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Activity Number:
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300
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Type:
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Contributed
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Date/Time:
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Tuesday, August 5, 2003 : 2:00 PM to 3:50 PM
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Sponsor:
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Biometrics Section
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| Abstract - #300346 |
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Title:
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Bayesian Analysis of Serial Dilution Assays
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Author(s):
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Michael Shnaidman*+ and Andrew Gelman
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Companies:
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Columbia University and Columbia University
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Address:
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6 York Dr., Princeton, NJ, 08540-7939,
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Keywords:
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assay ; Bayesian inference ; serial dilution ; detection limit ; measurement error models ; weighted average
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Abstract:
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In a serial dilution assay the concentration of a compound is estimated by combining measurements of several different dilutions of an unknown sample. The relation between concentration and measurement is nonlinear and heteroscedastic, and so it is not appropriate to weight these measurements equally. In the standard existing approach for analysis of these data, a large proportion of the measurements are discarded as being above or below detection limits. We present a Bayesian method for jointly estimating the response curve and the unknown concentrations using all the data. Compared to the existing method, our estimates have much lower standard errors and give estimates even when all the measurements are outside the "detection limits." We evaluate our method empirically using laboratory data on cockroach allergens measured in dust samples. Our estimates are much more accurate than those obtained using the usual approach. In addition, we developed a method for determining the "effective weight" attached to each measurement. The effective weight can give insight into the information conveyed by each data point and suggests improvements in design of serial dilution experiments.
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