calc_Wncdf: Calculate cdf of singletons W_n for CUSUM

In success: Survival Control Charts Estimation Software

Calculate cdf of singletons W_n for CUSUM

Description

Internal function to calculate cdf of singletons W_n of the Bernoulli CUSUM chart. The cdf is used to create the transition matrix when Markov Chain methodology is used or to determine the integral equation/probabilities of a Wald test when integral equation or Kemp's methodology is used.

Usage

calc_Wncdf(glmmod, theta, theta_true, p0, smooth_prob = FALSE)

Arguments

glmmod	Generalized linear regression model used for risk-adjustment as produced by the function glm(). Suggested: glm(as.formula("(survtime <= followup) & (censorid == 1) ~ covariates"), data = data). Alternatively, a list containing the following elements: formula: a formula() in the form ~ covariates; coefficients: a named vector specifying risk adjustment coefficients for covariates. Names must be the same as in formula and colnames of data.
theta	The \theta value used to specify the odds ratio e^\theta under the alternative hypothesis. If \theta >= 0, the average run length for the upper one-sided Bernoulli CUSUM will be determined. If \theta < 0, the average run length for the lower one-sided CUSUM will be determined. Note that p_1 = \frac{p_0 e^\theta}{1-p_0 +p_0 e^\theta}.
theta_true	The true log odds ratio \theta, describing the true increase in failure rate from the null-hypothesis. Default = log(1), indicating no increase in failure rate.
p0	The baseline failure probability at entrytime + followup for individuals.
smooth_prob	Should the probability distribution of failure under the null distribution be smoothed? Useful for small samples. Can only be TRUE when glmmod is supplied. Default = FALSE.

success documentation built on June 8, 2025, 1:50 p.m.