Descriptive statistical analyses of serial dilution data

Abstract

The serial dilution assay (for example, an in vitro antimicrobic susceptibility test or a serum antibody titer assay) is an important technique in biomedical research. The structure of the experiment forces grouping of the threshold concentrations into intervals. Statistical methods to analyse threshold concentrations from a batch of serial dilution assays should account for the grouping of the data. Many traditional subject area analyses, however, ignore the grouped nature of the data. This article discusses the discrepancy between the traditional subject area approach and the usual statistical approach for analysing such grouped data.

Handling Missing Data in Vaccine Clinical Trials for Immunogenicity and Safety Evaluation

“…Realizing that coarse data complicates the estimation and inference of immunological response, several authors have proposed different methods to address these concerns (Hamilton and Rinaldi, 1988;Moulton and Halsey, 1995). However, to date there has been no research comparing these methods for analyzing the serial dilution assay data where all three sets of coarse patterns (left censoring, right censoring, and interval censoring) coexist.…”

“…For example, serial dilution assays (Hamilton and Rinaldi, 1988), which are widely used in the measurement of antibody responses, usually report the antibody titers in terms of dilution factors. Let X be the results generated from a serial dilution assay with dilution levels d 1 d 2 d K , then the imprecise antibody titer can be categorized in the following three ways: (1) When Downloaded by [University of Tasmania] at 21:46 13 October 2014 the actual antibody concentration in the serum is very low such that no antibody response is detected at any dilution levels, then the antibody titer is left censored at the lower dilution limit (LDL) d 1 and is reported as "<d 1 "; (2) when the actual antibody concentration is very high such that antibody responses are detected at all dilution levels, then the antibody titer is right censored at the upper dilution limit (UDL) d K and is often reported as "≥d K "; and (3) when the highest dilution level with detectable antibody is achieved among dilution levels d 1 d K , then the antibody titer is reported as d j 1 ≤ j < K , even though the true antibody titer lies between d j and d j+1 .…”

Bayesian Analysis of Serial Dilution Assays

“…Recent formulations of dilution assays appear in Finney (1976), Hamilton and Rinaldi (1988), Racine-Poon, Weihs, and Smith (1991), Higgins et al (1998), and Lee and Whitmore (1999). Giltinan and Davidian (1994) and Davidian and Giltinan (1995) present a simulation study suggesting potential improvements using Bayesian methods, and Dellaportas and Stephens (1995) describe Bayesian computations for a model with a single unknown concentration.…”

“…It is hardly surprising that a Bayesian or likelihood approach works better than an inversion procedure that ignores estimation uncertainty. However, previous statistical treatments of serial dilution assay (see Hamilton and Rinaldi, 1988;Racine-Poon et al, 1991;Higgins et al, 1998;Lee and Whitmore, 1999) have focused on the estimation of the calibration curve or inference from discrete data rather than the problem considered here, of inference for several unknown concentrations from continuous assays. Dellaportas and Stephens (1995) consider a fully Bayesian approach but with a slightly simpler model in a nonhierarchical setting.…”

A Simple and Powerful Method for the Estimation of Intervention Effects on Serological Endpoints Using Paired Interval-Censored Data

“…Though such practice can avoid the difficulty in handling interval censoring, it causes other problems in the estimation and inference (Heitjan and Rubin, 1991;Helsel, 2010). Alternative approaches to handle interval censoring at a single time point have been investigated and discussed (Turnbull, 1976;Hamilton and Rinaldi, 1988;Heitjan, 1989;Helsel, 2005;Nauta, 2006). They are useful techniques for handling interval censoring in laboratory assays, but they are not directly relevant to the problem of interval censoring at two time points.…”