## The Annals of Applied Statistics

- Ann. Appl. Stat.
- Volume 8, Number 3 (2014), 1341-1371.

### A location-mixture autoregressive model for online forecasting of lung tumor motion

Daniel Cervone, Natesh S. Pillai, Debdeep Pati, Ross Berbeco, and John Henry Lewis

#### Abstract

Lung tumor tracking for radiotherapy requires real-time, multiple-step ahead forecasting of a quasi-periodic time series recording instantaneous tumor locations. We introduce a location-mixture autoregressive (LMAR) process that admits multimodal conditional distributions, fast approximate inference using the EM algorithm and accurate multiple-step ahead predictive distributions. LMAR outperforms several commonly used methods in terms of out-of-sample prediction accuracy using clinical data from lung tumor patients. With its superior predictive performance and real-time computation, the LMAR model could be effectively implemented for use in current tumor tracking systems.

#### Article information

**Source**

Ann. Appl. Stat., Volume 8, Number 3 (2014), 1341-1371.

**Dates**

First available in Project Euclid: 23 October 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.aoas/1414091216

**Digital Object Identifier**

doi:10.1214/14-AOAS744

**Mathematical Reviews number (MathSciNet)**

MR3271335

**Zentralblatt MATH identifier**

1303.62058

**Keywords**

Lung tumor tracking external beam radiotherapy nonlinear time series mixture autoregressive process time series motifs likelihood approximation multiple-step prediction

#### Citation

Cervone, Daniel; Pillai, Natesh S.; Pati, Debdeep; Berbeco, Ross; Lewis, John Henry. A location-mixture autoregressive model for online forecasting of lung tumor motion. Ann. Appl. Stat. 8 (2014), no. 3, 1341--1371. doi:10.1214/14-AOAS744. https://projecteuclid.org/euclid.aoas/1414091216

#### Supplemental materials

- Supplementary material: Code. R Code used for fitting and forecasting with the LMAR model.Digital Object Identifier: doi:10.1214/14-AOAS744SUPP