selBias {randomizeR}

Representing selection bias

Description

Represents the issue of selection bias in a clinical trial.

Usage

selBias(type, eta, method, alpha = 0.05, delta = 0)

Arguments

type

character string, should be one of "CS", "CS2" or "DS", see Details.

eta

numeric specifying the magnitude of selection bias.

method

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

alpha

significance level.

delta

parameter of selection bias used for calculating shape and scale of the Weibull distribution with exponential endpoints

Details

Selection bias can be an issue in the design of a clinical trial. The selBias function is a constructor function for an S4 object of the class selBias representing the issue of third order selection bias in a clinical trial. It supports two possible modes, method="sim" and method="exact". This representation is particularly useful in interaction with the assess function.

method="sim"

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 selBias 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.

method="exact"

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 selBias 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.

It also supports three types of selection bias:

type="DS"

Refers to the divergence strategy according to Blackwell and Hodges (1957). Under this guessing strategy, the investigator guesses that the upcoming treatment is the one that has so far been allocated *more* frequently.

type="CS"

Refers to the convergence strategy according to Blackwell and Hodges (1957). Under this guessing strategy, the investigator guesses that the upcoming treatment is the one that has so far been allocated *less* frequently. In multi-arm trials, type="CS" refers to the first generalization of the convergence strategy according to Uschner et al (2018). The investigator guesses the treatment that had been allocated less frequently whenever all the treatments of the opposite group are larger than the smallest of the present group.

type="CS2"

In trials with two treatment arms, type="CS2" is equivalent to type="CS". In multi-arm trials, type="CS2" refers to the second generalization of convergence strategy according to Uschner et al (2018). The investigator guesses the treatment that had been allocated less frequently whenever all the treatments of the opposite group are larger than the smallest of the present group.

Value

S4 object of class selBias, a formal representation of the issue of selection bias in a clinical trial.

References

D. Blackwell and J.L. Hodges Jr. (1957) Design for the control of selection bias. Annals of Mathematical Statistics, 25, 449-60.

M. Proschan (1994) Influence of selection bias on the type-I-error rate under random permuted block designs. Statistica Sinica, 4, 219-31.

D. Uschner, R.-D. Hilgers, N. Heussen (2018) The impact of selection bias in randomized multi-arm parallel group clinical trials PLOS ONE, 13(1), 1-18.

See Also

Compute exact or simulated rejection probability: assess.

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

Examples

# create a selection bias of the convergency strategy type with eta = 0.25 for which
# the exact rejection probabilities are calculated
sbias <- selBias("CS", 0.25, "exact")