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Table 1 Equations of applied models

From: Diabetes screening intervals based on risk stratification

Random effect model:

Y ij  = U ij  + ε ij

Observed HbA1c:

Y ij

Noise:

ε ij

Signal:

U ij  = α ij  + β ij  * T

α i  ~ N(α,σ a 2) , β i  ~ N(β,σ b 2), with covariance (αi ,β i ) = σ ab

ε ij  ~ N(0,σ w 2)

  1. Y is the observed HbA1c, equal to the true change and the measurement error, ε. U is the true change in HbA1c for individual for individual i at time j , α is the baseline HbA1c, β is the annual progression rate. T represents time since first measurement. The notation ~ N(x,y) refers to a normal distribution with a mean x and a variance y, so the other main assumption of the model is normality in the distributions of α, β and ε. From this model, the short-term variability is equal to the variance of the measurement error (σ2w) whereas the long-term variability is equal to the variance of the annual progression rate (σ2β)