chronBias {randomizeR}

Representing chronological bias

Description

Represents the issue of chronological bias in a clinical trial.

Usage

chronBias(type, theta, method, saltus, alpha = 0.05)

Arguments

type

character string, should be one of "linT", "logT", or "stepT", see Details.

theta

factor of the time trend for further details see type.

method

character string, should be one of "sim" or "exact", see Description.

saltus

integer or missing specifying the patient index (i.e. position) of the step in case of step time trend.

alpha

significance level

Details

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.

Types of chronological bias

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

Value

S4 object of class chronBias, a formal representation of the issue of chronological bias in a clinical trial.

References

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.

See Also

Other issues: combineBias(), corGuess, imbal, issue, selBias, setPower()

Examples

# 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)