Stability of visual outcome from 7 years in children treated surgically for bilateral dense congenital cataracts before 37 weeks of age
2009; Wiley; Volume: 89; Issue: 1 Linguagem: Inglês
10.1111/j.1755-3768.2009.01618.x
ISSN1755-3768
AutoresJohan Sjöstrand, Gunilla Magnusson, Alf Nyström, Robert Jönsson,
Tópico(s)Ophthalmology and Visual Impairment Studies
ResumoActa OphthalmologicaVolume 89, Issue 1 p. 30-36 Free Access Stability of visual outcome from 7 years in children treated surgically for bilateral dense congenital cataracts before 37 weeks of age Johan Sjöstrand, Johan Sjöstrand Department of Ophthalmology, University of Gothenburg, SwedenSearch for more papers by this authorGunilla Magnusson, Gunilla Magnusson Department of Ophthalmology, University of Gothenburg, SwedenSearch for more papers by this authorAlf Nyström, Alf Nyström Department of Ophthalmology, University of Gothenburg, SwedenSearch for more papers by this authorRobert Jonsson, Robert Jonsson Department of Statistics, University of Gothenburg, SwedenSearch for more papers by this author Johan Sjöstrand, Johan Sjöstrand Department of Ophthalmology, University of Gothenburg, SwedenSearch for more papers by this authorGunilla Magnusson, Gunilla Magnusson Department of Ophthalmology, University of Gothenburg, SwedenSearch for more papers by this authorAlf Nyström, Alf Nyström Department of Ophthalmology, University of Gothenburg, SwedenSearch for more papers by this authorRobert Jonsson, Robert Jonsson Department of Statistics, University of Gothenburg, SwedenSearch for more papers by this author First published: 27 January 2011 https://doi.org/10.1111/j.1755-3768.2009.01618.xCitations: 8 Johan Sjöstrand Department of OphthalmologyInstitute of Neuroscience and PhysiologyUniversity of GothenburgSahlgrenska University Hospital/MölndalSE-431 80 MölndalSwedenTel: + 46 31 3433254Fax: + 41 31 412904Email: [email protected] AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Abstract Acta Ophthalmol. 2011: 89: 30–36 Abstract. Purpose: To study the long-term visual outcome and the age at which final visual acuity can be predicted in a population sample of children treated surgically for bilateral dense congenital cataract before 37 weeks of age. In addition, we assessed the influence of associated risk factors and compared the visual development of these aphakic children with presumably blocked visual input before early surgery to that of normal children in Sweden. Methods: The 18 patients included were followed for at least 10 years postoperatively. The median age at last visit was 15.5 years (range 10–18). The best-corrected visual acuity (BCVA) was tested monocularly with a logarithmically scaled letter acuity test from 4 years of age to late teens. Other registered postoperative data were presence of manifest nystagmus, strabismus and complications. Results: The BCVA of the better-seeing eye reached a plateau at 7 years of age. Age at surgery of 80 days or less characterized the majority of cases with a logMAR ≤ 0.3 with a threshold effect between 80 and 130 days of age. Compared to normal children in Sweden, the long-term visual outcome showed a deficit of 0.5–0.6 logMAR. Conclusion: In spite of optimized care and surgery before 9 months, the BCVA was subnormal in our population compared to healthy children. The long-term visual outcome can be predicted at 7 years of age. Screening with early detection followed by surgery before the end of the third month is important to decrease the risk of marked acuity loss. Introduction The presence of media opacities in both eyes at birth may result in varying severity of form deprivation amblyopia and have a major impact on health-related quality of life (Chak & Rahi 2007). The outcome that is potentially the most dangerous for the individual is dense central bilateral congenital cataracts, blocking visual input of patterns to both eyes. Previous studies have shown that the development of both central and peripheral vision is delayed compared to normal children, and in spite of early surgery visual deficits are present during follow-up in childhood (Ellemberg et al. 1999; Maurer & Lewis 2001; Martin et al. 2008). However, information about the long-term outcome of visual acuity (VA) following early surgery of dense bilateral cataracts is sparse (Francois 1979; Lundvall & Kugelberg 2002; Ye et al. 2007). This lack of information has several explanations. The diagnosis of bilateral dense central congenital cataract has a low incidence. In our study of children born in western Sweden between 1980 and 1997, the incidence of bilateral dense congenital cataract was approximately 14 cases in 100 000 live births or approximately 40% of all with a diagnosis of congenital cataract in our region (Abrahamsson