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Advanced myopia, prevalence and incidence analysis

Abstract

Purpose

Various high-percentage high-incidence medical conditions, acute or chronic, start at a particular age of onset t1 (years), accumulate or progress rapidly, with a system time constant t0 (years), typically from 1 week to 5 years, and then level off at a plateau level \(\left\langle S \right\rangle\), ultimately affecting 10–95% of the population. This report investigates the prevalence and incidence functions for myopia and high myopia as a function of age.

Methods

Fundamental prevalence versus time and incidence versus time results allow continuous prediction of myopia and high myopia population fractions as a function of age. This is a retrospective study. Nine reports are calculated with N = 444,600 subjects. There were no interventions other than usual regular eye examinations and subsequent indicated refraction change.

Results

The main result is continuous prediction of myopia prevalence–time data along with incidence rate data (%/year), age of onset (years), system plateau level, and system time constant (years). These parameters apply to progressive myopia and high myopia (R < −6 D), useful over several decades.

Conclusions

The primary finding of this research is that the prevalence ratio of high myopes (R < −6.0 D) to common myopes is expected to increase from 15% entering college to 45% or more after college and graduate school. These statistics are particularly relevant to the many years of study required by M.D., Ph.D., and M.D./Ph.D. programs.

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Abbreviations

Pr(t):

Myopia prevalence fraction as a function of time (%)

In(t):

Myopia incidence rate as a function of time (%/year)

t0:

Myopia time constant (years)

t1:

Myopia onset age (years)

t2:

Onset age (years) for advanced myopia

\(\left\langle S \right\rangle\) :

Plateau level (%), 30–95% for myopia

95% CI:

95% conf. interval, r = correl. coefficient

\(\left\langle {{\text{std}} . {\text{err}} .} \right\rangle\) :

r.m.s. error @ regression line, typically ±2%

References

  1. 1.

    Fan DS, Lam DS, Lam RF, Lau JT, Chong KS, Cheung EY, Lai RY, Chew SJ (2004) Prevalence, incidence, and progression of myopia of school children in Hong Kong. Invest Ophthalmol Vis Sci 45(4):1071–1075

    Article  PubMed  Google Scholar 

  2. 2.

    Greene PR, Vigneau ES, Greene J (2015) Exponential prevalence and incidence equations for myopia. Clin Exp Opt 98(3):210–213

    Article  Google Scholar 

  3. 3.

    Greene PR, Grill ZW, Medina A (2016) Mathematical models of college myopia. Optik (Stuttg) 127(2):896–899. https://www.academia.edu/18233864/Greene_2016_Mathematical_Models_of_College_Myopia

  4. 4.

    Greene PR, Medina A (2016) Refraction data survey: 2nd generation correlation of myopia. Int Ophthalmol 36(5):609–615. file:///C:/Users/rasdpatron/Downloads/Greene_Medina_2016_Refraction_Data_Surve.pdf

  5. 5.

    Lam CS, Goh WS (1991) The incidence of refractive errors among school children in Hong Kong in relationship with the optical components. Clin Exp Opt 74(3):97–103. http://onlinelibrary.wiley.com/doi/10.1111/j.1444-0938.1991.tb04618.x/abstract

  6. 6.

    Lin LL, Shih YF, Hsiao CK, Chen CJ (2004) Prevalence of myopia in Taiwanese schoolchildren: 1983 to 2000. Ann Acad Med Singap 33(1):27–33

    CAS  PubMed  Google Scholar 

  7. 7.

    Pan CW, Ramamurthy D, Saw SM (2012) Worldwide prevalence and risk factors for myopia. Ophthalmic Physiol Opt 32(1):3–16

    Article  PubMed  Google Scholar 

  8. 8.

    Sun J, Zhou J, Zhao P, Lian J, Zhu H, Zhou Y, Sun Y, Wang Y, Zhao L, Wei Y, Wang L, Cun B, Ge S, Fan X (2012) High prevalence of myopia and high myopia in 5060 Chinese university students in Shanghai. Invest Ophthalmol Vis Sci 53(12):7504–7509

    Article  PubMed  Google Scholar 

  9. 9.

    Fan DS, Cheung EY, Lai RY, Kwok AK, Lam DS (2004) Myopia progression among preschool Chinese children in Hong Kong. Ann Acad Med Singap 33(1):39–43

    CAS  PubMed  Google Scholar 

  10. 10.

    Greene PR (1986) Gaussian and Poisson blink statistics: a preliminary study. IEEE Trans Biomed Eng. 33(3):359–361

    CAS  Article  PubMed  Google Scholar 

  11. 11.

    Greene PR, Medina A (2016) Analogue computer model of progressive myopia—refraction stability response to reading glasses. J Comput Sci Syst Biol 9:104. http://www.omicsonline.org/open-access/analogue-computer-model-of-progressive-myopiarefraction-stability-response-to-reading-glasses-jcsb-1000226.pdf

  12. 12.

    Medina A, Fariza E (1993) Emmetropization as a first-order feedback system. Vis Res 33(1):21–26

    CAS  Article  PubMed  Google Scholar 

  13. 13.

    Medina A (2015) The progression of corrected myopia. Graefes Arch Clin Exp Ophthalmol 253(8):1273–1277

    Article  PubMed  Google Scholar 

  14. 14.

    Medina A (2016) Detecting the effect of under-correcting myopia. Graefes Arch Clin Exp Ophthalmol 254(2):409–411

    Article  PubMed  Google Scholar 

  15. 15.

