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Table 2 Description of parameters for combined models of pre- and post-treatment data

From: Combined models for pre- and post-treatment longitudinal biomarker data: an application to CD4 counts in HIV-patients

Model parameter Description  
β 0 Pre-treatment mean intercept  
β 1 Pre-treatment mean slope  
U 00 Pre-treatment intercept subject-specific random effect variance  
ρ Correlation between pre-treatment intercept and slope subject-specific random effects  
U 11 Pre-treatment slope subject-specific random effect variance  
σ Standard deviation of residual error term for each measurement, shared by pre- and post-treatment parts of model  
κ pre Scale parameter for pre-treatment fBM process  
H pre Hurst index for pre-treatment fBM process  
ϕ1 model These parameters relate to the long-term maximum value of the response variable after treatment initiation  
At11,At12 Intercept and slope terms in relationship with \(u_{i}^{+}\) for patients treated within 6 months of seroconversion  
At21,At22 Intercept and slope terms in relationship with \(u_{i}^{+}\) for patients treated beyond 6 months but within 1 year of seroconversion  
A1,A2 Intercept and slope terms in relationship with \(u_{i}^{+}\) for linear or NCS models a  
A3,A4 Third and fourth coefficients for NCS models a  
ϕ2 model These parameters relate to the rate of recovery of the response variable after treatment initiation  
Bt11,Bt12 Intercept and slope terms in relationship with \(u_{i}^{+}\) for patients treated within 6 months of seroconversion  
Bt21,Bt22 Intercept and slope terms in relationship with \(u_{i}^{+}\) for patients treated beyond 6 months but within 1 year of seroconversion  
B1,B2 Intercept and slope terms in relationship with \(u_{i}^{+}\) for linear or NCS models a  
B3,B4 Third and fourth coefficients for NCS models a  
P Residual variance for long-term maximum (ϕ1:i) not explained by \(u_{i}^{+}\)  
κ post Scale parameter for post-treatment fBM process  
H post Hurst index for post-treatment fBM process  
d f pre Degrees of freedom parameter for pre-treatment stochastic process  
d f post Degrees of freedom parameter for post-treatment stochastic process  
ρ Moran Correlation parameter for latent scaling variables of pre- and post-treatment stochastic processes  
  1. aOnly applicable to patients with treatment initiation more than 1year after seroconversion when separate terms are included for earlier groups. fBM, fractional Brownian motion; NCS, natural cubic spline Some of the parameters relate to the link functions between the ‘true’ value of the response variable at treatment initiation, \(u_{i}^{+}\), and the post-treatment model