6. COMPUTATION OF CENTILES AND Z-SCORES FOR VELOCITIES BASED ON WEIGHT, LENGTH AND HEAD CIRCUMFERENCE
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1 6. COMPUTATION OF CENTILES AND Z-SCORES FOR VELOCITIES BASED ON WEIGHT, LENGTH AND HEAD CIRCUMFERENCE The same mehod used o calculae ceniles and -scores for he aained growh sandards based on weigh is used o calculae ceniles and -scores for he velociy sandards based on weigh, lengh and head circumference incremens. Briefly, he compuaion of perceniles and -scores for hese sandards uses formulae based on a resriced applicaion of he LMS mehod as used for he aained growh weigh-based icaors, limiing he Box-Cox normal disribuion o he inerval corresponding o -scores where empirical daa were available (i.e. beween -3 SD and +3 SD. Beyond hese limis, he sandard deviaion a each age was fixed o he disance beween ±2 SD and ±3 SD, respecively. This approach avoids making assumpions abou he disribuion of daa beyond he limis of he observed values (WHO Mulicenre Growh Reference Sudy Group, 2006a. Adjusmen o he basic mehodology had o be applied for weigh velociies condiional on age (see secion 2.5. Children experience weigh losses and, consequenly, weigh incremens occur in negaive values while he BCPE disribuion can handle only posiive values. Thus, before he BCPE could be applied o hese daa, i was necessary o add a consan value δ (dela o all incremens o sh heir disribuion above ero and, subsequenly, o subrac dela from he prediced ceniles. To calculae ividual scores, δ is firs added o he child's incremen and hen he L, M and S values of he model are fied on he shed observaions. When a child's incremen is less han -δ (i.e. he incremen is negaive and is absolue value is greaer han δ, he correcion applied for skewed aained growh sandards beyond -3 SD or +3 SD will be used, since in realiy such an incremen lies below -3 SD. For all icaors, he abulaed fied values of Box-Cox power, median and coefficien of variaion corresponding o he visi age are denoed by, M( and, respecively. Ceniles and -scores for weigh velociies condiional on age Noe ha in his case, he values of, M( and are based on he shed BCPE disribuion. Given he value of δ for he corresponding sandard, he ceniles were calculaed as follows: [ + Z ] L (, 3 3 C ( ( 00 M δ Z The following procedure is recommended o calculae a -score for an ividual child wih weigh incremen y a he visi age :. Calculae ( y + δ M (
2 224 Compuaion of ceniles and -scores 2. Compue he final -score ( of he child for ha icaor as: ( y + δ SD3pos 3 + SD23pos ( y + δ SD3neg 3 + SD23neg 3 > 3 < 3 where SD3 pos is he cu-off +3 SD calculaed a by he LMS mehod: [ (3 M ( + ; SD3 neg is he cu-off -3 SD calculaed a by he LMS mehod: [ + ( 3 SD3neg M ( ; SD23 pos is he dference beween he cu-offs +3 SD and +2 SD calculaed a by he LMS mehod: [ + (3 M ( [ (2 SD 23pos M ( + and SD23 neg is he dference beween he cu-offs -2 SD and -3 SD calculaed a by he LMS mehod: [ + ( 2 M ( [ + ( 3 SD23neg M ( ; To illusrae he procedure, examples wih he 2-monh inerval weigh velociy condiional on age for boys follow. Child : 6-monh-old boy wih an incremen, i.e. weigh gain 2200 g beween 4 and 6 monhs. L589; M ; S2030; δ600; ( >
3 Compuaion of ceniles and -scores 225 [ + ( (3] ( [ + ( (2] ( SD 3 pos SD 2 pos SD 23 pos ( Child 2: 8-monh-old boy wih an incremen of -500 g (weigh loss of 500 g beween 6 and 8 monhs. L; M009680; S365; δ600; ( <-3 [ + 365( 2 ] 43.0 [ + 365( 3 ] SD2neg SD 3neg SD 23 neg ( Child 3: 3-monh-old boy wih a weigh gain of 200 g beween and 3 monhs. L79; M ; S28462; δ600; ( and 3 (LMS -score
4 226 Compuaion of ceniles and -scores Ceniles and -scores for lengh and head circumference velociies condiional on age The ceniles were calculaed as follows: [ + Z ] L (, 3 Z 3 C ( ( 00 M The following procedure is recommended o calculae a -score for an ividual child wih lengh or head circumference incremen y a he visi age :. Calculae 2. Compue he final -score ( y M ( of he child for ha icaor as: y SD3pos 3 + SD23pos y SD3neg 3 + SD23neg 3 > 3 < 3 where SD3 pos is he cu-off +3 SD calculaed a by he LMS mehod: [ (3 M ( + ; SD3 neg is he cu-off -3 SD calculaed a by he LMS mehod: [ + ( 3 SD3neg M ( ; SD23 pos is he dference beween he cu-offs +3 SD and +2 SD calculaed a by he LMS mehod: [ + (3 M ( [ (2 SD 23pos M ( + ;
5 Compuaion of ceniles and -scores 227 and SD23 neg is he dference beween he cu-offs -2 SD and -3 SD calculaed a by he LMS mehod: [ + ( 2 M ( [ + ( 3 SD23neg M ( To illusrae he procedure, examples wih he 3-monh inerval lengh velociy condiional on age for girls follow. Child : 2-monh-old girl wih an incremen, i.e. lengh gain 7.5 cm beween 9 and 2 monhs. L; M3.8692; S23503; [ 7.5 ] >3 [ (3 ] [ (2 ] SD 2 pos SD 23 pos Child 2: 8-monh-old girl wih an incremen of 5 cm beween 5 and 8 monhs. L; M3.205; S28388; [ 5 ] < [ ( 2 ]. 47 [ ( 3 ] 70 SD2neg SD 3neg SD 23 neg Child 3: 6-monh-old girl wih a lengh gain of 8.0 cm beween 3 and 6 monhs. L; M5.9428; S7798; [ 8.0 ] and 3 (LMS -score 7798
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