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Published in:
2022 | OriginalPaper | Chapter
13. Initial Values
Author : Peter McCullagh
Published in: Ten Projects in Applied Statistics
Publisher: Springer International Publishing
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Abstract
Initial values, are values of a stochastic process measured at baseline, usually prior to the determination of patient eligibility, and certainly prior to randomization. Essentially all longitudinal studies are of this type. On the one hand, initial values are simply values of the process that happen to be made at time zero. In that sense, they are on a par with values recorded subsequently. On the other hand, initial values are pre-baseline and thus available for use as covariates on an equal footing with other baseline variables. Typically, initial and subsequent values on the same physical unit are positively correlated. The text discusses a number of issues and options for handling baseline values in a randomized trial. For example, the regression phenomenon suggests that patient selection may reduce the variability at baseline relative to variability at subsequent times.
If the initial values are initially regarded as random variables with distribution as specified by the model, it is essential that the distribution conform with the randomization scheme. In particular, the joint distribution of initial values cannot depend on the treatment effect. Chapter 5 provides an illustration of a stochastic model that clashes with the randomization.