Pediatric Nephrology
Pediatr Nephrol (1991) 5: 5-11 9 IPNA 1991
Original article Expressing glomerular filtration :rate in children David C. Heilbron 1, Malcolm A. Holliday 2, Amira AI-Dahwi2, and Barry A. Kogan3 Departments of a Epidemiologyand Biostatistics, 2 Pediatrics, and 3 Urology,Universityof California, San Francisco, San Francisco, CA 94143-0704, USA ReceivedNovember8, 1989; receivedin revised form March 27, acceptedJuly 2, 1990
Abstract. We have reviewed the studies that provide the current standards of reference for glomerular filtration rate (GFR) in normal children from 14 days to 12 years of postnatal age. These standards currently are presented as ml/min per 1.73 m 2, i.e., adjusted to average adult body surface area. Children from birth to 1 year of age have adjusted values below the adult range, making comparisons of observed to reference values difficult. Currently, there is no accepted way of obtaining reference values that vary smoothly with age. An analysis of the absolute GFR values in normal children taken from published studies led to an equation that estimates average GFR in relation to weight and term-adjusted age from - 2 months (7 months gestational age) to 12 years in children at least 14 days post delivery. When these data are transformed to percentage of normal (% nl) for age and weight (i. e., percentage of the estimated average), it is possible to describe approximate apparent lower limits of normal GFR as is now done for adults and older children. For children with loss of rel~al mass, GFR expressed as % nl for age and weight provides a convenient standardization which has several useful applications. First, results expressed as % nl for children of different ages, particularly under 1 year of age, can be combined with those of older children for summary purposes. Second, the course of GFR measured serially in children is more appropriately described using this method for expressing GFR. Reporting GFR in absolute values is also useful, particularly in patients whose body mass is significantly distorted or whose absolute GFR is low.
Key words: Glomerular filtration rate - Percentage of normal - Surface area
Introduction The assessment of renal function in patients with renal disease is made from estimates of glomerular filtration rate Offprint requests to: M. A. Holliday,Box 0314, Universityof California,
San Francisco, San Francisco, CA 94143-0314, USA
(GFR); serial estimates of GFR are used to follow the course of renal disease and its response to treatment. This approach has been applied to groups of patients to describe the natural history of renal disease [1, 2] or to compare results of a new versus a standard regimen [3, 4]. For statistical treatment of GFR data from groups, individual GFR values conventionally are adjusted to a standard body size - the average surface area for men and women, 1.73 m2 [5]. This practice also is used in children [6] inasmuch as GFR in normal children over 1 year of age, when adjusted to 1.73 m2 body size is in the same range as GFR for adults,which averages 127 ml/min per 1.73 m2 [5-9] (Table 1). However for children less than 1 year of age the reported average adjusted value is lower. In the 1st week of life it is 39 ml/min per 1.73 m2 and for 4 28 days of age it is 47 ml/min per 1.73 ma [7]. Not until 12 months does the average reach the "normal adult" value. These are the values cited in current texts [8, 9], although most of the data were obtained prior to 1960. For children less than 1 year of age there is no single standard value to reference as normal (Table 1). The study of the course of congenital renal disease in children would be aided by defining a standard value so that data from a group of children studied prior to 1 year of age could be related to a standard and treated by conventional statistical methods. This approach is even more valuable in following the course of renal disease in individual patients who have reduced function, to assess how kidney function is changing as growth proceeds. The imperative to grow and the effects of disease operate to change function in opposite directions. A child at 1 month who has a GFR estimated to be 50% of normal (% nl) may show improvement so that at 6 months it is 75% nl, it may show an increase proportional to growth so that although GFR increases it stays at 50% nl, or it may show a decline, e. g., to 25% nl. Change in absolute GFR also is valuable in certain exceptional circumstances, e.g., in children with changes in body composition or malformations, or with very low GFRs. The purpose of this study was to reevaluate the data on GFR from normal children to determine if a reference
6
Table 1. Normal adjusted glomerular filtration rate (GFR) values at different ages as currently reported [7] Age
Average GFR ml/min per 1.73 m 2
Range ml/min per 1.73 m 2
2 - 8 days ~ 4 - 2 8 days 37-95 days 1 - 6 months 6 - 1 2 months 12-19 months 2 - 1 2 years
39 47 58 77 103 127 127
17- 60 2 6 - 68 3 0 - 86 39-114 49-157 62-191 89-165
We used linear regression techniques to develop a model relating absolute GFR to term-adjusted age and weight. Power and logarithmic transformations of each of these variables were applied as needed to improve linearity and equality of error variance relative to different values of the predictors. A positive constant was added to age in months to avoid transformations of negative values of age for preterm infants; the value, +5, produced less error variance than other integer values. Given a particular choice of transformations of age and weight, an optimal transformation of absolute GFR was determined using the method of Box and Cox [18]. This was repeated with other choices of transformations of age and weight until no further reduction in error variance could be achieved. In converting the regression equation in transformed GFR back to the original scale, a correction term obtained by the retransfromation method of Taylor [19] was applied to reduce bias in the final equation for estimating the average of absolute GFR in normal children. Each GFR value was then expressed as % nl (i. e., 100 x (absolute GFR)/(estimated average nl GFR for age and weight)).
