R: Cumulative distribution function of a specified distribution

cdf {optimalThreshold}

R Documentation

Cumulative distribution function of a specified distribution

Description

The cdf function returns the cumulative distribution function relative to the S4 object passed in its argument. See details to know on what kind of S4 objects this function could be applied.

Usage

cdf(object)

## S4 method for signature 'normalDist'
cdf(object)

## S4 method for signature 'logNormalDist'
cdf(object)

## S4 method for signature 'gammaDist'
cdf(object)

## S4 method for signature 'studentDist'
cdf(object)

## S4 method for signature 'logisticDist'
cdf(object)

## S4 method for signature 'compoundEvtRefDist'
cdf(object)

## S4 method for signature 'compoundNoEvtRefDist'
cdf(object)

## S4 method for signature 'compoundEvtInnovDist'
cdf(object)

## S4 method for signature 'compoundNoEvtInnovDist'
cdf(object)

Arguments

object

Any S4 object for which a cdf method is defined. Should match with the definition of an S4 distribution object as defined in the optimalThreshold package.

Details

This method can be applied to the S4 distribution objects that are supported in the optimalThreshold package: normalDist, logNormalDist, gammaDist, studentDist, logisticDist, and userDefinedDist. These methods are applied internally, and you have no need to use it outside of the main functions trtSelThresh and diagThresh.

Normal distribution: the cdf method applied to a normalDist object is simply the pnorm function (see help on this function to have more details).
Log-normal distribution: the cdf method applied to a logNormalDist object is simply the plnorm function (see help on this function to have more details).
Gamma distribution: the cdf method applied to a gammaDist object is simply the pgamma function (see help on this function to have more details).
Scaled t distribution: the scaled t distribution with df = n, mu = \mu, and sd = \sigma has density:

f(x)=(\Gamma((n+1)/2)/(\sqrt{n\pi}\Gamma(n/2))(1+((x-\mu)/\sigma)^2/n)^-((n+1)/2))/\sigma
Logistic distribution: the cdf method applied to a logisticDist object is simply the plogis function (see help on this function to have more details).
User-defined distribution: the cdf method applied to a userDefinedDist object is simply the cumulative distribution function provided by the user when fitting a user-defined distribution with the fit function.

The S4 objects compoundEvtRefDist, compoundNoEvtRefDist, compoundEvtInnovDist, and compoundNoEvtInnovDist are created internally. The cdf function applied to these objects is defined dynamically depending on what types of distribution are fitted. The definition of the cdf function relies on the expression of the randomization constraint of a clinical trial that enforces the distribution of the marker in each treatment arm to be identical (see References for more details).

Value

Returns the cumulative distribution function of the specified distribution.

References

Blangero, Y, Rabilloud, M, Ecochard, R, and Subtil, F. A Bayesian method to estimate the optimal threshold of a marker used to select patients' treatment. Statistical Methods in Medical Research. 2019.