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CPS1419 Jinheum K. et al.
            4.  Illustrative real example
                PAQUID data were collected to investigate the effects of dementia
            on  mortality.  Samples  were  taken  from  community  residents  of  two
            southwestern regions (Gironde and Dordogne) of France (Helmer et al.,
            2001). The population consists of residents aged65 or above between
            1988 and 1990, whose socio-demographic characteristics and mental
            health status were recorded every two to three years. Among a total of
            3,675 persons selected to participate  in the study, 832 (22.6%) were
            diagnosed  with  dementia,  639  of  whom  died.  The  remaining  2,843
            participants  (77.4%)  did  not  experience  dementia  but  2,298  of  them
            died.
                In this article, we performed an analysis based on ‘paq1000’ data,
            which included 1,000 randomly selected observations from the PAQUID
            data (Touraine et al., 2015). The paq1000 data consist of several pieces
            of  information,  such  as  the  mental  health  status  (diagnosed  with
            dementia  or  dementia-free),  dead  or  alive  status,  ages  (including  a
            participant’s age at the start of study ( ), their age at the last dementia-
                                                     
            free visit ( ), their age when they were diagnosed with dementia ( ),
                        
                                                                                     
            their age at their time of death ( ), their age at censoring ( ), gender,
                                                
                                                                            
            and educational background (educated or non-educated in terms of
            graduation from elementary school, say certificate). For an illustration
            of the proposed method, we assume a subject’s age at death to be
            censored  in  an  interval  around  the  observed  value.  To  this  end,
            assuming  that   is  age-at-death  of  subject  , the  endpoints  of  the
                              
            interval ( ,  ] for  subject  are  defined  as  =  −   and  =  +
                                                                               
                                                                       1
                                                                  
                                                             
                       
                                                                                    
                          
             ,  where    and    are  random  variates  generated  from  (0,3).
                         1
             2
                                   2
            When a subject’s age at death is censored at time  , we set  =   and
                                                                             
                                                                                  
                                                                  
             = ∞, i.e., right-censored at  .
              
                                             
                For the 0 → 1 transition, men showed intensity that was 1.899 times
            higher than that of women, yielding a decently significant result with a
            -value of 0.0016. The non-educated group showed an intensity that
            was 1.277 times higher than the educated group, although this was not
            significant (a -value of 0.3293). For the 1 → 2 transition, the intensity
            for  women  is  1.222  times  higher  than  it  is  for  men,  but  this  is  not
            significant (a -value of 0.711). The intensity for the educated group is
            1.248  times  higher  than  the  non-educated  group,  but  this  is  not
            significant  (a -value  of  0.6808).  Finally,  for  the 0 → 2 transition,  the
            intensity for women is 6.816 times higher than it is for men with a very
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