pwrss.z.poisreg {pwrss}

Poisson 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 poisson regression. pwrss.z.poisson() and pwrss.z.poisreg() are the same functions. The distribution of the predictor variable can be one of the following: c("normal", "poisson", "uniform", "exponential", "binomial", "bernouilli", "lognormal"). 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.poisreg(exp.beta0 = 1.10, exp.beta1 = 1.16,
                beta0 = log(exp.beta0), beta1 = log(exp.beta1),
                mean.exposure = 1, n = NULL, power = NULL, r2.other.x = 0,
                alpha = 0.05, alternative = c("not equal", "less", "greater"),
                method = c("demidenko(vc)", "demidenko", "signorini"),
                distribution = "normal", verbose = TRUE)


pwrss.z.poisson(exp.beta0 = 1.10, exp.beta1 = 1.16,
                beta0 = log(exp.beta0), beta1 = log(exp.beta1),
                mean.exposure = 1, n = NULL, power = NULL, r2.other.x = 0,
                alpha = 0.05, alternative = c("not equal", "less", "greater"),
                method = c("demidenko(vc)", "demidenko", "signorini"),
                distribution = "normal", verbose = TRUE)

Arguments

exp.beta0

the base mean event rate

exp.beta1

event rate ratio: the relative increase in the mean event rate for one unit increase in the predictor X (similiar to odds ratio in logistic regression)

beta0

log(exp.beta0) or natural logarithm of the base mean event rate

beta1

log(exp.beta1) or natural logarithm of the relative increase in the mean event rate for one unit increase in the predictor X

mean.exposure

the mean exposure time (should be > 0). Usually 1

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 the 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; "signorini" stands for Signorini (1991) procedure. "demidenko" and "signorini" methods produce similiar results but "demidenko(vc)" is more precise

distribution

distribution family. Can be one of the c("normal", "poisson", "uniform", "exponential", "binomial", "bernouilli", "lognormal")

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.

Signorini, D. F. (1991). Sample size for poisson regression. Biometrika, 78(2), 446-450.

Examples

# predictor X follows normal distribution

## regression coefficient specification
pwrss.z.poisreg(beta0 = 0.50, beta1 = -0.10,
                alpha = 0.05, power = 0.80,
                dist = "normal")

## rate ratio specification
pwrss.z.poisreg(exp.beta0 = exp(0.50),
                exp.beta1 = exp(-0.10),
                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.poisreg(exp.beta0 = exp(0.50),
                exp.beta1 = exp(-0.10),
                alpha = 0.05, power = 0.80,
                dist = dist.x)


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

## regression coefficient specification
pwrss.z.poisreg(beta0 = 0.50, beta1 = -0.10,
                alpha = 0.05, power = 0.80,
                dist = "bernoulli")

## rate ratio specification
pwrss.z.poisreg(exp.beta0 = exp(0.50),
                exp.beta1 = exp(-0.10),
                alpha = 0.05, power = 0.80,
                dist = "bernoulli")

## change parameters associatied with predictor X
dist.x <- list(dist = "bernoulli", prob = 0.30)
pwrss.z.poisreg(exp.beta0 = exp(0.50),
                exp.beta1 = exp(-0.10),
                alpha = 0.05, power = 0.80,
                dist = dist.x)