ciss.binom: General purpose sample size calculation based on confidence...
In hoehleatsu/binomSamSize: Confidence Intervals and Sample Size Determination for a Binomial Proportion under Simple Random Sampling and Pooled Sampling

ciss.binom

R Documentation

General purpose sample size calculation based on confidence interval widths

Description

Calculate necessary sample size for estimating a binomial proportion with the confidence interval computed by an arbitrary binom.confint function

Usage

ciss.binom(p0, d, alpha=0.05, ci.fun=binom.confint,
           np02x = function(n, p0) round(n*p0), verbose=FALSE,
           nStart=1,nMax=1e6,...)

Arguments

`p0`	hypothesized value of the parameter `p` in the binomial distribution proportion. This is an upper bound if `p0` is below 1/2, and a lower bound if `p0` is above 1/2.
`d`	half width of the confidence interval. Note: The CI is not necessarily symmetric about the estimate so we just look at its width as determine by `d = 1/2*(CI_upper - CI_lower)`.
`alpha`	a two-sided `(1-\alpha)\cdot 100\%` confidence interval is computed
`ci.fun`	Any `binom.confint` like confidence interval computing function. The default is the `binom.confint` function itself. In this case one would have to specify the appropriate method to use using the `method` argument of the `binom.confint` function.
`np02x`	A function specifying how to calculate the value of `x` which results in an estimator of the proportion being as close as possible to the anticipated value `p_0`. Typically the value is obtained by rounding the result of `x\cdot p_0`.
`verbose`	If `TRUE`, additional output of the computations are shown. The default is `FALSE`.
`nStart`	Value where to start the search. The default `n=1` can sometimes lead to wrong answers, e.g. for the Wald-type interval
`nMax`	Max value of the sample size `n` to try in the iterative search. See details
`...`	Additional arguments sent to `ci.fun` function

Details

Given a pre set \alpha-level and an anticipated value of p, say p_0, the objective is to find the minimum sample size n such that the confidence interval will lead to an interval of length 2\cdot d.

Using ciss.binom this is done in a general purpose way by performing an iterative search for the sample size. Starting from n=nStart the appropriate x value, computed as round(x*p0), is found. For this integer x and the current n the corresponding confidence interval is computed using the function ci.fun. This function has to deliver the same type of result as the binom.confint function, i.e. a data frame containing the arguments lower and upper containing the borders of the confidence interval.

The sample size is iteratively increased until the obtained confidence interval has a length smaller than 2\cdot d. This might take a while if n is large. It is possible to speed up the search if an appropriate nStart is provided.

A brute force search is used within the function. Note that for many of the confidence intervals explicit expressions exists to calculate the necessary sample size.

Value

the necessary sample size n

Author(s)

M. Höhle

Examples

#Compute the classical Wald-type interval using brute force search
#Note that nStart=2 needs to be called, because the Wald-intervals
#for x=round(1*0.5)=0 is too short.
ciss.binom(p0=1/2, d=0.1, alpha=0.05, method="asymptotic",nStart=2)
#This could of course be done easier
ciss.wald(p0=1/2, d=0.1, alpha=0.05)

#Same for the Wilson intervals
ciss.binom(p0=1/2, d=0.1, alpha=0.05, method="wilson")
ciss.wilson(p0=1/2, d=0.1, alpha=0.05)

#Now the mid-p intervals 
ciss.binom(p0=1/2, d=0.1, alpha=0.05, ci.fun=binom.midp)
#This search in Fosgate (2005) is a bit different, because interest
#is not directly in the length, but the length is used to derive
#the upper and lower limits and then a search is performed until
#the required alpha level is done. The difference is negliable
ciss.midp(p0=1/2, d=0.1, alpha=0.05)

#Another situation where no closed formula exists
ciss.binom(p0=1/2, d=0.1, alpha=0.05, method="lrt")

#Pooled samples. Now np02x is a func taking three arguments
#The k argument is provided as additional argument
np02x <- function(n,p0,k) round( (1-(1-p0)^k)*n )
ciss.binom( p0=0.1, d=0.05, alpha=0.05, ci.fun=poolbinom.lrt,
            np02x=np02x, k=10,verbose=TRUE)

hoehleatsu/binomSamSize documentation built on March 25, 2024, 10:07 p.m.