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Advanced myopia, prevalence and incidence analysis



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.


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.


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.


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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Fig. 1
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Fig. 4
Fig. 5



Myopia prevalence fraction as a function of time (%)


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


Myopia time constant (years)


Myopia onset age (years)


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%


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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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Corresponding author

Correspondence to Peter R. Greene.

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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:

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

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

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

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

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

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).

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