Skip to main content
SpringerLink
Log in

Computing Theoretical Rates of Part C Eligibility Based on Developmental Delays

  • Published:
Maternal and Child Health Journal Aims and scope Submit manuscript

Abstract

Part C early intervention is a nationwide program that serves infants and toddlers who have developmental delays. This article presents a methodology for computing a theoretical estimate of the proportion of children who are likely to be eligible for Part C services based on delays in any of the 5 developmental domains (cognitive, motor, communication, social-emotional and adaptive) that are assessed to determine eligibility. Rates of developmental delays were estimated from a multivariate normal cumulative distribution function. This approach calculates theoretical rates of occurrence for conditions that are defined in terms of standard deviations from the mean on several variables that are approximately normally distributed. Evidence is presented to suggest that the procedures described produce accurate estimates of rates of child developmental delays. The methodology used in this study provides a useful tool for computing theoretical rates of occurrence of developmental delays that make children candidates for early intervention.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  1. Rosenberg, S. A., Zhang, D., & Robinson, C. C. (2008). Prevalence of developmental delays and participation in early intervention services for young children. Pediatrics, 121(6), e1503–e1509.

    Article  PubMed  Google Scholar 

  2. Data Resource Center for Child and Adolescent Health. (2012). 2005–2006 National survey of children with special health care needs. Cited January 4, 2012. Available at: http://childhealthdata.org/browse/survey/results?q=8&r=1&g=46.

  3. US Department of Education. (2011). Office of Special Education Programs, Data Analysis System (DANS), OMB #1820-0557: Infants and Toddlers Receiving Early Intervention Services in Accordance with Part C, 2010. Table 8–16. Number and percentage of infants and toddlers, ages birth to three, receiving early intervention services under IDEA, Part C, by state: 2010. Cited December 16, 2011. Available at: https://www.ideadata.org/arc_toc12.asp#partcCC.

  4. Shackelford, J. (2006). State and jurisdictional eligibility definitions for infants and toddlers with disabilities under IDEA. (NECTAC Notes No. 21). Chapel Hill: The University of North Carolina, FPG Child Development Institute, National Early Childhood Technical Assistance Center.

  5. Feinberg, E., Silverstein, M., Donahue, S., & Bliss, R. (2011). The impact of race on participation in Part C early intervention services. Journal of Developmental and Behavioral Pediatrics, 32(4), 1–8.

    Article  Google Scholar 

  6. Chao, A., Tsay, P. K., Lin, S. H., Shau, W. Y., & Chao, D. Y. (2001). The applications of capture-recapture models to epidemiological data. Statistics in Medicine, 20(20), 3123–3157.

    Article  PubMed  CAS  Google Scholar 

  7. Genz, A. (1992). Numerical computation of multivariate normal probabilities. Journal of Computational and Graphical Statistics, 1(2), 141–149.

    Google Scholar 

  8. Genz, A., Bretz, F., Miwa, T., Mi, X., Leisch, F., Scheipl, F., & Hothorn, T. (01/27/2010) Mvtnorm: Multivariate normal and t distributions. R package version 0.9-9. CRAN-Package mvtnorm: Cited December 16, 2011. Available at: http://CRAN.R-project.org/package=mvtnorm.

  9. Bayley, N. (2006). Bayley scales of infant and toddler development, third edition, technical manual, San Antonio, TX: Harcourt Assessment, Inc.

  10. Newborg, J. (2005). Battelle developmental inventory, 2nd edn: Examiner’s manual. Itasca, IL: Riverside.

    Google Scholar 

  11. Mathematica Positive definite matrix syntax. (2012). Cited January 4, 2012. Available at: http://reference.wolfram.com/mathematica/ref/PositiveDefiniteMatrixQ.html.

  12. Nord, C., Edwards, B., Andreassen, C., Green, J.L., & Wallner-Allen, K. (2006). Early childhood longitudinal study, birth cohort (ECLS-B), user’s manual for the ECLS-B longitudinal 9-month: 2-year data file and electronic codebook (NCES 2006-046). Washington, DC: US Department of Education, National Center for Education Statistics.

  13. Bayley, N. (1993). Bayley scales of infant development (2nd ed.). San Antonio, TX: Psychological Corporation.

    Google Scholar 

  14. Andreassen, C., & Fletcher, P. (2005). Early childhood longitudinal study, birth cohort (ECLS-B), psychometric characteristics. Volume 1 of the ECLS-B Methodology Report for the Nine-Month Data Collection (NCES 2005-100). Washington, DC: US Department of Education, National Center for Education Statistics.

  15. Connecticut Part C eligibility definition. (2012). Cited January 4, 2012. Available at: http://www.birth23.org/referrals/referrals.html.

  16. Florida Part C eligibility. (2012). Cited January 4, 2012. Available at: http://www.cms-kids.com/home/resources/es_policy_0710/3-FirstContactsEvaluationAssessment/Comp3_Handbook.html .

