Modeling Growth -- From Dinosaurs to Children

Growth-rate studies of dinosaurs reveal that the same statistical methods can be applied to better understanding a major issue in global health, child malnutrition.

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Modeling Growth -- From Dinosaurs to Children

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Growth-rate studies of dinosaurs reveal that the same statistical methods can be applied to better understanding a major issue in global health, child malnutrition.
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Slide Content
  1. 7 October 2014

    Slide 1 - 7 October 2014

    • Modeling
    • MODELING GROWTH: FROM DINOSAURS TO CHILDREN
  2. To better understand their biology, metabolism, and behavior

    Slide 3 - To better understand their biology, metabolism, and behavior

    • Why Model Dinosaur Growth?
  3. 4

    Slide 4 - 4

    • Commonalities with modeling child growth
    • The importance of best practices, especially when data is imperfect
    • Choosing appropriate variables
    • Choosing the mathematical model that objectively works best
    • Fitting curves appropriately
    • Understanding and respecting the limitations of data and models
  4. 6

    Slide 6 - 6

    • Lines of arrested growth (LAGS)
    • Velociraptor
    • Tenontosaurus
  5. 8

    Slide 8 - 8

    • Estimating age and size from fossilized bone
    • Lines of arrested growth (LAGs)
    • Estimate age from LAG count
    • Estimate mass from circumference of major bones:
    • M = a (cfemur + chumerus)b
    • for quadrupeds,
    • a = 0.078, b = 2.73
    • for bipeds,
    • a = 0.16, b =2.73
  6. Analyzed 31 Sets of Dinosaur Growth Data, Spanning 14 Taxa

    Slide 10 - Analyzed 31 Sets of Dinosaur Growth Data, Spanning 14 Taxa

  7. When complete data is not available on individuals, aggregating data can enable reconstruction of plausible growth trajectories

    Slide 12 - When complete data is not available on individuals, aggregating data can enable reconstruction of plausible growth trajectories

    • Some researchers do the fitting by eye
    • Least-squares optimization is replicable and more accurate
    • Need to use non-integer scaling factors (not every individual has the same birthday!)
    • 12
    • Constructing longitudinal seriesfrom sparse data
  8. Testing Fits to Multiple Models

    Slide 14 - Testing Fits to Multiple Models

    • 14
    • 21 increasing functions
    • 14 asymptotic attenuating
    • 49 asymptotic sigmoidal
    • 84 functions × 31 data sets = 2,604 fits
    • parameters
    • functions
    • 1
    • 4
    • 2
    • 21
    • 3
    • 31
    • 4
    • 28
    • Using more free parameters may improve the fit, but not always enough to justify the additional degrees of freedom
  9. 16

    Slide 16 - 16

    • Growth IS USUALLY (BUT NOT ALWAYS) heteroscedastic
    • Wandering albatross
    • Heteroscedastic growth: the distribution of body sizes widens substantially with age as individual growth trajectories diverge
    • At age 50d, σ = 1,115; at age 250d, σ = 1,505
  10. Increases the likelihood that an algorithm will find the best fit, and decreases the probability of algorithm failure

    Slide 18 - Increases the likelihood that an algorithm will find the best fit, and decreases the probability of algorithm failure

    • Tested using synthetic data set and six commonly used global fitting algorithms from R and Mathematica
    • A New Preprocessing transformation for Fitting Models
  11. 19

    Slide 19 - 19

    • From bone circumference and age estimates, we calculated the likely peak growth rate
    • Example: Tyrannosaurus
    • Maximum bone growth rate occurs at age 2
    • Bone circumference (cm)
    • Age (y)
    • Peak mass growth rate: 365 kg/yr
    • PER YEAR
  12. Almost all previous analyses in the literature were affected by one or more methodological issues

    Slide 21 - Almost all previous analyses in the literature were affected by one or more methodological issues

    • 21
    • Irreproducible fits
    • Use of subjective, rather than objective, criteria to select among models
    • Inappropriate choice of independent variable
    • Incorrect or hand-tweaked data and curve-fitting
    • Attempted replications of prior published results
    • Age
    • Mass
  13. 23

