Human Growth Curve Estimation through a Combination of Longitudinal and Cross-sectional Data
Parametric models have been quite popular for
studying human growth, particularly in relation to biological
parameters such as peak size velocity and age at peak size velocity.
Longitudinal data are generally considered to be vital for fittinga
parametric model to individual-specific data, and for studying the
distribution of these biological parameters in a human population.
However, cross-sectional data are easier to obtain than longitudinal
data. In this paper, we present a method of combining longitudinal
and cross-sectional data for the purpose of estimating the distribution
of the biological parameters. We demonstrate, through simulations in
the special case ofthePreece Baines model, how estimates based on
longitudinal data can be improved upon by harnessing the
information contained in cross-sectional data.We study the extent of
improvement for different mixes of the two types of data, and finally
illustrate the use of the method through data collected by the Indian
Statistical Institute.
[1] Albert, J. Bayesian Computation with R, Springer, New York. 2007.
[2] Bates, D.M. and Watts, D.G. Nonlinear Regression Analysis and Its
Applications. Wiley, New York. 2007.
[3] Cnaan A., Laird, N.M. Laird and Slasor, P. "Using the general linear
mixed model to analyseunblanced repeated measures and longitudinal
data."Statist. Med., vol. 16, 2349-2380. 1997.
[4] Carlin, B.P., and Louis, T.A. Bayes and Empirical Bayes Methods for
Data Analysis. Chapman and Hall, Boca Raton, FL. 2000.
[5] Cole, T.J. "Fitting smoothed centile curves to reference data." J. Roy.
Statist. Soc. Ser.A, vol. 151, 385-418. 1988.
[6] Diggle, P., Heagerty, P., Liang. K.-Y. and Zeger, S.L. Analysis of
Longitudinal Data. Oxford University Press, Oxford. 2002.
[7] Donnet, S., Foulley, J. L., Samson, A. "A Bayesian analysis of growth
curves using mixed models defined by stochastic differential equations."
Biometrics, vol. 66, 733-741. 2010.
[8] Duncan, T.E., Duncan, S.C., Strycker, L.A., Li, F. and Alpert, A. An
Introduction to Latent Variable Growth Curve Modeling: Concepts,
Issues and Applications, Lawrence Erlbaum Associates, Mahwah, NJ.
2006
[9] Falkner, F. and Tanner, J.M. Human Growth: A Comprehensive
Treatise, Vol. 3, second edition, Plenum Press, New York. 1986.
[10] Gasser, T., Muller, H.G., Kohler, W., Molinari, L. and Prader, A.
"Nonparametric regression analysis of growth curves", Ann. Statist., vol.
12, 210-229. 1984.
[11] Hamill , P.V., Drizd , T.A., Johnson , C.L., Reed, R.B., Roche, A.F. and
Moore, W.M. "Physical growth: National Center for Health Statistics
percentiles."Amer. J. Clinical Nutrition, vol. 32, 607-629. 1979.
[12] Hauspie, R.C., Cameron, N. and Molinari, L. Methods in Human
Growth Research. Cambridge University Press, Cambridge. 2004.
[13] Huggins R.M. and Loesch D.Z. "On the analysis of mixed longitudinal
growth data."Biometrics, vol. 54, 583-595. 1998.
[14] Laird, N.M. and Ware, J.H. "Random effects models for longitudinal
data: an overview of recent results."Biometrics, vol. 38, 963-974. 1982.
[15] McLachlan, G. and Krishnan, T. The EM Algorithm and Extensions,
Wiley, New York. 1997.
[16] Muller, H.G. Nonparametric Regression Analysis of Longitudinal Data.
Sringer-Verlag, Berlin. 1988.
[17] Potthoff, F. and Roy, S.N. "A generalized multivariate analysis of
variance model useful specially for growth curve problems." Biometrika,
vol. 51, 313-326. 1964.
[18] Preece M.A. and Baines M.J. "A new family of mathematical models
describing the human growth curve."Annals of Human Biology, vol. 5,
1-24. 1978.
[19] Rao, C.R. "The theory of least squares when the parameters are
stochastic and its application to the analysis of growth
curves."Biometrika, vol. 52, 447-458. 1965.
[20] Staniswalis, J.G. and Lee, J.J. "Nonparametric regression analysis of
longitudinal data."J. Amer. Statist. Assoc., vol. 93, 1403-1418. 1998.
[21] Wei, Y., Pere, A., Koenker, R. and He, X. "Quantile regression methods
for reference growth charts."Statist. Medicine, vol. 25, 1369-1382. 2006.
[22] Wulfsohn, M.S. Tsiatis, A.A. "A joint model for survival and
longitudinal data measured with error."Biometrics, vol. 53, 330-339.
1997.
[23] Zemel, B.S. and Johnston, F.E. "Application of the Preece-Baines
growth model to cross-sectional data: Problems of validity and
interpretation."Amer. J. Human Biol., vol. 6, 563-570. 1994.
[1] Albert, J. Bayesian Computation with R, Springer, New York. 2007.
