ss.nonadh {ssanv}

Find sample sizes accounting for nonadherence

Description

Calculate sample sizes needed for a two-sample difference in means test accounting for nonadherence (i.e., noncompliance) in a proportion of subjects.

Usage

ss.nonadh(mu0 = NULL, mu1 = NULL, delta = NULL, sigma0.sq = 1, 
    rho0 = 0, rho1 = 0, ss.ratio = 1, var.ratio = 1, deltaB = 0, 
    sig.level = 0.05, power = 0.8, alternative = c("two.sided", "one.sided"), 
    refinement = NULL,error.fisher=10^-6)

Arguments

mu0

mean of control group

mu1

mean of treatment group

delta

mu0 - mu1

sigma0.sq

variance of control group

rho0

probability that a subject randomized to control will switch to treatment

rho1

probability that a subject randomized to treatment will switch to control (or respond like control subjects)

ss.ratio

n1/n0, where n0 (n1) is sample size of control (treatment) group for proposed study

var.ratio

\sigma_1^2/\sigma_0^2, where \sigma_0 (\sigma_1) is standard deviation of control (treatment) group for proposed study

deltaB

boundary value between null and alternative hypotheses for one-sided tests (see details)

sig.level

significance level (Type I error)

power

minimum power that you want the sample size to achieve

alternative

One- or two-sided test

refinement

More precise sample size estimates for certain types of responses, possible values: NULL (use asymptotic method), ‘Normal’ or 'N','Bernoulli' or 'B', and 'Fisher.exact' or 'F'.

error.fisher

bound on the abolute error of the power calculations for the Fisher.exact refinement

Details

Calculates the sample sizes for a study designed to test the difference between the means of two groups, where a proportion of those randomized to the control regimin switch to the treatment regimin (rho0) and a proportion of those randomized to the treatment regimin switch to the control regimin (rho1).

You must supply either mu0 and mu1 or delta=mu0-mu1. The one-sided tests are designed to test either H_0: \delta \leq \delta_B vs. H_1: \delta > \delta_B or to test H_0: \delta \geq \delta_B vs. H_1: \delta < \delta_B. The choice of hypotheses is determined by the value of delta; if delta > deltaB then the former hypotheses are tested, otherwise the latter are.

The responses may be continuous, discrete, or even binary. The value refinement defines different methods related to the response type. When refinement=NULL, the method is based on asymptotic normal approximation. For refinement='Normal' the method is based on the t-distribution derived when the responses are normal. For refinement='Bernoulli' the sigma0.sq and var.ratio values are defined by mu0 and mu1, and the sample sizes do not use any continuity correction. For refinement='Fisher.exact' only the two-sided alternative is allowed and the sample size related to exact powers for the 2X2 Fisher exact test are calculated.

See Fay, Halloran and Follmann (2007) for details.

Value

Object of class "power.htest", a list of the arguments (including the computed sample sizes) augmented with 'METHOD' and 'NOTE' elements. The values 'n0' and 'n1' are the samples sizes for the two groups, rounded up to the nearest integer.

Note

If you have a two-sided hypotheses with binary data, then refinement='Fisher.exact' is more accurate than refinement='Bernoulli', but it takes considerably longer to run. If 'Fisher.exact' is chosen the method uses the uniroot.integer function, and if you ‘Esc’ during the calculation, intermediate exact powers will print.

Author(s)

Michael P. Fay

References

Fay, M.P., Halloran, M.E., and Follmann, D.A. (2007). 'Accounting for Variability in Sample Size Estimation with Applications to Nonadherence and Estimation of Variance and Effect Size' Biometrics 63: 465-474.

See Also

uniroot.integer, ss.fromdata.neff, ss.fromdata.pois, ss.fromdata.nvar

Examples

### Suppose treatment will not work on about 30 percent of subjects 
### then rho0=.3 and clinically significant difference in means is .5 
ss.nonadh(delta=.5,rho0=.3)

## Binary data, quick calculation
ss.nonadh(mu0=.1,mu1=.4,refinement="B")
# Calculate Fisher.exact before packaging, took about 8 seconds
#example.of.Fisher.exact<-ss.nonadh(mu0=.1,mu1=.4,refinement="Fisher.exact")
data(example.of.Fisher.exact)
example.of.Fisher.exact