@article{10.1093/ejo/cjaf088,
    author = {Sandhu, Satpal S and Leckie, George and Tilling, Kate and Hughes, Rachael A},
    title = {Studying the dynamics of mandibular growth spurts in individuals with Class I and Class II skeletal growth patterns using the Bayesian superimposition by translation and rotation (SITAR) model},
    journal = {European Journal of Orthodontics},
    volume = {47},
    number = {6},
    pages = {cjaf088},
    year = {2025},
    month = {11},
    issn = {1460-2210},
    doi = {10.1093/ejo/cjaf088},
    url = {https://doi.org/10.1093/ejo/cjaf088},
    eprint = {https://academic.oup.com/ejo/article-pdf/47/6/cjaf088/65268573/cjaf088.pdf},
}



@Manual{R-sitar,
    title = {sitar: Super Imposition by Translation and Rotation Growth Curve Analysis},
    author = {Tim Cole},
    year = {2022},
    note = {R package version 1.3.0},
    url = {https://CRAN.R-project.org/package=sitar},
  }


@Manual{R-brms,
  title = {brms: Bayesian Regression Models using Stan},
  author = {Paul-Christian Bürkner},
  year = {2022},
  note = {R package version 2.18.0},
  url = {https://CRAN.R-project.org/package=brms},
}


@Manual{R-Hmisc,
  title = {Hmisc: Harrell Miscellaneous},
  author = {Harrell, Jr., Frank E},
  year = {2022},
  note = {R package version 4.7-2},
  url = {https://hbiostat.org/R/Hmisc/},
}


@ARTICLE{Arnes2023,
  
AUTHOR={Arnes, Jo Inge  and Hapfelmeier, Alexander  and Horsch, Alexander  and Braaten, Tonje },
         
TITLE={Greedy knot selection algorithm for restricted cubic spline regression},
        
JOURNAL={Frontiers in Epidemiology},
        
VOLUME={Volume 3 - 2023},

YEAR={2023},

URL={https://www.frontiersin.org/journals/epidemiology/articles/10.3389/fepid.2023.1283705},

DOI={10.3389/fepid.2023.1283705},

ISSN={2674-1199},

ABSTRACT={Non-linear regression modeling is common in epidemiology for prediction purposes or estimating relationships between predictor and response variables. Restricted cubic spline (RCS) regression is one such method, for example, highly relevant to Cox proportional hazard regression model analysis. RCS regression uses third-order polynomials joined at knot points to model non-linear relationships. The standard approach is to place knots by a regular sequence of quantiles between the outer boundaries. A regression curve can easily be fitted to the sample using a relatively high number of knots. The problem is then overfitting, where a regression model has a good fit to the given sample but does not generalize well to other samples. A low knot count is thus preferred. However, the standard knot selection process can lead to underperformance in the sparser regions of the predictor variable, especially when using a low number of knots. It can also lead to overfitting in the denser regions. We present a simple greedy search algorithm using a backward method for knot selection that shows reduced prediction error and Bayesian information criterion (BIC) scores compared to the standard knot selection process in simulation experiments. We have implemented the algorithm as part of an open-source R-package, knutar.}}


@Manual{R-splines,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2022},
    url = {https://www.R-project.org/},
  }


@article{Cole2010,
	title = {{SITAR}—a useful instrument for growth curve analysis},
	volume = {39},
	issn = {0300-5771},
	url = {https://doi.org/10.1093/ije/dyq115},
	doi = {10.1093/ije/dyq115},
	number = {6},
	journal = {International Journal of Epidemiology},
	author = {Cole, Tim J and Donaldson, Malcolm D C and Ben-Shlomo, Yoav},
	year = {2010},
	note = {tex.eprint: https://academic.oup.com/ije/article-pdf/39/6/1558/18480886/dyq115.pdf},
	pages = {1558--1566},
}


@article{Lindstrom1995,
author = {Lindstrom, Mary J.},
title = {Self-modelling with random shift and scale parameters and a free-knot spline shape function},
journal = {Statistics in Medicine},
volume = {14},
number = {18},
pages = {2009-2021},
doi = {https://doi.org/10.1002/sim.4780141807},
abstract = {Abstract The shape invariant model is a semi-parametric approach to estimating a function relationship from clustered data (multiple observations on each of a number of individuals). The common response curve shape over individuals is estimated by adjusting for individual scaling differences while pooling shape information. In practice, the common response curve is restricted to some flexible family of functions. This paper introduces the use of a free-knot spline shape function and reduces the number of parameters in the shape invariant model by assuming a random distribution on the parameters that control the individual scaling of the shape function. New graphical diagnostics are presented, parameter identifiability and estimation are discussed, and an example is presented.},
year = {1995}
}


@article{Beath2007,
	title = {Infant growth modelling using a shape invariant model with random effects},
	volume = {26},
	doi = {10.1002/sim.2718},
	number = {12},
	journal = {Statistics in Medicine},
	author = {Beath, K. J.},
	year = {2007},
	note = {Type: Journal article},
	pages = {2547--2564},
	annote = {167ci Times Cited:23 Cited References Count:39},
}

@Article{brms2021,
  title = {Bayesian Item Response Modeling in {R} with {brms} and {Stan}},
  author = {Paul-Christian Bürkner},
  journal = {Journal of Statistical Software},
  year = {2021},
  volume = {100},
  number = {5},
  pages = {1--54},
  doi = {10.18637/jss.v100.i05},
  encoding = {UTF-8},
}


