bercusum {cgrcusum} R Documentation

### Description

This function can be used to construct a risk-adjusted Bernoulli CUSUM chart on survival data. Specify one of the following combinations for the parameters:

• glmmod + theta

• p0 + theta

• p0 + p1

### Usage

bercusum(data, followup, glmmod, theta, p0, p1, h, stoptime)


 data data.frame containing the following named columns: entrytime numeric - time of entry into study, survtime numeric - time from entry until event, censorid integer - (optional) censoring indicator (0 = right censored, 1 = observed), followup The followup time for every individual. At what time after entry do we consider the outcome? glmmod Generalized linear regression model used for risk-adjustment as produced by the function glm. Standard practice: glm(as.formula(paste("(survtime <= followup) & (censorid == 1)~" ,paste(covariates, collapse='+'))), data = data). Alternatively, a list containing: $formula (~ covariates),$coefficients (named vector specifying risk adjustment coefficients for covariates - names must be the same as in $formula and colnames of data). theta e^\theta is the odds ratio under the alternative hypothesis. Note that: p_1 = \frac{p_0 e^\theta}{(1-p_0) (1+p_0 e^\theta)} p0 The baseline failure probability at entrytime + followup for individuals. p1 The alternative hypothesis failure probability at entrytime + followup for individuals. h (optional) Control limit to be used for the procedure stoptime (optional) Time after which the value of the chart should no longer be determined ### Details The Bernoulli CUSUM chart is given by: S_n = \max(0, S_{n-1} + W_n) with W_n = X_n \ln \left( \frac{p_1 (1-p_0)}{p_0(1-p_1)} \right) + \ln \left( \frac{1-p_1}{1-p_0} \right) where X_n is the outcome of the n-th (chronological) subject in the data. Instead of displaying patient numbering on the x-axis, the time of outcome is displayed. ### Value An object of class bercusum containing: • CUSUM: A data.frame containing: •$time (times at which chart is constructed),

• $value (value of the chart at corresponding times), •$numobs (number of observations at corresponding times)

• call: the call used to obtain output

• glmmod: glm coefficients used for risk-adjustment, if specified

• stopind: indicator for whether the chart was stopped by the control limit

There are plot and runlength methods for "bercusum" objects.

### Author(s)

Daniel Gomon

plot.bercusum, runlength.bercusum

Other qcchart: bkcusum(), cgrcusum(), funnelplot()

### Examples

varsanalysis <- c("age", "sex", "BMI")
exprfitber <- as.formula(paste("(entrytime <= 365) & (censorid == 1)~",
paste(varsanalysis, collapse='+')))
surgerydat$instance <- surgerydat$Hosp_num
glmmodber <- glm(exprfitber, data = surgerydat, family = binomial(link = "logit"))
bercus <- bercusum(data = subset(surgerydat, Hosp_num == 14), glmmod = glmmodber,
followup = 100, theta = log(2))
plot(bercus)


[Package cgrcusum version 0.1.0 Index]