  17. Georgia Evaluation and Assessment. (2012). Cited January 4, 2012. Available at: http://health.state.ga.us/pdfs/bcw/EvalAssessment%20policy%20draft.pdf.

  18. Kentucky Evaluation and eligibility. (2012). Cited January 4, 2012. Available at: http://chfs.ky.gov/dph/firstSteps/pptablecontents.htm.

  19. Maine Eligibility Criteria for Children. (2012). Cited January 4, 2012. Available at: http://www.maine.gov/education/speced/documents/071c101-2010final2010.pdf.

  20. Oregon Children with Significant Delays in Development. (2012). Cited January 4, 2012. Available at: http://www.ode.state.or.us/gradelevel/pre_k/eiecse/medicalconditions.pdf.

  21. Salvia, J., Ysseldyke, J., & Bolt, S. (2007). Assessment: In Special and inclusive education (10th ed.). Boston: Houghton Mifflin Company.

    Google Scholar 

  22. Andersson, L. L. (2004). Appropriate and inappropriate interpretation and use of test scores in early intervention. Journal of Early Intervention, 27, 55–68.

    Article  Google Scholar 

Download references

Acknowledgments

This study was supported by grants from U.S. Department of Health and Human Services, Health Resources and Services Administration, Maternal and Child Health Research Program (R40 MC 05473), University Center of Excellence in Developmental Disabilities Education, Research and Service (UCEDD), U.S. Department of Health and Human Services, Administration on Developmental Disabilities (90DD0632), and the Colorado Intellectual and Developmental Disabilities Research Center (IDDRC), University of Colorado Denver. The authors thank Edward DeVos, Michael Gibbons, Kathy Green and Gary Zerbe for their valuable observations and suggestions.

Author information

Authors and Affiliations

  1. Department of Psychiatry and the Colorado Intellectual and Developmental Disabilities Research Center, University of Colorado School of Medicine, Aurora, CO, USA

    Steven A. Rosenberg

  2. Department of Biostatistics and Informatics, Colorado School of Public Health, Aurora, CO, USA

    Misoo C. Ellison

  3. Office of Information Technology, University of Colorado Boulder, Boulder, CO, USA

    Bruce Fast

  4. Departments of Pediatrics, Psychiatry, JFK Partners and the Colorado Intellectual and Developmental Disabilities Research Center, University of Colorado School of Medicine, Aurora, CO, USA

    Cordelia C. Robinson

  5. Robert H. Smith School of Business, University of Maryland, College Park, MD, USA

    Radu Lazar

Authors
  1. Steven A. Rosenberg
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Misoo C. Ellison
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bruce Fast
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Cordelia C. Robinson
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Radu Lazar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Steven A. Rosenberg.

Appendix

Appendix

Mathematically, the estimation of the probability of an individual falling between −4 SD and 4 SD on at least one of five domains is an evaluation of the joint probability of the following form, \( P(A \cup B \cup C \cup D \cup E) \) and for two domains it is \( P\{ [A \cap (B \cup C \cup D \cup E)] \cup [B \cap (C \cup D \cup E)] \cup [C \cap (D \cup E)] \cup (D \cap E)\} \), where \( \cup \) denotes union (‘or’), \( \cap \) denotes intersection (‘and’), and A, B, C, D, and E represent each of the five developmental domains satisfying certain conditions (e.g., A=Cognitive score less than 2.0 SD below the mean). Mvtnorm estimates probabilities of intersections, i.e., \( P(A \cap B), P(A \cap B \cap C), P(A \cap B \cap C \cap D), P(A \cap B \cap C \cap D \cap E) \), etc. Hence we needed to rewrite the above two expressions using only intersection symbols in order to use mvtnorm.

The interchange of union and intersection can be easily done by using the following general form of union probability.

$$ P\left( {\bigcup\limits_{i = 1}^{n} {A_{i} } } \right) = \mathop \sum \limits_{i = 1}^{n} P(A_{i} ) - \mathop \sum \limits_{i < j}^{n} P\left( {A_{i} \cap A_{j} } \right) + \mathop \sum \limits_{i < j < k}^{n} P\left( {A_{i} \cap A_{j} \cap A_{k} } \right) - \cdots + \left( { - 1} \right)^{n - 1} P\left( {\bigcap\limits_{i = 1}^{n} {A_{i} } } \right) $$

