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S  0X ``  >*  0 `   @*  0 `   @*  <"_  tAssess, York, Nov 2006 .@ 3f   <"`@  | University of Limerick, Ireland.@! 3f H  0޽h ? ̙33 Default Design 0 @8*( =(Uadb 8 8 0\ P    X*  8 0     Z* d 8 c $ ?   8 0   @  RClick to edit Master text styles Second level Third level Fourth level Fifth level!     S 8 6\ `P   X*  8 6H `   Z* H 8 0޽h ? ̙33 , G?(    64@ @ l&SCREENING MULTIVARIATE COMORBIDITIES *'&  6P9 `  Bby$  6= Pf  QGilbert MacKenzie$   6,B `  ZCentre of Biostatistics&   0F @ 2    C AC:\Documents and Settings\Gilbert.MacKenzie\My Documents\www\ul_web_logo_large.jpgFH  0޽h ? ̙33+ d 22nd April 2004 *CMS / GSK April 2004 o g 0 !  (     6(  L Introduction$ Z  0P8 There are two general problems The first is to understand the multivariate distribution of relevant comorbidities, say p in number. X$P   0 @0 :  6z A $  0   o!Descriptive Statistical Activity2"   6l'  A $  6ț PSo  A $  0p @V  :  0 P f ^"These are of course inter-related. #"  6PS3  A $7  08   oThe second is to understand which components of this distribution influence outcome, say Y (disease status) Lp[  0в   o!Explanatory Statistical Activity2" H  0޽h ? ̙33  / ' @  (    6Իu DFocus "  0  >The main focus in on the first question - taking into account 6?!  68L A $  6\pR P Binary (1,0) nature of comorbidities >)'   6k A $   6pL A $>   0P0  ^ Multivariate distribution p  dimensional d0  6w k  A $  6<w L  A $  0h` p0F  \ Resulting non-Normal correlation structure >/-  6g : ? "I  0x  Analysis is then in terms of a p-dimensional contingency table involving a log-linear model for the resulting frequencies, i.e., a GLM. DiH  0޽h ? ̙33 P( P  :  3 hj  6D* ERemark "  0 fHowever, the second question is also of interest  64 !  6L A $^  0T ` & |Requires a model for Y in terms of x  subset of comorbiditiesf?   6h k A $  60L A $&  0|0P ~ Burden of comorbidity - Index or Score  sometimes effective,@?  6w k  A $  6p w L  A $  0#` 03  z2 But no information on non-main effect complexity ,32  6p(g : ? "  0`,pf :  0/ :  0430   :  01   :  0: `  z2Also, may not take account of clinical severity ,32  0> 0 u%Hence loss of scientific information 4&H  0޽h ? ̙33h ` 0(  0 +0 6(G ? " 30 0K  {Primary data structure p =3 Br P  0 #"*M`??=HP " a0 <O?   *n222 p222R @`& `0 <b?  .n212 p212R @`" ^0 <l?    *n122 p122R @`& ]0 <v?  .n112 p112R @` \0 <?   o%C (+) A(-) A(+)&& @` Y0 <L?  ; B(-) B(+)<< @`  X0 <@? P (n221 p221R @`& W0 <0?P  .n211 p211R @`" U0 <@? P *n121 p121 R @`$ T0 <(? P ,n111 p111R @` S0 <? p&C (-) A(-) A(+)'' @` P0 <l?P 8 B(-) B(+) *9 @``B b0 0o ?PPZB c0 s *1 ?ZB e0 s *1 ?ZB f0 s *1 ?  `B h0 0o ?  `B i0 0o ?P `B l0 0o ?P ZB u0 s *1 ?ZB v0 s *1 ?  ZB x0 s *1 ?  ZB z0 s *1 ?  ZB }0 s *1 ?PPZB 0 s *1 ?   0 0@ 8Example, consider 3 binary comorbidities = A, B & C 49% 0 0  : 2 v 0 0   n NB: where SiSjSk nijk = n & SiSjSkpijk = 1. 8 2 ,,,$$,$ ,,,,$ H 0 0޽h ? ̙33=    p4} ( f0fP 4 4 0H  OStatistical Model" 4 0F . Basic assumption is mijk = E{ Nijk } = n.pijk = exp{j ijk} (1) with log-linear parametrization loge {mijk} = j ijk = m + ai + bj + gk + (ab)ij + (ag)ik + (bg)jk + (abg)ijk (2) and conditional Poisson Model Pr (Nijk= nijk) = exp{-mijk}.mijk nijk/ nijk! (3)` 2w(2 2,(2(2# ,$$$,$$$0,$,$! #"$,$,$$,$,$,4$$$,$$$,$$$,4$$, #! $$,$,$$,$,$,$,$ H 4 0޽h ? ̙33{ +#.f(     60pv =    61(  ? "p  f #":.  