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# Accession Number:

## ADA200203

# Title:

## Variance Functions and the Minimum Detectable Concentration in Assays

# Descriptive Note:

## Technical rept. no. 10, Aug 1987-Aug 1988

# Corporate Author:

## TEXAS A AND M UNIV COLLEGE STATION

# Report Date:

## 1988-08-01

# Pagination or Media Count:

##
28.0

# Abstract:

## Assay data are often fitted by a nonlinear regression model incorporating heterogeneity of variance. 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 resonable size, how one estimates the parameter Theta does not greatly affect how well one estimates the mean regression function. An additional component of assay analysis is the estimation of auxillary constructs such as the minimum detectable concentration, for which many definitions exist we focus on one such definition. The minimum detectable concentration depends both on Theta and the mean regression function. We compare standard methods of estimating the parameter Theta. When duplicate counts are taken at each concentration, the first method is only 20 efficient asymptotically in comparison to the fourth for normal data, and in an example the resulting estimate of the minimum detectable concentration is asymptotically 3.7 times more variable. Less dramatic results obtain for the second and third estimators compared to the fourth. Simulation results and an example support the asymptotic theory. The results have implications in applications other than the assay problem in which heterogeneity of variance and issues of calibration arise.

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#