Calculating Confidence, Uncertainty, and Numbers of Samples When Using Statistical Sampling Approaches to Characterize and Clear Contaminated Areas

Abstract

Executive SummaryThis report discusses selected methods, formulas, and inputs needed to make characterization and clearance decisions for Bacillus anthracis-contaminated and uncontaminated (or decontaminated) areas using a statistical sampling approach. Specifically, the report includes the methods and formulas for calculating the• number of samples required to achieve a specified confidence in characterization and clearance decisions• confidence in making characterization and clearance decisions for a specified number of samples for two common, statistically based, environmental sampling approaches. In particular, the report addresses an issue raised by the Government Accountability Office by providing methods and formulas to calculate the confidence that a decision area is uncontaminated (or successfully decontaminated) if all samples collected according to a statistical sampling approach have negative results. Key to addressing this topic is the probability that an individual sample result is a false negative, which is commonly referred to as the false negative rate (FNR).The two statistical sampling approaches currently discussed in this report are 1) hotspot sampling to detect small isolated contaminated locations during the characterization phase, and 2) combined judgment and random (CJR) sampling during the characterization or clearance phase. Typically, if contamination is widely distributed in a decision area, it will be detectable via judgment sampling during the characterization phrase. Hotspot sampling is appropriate for characterization situations where contamination is not widely distributed and may not be detected by judgment sampling. CJR sampling is appropriate during the characterization or clearance phase when it is desired to augment judgment samples with statistical (random) samples. Only these two statistical sampling approaches are addressed in this report because they are the only two approaches mentioned in a sampling reference document being developed by the Validated Sampling Plan Working Group (VSPWG). It was by agreement with the sponsor of this work (the Department of Homeland Security) that this report be limited to those two statistical sampling approaches for that reason. Other approaches which could reduce the number of samples required are being studied and may be included in future evaluations.The hotspot and CJR statistical sampling approaches are discussed in the report for four situations:1. qualitative data (detect and non-detect) when the FNR = 0 or when using statistical sampling methods that account for FNR > 0 2. qualitative data when the FNR > 0 but statistical sampling methods are used that assume the FNR = 0 3. quantitative data (e.g., contaminant concentrations expressed as CFU/cm 2 ) when the FNR = 0 or when using statistical sampling methods that account for FNR > 0 4. quantitative data when the FNR > 0 but statistical sampling methods are used that assume the FNR = 0.For Situation 2, the hotspot sampling approach provides for stating with Z% confidence that a ho...

False-negative rate, limit of detection and recovery efficiency performance of a validated macrofoam-swab sampling method for low surface concentrations ofBacillus anthracisSterne andBacillus atrophaeusspores

“…The FNR of a sampling and analysis method can have a significant impact on health‐risk decisions. One solution that compensates for FNR > 0 is to collect more samples, which increases the probability of detecting the contamination (Piepel et al ). Other options have been discussed by Amidan et al .…”

Recovery Efficiency, False Negative Rate, and Limit of Detection Performance of a Validated Macrofoam-Swab Sampling Method with Low Surface Concentrations of Two Bacillus anthracis Surrogates

“…The FNR estimates can in turn be used in responding to a future contamination event. For example, FNR estimates are required as inputs to formulas for calculating the number of samples required (with a given statistical sampling approach) to obtain the desired confidence in characterization and clearance decisions (Piepel et al 2013). Also, after samples are collected and analyzed following a contamination event, FNR values are needed as inputs to formulas for calculating the statistical confidence in characterization and clearance decisions (Piepel et al 2013).…”

Experimental Design for a Macrofoam-Swab Study Relating the Recovery Efficiency and False Negative Rate to Low Concentrations of Two Bacillus anthracis Surrogates on Four Surface Materials

“…The FNR equations will also serve as inputs to formulas for calculating the 1) numbers of samples required to make characterization and clearance decisions with specified levels of confidence and 2) confidence in characterization and clearance decisions for specific sampling plans implemented in BA contamination events. The work to develop these formulas is part of another task in the PNNL project supporting the VSPWG, which is being documented in separate reports (the first of which is Piepel et al 2013). The experimental design for the swab study discussed in this report will generate key data on the FNR for a single swab sample.…”

“…In actual contamination scenarios, before or after decontamination, concentrations of BA necessary to cause illness or symptoms may be low enough that the FNR > 0. Hence, for low concentrations, estimates of RE, FNR, and LOD for single samples taken under various sampling conditions are needed as inputs to calculate the confidence in detection or clearance decisions based on sampling and analysis 1.2 results after a contamination event (Piepel et al 2013). The macrofoam-swab study generated data to support developing FNR-concentration equations for combinations of the two surrogates, four surface materials, and two analytical methods.…”