power_continuous {samplesizelogisticcasecontrol}

Power for a continuous exposure

Description

Calculates the power of as case-control study with a continuous exposure variable

Usage

power_continuous(prev, logOR, distF=NULL, distF.support=c(-Inf, Inf), 
      data=NULL, size.2sided=0.05, sampleSize=1000, cc.ratio=0.5, interval=c(-100, 100), 
      tol=0.0001, distF.var=NULL) 

Arguments

prev

Number between 0 and 1 giving the prevalence of disease. No default.

logOR

Vector of ordered log-odds ratios for the confounders and exposure. The last log-odds ratio in the vector is for the exposure. If the option data (below) is specified, then the order must match the order of data. No default.

distF

NULL, a function or a character string giving the pdf of the exposure variable for the case of no confounders, or giving the function to generate random vectors from the distribution formed by the confounders and exposure. For the case of no confounders, examples are dnorm, "dnorm(x, mean=0.5, sd=2.1)", "dbeta(?, shape1=0.3, shape2=3)", "dchisq(whatever, df=1)". Notice that when distF is a character string, the first argument can be anything but must be given to serve as a place holder. For the case of two confounders, an example might be a random vector generator from a multivariate normal distribution "rmvnorm(x, c(0,0,0))". User defined functions are also allowed, provided the user-defined function has only one input argument. The input argument would be a vector of quantiles if the user-defined function is a pdf, or the input argument would be an integer specifiying the number of random vectors to generate if the user-defined function is a function to generate random vectors from the distribution of the confounders and exposure. An example pdf is the function H, where H <- function(x) { dunif(x, min=2, max=7) }. The default depends on other options (see details).

distF.support

Two element vector giving the domain of distF. This option is only used when distF is a pdf. The default is c(-Inf, Inf).

data

NULL, matrix, data frame or a list of type file.list that gives a sample from the distribution of the confounders and exposure. If a matrix or data frame, then the last column consists of random values for the exposure, while the other columns are for the confounders. The order of the columns must match the order of the vector logOR. The default is NULL.

size.2sided

Number between 0 and 1 giving the size of the 2-sided hypothesis test. The default is 0.05.

sampleSize

Sample size of the study. The default is 1000.

cc.ratio

Number between 0 and 1 for the proportion of cases in the case-control sample. The default is 0.5.

interval

Two element vector giving the interval to search for the estimated intercept parameter. The default is c(-100, 100).

tol

Positive value giving the stopping tolerance for the root finding method to estimate the intercept parameter. The default is 0.0001.

distF.var

The variance of the exposure variable for the case of no confounders. This option is for efficiency purposes. If not specified, the variance will be estimated by either the empirical variance of a random sample from the distribution of the exposure or by numerical integration. The default is NULL.

Details

The data option takes precedance over the other options. If data is not specified, then the distribution of the exposure will be N(0,1) or MVN(0, 1) depending on whether there are confounders.

Value

A list containing four powers, where two of them are for a Wald test and two for a score test. The two powers for each test correspond to the equations for n_{1} and n_{2}.

See Also

power_binary, power_ordinal, power_data

Examples

  prev  <- 0.01
  logOR <- 0.3

  # No confounders, exposure assumed to be N(0,1)
  power_continuous(prev, logOR) 

  # Two confounders and exposure assumed to be MVN(0,1)
  beta <- c(0.1, 0.1, logOR)
  power_continuous(prev, beta) 

  # No confounders, exposure is beta(0.3, 3)
  power_continuous(prev, logOR, distF="dbeta(m, shape1=0.3, shape2=3)",
                        distF.support=c(0, 1))