Modeling climate effects on hip fracture rate by the multivariate GARCH model in Montreal region, Canada

Changes in extreme meteorological variablesand the demographic shift towards an older population have made it important to investigate the association of climate variablesand hip fractureby advanced methods in order to determine the climate variablesthat most affect hip fractureincidence. The nonlinear autoregressive moving average with exogenous variable-generalized autoregressive conditional heteroscedasticity(ARMAX-GARCH) and multivariate GARCH (MGARCH) time series approaches were applied to investigate the nonlinear association between hip fracturerate in female and male patients aged 40–74 and 75+ years and climate variablesin the period of 1993–2004, in Montreal, Canada. The models describe 50–56 % of daily variation in hip fracturerate and identify snow depth, air temperature, day lengthand air pressure as the influencing variableson the time-varying mean and variance of the hip fracturerate. The conditional covariance between climate variablesand hip fracturerate is increasing exponentially, showing that the effect of climate variableson hip fracturerate is most acute when rates are high and climate conditions are at their worst. In Montreal, climate variables, particularly snow depth and air temperature, appear to be important predictors of hip fractureincidence. The association of climate variablesand hip fracturedoes not seem to change linearly with time, but increases exponentially under harsh climate conditions. The results of this study can be used to provide an adaptive climate-related public health program and ti guide allocation of services for avoiding hip fracturerisk.