MCbound {MChtest}

Create Monte Carlo stopping boundary

Description

Creates one of several different types of Monte Carlo stopping boundaries

Usage

MCbound(type, parms, conf.level = 0.99)

Arguments

type

a character vector of type of boundary, possible values: "fixed", "tsprt","Bvalue", and "BC"

parms

a numeric vector of parameter values, different for each type (see details)

conf.level

confidence level for intervals about Monte Carlo p-values

Details

Create Monte Carlo stopping boundaries for use with MCtest, where we keep resampling until hitting the stopping boundary. There are several possible types, each with a different length parameter vector.

type="fixed"	then names(parms)=c("Nmax")
type="tsprt"	then names(parms)=c("p0","p1","A","B","Nmax")
	or names(parms)=c("p0","p1","alpha0","beta0","Nmax")
type="Bvalue"	then names(parms)=c("Nmax","alpha","e0","e1")
type="BC"	then names(parms)=c("Nmax","Smax")

The object parms should be a named vector, although unnamed vectors will work if the parameters are in the above order (for the tsprt it assumes the first parameterization). For type="fixed" we keep reampling until N=Nmax resamples. For type="tsprt" we keep resampling until stopping for a truncated sequential probability ratio test for a binary parmaeter. The parameterizations are the usual Wald notation, except alpha0=alpha and beta0=beta, where A=(1-beta0)/alpha0 and B=beta0/(1-alpha0). The Bvalue is a test that p=alpha or not and we stop if the B-value at information time t, B(t), is B(t)<= qnorm(e0) or B >=qnorm(1-e1). Note that the B-value stopping boundary is just a reparameterization of the truncated sequential probability ratio test. For type="BC" we keep resampling until N=Nmax or S=Smax following a design recommended by Besag and Clifford (1991). For each stopping boundary we calculate valid p-values at each stopping point ordering by S/N. For details see Fay, Kim and Hachey, 2006.

Value

An object of class MCbound. A list with the following elements:

S

number of sucesses at points on the boundary

N

number of resamples at points on the boundary

p.value

valid p-value at each point on boundary, calculated using ordering by S/N

ci.lower

lower confidence limit of p-value at each boundary point

ci.upper

upper confidence limit of p-value at each boundary point

Kstar

number of ways to reach each point, (S,N), on boundary times beta(S+1,N-S+1)

conf.level

confidence level for intervals on p-values

type

type of boundary: either "fixed", "tsprt", "Bvalue" or "BC"

parms

parameter vector that defines boundary (see details)

Author(s)

Michael P. Fay

References

Besag, J. and Clifford, P. (1991). Sequential Monte Carlo p-values. Biometrika. 78: 301-304.

Fay, M.P., Kim, H-J. and Hachey, M. (2007). Using truncated sequential probability ratio test boundaries for Monte Carlo implementation of hypothesis tests. Journal of Computational and Graphical Statistics. 16(4):946-967.

Examples

MCbound("tsprt",c(alpha0=.001,beta0=.01,Nmax=99,p0=.06,p1=.04))