    Goh WS, Lam CS (1994) Changes in refractive trends and optical components of Hong Kong Chinese aged 19–39 years. Ophthalmic Physiol Opt 14(4):378–382

    CAS  Article  PubMed  Google Scholar 

  16. 16.

    Lin LL, Shih YF, Lee YC, Hung PT, Hou PK (1996) Changes in ocular refraction and its components among medical students—a 5-year longitudinal study. Optom Vis Sci 73(7):495–498

    CAS  Article  PubMed  Google Scholar 

  17. 17.

    Brinks R, Landwehr S, Icks A, Koch M, Giani G (2013) Deriving age-specific incidence from prevalence with an ordinary differential equation. Stat Med 32(12):2070–2078

    Article  PubMed  Google Scholar 

  18. 18.

    Brinks R, Landwehr S (2015) A new relation between prevalence and incidence of a chronic disease. Math Med Biol 32(4):425–435

    PubMed  PubMed Central  Google Scholar 

  19. 19.

    Saw SM, Tong L, Chua WH, Chia KS, Koh D, Tan DT, Katz J (2005) Incidence and progression of myopia in Singaporean school children. Invest Ophthalmol Vis Sci 46(1):51–57

    Article  PubMed  Google Scholar 

  20. 20.

    Holden BA, Fricke TR, Wilson DA, Jong M, Naidoo KS, Sankaridurg P, Wong TY, Naduvilath TJ, Resnikoff S (2016) Global prevalence of myopia and high myopia and temporal trends from 2000 through 2050. Ophthalmology 123(5):1036–1042. doi:10.1016/j.ophtha.2016.01.006 (Free Article)

    Article  PubMed  Google Scholar 

  21. 21.

    Pan CW, Dirani M, Cheng CY, Wong TY, Saw SM (2015) The age-specific prevalence of myopia in Asia: a meta-analysis. Optom Vis Sci 92(3):258–266

    Article  PubMed  Google Scholar 

  22. 22.

    Tay MT, Au Eong KG, Ng CY, Lim MK (1992) Myopia and educational attainment in 421,116 young Singaporean males. Ann Acad Med Singapore 21(6):785–791

    CAS  PubMed  Google Scholar 

  23. 23.

    Lee JH, Jee D, Kwon JW, Lee WK (2013) Prevalence and risk factors for myopia in a rural Korean population. Invest Ophthalmol Vis Sci 54(8):5466–5471

    Article  PubMed  Google Scholar 

  24. 24.

    Yip VC, Pan CW, Lin XY, Lee YS, Gazzard G, Wong TY, Saw SM (2012) The relationship between growth spurts and myopia in Singapore children. Invest Ophthalmol Vis Sci 53(13):7961–7966

    Article  PubMed  Google Scholar 

  25. 25.

    Quigley HA, Vitale S (1997) Models of open-angle glaucoma prevalence and incidence in the United States. Invest Ophthalmol Vis Sci 38(1):83–91

    CAS  PubMed  Google Scholar 

  26. 26.

    Podgor MJ, Leske MC (1986) Estimating incidence from age-specific prevalence for irreversible diseases with differential mortality. Stat Med 5(6):573–578

    CAS  Article  PubMed  Google Scholar 

  27. 27.

    Keiding N (1991) Age-specific incidence and prevalence: a statistical perspective. J R Stat Soc A 154(3):371–412. http://www.jstor.org/stable/2983150?seq=1#page_scan_tab_contents

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Acknowledgements

The authors thank F. Young, B. Curtin, O. Brown, A. Medina, D. Guyton, W. Baldwin, and S. Colgate for many helpful discussions. Funding was provided by National Eye Institute (Grant No. EY 005013).

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Correspondence to Peter R. Greene.

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The authors have no proprietary or financial conflicts of interest.

Appendix: Prevalence calculation details

Appendix: Prevalence calculation details

As a practical matter, the basic exponential equation (7) for prevalence as a function of time Pr(t) is somewhat difficult to work with, in terms of exactly determining the system time constant τ (t0) and the onset age t1:

$$\Pr \left( t \right) = \left\langle S \right\rangle \left[ {1{-}\exp \left( { - \left( {t - t1} \right) /\tau } \right)} \right]$$
(7)

Setting \(\left\langle S \right\rangle\) = 1, rearranging, taking natural log ln[] yields:

$$\ln \left[ {1{-}\Pr \left( t \right)} \right] = \left( {t - t1} \right) /\tau$$
(8)

For the more general situation with plateau at \(\left\langle S \right\rangle\) = 0.90, this is modified to

$$\ln \left[ {\left( {\left\langle S \right\rangle - \Pr \left( t \right)} \right) /\left\langle S \right\rangle } \right] = \left( {t{-}t1} \right) /\tau$$
(9)

Thus, using semi-log paper, plotting ln[1 − Pr(t)] versus time t, the slope and intercept will yield the system’s time constant τ (t0) and the onset age t1. For a general value of plateau \(\left\langle S \right\rangle\), several such plots must be generated, iterating over a range of values, to determine the optimal regression.

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Greene, P.R., Greene, J.M. Advanced myopia, prevalence and incidence analysis. Int Ophthalmol 38, 869–874 (2018). https://doi.org/10.1007/s10792-017-0510-x

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Keywords

  • Prevalence
  • Incidence
  • Myopia
  • High myopia
  • Exponential equations
  • Reading glasses
  • Time constant
  • Onset age
  • Plateau level