Comparison Of Constructing Growth Curve Methods And Its Medicalapplication

ObjectiveTo introduce four kinds of constructing growth curve methods,including the cubic spline function method,locally weighted scatterplot smoothing?LOWESS?,Lambda-Median-Sigma?LMS?method and Generalized Additive Model for Location Scale and Shape?GAMLSS?.To evaluate the advantages and disadvantages of these methods and to discuss the influence of different statistical methods on the construction of the growth curves under different sample sizes,which can provide theoretical basis for the choice of methods when constructing a reference curve.Methods1.The introduction of four kinds of constructing growth curve methods were applied in our study,including the cubic spline function method,locally weighted scatterplot smoothing,LMS method and GAMLSS method.2.Simulation study based on R software was adopted.The curves were smoothed by cubic spline function method,Locally weighted scatterplot smoothing,LMS method and GAMLSS method,respectively.The fitting results were compared and evaluated.3.A total of 1334 healthy children and adolescents aged 6 to 18 years in Chongqing were sampled with stratified cluster random sampling.The bone mineral content and bone mineral density were measured and recorded,and their gender,age were also collected.The growth curves were estimated using the GAMLSS method to verify the results of simulation study.Results1.In the simulation study,the mean square error and maximum norm error of the fitting results of the GAMLSS method and the LMS method were very close when the subgroup sample size was simultaneously,and they were smaller than those of the LOWESS method and the cubic spline method in turn.It showed that the fitting effects of GAMLSS and LMS were similar,and they were better than those of LOWESS and cubic spline.Longitudinal comparisons showed that the mean square error and maximum norm error of the fitting results of cubic splines,LOWESS,LMS method,and GAMLSS method gradually decreased,as the sample size of the subgroup increased.2.In the applied research,sex-and age-specific BMC and BMD percentile reference curves(3^rd,10^th,25^th,50^th,75^th,90^th,and 97^th)among children and adolescents aged 6-18 years in Chongqing were estimated using the GAMLSS method.Through model selection,it was found that most of the model agreed very well for the BCCG distribution but the fitted model of THBMC of boys and girls agreed very well for the BCPE distribution.The percentile values fitted by the GAMLSS method were very consistent with the actual percentiles.The residual distribution plot and Q-Q plot showed that the model fitted very well.By observing the fitted curves,we can find that:?Overall,LSBMC,THBMC,LSBMD,and THBMD increased steadily with age among children and adolescents aged6¹8 years.However,the way of growth was different.?The acceleration time of LSBMC and LSBMD appeared earlier.It accelerated from age of 8,continued to age of 15.After 15 years of age,the acceleration trend ended.Whereas,accelerated trend in boys was later two years than that in girls,which started from the age of 10 and keeps growing until age of 17.The acceleration time of THBMC and THBMD in boys and girls was earlier than that of LSBMC and LSBMD.Girls started at 6 years old,and boys started at 7 years old.ConclusionThe GAMLSS method allows the modeling of the fourth-order moments such as median,standard deviation,skewness,and kurtosis.The percentile curve constructed by GAMLSS method is smooth,the fitting errors are much smaller,and is better than those of LMS method,locally weighted scatterplot smoothing method,and cubic spline method.In this study,we established age-specific percentile values and percentile curves of LSBMC,LSBMD,THBMC,and THBMD for children and adolescents in Chongqing based on the GAMLSS method.These age-related values are valuable in determining the growth and developmental status,and the values should help in diagnosing of bone mineral content and bone mineral density disorders.