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A Bayesian Regression Model for Plasma Clearance

¹ University of Alabama Hospital and VA Medical Center, Birmingham, Alabama
² Emory University, Atlanta, Georgia

Nonlinear Bayesian regression permits curve fitting to a group of subjects simultaneously rather than individually. We evaluated this approach for interpreting plasma clearance curves with the goal of reducing curve-fitting failures and dealing objectively with problem datasets that may arise in clinical settings. Methods: ^99mTc-Diethylenetriaminepentaacetic acid plasma clearance curves from 79 subjects were analyzed. The data typically comprised 7–9 samples obtained from 5–10 to 180–240 min after injection. A 2-compartment model was fitted by Bayesian regression to yield compartmental hyperparameters V1, L21, and L12 corresponding to the volume of the compartment into which tracer was injected and the transfer rates from compartment 1 to compartment 2 and from compartment 2 to compartment 1, respectively. This also yielded a clearance estimate for each subject. Results: Estimated hyperparameters were V1 = 8.9 L, L21 = 0.026 min^-1, and L12 = 0.040 min^-1. Conventional methods led to fitting failures in 2 of the 79 subjects but there were no failures with the Bayesian method. The hyperparameters were used to calculate the glomerular filtration rate for each subject from a single plasma sample with a root-mean-square error of 7.3 mL/min, which was not significantly different from the widely used Christensen—Groth formula. Conclusion: Fewer fitting failures were encountered than with conventional methods, offering an objective means of dealing with problem data. This conceptually simple model can be used directly to calculate clearance from a single plasma sample. It requires only the 3 parameters described above, whereas the Christensen—Groth method requires 6 parameters.

Key Words: kidney function • glomerular filtration rate • renal clearance • plasma clearance

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