a term infants
value could be developed for use from early infancy through childhood. We excluded data obtained from child r e n in the first 2 w e e k s o f l i f e b e c a u s e G F R in this p e r i o d is c h a n g i n g r a p i d l y as t h e n e w b o r n adjusts to e x t r a u t e r i n e life. T h i s r e p o r t d e s c r i b e s the results o f this e v a l u a t i o n . W e also c o m m e n t o n o t h e r p o s s i b l e b a s e s f o r n o r m a l r e f e r e n c e v a l u e s f o r G F R in infants and s m a l l c h i l d r e n .
Results T h e e q u a t i o n f o r e s t i m a t i n g t h e a v e r a g e o f nl G F R for a g e and w e i g h t d e r i v e d f r o m the 99 i n s t a n c e s w e r e G F R , a g e and w e i g h t w e r e g i v e n is as f o l l o w s :
Patients and methods (a) nl G F R = z3 + 0.1293 9 z, w h e r e (b) z = 0 . 7 4 3 4 + 0 . 6 9 5 6 9 l o g ( a g e + 5) + 1.470 9 l o g (weight)
We reviewed published reports describing GFR in normal children and selected results from seven studies [10-16] that met the following criteria: (1) the children were at least 14 days post birth and not more than 12.0 years of age; (2) they were reported as being free of clinically apparent renal disease and were either convalescing from an illness or were admitted for a minor procedure; (3) GFR was measured by either inulin or mannitol that was infused and accurately timed serum and urine samples were collected; (4) age, surface area and GFR in each study were reported (Table 2). Results were available on 109 children and weights were available for 99. Of the 99, 26 were preterm infants of appropriate weight for gestational age who were studied at least 14 days post birth but prior to reaching 9 months gestational age; 31 were term infants studied at least 14 days post birth who were less than 12.0 months of age, and 42 were between 12.0 months and 12.0 years of age. Of the 99, 84 had gender identified; height and weight were reported in 47 so that surface area could be calculated independently from Eq. i [17] and checked against the original. Surface area = Height (cm) 0.3964M Weight (kg) 0.5378•
(2)
N o t e : a g e in m o n t h s is r e l a t i v e to t e r m , w e i g h t is in k i l o g r a m s , l o g = l o g a r i t h m b a s e 10. F o r m u l a (b) e s t i m a t e s the a v e r a g e o f the c u b e r o o t o f G F R . T h e e q u a t i o n f o r e x p r e s s i n g a g i v e n G F R v a l u e as % nl is as f o l l o w s : % nl G F R (for age and w e i g h t ) = 100 • ( a b s o l u t e G F R ) / ( n l G F R f o r a g e and w e i g h t )
(3)
T h e a b s o l u t e G F R s a n d a g e s for t h e 109 c h i l d r e n are illustrated; c u r v e s c o r r e s p o n d i n g to the e s t i m a t e d a v e r a g e o f nl G F R f o r g i v e n a g e f o r b o y s at the 10th, 5 0 t h and 9 0 t h c e n t i l e s o f w e i g h t for age are in Fig. 1 A ; f o r girls in Fig. 1 B [20]. S l i g h t d i f f e r e n c e s in the c u r v e s are d u e to d i f f e r e n c e s in w e i g h t f o r a g e b e t w e e n b o y s a n d girls. T h e 10th a n d 9 0 t h c e n t i l e s d e s c r i b e the a v e r a g e G F R at 10th a n d 9 0 t h w e i g h t c e n t i l e s , n o t the 10th and 9 0 t h c e n t i l e s for G F R at e a c h age. A p l o t o f G F R a d j u s t e d to 1.73 m 2 v e r s u s a g e f o r all 109 c h i l d r e n is illustrated in Fig. 2. I n t h o s e 47 cases w h e r e
(1)
Where GFR was reported only in absolute values (ml/min) we calculated the adjusted values (ml/min per 1.73 m 2) using the calculated surface area or, if height and weight weren't given, the reported surface area; where only adjusted GFR was reported we calculated the absolute value by transforming the value to the child's own surface area, which was provided.
