The minimal informative monitoring interval of N-terminal pro-B-type natriuretic peptide in patients with stable heart failure

Table 1 Equations used for the applied random-effects model

Equations or components	Interpretation
Y_it= β_i× t + α_i+ ε_it	Random-effects model predicting the observed value.
Y_it	The value of {log (NT-proBNP) – log (baseline NT-proBNP)} of individual i at time t.
α_i	Intercept for individual i in the model. \( {\alpha}_i\sim \mathrm{N}\left(\alpha, {\sigma}_{\alpha}^2\right) \)
β_i	Progression rate of Y_it over time \( {\beta}_i\sim \mathrm{N}\left(\beta, {\sigma}_{\beta}^2\right) \)
ε_it	Residual for individual i at time t in the model, reflecting measurement error and biological variability. \( {\varepsilon}_{it}\sim \mathrm{N}\left(0,{\sigma}_{\varepsilon}^2\right) \)
t	Time in month since baseline

The notation N(x, y) refers to a normal distribution with mean x and variance y. From this model, noise reflecting the scale of intra-individual variability equals the variance of the residual (i.e. \( {\sigma}_{\varepsilon}^2 \)), whereas signal reflecting the scale of between-individual variability equals the variance of the progression rate multiplied by time (i.e. \( {\sigma}_{\beta \mathrm{t}}^2={\sigma}_{\beta}^2\times {t}^2 \))
NT-proBNP N-terminal pro-B-type natriuretic peptide

ISSN: 1471-2261