Creates one of several different types of Monte Carlo stopping boundaries
MCbound(type, parms, conf.level = 0.99)a character vector of type of boundary, possible values: "fixed", "tsprt","Bvalue", and "BC"
a numeric vector of parameter values, different for each type (see details)
confidence level for intervals about Monte Carlo p-values
An object of class MCbound. A list with the following elements:
number of sucesses at points on the boundary
number of resamples at points on the boundary
valid p-value at each point on boundary, calculated using ordering by S/N
lower confidence limit of p-value at each boundary point
upper confidence limit of p-value at each boundary point
number of ways to reach each point, (S,N), on boundary times beta(S+1,N-S+1)
confidence level for intervals on p-values
type of boundary: either "fixed", "tsprt", "Bvalue" or "BC"
parameter vector that defines boundary (see 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.
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.
# NOT RUN {
MCbound("tsprt",c(alpha0=.001,beta0=.01,Nmax=99,p0=.06,p1=.04))
# }
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