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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\(  \ \ 0l "Results p = 8 and structural zerosJ# X \ 0A? z \ 0T!@  Not all 256 patterns are incident  only 140 of the 256 cells in the 8  dimensional table are non-zero*k(2jc  \ 0&0  These empty cells may be structural zeros  not merely sampling zeros. Will check whether all zeros are structural  but SPSS is tricky here. r(2cgPcgc \ 0#@p  [ S-zeros ? 2    \ 010 p  ZNon-zero 2  H \ 0޽h ? ̙33H    p (  B   6PI Flat Table Specification To specify structural zeros I must tell spss the address of each cell which is to be a structural zero. To do this correctly I should produce a flat contingency table. Suppose now I have 9 comorbities  the 8 in red below and C20. Then I need to output the 9- dimensional flat table comprising a column of frequencies and followed by columns of the design matrix (indices) of the table. Step1: Generate the flat table Problem: Crosstabs is the procedure which writes out this flat table, but only in integer mode and only for an 8 dimensional table!! It writes a .dat file TEMPORARY. SELECT IF ( c20 EQ 0). PROCEDURE OUTPUT OUTFILE='myflat_table.dat . CROSSTABS VARIABLES=C2 C3 C7 C10 C14 C17 C18 C19 (0,1) /TABLES=C2 BY C3 BY C7 BY C10 BY C14 BY C17 BY C18 BY C19 /WRITE=ALL /COUNT ROUND CELL . zEe%#!#,cg cgcgc ggcgc '&'&#''"#'#"<#"# '&#"g  , 6 <       <JGkH   0  This is only way to force crosstabs to write out the cells which have zero frequencies - freq is the variable written in the 1st column followed by the table indices in subsequent columnsZ!% H  0޽h ? ̙33    D (     6v``C Legacy Code Problems Step 2: Notice that I must repeat this operation for c20 =1 and then put the two flat tables together (ie by stacking them). Putting the tables together is most easily accomplished by converting the .dat files to .sav files and using the add files command Notice however that I have to add the table subscripts for C20 = 0 for the first table and c20 =1 for the second table in order to complete the 9 -dimensional table subscripts. C20 will be the last column and the table subscripts on the right vary slowest In what follows I assume that this has been done and that the final table was stored in  myflat_table.sav This whole procedure is a bind for higher dimensional tables but remember Crosstabs and Hiloglin can only handle 10 dimensions as a max!!  these restrictions are examples of LEGACY CODE PROBLEMS in SPSSLYeg/cgcgcgcg3fcg'cgg ca M  mH  0޽h ? ̙33z  * " (  z  6L8P hDefining the Structural Zero Indicator Step3 Read in the whole flat-table and define the structural zero indicator called cwht GET FILE=  myflat_table.sav Comment freq C2 C3 C7 C10 C14 C17 C18 C19 and c20 are in this file. IF (freq gt 0) cwht=1. IF (freq eq 0) cwht=0. Comment cwht = 0 implies a structural zero. SAVE OUTFILE= final_flat_table_.sav /KEEP= Freq c2 c3 c7 c10 c14 c17 c18 c19 c20 cwht /COMPRESSED. Comment the save step immediately above may be omitted and the code combined with the analysis on the next slide. (  2(e'V#' #'&'#'#'#'#'#'#'#'#'#'#&2''33('&#'#'#'#'#'l#h( L a  H  0޽h ? ̙33.     F (  Z  6` Analysing the Flat Table Step 4: Fit Final model. Method backward, maxorder = 3 and p =0.01 Get file =  final_flat_table.sav WEIGHT BY freq. HILOGLINEAR C2 C3 C7 C10 C14 C17 C18 C19 c20 (0,1) /CWEIGHT = cwht /METHOD=backward /MAXORDER=3 /CRITERIA =iterate(30) maxsteps(10000) p (0.01) /PRINT=none /PLOT = default. &C 2e%# ':#"#''"'& #'#'#"#'&#"#"3#"#"#"^ $  5    3     BGPH_   0 @   0<P  HReconstruct the 9-D contingency table Including c20 using weight command<I 2/H   BGH    @   00 0   <Specify the structural zeros to hiloglin using cwht variable<= 2.< H  0޽h ?/  ̙33 d9(  d d 0$ (Results with p = 8 and structural zerosJ)  d 0  dK-way Interactions6 2gg d 04 `  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#   X d <hGHi 0Pp >  d 0 C Max order = 3 2H d 0޽h ?d ̙33 x(  xX x 0A?