et al. 1999a). Secondly, many studies of VA outcome are difficult to interpret because dense or complete cataracts are not separated from partial or incomplete cataracts that may allow some visual experience before surgery. Finally, visual outcome is presented in several studies as VA at preschool ages, when the participants may be far from maturation of vision (Abrahamsson et al. 1999b). To our knowledge, no other long-term follow-ups of postoperative VA results presented earlier in the literature have evaluated individuals' continuous VA development related to the ages at which the measurements were taken during adolescence. The general purpose of the present study was to describe VA level and investigate VA development from the age of 4 years up to late teens, compared to Swedish normal populations from the literature (Larsson et al. 2005, 2006; Ohlsson & Villareal 2005). The primary aim of the present study was to characterize, in a population sample, the development of VA of the better eye up to late teens with respect to age at operation/optical correction in patients with presumably blocked visual input before early surgery. Secondly, we were interested in determining the age at which final VA can be predicted. In addition, we assessed the influence of associated risk factors and compared the visual development of aphakic children to that of normal children in Sweden. Materials and Methods Study population Twenty-one consecutive children born in Sweden who underwent cataract extraction without intraocular lens (IOL) implantation within the first 36 weeks of life were deducted from the longitudinal, prospective, population-based study of all children with congenital cataract born in south-western counties of Sweden between 1980 and 1996 (population approximately 2 million) (Abrahamsson et al. 1999a). Children were eligible if they fulfilled the following criteria: they had dense central cataracts in both eyes, the cataracts were presumed to be of congenital origin, the participants had been followed up to at least 10 years of age and regular measurements of letter VA had been performed. Cataracts defined as dense had no red reflex with the pupil undilated and the fundus view was blocked in both eyes. Eighteen cases fulfilled these criteria and had no changes of the retina or systemic abnormalities, and were therefore included in the present study. Two excluded cases had learning disabilities and thus were not able to participate in testing of letter acuity according to our protocol. One child was lost to follow-up. The characteristics of the included children are given in Table 1. Table 1. Characteristics of the children included in the study with bilateral dense congenital cataracts (n = 18). Median (range) Age (days) at operation 52 (2–253) Interval (days) between surgery on 1st and 2nd eye 2 (0–28) Age (years) at last follow-up 15.5 (10–18) LogMAR at last follow-up Better eye 0.35 (0.1–1.0) Worse eye 0.76 (0.19–1.7) Number of cases (%) Sex Male 9 Female 9 Optical correction Contact lenses 17 Spectacles 1 BCVA measurements Letter matching (before 10 years) 15 (83) Linear letter acuity (from 10 years) 18 (100) Manifest nystagmus postoperatively 13 (72) Strabismus postoperatively 15 (83) Complications postoperatively (better / worse eye) Glaucoma 2 (11) / 4 (22) VAO 3 (17) / 7 (39) Keratitis 1 (6) / 2 (11) Reoperation (not VAO) 1 (6) / 2 (11) BCVA, best-corrected visual acuity; VAO, visual axis opacity. The surgical procedure for cataract extraction was a limbal approach with capsulotomy and aspiration of lens material. Two patients had a secondary IOL implant at the time of the last visit (17 and 18 years of age, respectively). Postoperative data Fifteen of the included patients were followed continuously at Sahlgrenska University Hospital (SUH). These patients were all measured following a specific protocol with VA measurements using a HOTV letter matching chart with rows of four letters and logarithmic progression of letter size (Hedin et al. 1980) from 3 to 4 years of age up to 10 years of age. From 10 years of age up to the last visit (between 16 and 18 years of age) they had their VA measured using a linear letter chart with logarithmic steps (Hedin & Olsson 1984). For both charts inter-letter distance was equal to letter width and the threshold for best-corrected visual acuity (BCVA) was 75% of correctly read optotypes, expressed as logarithm of the minimal angle of resolution (logMAR); the testing distance was 3 and 5 m, respectively. Measurements were made using these charts at an age of 4, 7, 10, 12, 14 and 16– 18 years. Three patients were not followed at SUH. In these cases VA was measured regularly using letter optotypes but HOTV measures were not obtained. Some measurements were