[2] Bates, D.M. and Watts, D.G. Nonlinear Regression Analysis and Its
Applications. Wiley, New York. 2007.
[3] Cnaan A., Laird, N.M. Laird and Slasor, P. "Using the general linear
mixed model to analyseunblanced repeated measures and longitudinal
data."Statist. Med., vol. 16, 2349-2380. 1997.
[4] Carlin, B.P., and Louis, T.A. Bayes and Empirical Bayes Methods for
Data Analysis. Chapman and Hall, Boca Raton, FL. 2000.
[5] Cole, T.J. "Fitting smoothed centile curves to reference data." J. Roy.
Statist. Soc. Ser.A, vol. 151, 385-418. 1988.
[6] Diggle, P., Heagerty, P., Liang. K.-Y. and Zeger, S.L. Analysis of
Longitudinal Data. Oxford University Press, Oxford. 2002.
[7] Donnet, S., Foulley, J. L., Samson, A. "A Bayesian analysis of growth
curves using mixed models defined by stochastic differential equations."
Biometrics, vol. 66, 733-741. 2010.
[8] Duncan, T.E., Duncan, S.C., Strycker, L.A., Li, F. and Alpert, A. An
Introduction to Latent Variable Growth Curve Modeling: Concepts,
Issues and Applications, Lawrence Erlbaum Associates, Mahwah, NJ.
2006
[9] Falkner, F. and Tanner, J.M. Human Growth: A Comprehensive
Treatise, Vol. 3, second edition, Plenum Press, New York. 1986.
[10] Gasser, T., Muller, H.G., Kohler, W., Molinari, L. and Prader, A.
"Nonparametric regression analysis of growth curves", Ann. Statist., vol.
12, 210-229. 1984.
[11] Hamill , P.V., Drizd , T.A., Johnson , C.L., Reed, R.B., Roche, A.F. and
Moore, W.M. "Physical growth: National Center for Health Statistics
percentiles."Amer. J. Clinical Nutrition, vol. 32, 607-629. 1979.
[12] Hauspie, R.C., Cameron, N. and Molinari, L. Methods in Human
Growth Research. Cambridge University Press, Cambridge. 2004.
[13] Huggins R.M. and Loesch D.Z. "On the analysis of mixed longitudinal
growth data."Biometrics, vol. 54, 583-595. 1998.
[14] Laird, N.M. and Ware, J.H. "Random effects models for longitudinal
data: an overview of recent results."Biometrics, vol. 38, 963-974. 1982.
[15] McLachlan, G. and Krishnan, T. The EM Algorithm and Extensions,
Wiley, New York. 1997.
[16] Muller, H.G. Nonparametric Regression Analysis of Longitudinal Data.
Sringer-Verlag, Berlin. 1988.
[17] Potthoff, F. and Roy, S.N. "A generalized multivariate analysis of
variance model useful specially for growth curve problems." Biometrika,
vol. 51, 313-326. 1964.
[18] Preece M.A. and Baines M.J. "A new family of mathematical models
describing the human growth curve."Annals of Human Biology, vol. 5,
1-24. 1978.
[19] Rao, C.R. "The theory of least squares when the parameters are
stochastic and its application to the analysis of growth
curves."Biometrika, vol. 52, 447-458. 1965.
[20] Staniswalis, J.G. and Lee, J.J. "Nonparametric regression analysis of
longitudinal data."J. Amer. Statist. Assoc., vol. 93, 1403-1418. 1998.
[21] Wei, Y., Pere, A., Koenker, R. and He, X. "Quantile regression methods
for reference growth charts."Statist. Medicine, vol. 25, 1369-1382. 2006.
[22] Wulfsohn, M.S. Tsiatis, A.A. "A joint model for survival and
longitudinal data measured with error."Biometrics, vol. 53, 330-339.
1997.
[23] Zemel, B.S. and Johnston, F.E. "Application of the Preece-Baines
growth model to cross-sectional data: Problems of validity and
interpretation."Amer. J. Human Biol., vol. 6, 563-570. 1994.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:63433", author = "Sedigheh Mirzaei S. and Debasis Sengupta", title = "Human Growth Curve Estimation through a Combination of Longitudinal and Cross-sectional Data", abstract = "Parametric models have been quite popular for
studying human growth, particularly in relation to biological
parameters such as peak size velocity and age at peak size velocity.
Longitudinal data are generally considered to be vital for fittinga
parametric model to individual-specific data, and for studying the
distribution of these biological parameters in a human population.
However, cross-sectional data are easier to obtain than longitudinal
data. In this paper, we present a method of combining longitudinal
and cross-sectional data for the purpose of estimating the distribution
of the biological parameters. We demonstrate, through simulations in
the special case ofthePreece Baines model, how estimates based on
longitudinal data can be improved upon by harnessing the
information contained in cross-sectional data.We study the extent of
improvement for different mixes of the two types of data, and finally
illustrate the use of the method through data collected by the Indian
Statistical Institute.", keywords = "Preece-Baines growth model, MCMC method,
Mixed effect model", volume = "6", number = "7", pages = "780-6", }
