Factors affecting the stability and repeatability of gamma camera calibration for quantitative imaging applications based on a retrospective review of clinical data

Anizan, Nadège; Wang, Hao; Zhou, Xian C; Hobbs, Robert F; Wahl, Richard L; Frey, Eric C

doi:10.1186/s13550-014-0067-x

EJNMMI Research

Table 1 Mixed-effects models used for the different variables

From: Factors affecting the stability and repeatability of gamma camera calibration for quantitative imaging applications based on a retrospective review of clinical data

Model	Outcome variable	Model definition
1	Calibration factors CF_rA and CF_dA	$y_C F_{i k} = μ_{C F} + α_C F_{i} + β_{S_{E F}} \times S_{E F_{i k}} + β_{Constancy} \times Constanc y_{i k} + γ_{B k R_{i}} \times B k R_{i k} + ε_{i k}$ for calibration source i on day k, with $α_C F_{i} \sim N (0, σ_{C F}^{2})$ , $γ_{B k R_{i}} \sim N (0, σ_{γ_{B k R}}^{2})$ , and $ε_{i k} \sim N (0, σ_{ε}^{2})$
2	Background count rate	$y_B k R_{i k} = μ_{B k R} + α_B k R_{i} + β_{S_{E F}} \times S_{E F_{i k}} + ε_{i k}$ for calibration source i on day k, with $α_B k R_{i} \sim N (0, σ_{B k R}^{2})$ , and $ε_{i k} \sim N (0, σ_{ε}^{2})$
3	Calibration source count rate	$y_S R_{i k} = μ_{S R} + α_S R_{i} + β_{S_{E F}} \times S_{E F_{i k}} + γ_{B k R_{i}} \times B k R_{i k} + ε_{i k}$ for calibration source i on day k, with $α_S R_{i} \sim N (0, σ_{S R}^{2})$ , $γ_{B k R_{i}} \sim N (0, σ_{γ_{B k R}}^{2})$ , and $ε_{i k} \sim N (0, σ_{ε}^{2})$

y_ CF_ik denotes the standardized calibration factor for calibration source i and day k.
μ CF is the mean, and α _CF_i is the random intercept representing a contribution specific to calibration source i.
$σ_{C F}^{2}$ is the variance of the zero-mean normal distribution of the random intercept.
$σ_{γ B k R}^{2}$ is the variance of the zero-mean normal distribution representing the background count rate contribution.
$σ_{ε}^{2}$ is the variance of the zero-mean normal distribution representing the residual error.
S_EFik is the standardized camera sensitivity factor for source i and day k.
Constancy_ik is the standardized radionuclide activity meter constancy value for source i and day k.
BkR_ik is the standardized background count rate for source i and day k.
y _BkR_ik denotes the standardized background count rate for calibration source i and day k, μ BkR is the mean value, and α _BkR_i is the subject-specific effect.
y _SR_ik denotes the standardized calibration source count rate for calibration source i and day k.
μ_SR is the mean, and α _SR_i is the random intercept representing a contribution specific to calibration source i.
$β_{S_{E F}}$ is the slope of fixed effect representing the camera assessed using the standardized sensitivity factor.
β_Constancy is the slope of the fixed effect representing the radionuclide activity meter assessed using the standardized constancy.
$γ_{{BkR}_{ik}}$ is the random effect of the standardized background count rate.
ε_ik is the residual error.

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