missing at specific intervals: four patients at 4 and at 7 years, five patients at 12 years, six patients at 14 years and three patients at 16 years. Other registered postoperative data were presence of manifest nystagmus, strabismus and complications such as visual axis opacities (VAOs), glaucoma, keratitis and reoperations excluding those required for VAO (Table 1). Clinically significant VAO was treated with yttrium aluminum garnet (YAG) laser and in some cases with vitrectomy. Diagnosis of glaucoma was made if the optic disc was glaucomatous, intraocular pressure (IOP) was 25 mmHg or higher and treatment had started. Following surgery the refractive error was corrected using contact lenses in all patients except one, who intermittently used glasses. The contact lenses were applied at the operation or on the following day in the majority of patients. The compliance to refractive corrections was good in all patients. The median interval between the operation of the first and the second eye was 2 days. In two patients operated on elsewhere in the early 1980s the interval between operations was 4 weeks or more. Patching for amblyopia by adhesive eye patches or refractive penalization was started when indicated. This study was approved by the local ethics committee and was performed according to the Declaration of Helsinki. Data analysis and statistics Data from the better and worse eyes were analysed separately. To minimize confounding variables, our focus was on the better eye (the eye with the best average VA between 10 years of age and last visit). If the BCVA of the two eyes was similar, the right eye was chosen and defined as the better eye. Two of the better eyes had well-controlled aphakic glaucoma. The relationship between BCVA (expressed in logMAR) and age at surgery or age at VA measurements was assessed. Tests of the hypothesis that two sets of paired observations have the same distribution were carried out by Student's one-sample t-test (Wackerly et al. 2008, pp 520–522) and Wilcoxon Signed Rank test for pairs (Wackerly et al. 2008, pp 750–753). All tests were two-sided and statistical significance was claimed if p-values were below 0.05. The coefficient of determination (R2) was used to measure the goodness-of-fit of a linear model to data (Wackerly et al. 2008, p. 601 and p. 627). Prediction intervals (PIs) were based on standard expressions (Wackerly et al. 2008, p. 564 and pp 591–593). Results BCVA at different ages The BCVA of the better eye tested with the matching or linear letter chart from 4 years of age to last visit has reached a plateau and stabilized at the age of 7 years with no statistically significant changes during the time interval thereafter. Postoperative nystagmus seemed to affect the level (Fig.1). A marked increase in acuity occurred between 4 and 7 years (for several patients) that was statistically significant (p = 0.001, t-test and p = 0.002, rank test). The median logMAR at the last visit was 0.35 in the better eye and 0.76 in the worse eye (Table 1). Figure 1Open in figure viewerPowerPoint Mean logMAR plotted against years of age for children with nystagmus (upper curve) and without nystagmus (lower curve). Factors influencing visual outcome Plots of logMAR at 4, 7, 10, 12, 14 and 16 years versus age at surgery (days) did not show any clear structure, with one exception. A plot of logMAR at 16 years versus age at surgery revealed a threshold effect somewhere between 80 and 130 days (Fig. 2). Age at surgery < 90 days characterized the majority (eight out of nine) of patients with an acuity of 0.3 logMAR or less (≥ 0.5, decimal). Only one patients had a visual outcome of ≤ 0.3 logMAR following surgery later than 3 months of age (Fig 2). The mean logMAR at 10 years of age was 0.38 logMAR in patients who underwent surgery at an age of 90 days or less and 0.57 in those who had later surgery. Figure 2Open in figure viewerPowerPoint Dots represent logMAR at 16 years plotted against age at surgery (days). The solid line joins three-point moving averages of the logMAR values. Thirteen out of 18 patients had manifest nystagmus (Table 1) and in the group who had surgery later than 8 weeks all had nystagmus. At all ages the mean logMAR in the group with nystagmus was approximately 0.2 logMAR higher than in the group without nystagmus (Fig. 1). Two patients had a well-controlled glaucoma in their better eye and the patient operated for cataract extraction at 5 days of age (no. 4) had a satisfactory outcome (logMAR 0.3) whereas the patient with later cataract extraction (no. 18) had lower BCVA (logMAR 0.7). Keratitis and treated VAO (Table 1) were judged to have no major impact on the final visual outcome of the better eyes. The median BCVA of the worse eye at the last visit was 