The first probability can be written as:

$$ \begin{aligned} P( {A \cup B \cup C \cup D \cup E} ) & = P(A) + P(B) + P(C) + P(D) + P(E) - P(A \cap B) - P( {A \cap C} ) - P( {A \cap D} ) \\ & \quad - P( {A \cap E} ) - P( {B \cap C} ) - P( {B \cap D} ) - P( {B \cap E} ) - P( {C \cap D} ) \\ & \quad - P( {C \cap E} ) - P( {D \cap E} ) + P( {A \cap B \cap C} ) + P( {A \cap B \cap D} ) + P( {A \cap B \cap E} ) \\ & \quad + P( {A \cap C \cap D} ) + P( {A \cap C \cap E} ) + P( {A \cap D \cap E} ) + P( {B \cap C \cap D} ) \\ & \quad + P( {B \cap C \cap E} ) + P( {B \cap D \cap E} ) + P( {C \cap D \cap E} ) - P( {A \cap B \cap C \cap D} ) \\ & \quad - P( {A \cap B \cap C \cap E} ) - P( {A \cap B \cap D \cap E} ) - P( {A \cap C \cap D \cap E} ) \\ & \quad - P( {B \cap C \cap D \cap E} ) + P( {A \cap B \cap C \cap D \cap E} ). \\ \end{aligned} $$

The second probability expression can be written as:

$$ \begin{gathered} P\{ [A \cap (B \cup C \cup D \cup E)] \cup [B \cap (C \cup D \cup E)] \cup [C \cap (D \cup E)] \cup (D \cap E)\} \hfill \\ = P(A \cap B) + P(A \cap C) + P(A \cap D) + P(A \cap E) + P(B \cap C) + P(B \cap D) \hfill \\ \quad + P(B \cap E) + P(C \cap D) + P(C \cap E) + P(D \cap E) - 2P(A \cap B \cap C) - 2P(A \cap B \cap D) \hfill \\ \quad - 2P(A \cap B \cap E) - 2P(A \cap C \cap D) - 2P(A \cap C \cap E) - 2P(A \cap D \cap E) \hfill \\ \quad - 2P(B \cap C \cap D) - 2P(B \cap C \cap E) - 2P(B \cap D \cap E) - 2P(C \cap D \cap E) \hfill \\ \quad + 3P(A \cap B \cap C \cap D) + 3P(A \cap B \cap C \cap E) + 3P(A \cap B \cap D \cap E) + 3P(A \cap C \cap D \cap E) \hfill \\ \quad + 3P(B \cap C \cap D \cap E) - 4P(A \cap B \cap C \cap D \cap E). \hfill \\ \end{gathered} $$

Using the 1.5/2.0 criteria we first computed an estimate for 2 domains using correlations for cognitive and motor abilities. In addition we extended the procedure described above to create an estimate for 5 domains using the 1.5/2.0 eligibility criteria. This was accomplished by enumerating the following probability expression, which is the probability of union of 15 different sets. The capital letters are each domain being less than 2.0 SD below the mean and the small letters are each domain being less than 1.5 SD below the mean.