@article{Anna2022,
author = {Anna M. Hardin and Ryan P. Knigge and Hee Soo Oh and Manish Valiathan and Dana L. Duren and Kieran P. McNulty and Kevin M. Middleton and Richard J. Sherwood},
title ={Estimating Craniofacial Growth Cessation: Comparison of Asymptote- and Rate-Based Methods},
journal = {The Cleft Palate Craniofacial Journal},
volume = {59},
number = {2},
pages = {230-238},
year = {2022},
doi = {10.1177/10556656211002675},
note ={PMID: 33998905},
URL = {https://doi.org/10.1177/10556656211002675},
}



@Manual{teamStanReferenceManual,
	title = {Stan Reference Manual version 2.31},
	author = {{Stan Development Team}},
      year = {2023},
	url = {https://mc-stan.org/docs/reference-manual/},
}



@book{harrell2001regression,
	title = {Regression modeling strategies: with applications to linear models, logistic regression, and survival analysis},
	volume = {608},
	publisher = {Springer},
	author = {Harrell, Frank E and {others}},
	year = {2001},
}








@article{nembidzaneUsingSITARMethod2020,
	title = {Using the {SITAR} {Method} to {Estimate} {Age} at {Peak} {Height} {Velocity} of {Children} in {Rural} {South} {Africa}: {Ellisras} {Longitudinal} {Study}},
	volume = {7},
	issn = {2227-9067},
	shorttitle = {Using the {SITAR} {Method} to {Estimate} {Age} at {Peak} {Height} {Velocity} of {Children} in {Rural} {South} {Africa}},
	doi = {10.3390/children7030017},
	language = {en},
	number = {3},
	journal = {Children},
	author = {Nembidzane, Chris and Lesaoana, Maseka and Monyeki, Kotsedi Daniel and Boateng, Alexander and Makgae, Phuti J.},
	month = mar,
	year = {2020},
	pages = {17},
}





@article{mansukoskiLifeCourseAssociations2019,
	title = {Life course associations of height, weight, fatness, grip strength, and all‐cause mortality for high socioeconomic status {Guatemalans}},
	volume = {31},
	issn = {1042-0533, 1520-6300},
	url = {https://pubmed.ncbi.nlm.nih.gov/31090124/},
	doi = {10.1002/ajhb.23253},
	language = {en},
	number = {4},
	journal = {American Journal of Human Biology},
	author = {Mansukoski, Liina and Johnson, William and Brooke‐Wavell, Katherine and Galvez‐Sobral, J. Andres and Furlan, Luis and Cole, Tim J. and Bogin, Barry},
	month = jul,
	year = {2019},
}



@article{coleFiftyYearsChild2018,
	title = {Fifty years of child height and weight in {Japan} and {South} {Korea}: {Contrasting} secular trend patterns analyzed by {SITAR}},
	volume = {30},
	issn = {10420533},
	shorttitle = {Fifty years of child height and weight in {Japan} and {South} {Korea}},
	doi = {10.1002/ajhb.23054},
	language = {en},
	number = {1},
	journal = {American Journal of Human Biology},
	author = {Cole, T. J. and Mori, H.},
	month = jan,
	year = {2018},
	pages = {e23054},
}



@article{riddellClassifyingGestationalWeight2017,
	title = {Classifying {Gestational} {Weight} {Gain} {Trajectories} {Using} the {SITAR} {Growth} {Model}},
	volume = {31},
	issn = {02695022},
	doi = {10.1111/ppe.12336},
	language = {en},
	number = {2},
	journal = {Paediatric and Perinatal Epidemiology},
	author = {Riddell, Corinne A and Platt, Robert W. and Bodnar, Lisa M. and Hutcheon, Jennifer A.},
	month = mar,
	year = {2017},
	pages = {116--125},
}



@phdthesis{Sandhu2020,
	type = {Thesis},
	title = {Analysis of longitudinal jaw growth data to study sex differences in timing and intensity of the adolescent growth spurt for normal growth and skeletal discrepancies},
	school = {University of Bristol},
	author = {Sandhu, Satpal S.},
	year = {2020},
}




@article{Tuddenham1954,
	title = {Physical growth of {California} boys and girls from birth to eighteen years},
	volume = {1},
	language = {eng},
	number = {2},
	journal = {Publications in Child Development. University of California, Berkeley},
	author = {Tuddenham, R. D. and Snyder, M. M.},
	volume={1},
        number={2},
        pages={183--364},
        year={1954}
}


@Manual{R-fda,
    title = {fda: Functional Data Analysis},
    author = {J. O. Ramsay and Spencer Graves and Giles Hooker},
    year = {2022},
    note = {R package version 6.0.5},
    url = {https://CRAN.R-project.org/package=fda},
  }


@article{gelman2015,
	author = {Andrew Gelman and Daniel Lee and Jiqiang Guo},
	title ={Stan: A Probabilistic Programming Language for Bayesian Inference and Optimization},
	journal = {Journal of Educational and Behavioral Statistics},
	volume = {40},
	number = {5},
	pages = {530-543},
	year = {2015},
	doi = {10.3102/1076998615606113},
	URL = {https://doi.org/10.3102/1076998615606113},
}