0.76 logMAR. In seven patients the difference between the better and worse eye was < 0.1 logMAR. In all these patients the interval between operations was 2 days or less. In 11 of 18 patients the logMAR difference was ≥ 0.2 and the major cause of this BCVA difference was esotropia (three patients), pupillary membranes needing vitrectomy (three patients), remnants of VAOs following YAG laser capsulotomy (two patients), central keratitis (two patients) and glaucoma (one patient). In general, a diagnosis of glaucoma was recorded in six out of 36 eyes and no patient had bilateral glaucoma. Prediction of logMAR at 16 years There were strong within-patient correlations between logMAR at 16 years and logMAR at earlier ages. Therefore, the latter may be used as predictors. In order to be able to make predictions at early ages only logMAR at 4 years [logMAR(4]] and logMAR at 7 years [logMAR(7)] were considered. Also, the variable 'Age at surgery in days' (Days) was found to be associated with logMAR(16) (Fig. 2). Because there was sign of a threshold effect somewhere between 80 and 130 days, it was furthermore decided to consider a dichotomized predictor taking the values 1 if Days > d, say, and 0 if Days ≤ d. This predictor only uses the fact that Days is above or below a certain cut-off value. By performing predictions for all values of d from 80 to 130 it was found that d = 90 performed best, as judged by the value of R2 and the length of the PI. This predictor was denoted D90. The presence of nystagmus might also have been used as a predictor, because logMAR(16) was larger in this group (Fig. 1). However, the presence of nystagmus is closely tied up with Days (none without nystagmus was older than 55 days at surgery), so the presence of nystagmus did not contribute with further predictive ability beyond Days. A 90% PI, showing the limits inside which 90% of future predictions of logMAR(16) will fall, was calculated for each set of predictors. The quality of the predictors was judged by (the coefficient of determination) R2 and by the length of PI (cf. Statistical methods). The results are summarized in Table 2. The lengths of PI varied between the children except D90. Here, it was striking that the simple predictor D90 worked better than Days and that logMAR(7) worked better than logMAR(4). The best result at or before the age of 10 years was obtained by combining logMAR(7) or logMAR(10) and D90 with a predicted logMAR(16) of about ± 0.23 (PI 0.43–0.51) and ± 0.18 (PI 0.33–0.38), respectively. In the Appendix, expressions are given for predicting logMAR(16) based on Days, D90, logMAR(4), logMAR(7) and the combination (D90, logMAR[7]). Table 2. Quality of some predictors of logMAR at 16 years [logMAR(16)]. Predictor(s) R 2(%) Length of PI Days 50 0.61–0.71 logMAR(4) 52 0.59–0.63 D90 58 0.58 logMAR(7) 66 0.50–0.56 Days, logMAR(4) 66 0.54–0.60 D90, logMAR(4) 67 0.50–0.58 Days, logMAR(7) 75 0.46–0.51 D90, logMAR(7) 79 0.43–0.51 logMAR (10) 73 0.45–0.48 D90, logMAR (10) 87 0.33–0.38 D90, dichotomized variable that takes the value 1 if days > 90 and 0 otherwise; R2, coefficient of determination; PI, 90% prediction interval. Evaluation of BCVA loss compared to controls The mean logMAR at 10 and 16 years was 0.42 [95% confidence interval (CI) 0.31–0.60] and 0.42 (95% CI 0.29–0.55), respectively. The BCVA of the better eye at 10 years or 16 years in comparison to that of controls in Sweden at an age of 10 or 17–18 years (Larsson et al. 2005, 2006; Ohlsson & Villareal 2005) showed a mean logMAR deficit of 0.6 and 0.5, respectively. The relative logMAR loss in the subgroups with and without manifest nystagmus was 0.3 or 0.6, respectively, at both ages. Discussion Development of BCVA Our finding is that VA in general has stabilized at 7 years of age. The BCVA at 16 years was predicted within a 90% PI by testing at 7 years. The main developmental changes of BCVA occurred during the age period 4–7 years as tested with a letter matching chart, in agreement with our previous studies (Abrahamsson et al. 1999b; Magnusson et al. 2002). Long-term visual outcome, better-seeing eye At the last visit 50% of the better eyes had a satisfactory outcome (logMAR ≤ 0.3) in our prospective study of a geographically defined population sample. This outcome is similar to that reported in hospital-based studies of patients operated for dense bilateral congenital cataracts by Birch et al. (1998), Lundvall & Kugelberg (2002) and Lambert et al. (2006) tested at age 6–8, 4–9 and 5 years, respectively. Other hospital-based studies of visual outcome following surgery for dense bilateral congenital cataracts have reported less favourable results. In a study from southern China, Ye et al. (2007) have reported a long-term mean BCVA of the better eye of