    Slide 23 - 23

    • Choose the right independent variable
    • Linear regression methods assume it has no error
    • Monte Carlo analysis illustrates the consequence of choosing wrong: a different mean and a much greater standard deviation
    • Lessons Applicable to Modeling ChilD Growth
    • Age as the independent variable
    • Time as the independent variable
  14. 24

    Slide 24 - 24

    • Choose the right independent variable
    • Linear regression methods assume it has no error
    • Monte Carlo analysis illustrates the consequence of choosing wrong: a different mean and a much greater standard deviation
    • Lessons Applicable to Modeling ChilD Growth
    • Age as the independent variable
    • Time as the independent variable
  15. 26

    Slide 26 - 26

    • Try multiple alternative models
    • Don’t overfit by using too many parameters
    • Respect model constraints
    • Use an objective criterion, such as AICc, to select the best model
    • All goodness-of-fit metrics are local to the data points—there is no legitimate prediction beyond the limits of the data
    • Lessons Applicable to Modeling Child Growth
  16. 28

    Slide 28 - 28

    • If the shoe fits—it doesn’t necessarily mean anything
    • Every growth model has a linear phase!
    • Lessons Applicable to Modeling Child Growth
  17. 30

    Slide 30 - 30

    • Avoid unjustified extrapolation by estimating error and plotting confidence intervals
    • Outside the bounds of the data, CIs grow wide quickly
    • Lessons Applicable to Modeling Child Growth
  18. Cross-sectional data sets cannot accurately simulate longitudinal series

    Slide 32 - Cross-sectional data sets cannot accurately simulate longitudinal series

    • Longitudinal vs. Cross-sectional data
    • Standard curve-fitting algorithms assume uncorrelated errors
    • This assumption is violated by longitudinal data sets that follow individuals over time
  19. Cross-sectional data sets cannot accurately simulate longitudinal series

    Slide 34 - Cross-sectional data sets cannot accurately simulate longitudinal series

    • Longitudinal vs. Cross-sectional data
    • Source data: longitudinal growth measurements on 100 flamingos
    • 100 longitudinal fits: fit the same function to each individual series
    • 100 cross-sectional fits: fit the same function as above to data sets of randomly selected points representing the
    • entire life span
    • Values of coefficient a b c
  20. Following individuals for many years enables insights into the effects of path history

    Slide 36 - Following individuals for many years enables insights into the effects of path history

    • Need to use models and measures designed for longitudinal series
    • The Power of Longitudinal Data
  21. 38

    Slide 38 - 38

    • Weighted Least Squares Analysis
  22. Improper measurement of the independent variable attenuates relationships.

    Slide 39 - Improper measurement of the independent variable attenuates relationships.

    • Jerry Hausman, M.I.T., in Journal of Economic Perspectives 15:4 (2001)
    • 39
    • The Iron Law of econometrics
    • Nigeria: +89%
    • Oshodi BA. Energy Economics and Project Financing Options in Nigeria. Rochester, NY: Social Science Research Network, 2014
    • Zambia: +24%
    • Jerven M. Poor Numbers: How We Are Misled by African Development Statistics and What to Do about It. Ithaca, NY: Cornell University Press, 2013.
    • Ghana: +63%
    • Jerven M, Duncan ME. Revising GDP estimates in sub-Saharan Africa: lessons from Ghana. Afr Stat J 2012; 15: 13–24.
    • GDP measurements are noisy and often inaccurate even in developed economies
    • Changes to national accounting systems can cause large artificial changes
  23. Consensus view: Stunting Falls as GDP Rises

    Slide 41 - Consensus view: Stunting Falls as GDP Rises

    • Absolute decline in prevalence
    • Relative decline (% of previous prevalence)
  24. Underweight Also goes down when GDP goes up

    Slide 43 - Underweight Also goes down when GDP goes up

    • Absolute decline in prevalence
    • Relative decline (% of previous prevalence)
  25. Slide 44

    • Countries where GDP per capita was growing were 67% more likely to reduce the prevalence of child stunting
  26. Slide 46

    • Causal or Simply Correlated?
    • Stunting and sanitation
  27. Slide 48

    • Causal or Simply Correlated?
    • Stunting and maternal education