The Use of Quantile Regression to Forecast Higher Than Expected Respiratory Deaths in a Daily Time Series: A Study of New York City Data 1987-2000

Ireneous N Soyiri,Daniel D Reidpath

doi:10.1371/journal.pone.0078215

Abstract

Forecasting higher than expected numbers of health events provides potentially valuable insights in its own right, and may contribute to health services management and syndromic surveillance. This study investigates the use of quantile regression to predict higher than expected respiratory deaths.Data taken from 70,830 deaths occurring in New York were used. Temporal, weather and air quality measures were fitted using quantile regression at the 90th-percentile with half the data (in-sample). Four QR models were fitted: an unconditional model predicting the 90th-percentile of deaths (Model 1), a seasonal / temporal (Model 2), a seasonal, temporal plus lags of weather and air quality (Model 3), and a seasonal, temporal model with 7-day moving averages of weather and air quality. Models were cross-validated with the out of sample data. Performance was measured as proportionate reduction in weighted sum of absolute deviations by a conditional, over unconditional models; i.e., the coefficient of determination (R1).The coefficient of determination showed an improvement over the unconditional model between 0.16 and 0.19. The greatest improvement in predictive and forecasting accuracy of daily mortality was associated with the inclusion of seasonal and temporal predictors (Model 2). No gains were made in the predictive models with the addition of weather and air quality predictors (Models 3 and 4). However, forecasting models that included weather and air quality predictors performed slightly better than the seasonal and temporal model alone (i.e., Model 3 > Model 4 > Model 2)This study provided a new approach to predict higher than expected numbers of respiratory related-deaths. The approach, while promising, has limitations and should be treated at this stage as a proof of concept.

Highlights

There is an increasing body of literature looking at the causal relationship between weather, air quality factors, and health outcomes [1,2,3,4]
There is no requirement for the factors explaining low birth weight to be the same factors that explain average birth weight or for the explanation to be of the same form as for the central part of the conditional distribution
We investigated the use of quantile regression to forecast the 90th percentile of daily, respiratory related deaths for New York City, in the period 1 January 1987 to 31 December 2000

Summary

Introduction

There is an increasing body of literature looking at the causal relationship between weather, air quality factors, and health outcomes [1,2,3,4]. Forecasting health outcomes has attracted less attention, but it too has a developing base in the scientific literature [5,6,7,8,9]. Both the causal modelling and the forecast research have focused on the central tendencies of the distribution of data; i.e., the expected and conditional expected value. There is no requirement for the factors explaining low birth weight to be the same factors that explain average birth weight or for the explanation to be of the same form as for the central part of the conditional distribution

Methods

Results

Discussion

Conclusion