Table 2. Sources for GFR data on normal children with relevant characteristics Date of publication
n
Age range
Number of subjects/preterm
Pediatr Nephrol (1991) 5: 5-11 9 IPNA 1991
Original article Expressing glomerular filtration :rate in children David C. Heilbron 1, Malcolm A. Holliday 2, Amira AI-Dahwi2, and Barry A. Kogan3 Departments of a Epidemiologyand Biostatistics, 2 Pediatrics, and 3 Urology,Universityof California, San Francisco, San Francisco, CA 94143-0704, USA ReceivedNovember8, 1989; receivedin revised form March 27, acceptedJuly 2, 1990
Abstract. We have reviewed the studies that provide the current standards of reference for glomerular filtration rate (GFR) in normal children from 14 days to 12 years of postnatal age. These standards currently are presented as ml/min per 1.73 m 2, i.e., adjusted to average adult body surface area. Children from birth to 1 year of age have adjusted values below the adult range, making comparisons of observed to reference values difficult. Currently, there is no accepted way of obtaining reference values that vary smoothly with age. An analysis of the absolute GFR values in normal children taken from published studies led to an equation that estimates average GFR in relation to weight and term-adjusted age from - 2 months (7 months gestational age) to 12 years in children at least 14 days post delivery. When these data are transformed to percentage of normal (% nl) for age and weight (i. e., percentage of the estimated average), it is possible to describe approximate apparent lower limits of normal GFR as is now done for adults and older children. For children with loss of rel~al mass, GFR expressed as % nl for age and weight provides a convenient standardization which has several useful applications. First, results expressed as % nl for children of different ages, particularly under 1 year of age, can be combined with those of older children for summary purposes. Second, the course of GFR measured serially in children is more appropriately described using this method for expressing GFR. Reporting GFR in absolute values is also useful, particularly in patients whose body mass is significantly distorted or whose absolute GFR is low.
Key words: Glomerular filtration rate - Percentage of normal - Surface area
Introduction The assessment of renal function in patients with renal disease is made from estimates of glomerular filtration rate Offprint requests to: M. A. Holliday,Box 0314, Universityof California,
San Francisco, San Francisco, CA 94143-0314, USA
(GFR); serial estimates of GFR are used to follow the course of renal disease and its response to treatment. This approach has been applied to groups of patients to describe the natural history of renal disease [1, 2] or to compare results of a new versus a standard regimen [3, 4]. For statistical treatment of GFR data from groups, individual GFR values conventionally are adjusted to a standard body size - the average surface area for men and women, 1.73 m2 [5]. This practice also is used in children [6] inasmuch as GFR in normal children over 1 year of age, when adjusted to 1.73 m2 body size is in the same range as GFR for adults,which averages 127 ml/min per 1.73 m2 [5-9] (Table 1). However for children less than 1 year of age the reported average adjusted value is lower. In the 1st week of life it is 39 ml/min per 1.73 m2 and for 4 28 days of age it is 47 ml/min per 1.73 ma [7]. Not until 12 months does the average reach the "normal adult" value. These are the values cited in current texts [8, 9], although most of the data were obtained prior to 1960. For children less than 1 year of age there is no single standard value to reference as normal (Table 1). The study of the course of congenital renal disease in children would be aided by defining a standard value so that data from a group of children studied prior to 1 year of age could be related to a standard and treated by conventional statistical methods. This approach is even more valuable in following the course of renal disease in individual patients who have reduced function, to assess how kidney function is changing as growth proceeds. The imperative to grow and the effects of disease operate to change function in opposite directions. A child at 1 month who has a GFR estimated to be 50% of normal (% nl) may show improvement so that at 6 months it is 75% nl, it may show an increase proportional to growth so that although GFR increases it stays at 50% nl, or it may show a decline, e. g., to 25% nl. Change in absolute GFR also is valuable in certain exceptional circumstances, e.g., in children with changes in body composition or malformations, or with very low GFRs. The purpose of this study was to reevaluate the data on GFR from normal children to determine if a reference
6
Table 1. Normal adjusted glomerular filtration rate (GFR) values at different ages as currently reported [7] Age
Average GFR ml/min per 1.73 m 2
Range ml/min per 1.73 m 2
2 - 8 days ~ 4 - 2 8 days 37-95 days 1 - 6 months 6 - 1 2 months 12-19 months 2 - 1 2 years
39 47 58 77 103 127 127
17- 60 2 6 - 68 3 0 - 86 39-114 49-157 62-191 89-165
We used linear regression techniques to develop a model relating absolute GFR to term-adjusted age and weight. Power and logarithmic transformations of each of these variables were applied as needed to improve linearity and equality of error variance relative to different values of the predictors. A positive constant was added to age in months to avoid transformations of negative values of age for preterm infants; the value, +5, produced less error variance than other integer values. Given a particular choice of transformations of age and weight, an optimal transformation of absolute GFR was determined using the method of Box and Cox [18]. This was repeated with other choices of transformations of age and weight until no further reduction in error variance could be achieved. In converting the regression equation in transformed GFR back to the original scale, a correction term obtained by the retransfromation method of Taylor [19] was applied to reduce bias in the final equation for estimating the average of absolute GFR in normal children. Each GFR value was then expressed as % nl (i. e., 100 x (absolute GFR)/(estimated average nl GFR for age and weight)).
