Appendix
To aid in establishing the parameter values in the model, a comprehensive literature search
was performed, including searches of PubMed, EMBASE and the China National Knowledge
Infrastructure database for 1990–2008 (accessed October, 2014). Due to limited publications in
this area, no transition probabilities for Chinese patients were found in the published data.
Using the disease model, we calibrated the parameter sets of transition probabilities to ensure
that the model outputs were consistent with observed Chinese epidemiologic data, including the
prevalences of DR, PDR, NPDR and DME stratified by the duration of diabetes 1-5, which were
defined as the calibration targets. Our approach to model calibration was based on a genetic
algorithm in which the parameter search method is based on the principle of “survival of the fittest”
6
. The goodness-of-fit (GOF) of modeled outputs resulting from each candidate set of input
parameter values was evaluated with the chi-square (χ2) GOF score using the following formula:
𝜒 2 = ∑𝑘𝑖=1
(𝑂𝑖 −𝐸𝑖 )2
𝐸𝑖
,
where Ei and Oi indicate the expected and observed values, respectively. The upper limit, k,
corresponds to the total number of observations, and i indicates the index for the observation.
The best-fitting parameter would be identified by the lowest overall GOF score – the
searched input parameter set whose model outputs were simultaneously closest to all calibration
targets. We then identified a subset of parameter sets whose GOF scores were statistically
indistinguishable from the GOF score of the best-fitting set (α = 0.05) using a likelihood ratio test
and assuming that the distribution of the GOF scores approximate a χ2 distribution (degrees of
freedom-number of calibration targets) 7.
Figure A1 depicts the model output for fitting our calibration targets, the prevalences of DR,
PDR, NPDR and DME, using a random sample of 100 sets from the subset of good-fitting
parameter sets. The fit for the DR prevalence is good, as model outputs are consistent with the
observed data (Fig A1 A). Although modeled ranges overlap the 95% confidence intervals of the
observed data, they are narrower.
Figure A1 B-D shows the 95% confidence intervals or single points for the prevalences of
PDR, NPDR and DME compared to the 95% confidence interval modeled outputs. Model output
is consistent with the general trend of the increasing prevalences of PDR, NPDR and DME as the
duration of diabetes increases. The modeled ranges are close to the observed data, but they are
wider and more variable for PDR and NPDR because of the paucity of epidemiological data in
China. The uncertainty was tested in the sensitivity analysis.
A.
B.
0.7
0.16
0.14
0.6
Prevalence of PDR
Prevalence of DR
0.12
0.5
0.4
0.3
0.10
0.08
0.06
0.04
0.02
0.2
0.00
−0.02
0.1
1-4 years 5-10 years 11-15 years >15 years >10 years
Diabetes duration
=8 years
D.
0.45
0.30
0.40
0.25
Prevalence of DME
Prevalence of NPDR
C.
1-4 years 5-10 years 11-15 years >15 years
Diabetes duration
0.35
0.30
0.25
0.20
0.20
0.15
0.10
0.05
0.15
0.00
1-4 years
5-10 years
>10 years
Diabetes duration
=12 years
1-4 years
5-10 years
<10 years
Diabetes duration
>10 years
Observed values
Predicted values
Figure A1. Observed and mean model-projected prevalence of DR (A), PDR (B), NPDR (C) and
ME (D) in Chinese diabetic patients stratified by disease duration. We superimposed 95%CIs
reflecting uncertainty. DR, diabetic retinopathy; NPDR, nonproliferative diabetic retinopathy;
PDR, proliferative diabetic retinopathy; DMR, diabetic macular edema.
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1.
Liu L, Wu X, Liu L, et al. Prevalence of diabetic retinopathy in mainland China: a
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2.
Lin CC, Li CI, Hsiao CY, et al. Time trend analysis of the prevalence and incidence of
diagnosed type 2 diabetes among adults in Taiwan from 2000 to 2007: a population-based
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3.
Lin JC, Shau WY, Lai MS. Sex- and age-specific prevalence and incidence rates of
sight-threatening diabetic retinopathy in Taiwan. JAMA ophthalmology. 2014;132:922-928.
4.
Tu Y, Xu L, Wei WB, Wang S, Wang YX, Jonas JB. Progression of diabetic retinopathy: the
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Wang FH, Liang YB, Zhang F, et al. Prevalence of diabetic retinopathy in rural China: the
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Yeh JM, Kuntz KM, Ezzati M, Hur C, Kong CY, Goldie SJ. Development of an empirically
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