calc_Wncdf function

Calculate cdf of singletons W_n for CUSUM

Internal function to calculate cdf of singletons $Wn$

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)

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

• 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.