Z <4=?   K1 @` X <XD?  T 2-way Int.   @` V <M?  PAB" @` J <HO? `Dependence Structure @`. 7 <_?  J Total = 2p-1 =7>KD"." @` 6 <\f?   K1 @` 5 <n?   T 3-way int.   @` 4 <p?   QABC" @` 3 <x?   K1 @` 2 <z?  L  @` 1 <?   PBC" @` 0 <8?   K1 @` / < ?  L  @` . <0?   PAC" @` - <@? k K1 @` , <P?k  L  @` + <`?k OC" @` * <̹? Mk K1 @` ) <?M k L  @` ( <8?Mk OB" @` ' < ? /M K1 @` & <?/ M W Main Effect @` % <t?/M OA" @` $ <? / Ndf @` # <$? / QType  @` " <H ?/ UEffect " @``B : 0o ?ZB ; s *1 ?//ZB < s *1 ?MMZB = s *1 ?kkZB > s *1 ?ZB ? s *1 ?  ZB @ s *1 ?  ZB A s *1 ?  `B B 0o ?`B C 0o ?`B F 0o ?ZB K s *1 ?ZB R s *1 ? ZB S s *1 ?   ZB W s *1 ?   c 0  SDependence Structure "H  0޽h ? ̙33M  ( YdZ    6w1l A $   6x8P A $  6H 1l A $  6$P  A $  6<(1l  A $  6p, P  N $  6p/ P  J $   6t4 ?z  A $  0,8  MInterpretation "  0Fp  ^Main Effects Model => SI For example, when the 2-way & 3-way interaction terms in (2) are zero we have a main effects model pijk = exp{ai + bj + gk} (4) then the comorbidities are SI, ie, A ^B ^C Conditional Independence Model A model in which, say pijk = exp{ai+bj + gk + (ab)ij + (bg)jk} (5) implies that A & C are SI given B and is denoted A ^ C | B.8 2(2#''e $,$,$,$,$$ e      # * ,$,$,$,$$$,$$$,$     e          H  0޽h ? ̙33  z r   (    0u "How does SPSS handle these models?B#   0z0` tHiloginlear - finds mle s of expected numbers in cells of a hierarchical loglinear model by IPF <l   0Ā0`  Loglinear - finds mle s of parameters by Newton Raphson vW 9H     0p0  Fp Genlog - similar to Loglin  different interface9  ,  0x0P :  0H0P@ :  0LP@  :k  6@ J iIPF = Iterative proportional fitting (Haberman, 1972) NB: Some incompatibilities between procedures `j0)i    0 @  #Above procedures restrict p =10 !! L$ 2# H  0޽h ? ̙330 # p( d   ! 0x  rExample when p = 10 B ^ " 0 pv  Data Example: Obesity study data comprising 5550 cases and p = 100 comorbidities. Selecting Candidate Co-morbidities Usually based on clinical criteria  here p = 10 selected on basis of most frequently occurring. Clinical Relevance However, no suggestion that these 10 are the most clinically relevant  rather they provide a stern test of the technique.  2i(2#'6"&" c "a *"&5"" c"" H  0޽h ? ̙33( (Z$h(   $L 0@0\ Z$ #">2 )))@00\ N$ <t?P T0h R12.9" @` L$ <?0TP h b1. com3 - Alcoholb @` D$ <<?P @0T U Frequency   @` B$ <P?0@P T OName  @` =$ <?P h0} Q9.4" @` ;$ <,?0hP } d2. com6 - Athralgiab @` -$ <?P H 0\ R20.7" @` ,$ < ?0H P \ `10. com99 - Weightb @` +$ < ?P  0H  R16.7" @` *$ <?0 P H  a9. com90 - Smokerb @` )$ <x?P 0  V21.6 & @` ($ <+?0 P   >8. com89  Smear Cervix Normal  f @` '$ < 3?P 0  Q9.0" @` &$ <:?0 P  :7. com38  Exercise Adequateb @` %$ <xB?P 0  R10.5" @` $$ <8K?0P  _6. com21 - Coughb @` #$ <$M?P 0 U9.8 & @` "$ <T?0P  l5. com20 - Contraception f @` !$ <b?P 0 R49.7" @`  $ <( <  @ 0 A Max order = 4 2 @ <$GH: P  @   @ 0T '  lLR is a measure of discrepancy here. So the 4-way interaction is required to provide a minimal fit  maybe not very good !!:} 2t| H @ 0޽h ?/ @@ ̙33> D~(  Dd D 6Զ t Backwards elimination with P=0.01 & maxorder =4. 