Variance functions and the minimum detectable concentration in assays. Technical report, August 1985-August 1986

Technical Report · Tue Jul 01 04:00:00 EDT 1986

OSTI ID:7030092

Carroll, R J; Davidian, M; Smith, W

Assay data are often fit by a nonlinear regression model incorporating heterogeneity of variance, as ion radioimmunoassay, for example. Typically, the standard deviation of the response is taken to be proportional to a power theta of the mean. There is considerable empirical evidence suggesting that, for assays of a reasonable size, how one estimates the parameter theta does not greatly affect how well one estimates the the mean regression function. An additional component of assay analysis is the estimation of auxiliary constructs such as the minimum detectable concentration, for which many definitions exist; focus here is on one such definition. The minimum detectable concentration depends both on theta and the mean regression function. Three standard methods of estimating the parameter theta are compared. When duplicate counts are taken at each concentration, the first method is only 20% efficient asymptotically in comparison to the third, and the resulting estimate of the minimum detectable concentration is asymptotically 3.3 times more variable for first than the third. Less-dramatic results obtain for the second estimator compared to the third; this estimator is still not efficient, however. Simulation results and an example are supportive of the asymptotic theory.

• Research Organization: North Carolina Univ. at Chapel Hill (USA). Inst. of Statistics
• OSTI ID: 7030092
• Report Number(s): AD-A-174983/7/XAB; MIMEO-SER-1701
• Country of Publication: United States
• Language: English

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62 RADIOLOGY AND NUCLEAR MEDICINE
ACCURACY
BIOASSAY
CHARGED PARTICLES
FUNCTIONS
IMMUNOASSAY
IMMUNOLOGY
IONS
ISOTOPE APPLICATIONS
MATHEMATICAL MODELS
MATHEMATICS
RADIOASSAY
RADIOIMMUNOASSAY
RADIOIMMUNOLOGY
REGRESSION ANALYSIS
SIMULATION
STANDARDIZATION
STATISTICS
TRACER TECHNIQUES
VARIATIONS