calc_Wncdf: Calculate cdf of singletons W_n for CUSUM
In success: Survival Control Charts Estimation Software

calc_Wncdf

R Documentation

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.