Alex Trindade Assoc. Prof. TTU Mathematics & Statistics Dept. ([email protected])
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Transcript of Alex Trindade Assoc. Prof. TTU Mathematics & Statistics Dept. ([email protected])
![Page 2: Alex Trindade Assoc. Prof. TTU Mathematics & Statistics Dept. (alex.trindade@ttu.edu)](https://reader036.fdocuments.us/reader036/viewer/2022081809/5697bf981a28abf838c914e7/html5/thumbnails/2.jpg)
I’m a Statistician… Your toolbox…
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Problem 1. A Model for Predicting Outcomes in
Longitudinal Data (Naranjo, Trindade & Casella, Journal American Statistical Association, 2013)
• Advantages of a State-Space Approach– Flexible, handles trends over time;– Can have multivariate outcomes, covariates, and
missing data (in both outcomes & covariates);– Ease of forecasting.
![Page 4: Alex Trindade Assoc. Prof. TTU Mathematics & Statistics Dept. (alex.trindade@ttu.edu)](https://reader036.fdocuments.us/reader036/viewer/2022081809/5697bf981a28abf838c914e7/html5/thumbnails/4.jpg)
State-Space Model
Outcomes @ time t = FUNCTION( X, Y)• Y: outcomes at earlier times, • X: covariates at current and earlier times.
![Page 5: Alex Trindade Assoc. Prof. TTU Mathematics & Statistics Dept. (alex.trindade@ttu.edu)](https://reader036.fdocuments.us/reader036/viewer/2022081809/5697bf981a28abf838c914e7/html5/thumbnails/5.jpg)
• Lagorio et al (2006) data: 8 patients suffering from Chronic Obstructive Pulmonary Disease (COPD).
• Response: 2-vector of lung function (FVC, FEV1).
• Exogenous covariates: nitrogen dioxide and fine particulate matter.
• Time period: 32 consecutive days in winter 1999, Rome (Italy).
• Missing: 60% in response; 10% in covariates.• Main focus: prediction.
Data Analysis
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Individual Forecasts
![Page 7: Alex Trindade Assoc. Prof. TTU Mathematics & Statistics Dept. (alex.trindade@ttu.edu)](https://reader036.fdocuments.us/reader036/viewer/2022081809/5697bf981a28abf838c914e7/html5/thumbnails/7.jpg)
Problem 2. Smoothing Reconstructed Non-
Parametric Survival Curves (Paige & Trindade, in progress…)
• Advantages of a Saddlepoint-Based Approach– Starts from classical Kaplan-Meier weights;– Does not need user-specified tuning parameters;– Accurate reproduction of “true” curve.
![Page 8: Alex Trindade Assoc. Prof. TTU Mathematics & Statistics Dept. (alex.trindade@ttu.edu)](https://reader036.fdocuments.us/reader036/viewer/2022081809/5697bf981a28abf838c914e7/html5/thumbnails/8.jpg)
• Classic dataset (c.1980): survival times (days) of 184 patients who underwent heart transplantation.
• Events: 113 died.o First died at day 0.5;o Last died at day 2878.
• Censored: 71 still alive at end of study (day 3695).
Stanford Heart Transplant Data
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