rsimsum (version 0.13.0)

nsim: Compute number of simulations required

Description

The function nsim computes the number of simulations \(B\) to perform based on the accuracy of an estimate of interest, using the following equation: $$B = \left( \frac{(Z_{1 - \alpha / 2} + Z_{1 - theta}) \sigma}{\delta} \right) ^ 2,$$ where \(\delta\) is the specified level of accuracy of the estimate of interest you are willing to accept (i.e. the permissible difference from the true value \(\beta\)), \(Z_{1 - \alpha / 2}\) is the \((1 - \alpha / 2)\) quantile of the standard normal distribution, \(Z_{1 - \theta}\) is the \((1 - \theta)\) quantile of the standard normal distribution with \((1 - \theta)\) being the power to detect a specific difference from the true value as significant, and \(\sigma ^ 2\) is the variance of the parameter of interest.

Usage

nsim(alpha, sigma, delta, power = 0.5)

Value

A scalar value \(B\) representing the number of simulations to perform based on the accuracy required.

Arguments

alpha

Significance level. Must be a value between 0 and 1.

sigma

Variance for the parameter of interest. Must be greater than 0.

delta

Specified level of accuracy of the estimate of interest you are willing to accept. Must be greater than 0.

power

Power to detect a specific difference from the true value as significant. Must be a value between 0 and 1. Defaults to 0.5, e.g. a power of 50%.

References

Burton, A., Douglas G. Altman, P. Royston. et al. 2006. The design of simulation studies in medical statistics. Statistics in Medicine 25: 4279-4292 tools:::Rd_expr_doi("10.1002/sim.2673")

Examples

# Number of simulations required to produce an estimate to within 5%
# accuracy of the true coefficient of 0.349 with a 5% significance level,
# assuming the variance of the estimate is 0.0166 and 50% power:
nsim(alpha = 0.05, sigma = sqrt(0.0166), delta = 0.349 * 5 / 100, power = 0.5)

# Number of simulations required to produce an estimate to within 1%
# accuracy of the true coefficient of 0.349 with a 5% significance level,
# assuming the variance of the estimate is 0.0166 and 50% power:
nsim(alpha = 0.05, sigma = sqrt(0.0166), delta = 0.349 * 1 / 100, power = 0.5)