Calculates the power of as case-control study with a continuous exposure variable
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)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 \(n_{2}\).
Number between 0 and 1 giving the prevalence of disease. No default.
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.
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).
Two element vector giving the domain of distF. This option is only used
when distF is a pdf.
The default is c(-Inf, Inf).
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.
Number between 0 and 1 giving the size of the 2-sided hypothesis test. The default is 0.05.
Sample size of the study. The default is 1000.
Number between 0 and 1 for the proportion of cases in the case-control sample. The default is 0.5.
Two element vector giving the interval to search for the estimated intercept parameter. The default is c(-100, 100).
Positive value giving the stopping tolerance for the root finding method to estimate the intercept parameter. The default is 0.0001.
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.
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.
power_binary, power_ordinal, power_data
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))
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