Sequential Comparison of Changes With Repeated Measurements Data

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Abstract
There are many clinical trials in which the patients enter sequentially, and a response variable is measured repeatedly over time for each patient. A group sequential procedure is proposed for comparing the rates of change between two treatment groups. Some existing procedures for testing the equality of means between two treatment groups with repeated measurements data, such as those proposed by Armitage, Stratton, and Worthington and by Geary, can be interpreted as special cases of the proposed procedure. Under a linear mixed effects model, the asymptotic joint distribution of the sequentially computed statistics is derived. Construction of the group sequential boundaries is based on this distribution theory. The extension to nonnormal distributions of errors is also discussed. The proposed procedure allows for using either the sequential method of Slud and Wei or that of Lan and DeMets. This procedure is then applied to repeated bone density measurements on a sample of 74 middle-aged women and implemented by the method of Lan and DeMets.

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