Represents the issue of chronological bias in a clinical trial.
chronBias(type, theta, method, saltus, alpha = 0.05)
S4
object of class chronBias
, a formal representation of the
issue of chronological bias in a clinical trial.
character string, should be one of "linT
", "logT
", or "stepT
",
see Details.
factor of the time trend for further details see type
.
character string, should be one of "sim"
or "exact"
, see Description.
integer or missing
specifying the patient index (i.e. position)
of the step in case of step time trend.
significance level
Chronological bias can be an issue in the design of a clinical trial. The
chronBias
function is a constructor function
for an S4 object of the class chronBias
representing the issue of
chronological bias, s.a. time trends, in a clinical trial. It supports two possible modes,
method="sim"
and method="exact"
, and three different types of trend.
If method="sim"
, the object represents the simulated type-I-error rate given
the level alpha
, the selection effect eta
and the biasing
strategy type
. When calling assess
for a chronBias
object
with method="sim"
, one test decision is computed for each sequence of
randSeq
. The type-I-error rate (power) is the proportion of falsely
(correctly) rejected null hypotheses.
If method="exact"
, the object represents the exact type-I-error probability
given the level alpha
, the selection effect eta
and the
biasing strategy type
. When calling assess
for a chronBias
object with method="exact"
, the p-value of each randomization
sequence is computed. For normal endpoints and two treatment groups these p-values
are exact values which can be calculated from the sum of the corresponding quantiles
of the doubly noncentral t-distribution. For more than two treatment groups, exact
p-values are computed using a doubly noncentral F distribution. For exponential
endpoints the p-values are obtained using an approximation formula.
type = "linT"
Represents linear time trend. Linear time trend means that the time trend function of the patients,
i.e. expected response for normal endpoints, increases evenly by theta/(N-1)
with
every patient included in the study, until reaching theta
after N
patients.
Linear time trend may occur as a result of gradually relaxing in- or exclusion criteria
throughout the trial.
It can be represented by the formula:
$$f(i) = (i-1)/(N-1) \theta$$
type = "logT"
Represents logarithmic time trend. Logarithmic time trend means that the time trend function of
the patients, i.e. expected response for normal endpoints, increases logarithmically in the
patient index by theta/log(N)
with every patient included in the study, until reaching
theta
after N
patients. Logarithmic time trend may occur as a result of a learning
curve, i.e. in a surgical trial.
It can be represented by the formula:
$$\log(i)/\log(N) \theta$$
type = "stepT"
Represents step trend. Step trend means that the expected response of the patients increases
by theta
after a given point ("saltus"
) in the allocation process.
Step trend may occur if a new device is used after the point \(c\) = "saltus"
, or if
the medical personal changes after this point.
Step time trend can be represented by the formula:
$$f(i) = 1_{c < i \leq N} \theta$$
G. K. Rosenkranz (2011) The impact of randomization on the analysis of clinical trials. Statistics in Medicine, 30, 3475-87.
M. Tamm and R.-D. Hilgers (2014) Chronological bias in randomized clinical trials under different types of unobserved time trends. Methods of Information in Medicine, 53, 501-10.
Other issues:
combineBias()
,
corGuess
,
imbal
,
issue
,
selBias
,
setPower()
# create a linear time trend with theta = 0.5 for which the exact rejection probabilities
# are calculated
cbias <- chronBias("linT", 0.5, "exact")
# create a stepwise time trend with theta = 1 after 10 allocations for which the test
# decision is simulated
cbias <- chronBias("stepT", 1, "sim", 10)
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