Alain Duhamel wrote: Hi, Could you help me to solve the following problem : 1. P measures are made for a patient at times T1, T2, ... Tp : X1,...,Xp 2. A reference's curve have been etablished. This curve reflect the "normal" evolution at times T1, ... Tp : C1,...,Cj,... Cp. We have also the confidence intervals of the Cj's. 3. We want to decide : - The observed values Xj (or the observed curve) are (is) compatible with the standard curve, - On the contrary, there is a significant diffrence between the curve and the standard. How this problem could be solved ?? Thanks for advance ------------------------------------------------------------ I Alain DUHAMEL Statisticien I I Centre d' Etude et de Recherche en Informatique Medicale I I Universite de LILLE II --- http://www.univ-lille2.fr I I Tel : 03-20-62-68-01 Fax : 03-20-52-10-22 I ------------------------------------------------------------
This is a very interesting problem. One approach is to consider this as a pooled cross-sectional time series problem or as it is sometimes known panel data. Consider identifying the underlying equation for these p equally spaced measures X1,X2,,,,,Xp as an ARIMA model of some order. Now, identify an ARIMA model for the C1,C2,,,,,Cp series. Determine a common model, i.e.one that describes both , albeit one being slightly over parameterized.
Now estimate the potentially over parameterized model for both traces, i.e. the X's and the C's separately leading to totally separate sets of coefficients and error sums of squares.
Now, under the null hypothesis of a common set of parameters, estimate this slightly over parameterized model using ALL of the data. This model will have one set of parameters being based on the joint set of X and C thus 2p values. The test of the hypothesis of a single set of coefficients is the same as a test of the hypothesis of the equality of X and C. This test is a quadratic form and leads to an F test following the work of Gregory Chow (tests for the equivalence of regression). AUTOBOX, see http://www.autobox.com, has this option as part of it's tour de force. If I can help please get in touch with me. Dave Reilly