pwrss.z.logreg {pwrss}

Logistic Regression: Single Coefficient (Large Sample Approx. Wald's z Test)

Description

Calculates statistical power or minimum required sample size (only one can be NULL at a time) to test a single coefficient in logistic regression. pwrss.z.logistic() and pwrss.z.logreg() are the same functions. The distribution of the predictor variable can be one of the following: c("normal", "poisson", "uniform", "exponential", "binomial", "bernouilli", "lognormal") for Demidenko (2007) procedure but only c("normal", "binomial", "bernouilli") for Hsieh et al. (1998) procedure. The default parameters for these distributions are

distribution = list(dist = "normal", mean = 0, sd = 1)
distribution = list(dist = "poisson", lambda = 1)
distribution = list(dist = "uniform", min = 0, max = 1)
distribution = list(dist = "exponential", rate = 1)
distribution = list(dist = "binomial", size = 1, prob = 0.50)
distribution = list(dist = "bernoulli", prob = 0.50)
distribution = list(dist = "lognormal", meanlog = 0, sdlog = 1)

Parameters defined in list() form can be modified, but the names should be kept the same. It is sufficient to use distribution's name for default parameters (e.g. dist = "normal").

Formulas are validated using Monte Carlo simulation, G*Power, and tables in PASS documentation.

Usage

pwrss.z.logreg(p1 = 0.10, p0 = 0.15,
               odds.ratio  = (p1/(1-p1))/(p0/(1-p0)),
               beta0 = log(p0/(1-p0)), beta1 = log(odds.ratio),
               n = NULL, power = NULL, r2.other.x = 0, alpha = 0.05,
               alternative = c("not equal", "less", "greater"),
               method = c("demidenko(vc)", "demidenko", "hsieh"),
               distribution = "normal", verbose = TRUE)


pwrss.z.logistic(p1 = 0.10, p0 = 0.15,
                 odds.ratio  = (p1/(1-p1))/(p0/(1-p0)),
                 beta0 = log(p0/(1-p0)), beta1 = log(odds.ratio),
                 n = NULL, power = NULL, r2.other.x = 0, alpha = 0.05,
                 alternative = c("not equal", "less", "greater"),
                 method = c("demidenko(vc)", "demidenko", "hsieh"),
                 distribution = "normal", verbose = TRUE)

Arguments

p0

base probability under null hypothesis (probability that an event occurs without the influence of the predictor X - or when the value of the predictor is zero)

p1

probability under alternative hypothesis (probability that an event occurs when the value of the predictor X is increased by one unit)

beta0

regression coefficient defined as
beta0 = log( p0/(1-p0) )

beta1

regression coefficient for the predictor X defined as
beta1 = log( (p1/(1-p1)) / (p0/(1-p0)) )

odds.ratio

odds ratio defined as
odds.ratio = exp(beta1) = (p1/(1-p1)) / (p0/(1-p0))

n

total sample size

power

statistical power (1-\beta)

r2.other.x

proportion of variance in the predictor X explained by other covariates. Not to be confused with pseudo R-squared

alpha

probability of type I error

alternative

direction or type of the hypothesis test: "not equal", "greater", "less"

method

calculation method. "demidenko(vc)" stands for Demidenko (2007) procedure with variance correction; "demidenko" stands for Demidenko (2007) procedure without variance correction; "hsieh" stands for Hsieh et al. (1998) procedure. "demidenko" and "hsieh" methods produce similiar results but "demidenko(vc)" is more precise

distribution

distribution family. Can be one of the c("noramal", "poisson", "uniform", "exponential", "binomial", "bernouilli", "lognormal") for Demidenko (2007) procedure but only c("normal", "binomial", "bernouilli") for Hsieh et al. (1998) procedure

verbose

if FALSE no output is printed on the console

Value

parms

list of parameters used in calculation

test

type of the statistical test (z test)

ncp

non-centrality parameter

power

statistical power (1-\beta)

n

total sample size

References

Demidenko, E. (2007). Sample size determination for logistic regression revisited. Statistics in Medicine, 26(18), 3385-3397.

Hsieh, F. Y., Bloch, D. A., & Larsen, M. D. (1998). A simple method of sample size calculation for linear and logistic regression. Statistics in Medicine, 17(4), 1623-1634.

Examples

# predictor X follows normal distribution

## probability specification
pwrss.z.logreg(p0 = 0.15, p1 = 0.10,
               alpha = 0.05, power = 0.80,
               dist = "normal")

## odds ratio specification
pwrss.z.logreg(p0 = 0.15, odds.ratio = 0.6296,
               alpha = 0.05, power = 0.80,
               dist = "normal")

## regression coefficient specification
pwrss.z.logreg(p0 = 0.15, beta1 = -0.4626,
               alpha = 0.05, power = 0.80,
               dist = "normal")

## change parameters associated with predictor X
dist.x <- list(dist = "normal", mean = 10, sd = 2)
pwrss.z.logreg(p0 = 0.15, beta1 = -0.4626,
               alpha = 0.05, power = 0.80,
               dist = dist.x)


# predictor X follows Bernoulli distribution (such as treatment/control groups)

## probability specification
pwrss.z.logreg(p0 = 0.15, p1 = 0.10,
               alpha = 0.05, power = 0.80,
               dist = "bernoulli")

## odds ratio specification
pwrss.z.logreg(p0 = 0.15, odds.ratio = 0.6296,
               alpha = 0.05, power = 0.80,
               dist = "bernoulli")

## regression coefficient specification
pwrss.z.logreg(p0 = 0.15, beta1 = -0.4626,
               alpha = 0.05, power = 0.80,
               dist = "bernoulli")

## change parameters associated with predictor X
dist.x <- list(dist = "bernoulli", prob = 0.30)
pwrss.z.logreg(p0 = 0.15, beta1 = -0.4626,
               alpha = 0.05, power = 0.80,
               dist = dist.x)