Another topic is about the hypothesis testing for current leukemia-free
survival. Relapse after bone marrow transplant for patients with leukemia is
looked on as failure of the treatment. In recent years, donor lymphocyte
infusion (DLI) has been suggested as a new approach to treat the patients who
relapse. Of clinical interest would then be the probability that a patient is
alive and leukemia-free at a given time point after the transplant with or
without DLI. This probability is called the current leukemia-free survival
probability (CLFS). Klein (2000, British Journal of Hematology) introduced a
linear combination of three survival curves as an estimator of CLFS. Based on
this estimator, we construct a series of test statistics to compare CLFS
between two groups. We present simulation results to estimate type I error
rates and power of these testing methods under different scenarios. Real data
are analyzed as an illustration of these testing methods. Practical
recommendations are provided.

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We approach this problem with a sequential search. Use data to fit a spatial process that approximates f. This process gives an estimate of the L-contour, and can be used to estimate how much information would be gained if f is evaluated at point p. Choose points where the estimated value of f is L, but where uncertainty is high. Evaluate f at chosen points. Augment set of data points and set of data values. Repeat procedure with augmented data. Calculate convergence criteria after each iteration, and stop when criteria reach set goals.

The search process is applied to several functions
defined in low dimensional space. Finally, it is applied to
an actual simulation function.

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Based on joint work with Andy Tremayne and John Naylor

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Extending the influence function approach to non-linear or hierarchical models is however far less simple, leading to an absence of this form of robustness in many areas. We therefore propose a simple location-scale family based around the heavy-tailed 'Huber distribution', which provides a model-based analogue of Huber's estimation methods. For simultaneously robust inference on both location and scale, standard likelihood methods applied to this family give results extremely closely related to Huber's well-known but more ad-hoc "Proposal 2".

Further justification for our empirical approach is provided by examining
this fully-specified model in terms of constituent 'signal' and 'contaminant'
parts. These have several attractive operating characteristics which are both
simply understood and of broad practical appeal. The full specification of a
likelihood for the data allows simple extensions to be made for robust
inference in many complex models; a selection of examples will be given.

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Lawton et al. (1972) propose the self-modeling approach for functional data. Their method is based on the assumption that all individuals response curves have a common shape and that a particular individual's curve is some simple transformation of the common shape curve. This basic model can be expanded by adding the assumption that the transformation parameters are random in the population (Lindstrom, 1995). This allows a more natural approach to complex data.

This methodology can also be generalized to two-dimensional response curves such as those that arise in speech kinematics and other areas of research on motion (Ladd and Lindstrom, 2000). These parameterized curves are usually obtained by recording the two-dimensional location of an object over time. In this setting, time is the independent variable, and the (two-dimensional) location in space is the response. Collections of such parameterized curves can be obtained either from one subject or from a number of different subjects, each 1 producing one or more repetitions of the response curve.

Finally, the methods for two-dimensional, time-parameterized curves can be
extended to model outlines (closed curves) collected from medical or other
images. For example, in a study of autistic and normally developing children,
the outlines of the corpus callosum were collected from brain MRIs.
Self-modeling allows us to model the outlines, describe the variability within
each group and also assess the existance of meaninful difference between the
groups.

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