`	alternative hypothesis type
`method`	description of the method
`data.name`	description of the data

References

Dobson, AJ, Kuulasmaa, K, Eberle, E and Scherer, J (1991) 'Confidence intervals for weighted sums of Poisson parameters', Statistics in Medicine, 10: 457–462. doi:10.1002/sim.4780100317

Swift, MB (1995). 'Simple confidence intervals for standardized rates based on the approximate bootstrap method', Statistics in Medicine, 14, 1875–1888. doi:10.1002/sim.4780141704.

Fay MP & Feuer EJ (1997). 'Confidence intervals for directly standardized rates: a method based on the gamma distribution. Statistics in Medicine*. 16: 791–801. doi:10.1002/(sici)1097-0258(19970415)16:7<791::aid-sim500>3.0.co;2-# Tiwari RC, Clegg LX, & Zou Z (2006). 'Efficient interval estimation for age-adjusted cancer rates.' Statistical Methods in Medical Research 15: 547–569. doi:10.1177/0962280206070621

Ng HKT, Filardo, G & Zheng G (2008). 'Confidence interval estimating procedures for standardized incidence rates.' Computational Statistics and Data Analysis 52 3501–3516. doi:10.1016/j.csda.2007.11.004