The gradient function returns the probability density 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.
gradient(object)# S4 method for normalDist
gradient(object)
# S4 method for logNormalDist
gradient(object)
# S4 method for gammaDist
gradient(object)
# S4 method for studentDist
gradient(object)
# S4 method for logisticDist
gradient(object)
# S4 method for compoundEvtRefDist
gradient(object)
# S4 method for compoundNoEvtRefDist
gradient(object)
# S4 method for compoundEvtInnovDist
gradient(object)
# S4 method for compoundNoEvtInnovDist
gradient(object)
Any S4 object for which a gradient method is defined. Should match with the definition of an S4 distribution object as defined in the optimalThreshold package.
Returns the probability density function of the specified distribution.
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 gradient method applied to a normalDist object is simply the dnorm function (see help on this function to have more details).
Log-normal distribution: the gradient method applied to a logNormalDist object is simply the dlnorm function (see help on this function to have more details).
Gamma distribution: the gradient method applied to a gammaDist object is simply the dgamma 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 gradient method applied to a logisticDist object is simply the dlogis function (see help on this function to have more details).
User-defined distribution: the gradient method applied to a userDefinedDist object is simply the gradient 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 gradient function applied to these objects is defined dynamically depending on what types of distribution are fitted. The definition of the gradient 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).
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.