n1.get {exact.n}

Find smallest value of n1 that achieves target power

Description

Function calculates minimum value of n1 that achieves power beta. If there is no solution less than 500, it models observed powers as a function of n1 and then extrapolates. It returns an infinite value if the power is unattainable.

Usage

n1.get(data, n0, beta, delta, alpha, type = 1, plt = FALSE)

Arguments

data

a matrix with column names beta, p0.vals, n0, n1 and 481^2 rows (See details)

n0

scalar value of n0 between 20 and 500 inclusive

beta

scalar target for power

delta

value of clinically relevant difference

alpha

value of nominal size of test

type

type of minimum solution (See details)

plt

if true produce diagnostic plots

Details

This function is called by n1.get.vector and will likely never be run by the user.

The data matrix will be a subset of one of the 85 main databases. Supplying alpha and delta loads the appropriate database and selecting a value of p0 further subsets this data base. The resulting matrix will have 4 columns and 481^2 rows corresponding to all values of n0 and n1 from 20 to 500 inclusive and is suitable for input into n1.get.

If type=1, the smallest value N1 of n1 so that power > beta is returned. If type=2, the smallest value N1 of n1 so that power > beta for all n1>=N1 is returned.

Value

a single scalar value of n1. An integer indicates a solution was found in the database. A non-integer indicates an extrapolated solution. An Inf value indicates no extrapolated solution was found.

Author(s)

Chris J. Lloyd

References

C.J. Lloyd (2022) Exact samples sizes for clinical trials subject to size and power constraints. Preprint. doi:10.13140/RG.2.2.11828.94085

Examples

# Load toy version of power library for alpha=0.025, delta=0.20.
# Alternatively, load the full library using fetch.data(alpha=0.025,delta=0.20)
rdata_file = system.file('files', 'LIB.a025.d20.Rdata', package = 'exact.n')
load(rdata_file)
data=LIB.a025.d20[LIB.a025.d20[,2]==0.5,] # select subset with p0=.5
# For given value of n0, what minimum value of n1 ensures power at least 0.7?
n1.get(data, n0=70, beta=.7, delta=.2, alpha=0.025,
       type = 1, plt = TRUE) # Explicit solution 63 found in data base
n1.get(data, n0=50, beta=.7, delta=.2, alpha=0.025,
       type = 1, plt = TRUE) # Approximate solution 131 extrapolated from toy data base
# You can check the accuracy of this extrapolated result:
# POWER(n0=50,n1=131,alpha=0.025,delta=0.2,p0=0.5,type="elr")
# The minimum power at p0=0.5 is 0.699, slightly less than 0.7.
# With the full library n1.get returns the correct answer of n1=136.
n1.get(data, n0=30, beta=.7, delta=.2, alpha=0.025,
       type = 1, plt = TRUE) # Extrapolated solution is infinite