Alex TrindadeAssoc. Prof.

TTU Mathematics & Statistics Dept.(alex.trindade@ttu.edu)

I’m a Statistician… Your toolbox…

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.

State-Space Model

Outcomes @ time t = FUNCTION( X, Y)• Y: outcomes at earlier times, • X: covariates at current and earlier times.

• 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

Individual Forecasts

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.

• 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

Your data?

(alex.trindade@ttu.edu)