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1 2006 4

2 UDC Research and application of synthetical evaluation in the Down s syndrome screening system

3 I

4 5% Meta II

5 Abstract Bioinformatics is the interdiscipline of computational molecular biology and information processing science. With the rapid development of computing techniques biological technologies are reshaping the human society. It brings new development for the screening of Down s syndrome by combining the computing techniques with the bioinformatics. Down s syndrome is an usual chromosome disease because of the abnormality of fetus chromosome. It will take big tragedy to the family. So it is a very meaningful job to study the method of screening the DS in the first and second trimester especially using the computing technique. The workload of the collection statistics and analyzing for the information can be depressed through using the DS screening software. The accuracy of the screening result is also improved. Using the software the data can be stored integrally. This is useful for the further study and diagnoses. The information for screening DS in the pregnancy period and the revise information are concluded here the main point and innovation are listed below: 1. The measures used for screening DS pregnancies in the first and second trimester has been concluded here; 2. The information related to the DS in the first and second trimester has been concluded here such as ultrasonic screening methods maternal serum biochemistry ; 3. The efficacy of the respective information are analyzed by combining theory of information and synthetical evaluation; 4. The screen information and its revise information for our system has been chosen though the statistical methods using single diathesis methods and multiple diathesis methods; 5. Three screen fields were evaluated by meta-analysis method. After the evaluation the best field has been chosen for the further study; 6. The function of the screening system is realized at last though the software. This screening system is used for determining the risk of DS pregnancies in the second trimester the risk of the NTD pregnancies is determined at the same time. It is proved that this system is according to the requirement of the DS screening system. Key words: Down s Syndrome Synthetical evaluation information theory meta-analysis III

6 SROC β-hcg...28 i

7 Meta SROC ii

8 J.Langdon.Down 21 (trisomy 21) J.Langdon.Down Down's Syndrome 1959 Lejune G /

9 % % % ( ) 21 2

10 ~ ml 99% 0.3%(0.1%--0.4%) [1] Simoni 1 DS [2] % [1] %-1.5% 0.3%-1.5% 3

11 99% % (Crown Rump Length CRL) (Nichol Translucency NT) NT 2.5mm (NT (Cut-off) 2.5 [3][4] ) NT CRL

12 / (gold immunochromatographic assay GICA) 90 [5] 3. 69% % % [6] 4. Duchenne' s 5

13 [7] 1/ / [10]

15 X N a 1, a 2, L an x a1 a2 K a n = px ( ) p1 p2 K a1 (2-1) Shannon p 1, p 2, pn 3 [11] f ( p p p ) 1 2 L f ( p p L p ),, n 1 2,, L n pi ( i = 1,2, L, N) f (,,, ) gn ( ) N N L N = (2-2) ' ' ' ( ) = ( + + ) f pp,, L, p f( p p L p), p, L, p ( p p L p) fpp (,, L, p) (2-3) 1 2 n 1 2 k k+ 1 N 1 2 k 1 2 k ' pk p = k k 1, 2,, K p + p + + p = L (2-4) L 1 2 Shannon f ( p p L p ) 1 2 k,,, n N n i i i= 1 3 f ( p1, p2, L, p ) = C p log p (2-5) 8

16 C 2 10 e bit Hartley nat Shannon H( p p L p ) N i i i= 1,,, N 1 2 N H( p1, p2, L, p ) = p log p (2-6) X X H( p ) = 0 Shannon

17 U={u 1 u 2 u m } V={v 1 v 2 v n } m n v11 v12 v13 R = L L L (2-7) vn 1 vn2 v n3 A={ a 1 a 2 a m } A R = B (2-8) B={ b 1 b 2 b n } 1 M (, ) b = max[min( a, r ),min( a, r ), L,min( a, r )], j = 1,2 L, n (2-9) j 1 1j 2 2 j m mj min max ( ) 2 M( ) b = max[ ar, a r, L, a r ], j = 1, 2 L, n (2-10) j 11j 2 2j m mj 1 3 M( ) b = min[min( a, r ) + min( a, r ) + L + min( a, r )], j = 1, 2 L, n (2-11) j 1 1j 2 2 j m mj a b = min(1, a+ b) m k = 1 ( a r ) 1 k kj m k = 1 a k = 1 4 M( +) bj = ar 11j + a2r2 j + L + amrmj, j = 1,2 L, n (2-12) 10

18 5 M( ) b = min( ar + a r + L + a r ), j = 1, 2 L, n (2-13) j 11j 2 2j m mj M (, ) M( ) M( ) M (, ) M( +) M( ) Logistic OR OR 95% P t Logistic P<0.10 ( ) Logistic (stepwise ) α=0.10 Logistic 11

19 2.2.3 (Meta- analysis) Meta Meta [10] Cohen [11] (NHST Null Hypothesis Significance Testing) Schmidt [12] Meta Abrahantes [17] Meta Meta-analysis Meta above beyond behind after Glass 1976 (American Education Research Association) Glass Glass 12

20 [53] Glass 1. Meta 2. Meta 3. Meta [14] Meta [15] Meta Meta Meta ( ) (effect size) d (effect size) Meta ( t z F ) d d = ( Me Mc)/ Sc (2-14) t r d [15][16] d d Hedge d = wd / w (2-15) d w Meta w 13

21 2 = 2 /(8 + ) (2-16) w N d N Cohen [15] d Meta 50 [14] ( ) ( homogeneity of effect size) Meta Meta [17] Rosenthal Rubin (1982) 2 2 x = ( w( d d) ) (2-17) d d w x 2 k 1 k [22] ( ) Hox Meta ( 2 ) [18] 14

