Wright State
Harry Khamis
Statistical Consulting Center Department of Mathematics and Statistics College of Science and Mathematics Wright State Home
Information for my students
Students, See This!
Publication List
Semi-Symmetric Intraclass Contingency Table
Buffon's Needle Problem
Swedish Language
(Det Svenska Språket)
Kolmogorov-Smirnov Test
Graphical Models and Multigraph Representations
Stature Prediction  
Return to Harry Khamis home page
Harry Khamis Home
spacer bar

Stature Prediction 

Numbers in parentheses correspond to the numbered references in my publication list.

From 1990 to 1993, I worked one day a week for the Department of Community Health in the School of Medicine. I worked at a unit which at that time was called the Division of Human Biology; now it's called the Lifespan Health Research Center (LHRC). The LHRC maintains the massive database for the Fels Longitudinal Study. The Fels Longitudinal Study is the largest and longest running (started in 1929) longitudinal study of human growth and development in the world. See Roche, 1992 for a full description of the Study. 

Although I worked on many projects at LHRC, the focus of my work involved the prediction of adult (age 18) stature in children, and most of my work was done in collaboration with Alex Roche, M.D., Ph.D., D.Sc., now retired. Some of the research was contract work for Genentech pharmaceuticals and some was independent research.

Let me first motivate this work by answering the question, "Why predict adult stature?" Of course, there is always the anxious curiosity of doting parents, but that by itself might not justify the effort we make in predicting adult stature. Other important reasons include the following.

  • It is used in medical and psychological management of child growth. Many children experience erratic growth behavior near the age of puberty which may lead to adverse psychological effects. We may be able to avoid therapeutic intervention if we can determine that the child will achieve a normal stature despite the erratic growth behavior.
  • Shortness has been correlated with hyperactivity, poor concentration, low attainment in reading, seriously elevated blood pressure, and increased risk of heart disease. Hence the desire by many for therapeutic intervention to avoid short adult stature. 
  • Adult stature prediction is an important part of treatments involving regulation of dosages for human growth hormone or anabolic steroids.
  • It plays an important role in studying the effects of surgery for congenital heart disease and for the surgical management of anisomelic children.
  • It is an important part of intervention programs involving nutrition and incidence of disease.
In the mid-1970s, researchers at the Division of Human Biology used the Fels Longitudinal Study data to conduct an exhaustive investigation in an attempt to determine the most important predictors of adult stature. Their conclusion: the most important predictors of adult stature for a child of a given age and gender are (i) current stature (big surprise!), (ii) current weight, (iii) midparent stature (another no-brainer), and (iv) skeletal age (a measurement of bone age based on a skeletal X-ray of the hand and wrist). They then proceeded to develop a prediction model based on these four predictors from which the adult stature of a given child could be predicted with a high degree of accuracy; see Roche et al. (1975) for details.

Improvements in the methodology described above have since been incorporated - see (34). The new method is called MCS**2(1); this stands for "multivariate cubic spline smoothing with one knot." In an attempt to make the method more accessible to everyone, the skeletal age predictor (which requires a hand X-ray to obtain) was omitted. The remaining three predictors, the child's stature, the child's weight, and the average stature of the two parents, can be measured by anyone (e.g., the parents themselves). And interestingly, the deterioration in prediction accuracy after dropping the skeletal age predictor is not serious; see (39). The resulting method is called the Khamis-Roche Method and can now be accessed through the world-wide web (see the end of this article). Be aware, however, that the height predictor on the web, based on the tables in (39), are valid only for White Americans who are free from any growth-related condition or disease. The 90% error margin of such individuals is 2.1 inches for boys and 1.7 inches for girls on the average - somewhat higher during the puberty years, and lower for other years. Unfortunately, there is not a sufficient number of African-American participants, or other ethnic groups, in the Fels Longitudinal Study data set from which to produce reliable stature prediction equations. 

A very rough rule of thumb that many parents have used to predict their child's adult stature in inches is to double their child's stature (in inches) at age two:

Adult stature = 2 x (stature at age 2).
This prediction can be improved substantially by using simple linear regressions, separately for boys and girls, of adult stature on stature at age two. These regressions, based on the Fels Longitudinal Study data, are:
Adult stature = 22.7 + 1.37 x (stature at age 2) for boys, and

Adult stature = 25.0 + 1.17 x (stature at age 2) for girls.

The prediction is improved further by using the Khamis-Roche method, based on three predictors: the child's stature, the child's weight, and the midparent stature, and can be done at any age, years 4 - 17.

Finally, the best prediction is obtained by using MCS**2(1), which uses the three predictors listed above in addition to the child's skeletal age. For comparison purposes, the median absolute deviation (MAD) for each of these cases is given below (MAD is the median deviation, in absolute value, between the predicted adult stature and the observed adult stature):
MAD (inches)
Method Male Female
2 x stature at age two 1.6 3.7
Simple linear
1.3 1.2
Khamis-Roche 0.9 0.7
MCS**2(1) 0.8 0.6

Note that doubling the child's stature at age two is a very unreliable method for girls. Separate simple linear regressions not only produce more reliable (lower MAD) predictions, but also predictions that have about the same reliability for boys and girls. The Khamis-Roche method produces a substantial improvement, and is only slightly inferior to MCS**2(1).

To calculate the predicted adult stature of a White, American child using the Khamis-Roche method, see: 



Roche, A.F. (1992). Growth, Maturation and Body Composition, The Fels Longitudinal Study, 1929 - 1991. Cambridge University Press.

Roche, A.F., Wainer, H., and Thissen, D. (1975). Predicting Adult Stature for Individuals. Monogr. Pediatr. 3: 1 - 115.



spacer bar
Prof. Harry Khamis, Director [e-mail]
Statistical Consulting Center [home][e-mail]
130 Mathematics and Microbiological Sciences Building
Wright State University
3640 Colonel Glenn Highway
Dayton OH 45435 USA
office phone: (937) 775-2433
or stat consulting center (937) 775-4205

fax: (937) 775-2081
Last updated: July 18, 2001
spacer bar

All Wright State University Webpages must publish this disclaimer.
Please send your comments, questions and suggestions regarding this webpage to me. (sjm)