a term infants
value could be developed for use from early infancy through childhood. We excluded data obtained from child r e n in the first 2 w e e k s o f l i f e b e c a u s e G F R in this p e r i o d is c h a n g i n g r a p i d l y as t h e n e w b o r n adjusts to e x t r a u t e r i n e life. T h i s r e p o r t d e s c r i b e s the results o f this e v a l u a t i o n . W e also c o m m e n t o n o t h e r p o s s i b l e b a s e s f o r n o r m a l r e f e r e n c e v a l u e s f o r G F R in infants and s m a l l c h i l d r e n .
Results T h e e q u a t i o n f o r e s t i m a t i n g t h e a v e r a g e o f nl G F R for a g e and w e i g h t d e r i v e d f r o m the 99 i n s t a n c e s w e r e G F R , a g e and w e i g h t w e r e g i v e n is as f o l l o w s :
Patients and methods (a) nl G F R = z3 + 0.1293 9 z, w h e r e (b) z = 0 . 7 4 3 4 + 0 . 6 9 5 6 9 l o g ( a g e + 5) + 1.470 9 l o g (weight)
We reviewed published reports describing GFR in normal children and selected results from seven studies [10-16] that met the following criteria: (1) the children were at least 14 days post birth and not more than 12.0 years of age; (2) they were reported as being free of clinically apparent renal disease and were either convalescing from an illness or were admitted for a minor procedure; (3) GFR was measured by either inulin or mannitol that was infused and accurately timed serum and urine samples were collected; (4) age, surface area and GFR in each study were reported (Table 2). Results were available on 109 children and weights were available for 99. Of the 99, 26 were preterm infants of appropriate weight for gestational age who were studied at least 14 days post birth but prior to reaching 9 months gestational age; 31 were term infants studied at least 14 days post birth who were less than 12.0 months of age, and 42 were between 12.0 months and 12.0 years of age. Of the 99, 84 had gender identified; height and weight were reported in 47 so that surface area could be calculated independently from Eq. i [17] and checked against the original. Surface area = Height (cm) 0.3964M Weight (kg) 0.5378•
(2)
N o t e : a g e in m o n t h s is r e l a t i v e to t e r m , w e i g h t is in k i l o g r a m s , l o g = l o g a r i t h m b a s e 10. F o r m u l a (b) e s t i m a t e s the a v e r a g e o f the c u b e r o o t o f G F R . T h e e q u a t i o n f o r e x p r e s s i n g a g i v e n G F R v a l u e as % nl is as f o l l o w s : % nl G F R (for age and w e i g h t ) = 100 • ( a b s o l u t e G F R ) / ( n l G F R f o r a g e and w e i g h t )
(3)
T h e a b s o l u t e G F R s a n d a g e s for t h e 109 c h i l d r e n are illustrated; c u r v e s c o r r e s p o n d i n g to the e s t i m a t e d a v e r a g e o f nl G F R f o r g i v e n a g e f o r b o y s at the 10th, 5 0 t h and 9 0 t h c e n t i l e s o f w e i g h t for age are in Fig. 1 A ; f o r girls in Fig. 1 B [20]. S l i g h t d i f f e r e n c e s in the c u r v e s are d u e to d i f f e r e n c e s in w e i g h t f o r a g e b e t w e e n b o y s a n d girls. T h e 10th a n d 9 0 t h c e n t i l e s d e s c r i b e the a v e r a g e G F R at 10th a n d 9 0 t h w e i g h t c e n t i l e s , n o t the 10th and 9 0 t h c e n t i l e s for G F R at e a c h age. A p l o t o f G F R a d j u s t e d to 1.73 m 2 v e r s u s a g e f o r all 109 c h i l d r e n is illustrated in Fig. 2. I n t h o s e 47 cases w h e r e
(1)
Where GFR was reported only in absolute values (ml/min) we calculated the adjusted values (ml/min per 1.73 m 2) using the calculated surface area or, if height and weight weren't given, the reported surface area; where only adjusted GFR was reported we calculated the absolute value by transforming the value to the child's own surface area, which was provided.
Table 2. Sources for GFR data on normal children with relevant characteristics Date of publication
n
Age range
Number of subjects/preterm
