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Probability and Statistics in Aerospace Engineering: by M.H. Rheinfurth

By Rheinfurth, M. H.

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Book Id: WPLBN0000659548
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Title: Probability and Statistics in Aerospace Engineering: by M.H. Rheinfurth  
Author: Rheinfurth, M. H.
Volume:
Language: English
Subject: Government publications, National Aeronautics and Space Administration (U.S.), NASA reference publication
Collections: NASA Publication Collection
Historic
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Publisher: National Aeronautics and Space Administration Publication

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H, R. M. (n.d.). Probability and Statistics in Aerospace Engineering. Retrieved from http://worldlibrary.org/


Excerpt
Description: This document contains information regarding topics such as Proportion of DCS by TR360 and EXER, Proportion of DCS by P2 and, and Maximum Partial Likelihood Estimates for Fitted Cox Models...

Table of Contents
Contents Abstract ................................................................................................................................................ 1 1. Introduction ................................................................................................................................ 1 2. Cox Proportional Hazards Model.................................................................................................. 2 2.1 Stratified Cox Models........................................................................................................ 3 3. Description of Data ...................................................................................................................... 3 3.1 Exploratory Analysis ......................................................................................................... 5 4. Assessment of Proportional Hazards............................................................................................. 8 4.1 Initial Fit of a Cox PH Model ............................................................................................. 9 4.2 Test of Time-varying Coefficients in a Cox PH Model ....................................................... 10 4.3 Graphical Tests for PH After Fitting a Cox Model .............................................................. 14 5. Stratified Cox Proportional Hazards Model................................................................................... 16 5.1 Fit of Stratified Cox Proportional Hazards Models ............................................................. 16 5.2 Test of PH Assumption for Stratified Cox Models: Test for Time-varying Coefficients....... 17 5.3 Graphical Tests for PH After Fitting a Stratified Cox Model............................................... 19 5.4 Expected Survival from a Stratified Cox Model.................................................................. 20 5.5 Lack of Fit in the Stratified Cox Model .............................................................................. 21 5.5.1 Deviance Residuals and Normal Deviate Residuals for Assessing Poorly Predicted Individuals ................................................................................. 21 5.5.2 Global Goodness-of-Fit Using Martingale Residuals ............................................. 24 5.5.3 Assessment of Influential Observations................................................................. 25 6. Interpretation of the Stratified Cox Model..................................................................................... 29 7. Discussion On the Use of Frailty Models for DCS Data ................................................................ 30 8. Model Validation ......................................................................................................................... 32 8.1 Predictive Accuracy of Cox Models ................................................................................... 33 8.2 Model Calibration of Survival Predictions.......................................................................... 34 9. Concluding Remarks.................................................................................................................... 35 Appendix ? Arjas Plots.......................................................................................................................... 36 References ............................................................................................................................................ 37

 

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