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.
calc_Wncdf(glmmod, theta, theta_true, p0, smooth_prob = FALSE)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.
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 $$p_1 = \frac{p_0 e^\theta}{1-p_0 +p_0 e^\theta}.$$
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.
The baseline failure probability at entrytime + followup for individuals.
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.