logMAR 0.6. Parks et al. (1993) reported a median VA of logMAR 1.0 in patients with bilateral nuclear cataract following early surgery. In the latter study a more favourable outcome was found in partial types of cataract, as has also been reported by others (Mioche & Perenin 1986; Magnusson et al. 2002). In a study before the era of modern surgery, Francois (1979) states a long-term visual outcome of more than logMAR 1.0 (< 0.1, decimal) in 50% of children operated for total bilateral cataracts. Factors influencing long-term outcome The BCVA of the better eyes in the subgroup who underwent surgery during the first 2 months was significantly better compared to those patients operated later. Our finding of a threshold effect during the third and fourth months of age underlines the importance of early surgery. Good postoperative BCVA following bilateral surgery during the first 2 months has also been reported by Gelbart et al. (1982), Lambert et al. (2006) and Lundvall & Kugelberg (2002). However, Bradford et al. (1994) found no clear-cut difference between early (before 8 weeks) and late surgery and reported three cases with satisfactory outcome [defined as logMAR ≤ 0.3 (decimal ≥ 0.5)] undergoing late surgery at 4–5 months. Such a favourable visual outcome was found in only one case in our study, who underwent surgery at approximately 4 months. Our finding of a threshold effect between 80 and 130 days of age favours a bilinear model of visual development, as has also been proposed for patients with unilateral cataract (Birch & Stager 1996) with a threshold at 6 weeks. The indications of the presence of a longer latent period in bilateral compared to unilateral cataracts fits with the general finding of weaker functional effects of bilateral compared to unilateral form deprivation in monkey studies (Harwerth et al. 1991). The association of early surgery and better visual outcome makes it urgent to detect babies with cataract early. In Sweden a national study has shown that screening in maternity wards is most effective in recruiting cases for early surgery (Magnusson et al. 2003). In a report from the British Congenital Cataract Interest Group (Chak et al. 2006) of all operated eyes (mean age at surgery 4.57 months) with newly diagnosed bilateral dense or partial congenital/infantile cataract, a satisfactory outcome (defined as described earlier) was recorded in approximately half of the eyes compared to one third of all eyes (better or worse) at 10 years in our study of dense bilateral congenital cataracts. The association of final VA and manifest nystagmus is important to elucidate. In our study the presence of manifest nystagmus was closely associated with later age at surgery and did not contribute to predictive ability beyond age at surgery. However, Lambert et al. (2006) describe the absence of preoperative nystagmus as a better predictor of a good visual outcome than age at surgery. Furthermore, some patients operated early have postoperative nystagmus. In agreement, Abadi et al. (2006) concluded that following optimal postoperative management of cataracts with major form deprivation a manifest nystagmus was frequent even when the surgery was performed early. Similarly, Robb & Petersen (1992), Bradford et al. (1994) and Lundvall & Kugelberg (2002) found that early surgery did not seem to prevent the development of nystagmus. In children without postoperative nystagmus we observed that the visual outcome in general was far better than in children with postoperative nystagmus; in another Swedish study (Lundvall & Kugelberg 2002), the finding was similar. At the same time it is obvious from our study that in the individual case the presence of postoperative nystagmus does not preclude a satisfactory visual outcome in a small proportion of patients (Bradford et al. 1994). The less satisfactory visual outcome of the majority of worse eyes was associated with strabismus and various complications. The prevalence and visual impact of aphakic glaucoma in our group with bilateral dense cataracts were similar to those reported previously for all types of congenital cataract in our population sample (Magnusson et al. 2000). Limitations Because our population sample included children born during a period of 16 years the visual outcome may have been influenced by changes in surgical technique and age at detection. However, the postoperative treatment and measurement followed the same protocol during the entire study period. A sample size of 18 patients may seem small in order to study factors influencing visual outcome. However, the sample was large enough to get statistically significant results at 16 years and to produce relatively compact PIs. Nevertheless, small numbers limit our ability to study various