bkcusum {cgrcusum}  R Documentation 
This function performs the BKCUSUM procedure based on the
Biswas & Kalbfleisch (2008) CUSUM. For detection purposes, it is sufficient
to only determine the value of the chart at the times of failure. This can be
achieved by leaving ctimes
empty.
bkcusum(data, theta, coxphmod, cbaseh, ctimes, h, stoptime, C, pb = FALSE)
data 
and optionally additional covariates used for riskadjustment. 
theta 
expected ln(hazard ratio) 
coxphmod 
(optional) a cox proportional hazards regression model as produced by
the function

cbaseh 
a function which returns the non riskadjusted cumulative
baseline hazard 
ctimes 
(optional) vector of construction times at which the value of the chart should be determined. When not specified, the chart is constructed at all failure times. 
h 
(optional) value of the control limit. The chart will only be constructed until the value of the control limit has been reached or surpassed. 
stoptime 
(optional) time after which the value of the chart should no longer be determined. Default = max(failure time). Useful when ctimes has not been specified. 
C 
(optional) a numeric value indicating how long after entering the study
patients should no longer influence the value of the chart. This is
equivalent to rightcensoring every observation at time 
pb 
(optional) boolean indicating whether a progress bar should be shown. Default = FALSE 
The BKCUSUM can be used to test the hypothesis of an instant change
of fixed size e^\theta
in the subject specific hazard rate from h_i(t)
to
h_i(t) e^\theta
. The parameter C
can be used
to ignore information provided by subjects C time units after their entry
into the study.
The BKCUSUM is constructed as:
G(t) = \max_{0 \leq k \leq t} \left( \theta N(k,t)  \left( e^\theta 1 \right) \Lambda(k,t) \right)
with \theta
the ln(expected hazard ratio) and
N(k,t) = N(t)  N(k)
with N(t)
the counting process of all failures at time t and
\Lambda(k,t) = \Lambda(t)  \Lambda(k)
the
with \Lambda(t)
the summed cumulative intensity of all subjects at time t.
An object of class "bkcusum" containing:
BK
: list containing
$time (times at which chart is constructed),
$value (value of the chart at corresponding times),
stopind
: indicator for whether the chart was stopped by the control limit
call
: the call used to obtain output
There are plot
and
runlength
methods for "bkcusum" objects.
Daniel Gomon
Biswas P. and Kalbfleisch J.D. (2008), A riskadjusted CUSUM in continuous time based on the Cox Model, doi: 10.1002/sim.3216
plot.bkcusum
, runlength.bkcusum
Other qcchart:
bercusum()
,
cgrcusum()
,
funnelplot()
require(survival)
tdat < subset(surgerydat, Hosp_num == 14)
tcbaseh < function(t) chaz_exp(t, lambda = 0.01)
varsanalysis < c("age", "sex", "BMI")
exprfit < as.formula(paste("Surv(survtime, censorid) ~" ,paste(varsanalysis, collapse='+')))
tcoxmod < coxph(exprfit, data= surgerydat)
#Alternatively, cbaseh can be left empty when specifying coxphmod through coxph()
bk < bkcusum(data = tdat, theta = log(2), coxphmod = tcoxmod, cbaseh = tcbaseh, pb = TRUE)
plot(bk)