Applied Functional Data Analysis: Methods and Case Studies by J.O. Ramsay

By J.O. Ramsay

"What do juggling, outdated bones, legal careers, and human development styles have in universal? all of them provide upward thrust to sensible facts, which are available in the shape of curves or features instead of the numbers, or vectors of numbers, which are thought of in traditional information. The authors' booklet practical info research (1997) offered a thematic method of the statistical research of such information. against this, the current e-book introduces and explores the guidelines of sensible facts research through the dignity of a few case reviews, a lot of them awarded for the 1st time. the 2 books are complementary, yet nor is a prerequisite for the opposite. The case stories are available to investigate employees in quite a lot of disciplines. each reader, even if skilled researcher or graduate pupil, should still achieve not just a particular realizing of the tools of practical information research, yet, extra importantly, a common perception into the underlying styles of inspiration. a few of the stories call for the improvement of novel points of the method of practical info research, yet technical information aimed toward the expert statistician are limited to sections that the extra common reader can correctly forget. there's an linked site with MATLAB and S-PLUS implementations of the equipment mentioned, including all of the info units that aren't proprietary.

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In calculating the estimate, we assume that the censored observation occurs after the death (in this case, just past 24 months), and hence is treated as being in a later time period. The successive products of the individual proportions surviving gives this estimate the name product-limit estimator. 49. 7. The curve is graphed as a step function, meaning it remains constant except at the death times. Statistically this is the most appropriate; attempting to interpolate between points can lead to biased estimates.

The statement “To compare A and B,” for instance, is not a sufficient statement of objectives. Is the goal to identify one of the arms for further study? To reach a definitive conclusion about which arm to use in the future to treat a specific type of patient? To decide if addition of a new agent improves treatment outcome? To determine if A and B are equivalent? To generate evidence for or against a biologic hypothesis? Each of these objectives has different design implications. For the first, a relatively small randomized Phase II selection design might be appropriate.

One problem with this is that the choice of the time point for testing is rather arbitrary. In addition, there are many situations for which the 2-year survival probabilities are the same, but the overall survival is very different. 2b displays three situations, all giving rise to the same 2-year probabilities. One would usually prefer an overall test of the equality of the survival curves. There are a number of ways to do this. The general idea is the following: Begin by ordering the survival times (and censored observations), disregarding treatment assignment.

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