` x < H&    @  x 0 @ 0` @ 2  x 0p e  [This model is much worse suggesting that not all the observed zeros can be structural zeros\ 2\[ H x 0޽h ?x ̙33 <4h(  h h 0 R Model Wrapping - up" h 0x nf^___PPT9@8 6Generally Examine model sets with and without patterns of structural zeros 2. Refit models by Newton-Raphson to obtain MLE estimates, standard errors and variance-covariance matrix Explore Fit issues Check Biologic & Clinical plausibility Decide on Final Model  Parsimony first  2A 2k 2e 2 cAckcc c  "  &  @`H h 0޽h ? ̙33 xl(  l l 06Q  Advantages Multivariate, p-dimensional method Natural statistical parametrization for binary data Dependence measured in terms of interactions Fast IPF-based structured search procedure for MLEs Interaction test Backward elimination Final N-R fit Can incorporate binary response variable Y in analysis Can handle structural zeros when encountered. 2 2@ 2h 2 c""" cgcccccc)cg cc.c e l 0E T Summary of Technique "H l 0޽h ? ̙33 p*(  p p 0LM T Scope for Development"6 p 0,Qp  |Restrictions Basic model-building Philosophy is out-dated in SPSS Extension of the maximum dimension - currently p=10 max More general search procedure basically involves a re-programming of the structured search procedure Handling Structural Zeros  new procedure required Also Hiloglin does not tie-up with Genlog easily  Genlog does not accept Generating Sets as input User-selected reference categories required  2 2S 2o 2. 20 2c0cg_cMcc">*  ZH p 0޽h ? ̙33t $(    0 hP6 L In Summary "  0l`Ps  ht Log-linear Modelling in SPSS is not  Joined Up Main restriction to usefulness is p=10 Structural Zero handling is antiquated Modern search strategy tools needed IPF is useful, but some models produced are not estimable by ML. Output needs modernisation Nevertheless the Basic procedures are useful  2 2K 2  %: H  0޽h ? ̙33E  P(  P P 0y M Key References" P 0,w 8Birch (1963). Maximum Likelihood in three-way contingency tables. JRSS, Series B, 25, 220-233. Bishop (1969). Full contingency tables, logits and split contingency tables. Biometrics, 25, 383-400. Fienberg (1972). The analysis of incomplete multi-way contingency tables. Biometrics. 24, 177-202. Goodman (1971). The analysis of multi-dimensional contingency tables. Technometrics, 13, 1, 33-61. Haberman (1972). Log-linear fit for contingency tables. JRSS, Applied Stats., 21; 2, 218-225 MacKenzie & O Flaherty (1982). Direct design matrix generation for balanced factorial experiments  algorithm AS173. JRSS, Applied Stats, 31,75-80. O Flaherty & MacKenzie (1982) Direct simulation of nested Fortran Do-loops  Algorithm AS172, JRSS, 31,71-74.B` 2 2c"H P 0޽h ? ̙33 0 0(  X  C 8     S 08 @    H  0޽h ? ̙33r y,"_-8}l'_G8aD`|qu .&:#'mx+~l6tAebUXN'Oh+'0Q `h   No Slide TitleGilbert MacKenziee Brian.Sextonnzi68aMicrosoft PowerPointP@л@{i@`ŲGPg  R('& &&#TNPPp2OMi & TNPP &&TNPP     'A x(xKʦ """)))UUUMMMBBB999|PP3f3333f333ff3fffff3f3f̙f3333f3333333333f3333333f3f33ff3f3f3f3333f3333333f3̙33333f333ff3ffffff3f33f3ff3f3f3ffff3fffffffff3fffffff3f̙ffff3ff333f3ff33fff33f3ff̙3f3f3333f333ff3fffff̙̙3̙f̙̙̙3f̙3f3f3333f333ff3fffff3f3f̙3ffffffffff!___wwwhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh޴ݵ⴦ݵݴⵦݼݼݼݼݼݼݼݼFiFoFiFiLiFo—rrrrr @ @  Fޘ--.--.---.-- ooF @ -.-.--.-.-.- @ @  F-N---.------ F @ .-.-.---.-.- @ @  @------.----- F @ %ޟrVPUrVqVrUrV @ @»™»™ F %ޞO..N.OO.O-O- @ @----Vx--.-.--&TNPP &՜.+,0     OOn-screen ShowKeele UniversityeJ]! *Times New RomanComic Sans MS Arial BlackMonotype SortsSymbolArial Courier New WingdingsDefault DesignPowerPoint PresentationPowerPoint PresentationPowerPoint PresentationPowerPoint PresentationPowerPoint PresentationPowerPoint PresentationPowerPoint PresentationPowerPoint PresentationPowerPoint PresentationPowerPoint PresentationPowerPoint PresentationPowerPoint PresentationPowerPoint PresentationPowerPoint PresentationPowerPoint PresentationPowerPoint PresentationPowerPoint PresentationPowerPoint PresentationPowerPoint PresentationPowerPoint PresentationPowerPoint PresentationPowerPoint PresentationPowerPoint PresentationPowerPoint PresentationPowerPoint PresentationPowerPoint PresentationPowerPoint PresentationPowerPoint PresentationPowerPoint PresentationPowerPoint PresentationPowerPoint PresentationPowerPoint PresentationPowerPoint Presentation  Fonts UsedDesign Template Slide Titles!$_: Brian.SextonBrian.Sexton  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`bcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXZ[\]^_`bcdefghmRoot EntrydO)PicturesCurrent UseraSummaryInformation(0QPowerPoint Document(a^DocumentSummaryInformation8Y