Turkiye Klinikleri Journal of Medical Sciences

.: ORIGINAL RESEARCH
The Use of Nonparametric Quantile Regression and Least Median of Squares Regression for Construction of Growth Curves of Weight
Ağırlıkça Büyüme Eğrilerinin Oluşturulmasında Nonparametrik Kantil Regresyon ve En Küçük Medyan Kareler Regresyonunun Kullanımı
Handan ANKARALIa, Özge YILMAZa, Münevver KIZILAYb, İlknur ARSLANOĞLUb, Duygu AYDINa
Departments of
aBiostatistics,
bPediatrics, Düzce University Faculty of Medicine, Düzce
Turkiye Klinikleri J Med Sci. 2013;33(3):692-701
doi: 10.5336/medsci.2012-30442
Article Language: EN
Full Text
ABSTRACT
Objective: This study aimed to investigate the use of the Least Median Squares (LMS) regression and nonparametric quantile regression model comparatively to describe children's weight growth. Material and Methods: Two different models were used to obtain the percentile curves to identify the weight growth in girls. The first model was obtained by LMS regression, which is a member of the family of nonlinear parametric quantile regression. In addition, in this model percentile curves used to define growth were generated using the Box-Cox transformation and the cubic spline. The second model was obtained by nonparametric quantile regression that did not require the assumption of a normal distribution for construction of percentile curves. This method is a flexible approach, as well as being computationally simple. The weight values obtained from 1771 healthy girls aged between 6 and 14 years were used in both methods. The data were collected from the cross-sectional study conducted in schools in Düzce city. Results: The distributions of weight measurements according to ages revealed that there were deviations from normality at some ages, there were deviated values in the tail regions of the distribution, and the variances changed according to ages. Using both methods, growth curves were constructed separately for each age group. Predicted values of the LMS and the non-parametric quantile regression models were similar for each age. In addition, the error sum of squares derived from non-parametric quantile regression was lower than that derived from LMS regression for each percentile curve. Moreover, the estimations obtained from both methods were highly correlated with the estimation values of the province İstanbul, which was considered the reference. Conclusion: When the assumptions about the distribution and variances of the data are violated and these assumptions cannot be achieved with the transformation, nonparametric quantile regression method gives more reliable results for the creation of percentile curves.

Keywords: Growth&development; growth charts
ÖZET
Amaç: Bu çalışmada, çocuklardaki ağırlıkça büyümeyi tanımlamada, En Küçük Medyan Kareler (LMS) regresyonu ve nonparametrik kantil regresyon modellerinin karşılaştırmalı olarak incelenmesi amaçlanmıştır. Gereç ve Yöntemler: Çalışmada, kız çocuklarının ağırlıkça büyümesini tanımlamak için persentil eğrilerinin elde edilmesinde iki farklı büyüme modeli kullanılmıştır. Bu yöntemlerden birisi olan LMS regresyonu, doğrusal olmayan parametrik kantil regresyon ailesinden olup, Box-Cox transformasyonu ve kübik eğri yardımıyla persentil eğrilerini oluşturur. İkinci yöntem, LMS yöntemine alternatif olabilecek ve dağılım ön şartı gerektirmeyen nonparametrik kantil regresyondur. Bu yöntem, hesaplama kolaylıklarının yanı sıra esnek bir yaklaşımdır. Her iki yöntemin uygulamasında, yaşları 6 ile 14 arasında değişen toplam 1771 sağlıklı kız çocuğundan elde edilen ağırlık değerleri kullanılmıştır. Bu veriler, Düzce ilindeki okullarda yürütülen kesitsel bir çalışmaya aittir. Bulgular: Yaşlara göre ağırlık ölçümlerinin dağılımı incelendiğinde, bazı yaşlarda normal dağılımdan sapmaların gözlendiği, dağılımın kuyruk bölgelerinde sapan değerlerin olduğu ve varyansların yaşlara göre değiştiği belirlenmiştir. Her iki yöntem yardımıyla, her bir yaş grubu için ayrı ayrı büyüme eğrileri oluşturulmuştur. Bu eğrilerden elde edilen tahmini ağırlık değerleri birbirine benzer çıkmıştır. Bunun yanı sıra oluşturulan her bir persentil eğrisi için parametrik olmayan kantil regresyon tahminlerinin hatası, LMS yöntemine göre daha küçük bulunmuştur. Ayrıca her iki yöntem sonucunda elde edilen tahminlerin, referans olarak kabul edilen İstanbul ili tahmin değerleri ile hayli kuvvetli bir ilişki içinde olduğu belirlenmiştir. Sonuç: Verilerin dağılımı ve varyanslar ile ilgili varsayımların bozulduğu durumlarda ve transformasyonla bu varsayımların sağlanamadığı koşullarda, nonparametrik kantil regresyon metodu, persentil eğrilerinin oluşturulmasında daha güvenilir sonuçlar vermektedir.

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