$$ \begin{gathered} P\{ A \cup [\left( {a \cap b} \right) \cup \left( {a \cap c} \right) \cup \left( {a \cap d} \right) \cup \left( {a \cap e} \right) \cup \left( {b \cap c} \right) \cup \left( {b \cap d} \right) \cup \left( {b \cap e} \right) \cup \left( {c \cap d} \right) \cup \left( {c \cap e} \right) \hfill \\ \cup \left( {d \cap e} \right)] \cup B \cup [\left( {a \cap b} \right) \cup \left( {a \cap c} \right) \cup \left( {a \cap d} \right) \cup \left( {a \cap e} \right) \cup \left( {b \cap c} \right) \cup \left( {b \cap d} \right) \cup \left( {b \cap e} \right) \cup \left( {c \cap d} \right) \hfill \\ \cup \left( {c \cap e} \right) \cup \left( {d \cap e} \right)] \cup C \cup [\left( {a \cap b} \right) \cup \left( {a \cap c} \right) \cup \left( {a \cap d} \right) \cup \left( {a \cap e} \right) \cup \left( {b \cap c} \right) \cup \left( {b \cap d} \right) \cup \left( {b \cap e} \right) \hfill \\ \cup \left( {c \cap d} \right) \cup \left( {c \cap e} \right) \cup \left( {d \cap e} \right)] \cup D \cup [\left( {a \cap b} \right) \cup \left( {a \cap c} \right) \cup \left( {a \cap d} \right) \cup \left( {a \cap e} \right) \cup \left( {b \cap c} \right) \cup \left( {b \cap d} \right) \hfill \\ \cup \left( {b \cap e} \right) \cup \left( {c \cap d} \right) \cup \left( {c \cap e} \right) \cup \left( {d \cap e} \right)] \cup E \cup [\left( {a \cap b} \right) \cup \left( {a \cap c} \right) \cup \left( {a \cap d} \right) \cup \left( {a \cap e} \right) \cup \left( {b \cap c} \right) \hfill \\ \cup \left( {b \cap d} \right) \cup \left( {b \cap e} \right) \cup \left( {c \cap d} \right) \cup \left( {c \cap e} \right) \cup \left( {d \cap e} \right)] = P[A \cup B \cup C \cup D \cup E \cup \left( {a \cap b} \right) \cup \left( {a \cap c} \right) \hfill \\ \cup \left( {a \cap d} \right) \cup \left( {a \cap e} \right) \cup \left( {b \cap c} \right) \cup \left( {b \cap d} \right) \cup \left( {b \cap e} \right) \cup \left( {c \cap d} \right) \cup \left( {c \cap e} \right) \cup \left( {d \cap e} \right)] \hfill \\ \end{gathered} $$
$$ \begin{gathered} = P\left( A \right) + P\left( B \right) + P\left( C \right) + P\left( D \right) + P\left( E \right) - P\left( {Ab} \right) - P\left( {Ac} \right) - P\left( {Ad} \right) - P\left( {Ae} \right) - P\left( {Bc} \right) - P\left( {Bd} \right) \hfill \\ \quad - P\left( {Be} \right) - P\left( {Cd} \right) - P\left( {Ce} \right) - P\left( {De} \right) - P\left( {aB} \right) - P\left( {aC} \right) - P\left( {aD} \right) - P\left( {aE} \right) - P\left( {bC} \right) - P\left( {bD} \right) \hfill \\ \quad - P\left( {bE} \right) - P\left( {cD} \right) - P\left( {cE} \right) - P\left( {dE} \right) + P\left( {ab} \right) + P\left( {ac} \right) + P\left( {ad} \right) + P\left( {ae} \right) + P\left( {bc} \right) + P\left( {bd} \right) \hfill \\ \quad + P\left( {be} \right) + P\left( {cd} \right) + P\left( {ce} \right) + P\left( {de} \right) + P\left( {Abc} \right) + P\left( {Abd} \right) + P\left( {Abe} \right) + P\left( {Acd} \right) + P\left( {Ace} \right) \hfill \\ \quad + P\left( {Ade} \right) + P\left( {Bcd} \right) + P\left( {Bce} \right) + P\left( {Bde} \right) + P\left( {Cde} \right) + P\left( {aBc} \right) + P\left( {aBd} \right) + P\left( {aBe} \right) + P\left( {aCd} \right) \hfill \\ \quad + P\left( {aCe} \right) + P\left( {aDe} \right) + P\left( {abC} \right) + P\left( {abD} \right) + P\left( {abE} \right) + P\left( {acD} \right) + P\left( {acE} \right) + P\left( {adE} \right) + P\left( {bCd} \right) \hfill \\ \quad + P\left( {bCe} \right) + P\left( {bDe} \right) + P\left( {bcD} \right) + P\left( {bcE} \right) + P\left( {bdE} \right) + P\left( {cDe} \right) + P\left( {cdE} \right) - P\left( {Abcd} \right) - P\left( {Abce} \right) \hfill \\ \quad - P\left( {Abde} \right) - P\left( {Acde} \right) - P\left( {Bcde} \right) - P\left( {aBcd} \right) - P\left( {aBce} \right) - P\left( {aBde} \right) - P\left( {aCde} \right) - P\left( {abCd} \right) \hfill \\ \quad - P\left( {abCe} \right) - P\left( {abDe} \right) - P\left( {abcD} \right) - P\left( {abcE} \right) - P\left( {abdE} \right) - P\left( {acDe} \right) - P\left( {acdE} \right) - P\left( {bCde} \right) \hfill \\ \quad - P\left( {bcDe} \right)--P\left( {bcdE} \right) + P\left( {Abcde} \right) + P\left( {aBcde} \right) + P\left( {abCde} \right) + P\left( {abcDe} \right) + P\left( {abcdE} \right) \hfill \\ \quad - 2P\left( {abc} \right) - 2P\left( {abd} \right) - 2P\left( {abe} \right) - 2P\left( {acd} \right) - 2P\left( {ace} \right) - 2P\left( {ade} \right) - 2P\left( {bcd} \right) \hfill \\ \quad - 2P\left( {bce} \right) - 2P\left( {bde} \right) - 2P\left( {cde} \right) + 3P\left( {abcd} \right) + 3P\left( {abce} \right) + 3P\left( {abde} \right) + 3P\left( {acde} \right) \hfill \\ \quad + 3P\left( {bcde} \right) - 4P\left( {abcde} \right). \hfill \\ \end{gathered} $$

Intersection symbols are omitted for simplicity in the last expression, i.e., \( abcde = a \cap b \cap c \cap d \cap e. \)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rosenberg, S.A., Ellison, M.C., Fast, B. et al. Computing Theoretical Rates of Part C Eligibility Based on Developmental Delays. Matern Child Health J 17, 384–390 (2013). https://doi.org/10.1007/s10995-012-0982-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10995-012-0982-2

Keywords

Search

Navigation