wr.ci {WRestimates}

Confidence Interval (CI) for Win Ratio

Description

Calculate the confidence interval for a win ratio.

CI = exp((ln(WR) +/- Z\sqrt{var})

Where;

ln(WR) = Natural log of the true or assumed win ratio.

Z = Z-score from normal distribution.

\sqrt{var} = Standard deviation of the natural log of the win ratio.

Usage

wr.ci(WR = 1, Z = 1.96, var.ln.WR, N, sigma.sqr, k, p.tie)

Arguments

WR

Win ratio; Default: WR = 1 for an assumed true win ratio where H₀ is assumed true.

Z

Z-score from normal distribution; Default: Z = 1.96 for a 95% CI.

var.ln.WR

Variance of the natural log (ln) of the win ratio.

N

Sample size.

sigma.sqr

Population variance of the natural log (ln) of the win ratio.

k

The proportion of subjects allocated to one group i.e. the proportion of patients allocated to treatment.

p.tie

The proportion of ties.

Value

wr.ci returns an object of class "list" containing the following components:

ci

The confidence interval of a win ratio.

WR

The win ratio.

Z

Z-score from normal distribution.

var.ln.WR

Variance of the natural log (ln) of the win ratio.

N

Sample size.

sigma.sqr

Population variance of the natural log (ln) of the win ratio.

k

The proportion of subjects allocated to one group.

p.tie

The proportion of ties.

Author(s)

Autumn O'Donnell [e-mail]

References

Yu, R. X. and Ganju, J. (2022). Sample size formula for a win ratio endpoint. Statistics in medicine, 41(6), 950-963. doi:10.1002/sim.9297.

See Also

wr.sigma.sqr; wr.var

Examples

## N = 100 patients, 1:1 allocation, one-sided alpha = 2.5%, power = 90%
## (beta = 10%), a small proportion of ties p.tie = 0.1, and 50% more wins
## on treatment than control.

### Calculation 95% CI
wr.ci(N = 100, WR = 1.5, k = 0.5, p.tie = 0.1)