# dsr: Calculate directly standardized rate In mnel/dsrci: Confidence Intervals on Directly Standardized Rates for Several Parameterizations

## Description

Calculate a directly standardised rate with confidence interval based on a specified method.

## Usage

 ```1 2``` ```dsr(x, n, w, ci.method = c("asymptotic", "moments", "gamma", "beta", "bootstrap"), level = 0.95, mult = 1000, ...) ```

## 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) `ci.method` method used to calculate the confidence interval. See details `level` the confidence level required `mult` a factor to multiply the estimate to give rates per `mult` `...` Further arguments passed to the confidence interval function.

## Details

Five groupds of methods can be specified using `'ci.method'`, with variations on each depending on the method. five groups are:

 `'asymptotic'` Using the normal approximation of the MLE distribution (or transformed MLE distribution). See `ci.asymptotic` for more details and the currently implemented transformations. `'moments'` Moment matching based on Dobson et al (1991). A variety methods for constructing the confidence interval on the unweighted sum of `x`. - See `ci.moments` for more details. `'gamma'` Based on the gamma distribution (Fay & Feuer 1997). See `ci.gamma` for more details and modifications implemented. `'beta'` Based on the beta distribution as proposed by Tiwari et al (2006). See `ci.beta` for details and the modifications implemented. `'bootstrap'` Appromiximate Bootstrap Confidence proposed by Swift (1995).

## Value

`dsr` returns an object of class "`dsr`" . The function `confint` is used to return a confidence interval using a specified method

An object of class "`dsr`" is a list containing the following components:

 `estimate` the estimate of the directly standardised rate `lower` lower bound of the confidence interval `upper` upper bound of the confidence interval `level` the level of confidence `ci.method` method used to calcalate the confidence interval `method.arg` additional argument passed to ci method function `call` the matched call `mult` The multiplicative factor to scale the final estimate `strata` number of strata or summands

## 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 & Feuer (1997). 'Confidence intervals for directly standardized rates: a method based on the gamma distribution. Statistics in Medicine*. 16: 791–801. https://doi.org10.1002/(SICI)1097-0258(19970415)16:7<791::AID-SIM500>3.0.CO;2-%23

Tiwari, Clegg, & Zou (2006). 'Efficient interval estimation for age-adjusted cancer rates.' Statistical Methods in Medical Research 15: 547–569. doi: 10.1177/0962280206070621

Ng, Filardo, & Zheng (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

mnel/dsrci documentation built on May 22, 2017, 11:58 a.m.