regression.logistic: Power Analysis for Logistic Regression Coefficient (Wald's...

In pwrss: Statistical Power and Sample Size Calculation Tools

Power Analysis for Logistic Regression Coefficient (Wald's Z-Test)

Description

Calculates power or sample size (only one can be NULL at a time) to test a single coefficient in logistic regression. power.z.logistic() and power.z.logreg() are the same functions, as well as pwrss.z.logistic() and pwrss.z.logreg().

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 element names should be kept the same. It is sufficient to use distribution's name for default parameters (e.g. dist = "normal").

NOTE: The pwrss.z.logistic() and its alias pwrss.z.logreg() are deprecated. However, they will remain available as wrappers for the power.z.logistic() function.

Formulas are validated using G*Power and tables in PASS documentation.

Usage

power.z.logistic(prob = NULL, base.prob = NULL,
                 odds.ratio  = (prob/(1-prob))/(base.prob/(1-base.prob)),
                 beta0 = log(base.prob/(1-base.prob)), beta1 = log(odds.ratio),
                 n = NULL, power = NULL, r.squared.predictor = 0,
                 alpha = 0.05, alternative = c("two.sided", "one.sided"),
                 method = c("demidenko(vc)", "demidenko", "hsieh"),
                 distribution = "normal", ceiling = TRUE,
                 verbose = TRUE, pretty = FALSE)

Arguments

base.prob	base probability under null hypothesis (probability that an event occurs without the influence of the predictor - or when the value of the predictor is zero).
prob	probability under alternative hypothesis (probability that an event occurs when the value of the predictor is increased from 0 to 1). Warning: This is base probability + incremental increase.
beta0	regression coefficient defined as beta0 = log(base.prob/(1-base.prob))
beta1	regression coefficient for the predictor X defined as beta1 = log((prob/(1-prob))/(base.prob/(1-base.prob)))
odds.ratio	odds ratio defined as odds.ratio = exp(beta1) = (prob/(1-prob))/(base.prob/(1-base.prob))
n	integer; sample size
power	statistical power, defined as the probability of correctly rejecting a false null hypothesis, denoted as 1 - \beta.
r.squared.predictor	proportion of variance in the predictor accounted for by other covariates. This is not a pseudo R-squared. To compute it, regress the predictor on the covariates and extract the adjusted R-squared from that model.
alpha	type 1 error rate, defined as the probability of incorrectly rejecting a true null hypothesis, denoted as \alpha.
alternative	character; direction or type of the hypothesis test: "not equal", "greater", "less"
method	character; analytic 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 similar results but "demidenko(vc)" is more precise
distribution	character; 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.
ceiling	logical; whether sample size should be rounded up. TRUE by default.
verbose	logical; whether the output should be printed on the console. TRUE by default.
pretty	logical; whether the output should show Unicode characters (if encoding allows for it). FALSE by default.

Value

parms	list of parameters used in calculation.
test	type of the statistical test (Z-Test).
mean	mean of the alternative distribution.
sd	standard deviation of the alternative distribution.
null.mean	mean of the null distribution.
null.sd	standard deviation of the null distribution.
z.alpha	critical value(s).
power	statistical power (1-\beta).
n	sample size.

References

Demidenko, E. (2007). Sample size determination for logistic regression revisited. Statistics in Medicine, 26(18), 3385-3397. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/sim.2771")}

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
power.z.logistic(base.prob = 0.15, prob = 0.20,
                 alpha = 0.05, power = 0.80,
                 dist = "normal")

## odds ratio specification
power.z.logistic(base.prob = 0.15, odds.ratio = 1.416667,
                 alpha = 0.05, power = 0.80,
                 dist = "normal")

## regression coefficient specification
power.z.logistic(beta0 = -1.734601, beta1 = 0.3483067,
                 alpha = 0.05, power = 0.80,
                 dist = "normal")

## change parameters associated with predictor X
pred.dist <- list(dist = "normal", mean = 10, sd = 2)
power.z.logistic(base.prob = 0.15, beta1 = 0.3483067,
                 alpha = 0.05, power = 0.80,
                 dist = pred.dist)


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

## odds ratio specification
power.z.logistic(base.prob = 0.15, odds.ratio = 1.416667,
                 alpha = 0.05, power = 0.80,
                 dist = "bernoulli")

## change parameters associated with predictor X
pred.dist <- list(dist = "bernoulli", prob = 0.30)
power.z.logistic(base.prob = 0.15, odds.ratio = 1.416667,
                 alpha = 0.05, power = 0.80,
                 dist = pred.dist)

####################################
# predictor X is an ordinal factor #
####################################

## generating an ordinal predictor
x.ord <- sample(
  x = c(1, 2, 3, 4), # levels
  size = 1e5, # sample size large enough to get stable estimates
  prob = c(0.25, 0.25, 0.25, 0.25), # category probabilities
  replace = TRUE
)

## dummy coding the ordinal predictor
x.ord <- factor(x.ord, ordered = TRUE)
contrasts(x.ord) <- contr.treatment(4, base = 4)
x.dummy <- model.matrix( ~ x.ord)[,-1]
x.data <- as.data.frame(x.dummy)

## fit linear regression to get multiple r-squared
x.fit <- lm(x.ord1 ~ x.ord2 + x.ord3, data = x.data)

## extract parameters
bern.prob <- mean(x.data$x.ord1)
r.squared.pred <- summary(x.fit)$adj.r.squared

## change parameters associated with predictor X
pred.dist <- list(dist = "bernoulli", prob = bern.prob)
power.z.logistic(base.prob = 0.15, odds.ratio = 1.416667,
               alpha = 0.05, power = 0.80,
               r.squared.pred = r.squared.pred,
               dist = pred.dist)

pwrss documentation built on Sept. 16, 2025, 9:11 a.m.