surgical factors, postoperative complications and compliance to amblyopia treatment that may impact on the vision of the worse eye. Therefore, our rationale has been to focus on the better-seeing eye, which is not under the possible influence of superimposed unilateral amblyopia. The change at 10 years of age to a linear letter chart with more optotypes may have concealed a small improvement of VA between 7 and 10 years. However, this possibility does not limit the use of HOTV letter-matching chart acuities for the prediction of long-term visual outcome. The major strength of the current prospective population-based study is the long-term follow-up of children with dense bilateral congenital cataract with stringent criteria for acuity measurement from 4 years up to late teens. Conclusion Half of the children in our study reached a satisfactory visual outcome of the better eye following surgery. Compared to age-matched control children, the VA if subnormal with a deficit corresponding to 0.5–0.6 logMAR. The major predictive factor for long-term visual outcome is age at surgery. Therefore, screening with early detection followed by surgery before the end of the third month is important to decrease the risk of marked acuity loss. Acknowledgements This study was supported by grants from the Gothenburg Medical Society and the Royal Society of Arts and Sciences in Gothenburg. Appendix 90% PIs at the individual level a) Prediction of Y =logMAR(16) based on a single predictor (X) The general expression for a 90% PI of Y based on a new value X is [cf. p. 564 in Wackerly et al. (2008).]: The quantities in this expression are obtained by first performing a linear regression analysis with Y as dependent variable and X as independent variable in the old data set. The latter consists of n observations on (X, Y), missing values being excluded. a and b are the intercept and slope, respectively. S is the square root of the mean squared error, is the mean of the x-values and . t.95(n – 2) is the upper 95% percentile in Student's t-distribution with n – 2 degrees of freedom, the latter being 1.771 for Days and D90 and 1.812 for logMAR(4) and logMAR(7). The following expressions are obtained: X = days X = logMAR(4) X = D90 X = logMAR(7) Consider, for example, child no. 8 with logMAR(7) = 0.6021. From above one gets the 90% PI for logMAR(16) as 0.45 ± 0.25. The observed value was 0.52, which is well inside the interval. In fact, 100% of all predictions of logMAR(16) fell within the PIs, which illustrates the fact that a PI is intended for new individuals that have not already been included in the study. In that case 90% of the observations will be found inside the PI in the long run. b) Prediction of logMAR(16) based on a pair of predictors (X1 and X2). The expression for a 90% PI for Y = logMAR(16) based on two new values of X1 and X2 is more complicated. [For an expression involving vectors and matrices refer to pp 591–593 in Wackerly et al. (2008).] Because the computations are heavy, a computer program (in sas®) is presented that easily computes 90% PIs for child no. 8 based on X1 = D90 = 1 and X2 = logMAR(7) = 0.8021. A preceding regression analysis with Y as dependent variable and X1 and X2 as independent variables has given the intercept a = 0.111583, regression coefficients b1 = 0.170196 and b2 = 0.442229, and mean squared error S2 = 0.012068. The following program solves the task: (Data are stored on the file 'children', containing nine columns.) data a; /* read data from the file 'children'*/ infile 'children'; input obs nyst days va4 va7 va10 va12 va14 va16; /* transformations */ lm4 = log10(1/va4); lm7 = log10(1/va7); lm10 = log10(1/va10); lm12 = log10(1/va12); lm14 = log10(1/va12); lm16 = log10(1/va16); if days= 90 then d90 = 1; /* exclude missing values */ data b; set a; if lm7 > '.' and lm16 > '.'; /* calculate matrix elements */ x=d90; z=lm7; x2 = x*x; xz=x*z; z2 = z*z; proc means noprint n sum; var x z x2 xz z2; output out=sas1 n=n n2 n3 n4 n5 sum=sx sz sx2 sxz sz2; data c; set sas1; m1 = sx/n; m2 = sz/n; s11 = sx2-sx*sx/n; s12 = sxz-sx*sz/n; s22 = sz2-sz*sz/n; d=s11*s22-s12*s12; a11 = 1/n+(m1*m1*s22-2*m1*m2*s12+m2*m2*s11)/d;a12 = -(m1*s22-m2*s12)/d;a13 = -(m2*s11-m1*s12)/d;a22 = s22/d;a23 = -s12/d;a33 = s11/d; data d; set c; /* calculate 90% pi for children no 8 with d90 = 1 and logmar(7)=0.6021 */ x1 = 1; x2 = 0.6021; k90 = 1.833; a = 0.111583; b1 = 0.170196; b2 = 0.442229; s=sqrt(0.012068); h=a11+2*(a12*x1+a13*x2+a23*x1*x2)+a22*x1*x1+a33*x2*x2; int=k90*s*sqrt(1+h); mean=a+b1*x1+b2*x2; upper=mean+int; lower=mean-int; proc print; var lower upper title '90% pi for logmar(16), ind=8'; run; Here all lines containing '/*…*/' are only comments and can be excluded. 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