22 d j = δ j + ej (2-18) d j j δ j e j j e j δ 2 j d j 2 r Fisher Z δ j 2 δ j = 1( n j 3) (2-19) n j [23] δ j δ j = β0 + β1z1j + β2z2 j + L + βpzpj + μj (2-20) Z ( ) p 2 μ j 2 [19] μ j δ 2 jp d j = β0 + β1z1j + β2z2 j + L + βpzpj + μj + ej (2-21) 2 d j = β0 + μj + ej (2-22) β 0 δ 2 μ (homogeneous) μ δ 0 δ 0 j 2 μ (heterogeneous) 2 ( ) 2 [19] 2 ID 1 ID CONS( 1) ( Fisher Z) CONS 2 ( Fisher Z) ( ) δ x 2 x 2 2 μ 2 μ 15

23 d j se..( dj ) x 2 2 d j d j = (2-23) se..( dj ) [19] Meta Meta Meta Meta ROC Meta (true positive rate TPR) (false positive rate FPR) logit ROC SROC (Summary Receiver Operating Characteristic SROC) SROC SROC SROC X ( ) X ( ) S (True positive rate TPR ) (False positive rate FPR ) (1 ) (TPR ) ( FPR ) S TPR FPR logit 16

24 U V TPR = ln( ) 1 TPR FPR = ln( ) 1 FPR (2-24) (2-25) U V U V Kardau D=V-U S=V+U (2-24 ) ( TPR) ( FPR) TPR /1 D = ln FPR /1 = ln (2-26) TPR FPR S= ln 1 TPR 1 FPR = ln D S [20] D ( ) ( ) D S (2-27) S=0 S>0 S<0 U V D S D S D=A+B S (2-28) A S=0 B (D) (S) 0 0 A TPR FPR TPR FPR 17

25 SROC (2-28) 1 ( ) A B 2 D a,b,c,d W W= var ( D) = a b c d 1 (2-29) a,b,c,d ( a ),( b ),( c ),( d + 0.5) Moses Shapiro Littenberg 1993 SROC 3 S D (S D) (S D) 1/ S D B ( S,D 1 1) ( S,D 2 2) ( S D ) A B 18

26 A B DS -DS S-S = (2-30) 2 1 D D S-S 2 1 = (2-31) 2 1 SROC 1. TPR FPR (2-28) D S TPR FPR TPR FPR -A/( 1-B) 1 FPR TPR= 1+e FPR (1+ B) /(1 B) 1 (2-32) SROC 2. AUC (area under the curve) [22] a x a x AUC = + 1 b 1 x 1 b 1 x 1 (1 + b)(1 b) (1 + b)(1 b) exp( )( ) 1 exp( )( ) dx 0 (2-33) 2 2 AUC var( ) var( $ AUC AUC AUC AUC = a) + var( b$ ) + 2 cov( a$, b$ ) a b a b (2-34) a b 1 (1 + b) /(1 b) (1 + b) /(1 b) dx 0 (2-35) AUC 1 a x a x = ( )exp( ) ( ) 1+ exp( )( ) a 1 b 1 b 1 x 1 b 1 x SROC b 0 AUC OR AUChom = 2 [( OR 1) ln( OR) ] ( OR 1) (2-36) OR=exp(a) AUChom OR SE( AUC $ hom) = [( OR + 1) ln( OR) 2( OR 1)] SE( a) 3 ( OR 1) SROC b 0 AUC (2-37) 19

27 OR AUChom = ( OR 1) ln( OR) 2 ( OR 1) [ ] (2-36) OR=exp(a) AUChom OR SE( AUC $ hom) = [( OR + 1) ln( OR) 2( OR 1)] SE( a) (2-37) 3 ( OR 1) 3. Q* Q* ROC SROC TPR =1- FPR ROC exp(a/2) Q*= = OR [1+ OR ] (2-38) 1+exp(a/2) 2 SE(Q*)= OR 2( OR +1) SE(a) $ (2-39) 4. Z Q * [20] ( ) z= Q Q SE (Q ) + SE (Q ) (2-40) * * 2 * 2 * Meta SROC 20

28 NT (Nuchal Translucency) XO Benacerraf [23] (NT) 2. (CRL) [24] 62.5% CRL 5 CRL (Crown Rump Length CRL) (Nuchal Translucency NT) NT 2.5mm (NTCut-off 2.5 [25][26] ) 21

29 CRL CRL NT ( [27] ) 3-1 CRL(mm) NT(mm) CRL(mm) NT(mm) CRL(mm) NT(mm) CRL(mm) NT(mm) Awwad [28] Aloka SSD ( ) Nybery [34] 18 4 (22.2%) 22

30 / 0.9 [35] = (BPD) [35] 6. (umbilical artery pulsatility index UAPI) Martinez [36] UAPI UAPI % 95.1% UAPI UAPI 7. Jauniaux [37] ( ) 5 (30.8%) Jauniaux [38] / Grandjean [39] / % 4.6% % 2.3% BPD( )/ (FL) PBD/ % 97.8% 2.2% [35] 3-2 BPD/FL [36] BPD/FL( 1.5SD) BPD/FL( 1.5SD)

31 ( + )/ Johnson [37] ( + )/ 1.75 OR % 93% % % 21 8% 2% 21 20% 3-3 [38] 30 <1/ / / / / / / / / / / / /135 24

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