bernoulli_ARL_SPRT() R function from [success]

Average run length for Bernoulli CUSUM using Integral Equation methodology

Internal function that calculates the ARL using the connection between the ARL of a Wald SPRT and a CUSUM.


bernoulli_ARL_SPRT(h, n_grid, Wncdf, glmmod, theta, theta_true, p0,
  tol = 1e-06)

h: Control limit for the Bernoulli CUSUM
n_grid: Number of state spaces used to discretize the outcome space (when method = "MC") or number of grid points used for trapezoidal integration (when method = "SPRT"). Increasing this number improves accuracy, but can also significantly increase computation time.
Wncdf: A function returning the values of the (risk-adjusted) cumulative distribution function (cdf) for the singletons Wn.
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}.p1 = (p0 * e^\theta)/(1-p0+p0 * 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.