chronBias() R function from [randomizeR]

Representing chronological bias

Represents the issue of chronological bias in a clinical trial.


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

Returns

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

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) \thetaf(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) \thetaf(i) = 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} \thetaf(i) = 1_{c < i \le N} \theta

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)

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.

chronBias function