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CPS1944 Oyelola A.
                Ethical  approval  was  obtained  from  the  THHS  Human  Research  Ethics
            Committee  (HREC/16/QTHS/221)  and  the  Queensland  Public  Health  Act
            (RD007802) for the data linkage project.

            Statistical analysis
            Estimation of the climate-pneumonia association
                Weekly cases of pneumonia and climatic variables (rainfall, temperature)
            were  analysed  using  distributed  lag  non-linear  model  (DLNM)  [13-16]  to
            investigate  the  association  between  pneumonia  cases  and  rainfall  or
            temperature in THHS from 2006 to 2016.
                The  weekly  counts  of  pneumonia  cases  was  fitted  via  quasi-Poisson
            generalized linear regression models adjusting for season, long-term trend,
            weekly  mean  temperature  (ºC)  and  total  weekly  rainfall  (mm).  We  used
            distributed  lag  non-linear  models  (DLNMs)  [13-16]  to  model  the  potential
            non-linear and delayed (lagged) effects of temperature and rainfall.

                                         ~( )
                                         
                                                          
                                                            
                             ( ) =∝ + ∑   (  ) + ∑   
                                                     
                                                 
                                                                    
                                  
                                             =1             =1

            Where   represents the weekly observed pneumonia cases on week t with
                    
            mean  , ∝ is  the  model  intercept.  The  function,   is  used  to  specify  the
                    
                                                               
            functional  relationship  between  variables    and  the  nonlinear  exposure-
                                                        
            response curve, defined by the parameter vectors  . The variables   include
                                                                              
                                                              
            other predictors with linear effects specified by the related coefficients  .
                                                                                  
                Previous  studies  have  suggested  that  the  effect  of  a  specific  exposure
            event is not limited to the period when it is observed, association may spread
            over a few time periods [15, 17]. Therefore, we modelled the non-linear and
            delayed effects of a rainfall and temperature through functions   which define
                                                                          
            the relationship along the two dimensions of predictor and lags. That is, the
            exposure-lag-response  was  modelled  by  applying  a  bi-dimensional  cross-
            basis  spline  function  describing  simultaneously  the  dependency  of  the
            relationship along the temperature range and its distributed lag effects.
            The relaxed cross-basis parameterization for exposure-lag-response is given
            by:
                                                      
                                   
                                                                        
                         (, ) = ∫  ∙ ( − , ) ≈ ∑  ∙ ( − , ) =  
                         
                                                                        ,
                                   0
                                                       0
            Where  the  bi-dimensional  function  ∙ ( − , )  define  the  exposure–lag–
            response function, and models simultaneously the exposure–response ()
            curve along temperature/rainfall range and lag–response curve, ()  [14].


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