1. COM3*COM20*COM89*COM90 2. COM38*COM90*COM99 3. COM9*COM38*COM99 4. COM6*COM21 5. COM9*COM20*COM89 6. COM3*COM38 7. COM6*COM9 8. COM6*COM8 9. COM3*COM99 10. COM9*COM21*COM90 11. COM89*COM99 12. COM6*COM89 13. COM3*COM9*COM90 14. COM8*COM9 @u 24=&%  H  D 0 zBest Subset of terms p = 10BH D 0޽h ? ̙33 ~vH(  H  H C "@`   L-Ratio test - elimination of any interaction DF L.R. Prob 1. COM3*COM20*COM89*COM90 1 8.072 .0045 2. COM38*COM90*COM99 1 13.313 .0003 3. COM9*COM38*COM99 1 9.493 .0021 4. COM6*COM21 1 16.863 .0000 5. COM9*COM20*COM89 1 8.990 .0027 6. COM3*COM38 1 299.468 .0000 7. COM6*COM9 1 27.956 .0000 8. COM6*COM8 1 42.888 .0000 9. COM3*COM99 1 149.623 .0000 10. COM9*COM21*COM90 1 18.485 .0000 11. COM89*COM99 1 13.916 .0002 12.COM6*COM89 1 9.810 .0017 13 COM3*COM9*COM90 1 11.838 .0006 14 COM8*COM9 1 11.239 .0008  -  -n&i  o  H 0 d&Confirmation of Best Subset of terms "'&H H 0޽h ? ̙33  +0L)(  Li 0@0\ L #">2 )))@00\ L <?P T0h R12.9" @` L <?0TP h b1. com3 - Alcoholb @` L <?P @0T U Frequency   @` L <x?0@P T OName  @` L <8 ?P h0} Q9.4" @`  L < ?0hP } e2. com6 - Arthralgiab @`  L <?P H 0\ R20.7" @`  L <,!?0H P \ `10. com99 - Weightb @`  L <@#?P  0H  R16.7" @`  L <*?0 P H  a9. com90 - Smokerb @` L <9?P 0  ` 21.6 X & @` L <l;?0 P   >8. com89  Smear Cervix Normal  f @` L <,I?P 0  Q9.0" @` L <$K?0 P  :7. com38  Exercise Adequateb @` L <S?P 0  R10.5" @` L <db?0P  _6. com21 - Coughb @` L <j?P 0 ^ 9.8 X  & @` L <Ll?0P  o5. com20 - Contraception  f @` L < z?P 0 R49.7" @` L <|?0P  44. com9  Blood Pressureb @` L <?P }0 Q9.9" @` L <D?0}P  x*3. com8  Back-painb @``B L 0o ?0@0@ZB L s *1 ?00ZB L s *1 ?00ZB L s *1 ?00ZB L s *1 ?0 0 ZB L s *1 ?0 0 ZB  L s *1 ?0 0 ZB !L s *1 ?0H 0H `B "L 0o ?0\0\`B #L 0o ?0@0\ZB $L s *1 ?P @P \`B %L 0o ?0@0\ZB &L s *1 ?0}0}ZB 'L s *1 ?0T0TZB (L s *1 ?0h0h )L 0h {Comorbidities Selected p = 8 B ,L 0@  /  }Eliminate gender variables ( 2 XB /L@ 0DԔ@@P@XB 0L@ 0DԔ  H L 0޽h ? ̙33 VN0T(  T T 0| jResults when p = 8 : T 0  dK-way Interactions6 2g33g33 T 0p ; Tests that K-way effects are zero. K DF L.R. Prob 1 8 24821.005 .0000 2 28 6603.913 .0000 3 56 101.278 .0002 4 70 80.517 .1831 5 56 28.047 .9993 6 28 2.248 1.0000 7 8 .000 1.0000 8 1 .000 .9966  2 # w T <HGHi @ >  T 0 C Max order = 3 2H T 0޽h ?T ̙33n @`(  `[ ` 0p  Terms DF L.R. Prob 1. C3*C6*C9 1 10.649 .0011 2. C3*C9*C38 1 10.724 .0011 3. C6*C9*C38 1 10.149 .0014 4. C8*C9*C38 1 10.032 .0015 5. C3*C9*C90 1 10.306 .0013 6. C9*C21*C90 1 21.822 .0000 7. C3*C8*C99 1 6.951 .0084 8. C38*C90*C99 1 12.572 .0004 9. C6*C8 1 51.814 .0000 10 C6*C21 1 17.589 .0000 11.C9*C99 1 567.225 .0000 ( 2  33/33 33h33, 33633f ` 0  }Best Subset of terms p = 8 : B . ` B@ : 0Backwards elimination with P=0.05 & maxorder =3.:1.$   H ` 0޽h ? ̙33 {sPX (  X X 0` \ DF L.R. Prob 1. C3*C9*C90 1 11.891 .0006 2. C9*C21*C90 1 14.609 .0001 3. C9*C38*C99 1 9.510 .0020 4. C38*C90*C99 1 13.539 .0002 5. C21*C38 1 7.403 .0065 6. C6*C21 1 16.766 .0000 7. C3*C38 1 299.649 .0000 8. C3*C99 1 156.962 .0000 9. C6*C8 1 42.889 .0000 10. c8*C9 1 11.236 .0008 11. C6*C9 1 22.880 .0000 6 2) 5 5 5 s   . X B@ : 0Backwards elimination with P=0.01 & maxorder =3.:1.$    X 0l yBest Subset of terms p = 8BH X 0޽h ? ̙33 bZ`t(  tX t 0A? t <PG@6H 0pp  @  t 0`  .Always some outliers & we are just looking for the largest effects with the crude selection methods on offern 2nm H t 0޽h ?t ̙33Y  p\(