# Estimating Upper Centile Pesticide Concentrations and Sample Size Requirement

Wenlin Chen, Syngenta Crop Protection, LLC Paul Mosquin, RTI International Roy W. Whitmore, RTI International Paul Hendley, Syngenta Crop Protection, LLC

# Introduction

 

# Use of available monitoring data to estimate potential pesticide peak concentrations or very high centiles (e.g. 99th) provides a useful reality check for comparison with exposure model output in regulatory assessment.

 

# Technical challenges:

 

# Certain data sets have relatively low annual sample frequency across many years for many sites.

 

# Variably stratified monitoring (i.e. sampling timing is generally targeted and not simple random sampling) due to seasonal residue patterns and other variables.

2

# Introduction

 

# Objective is to

 

# propose a survey sampling approach to account for complexities in pesticide monitoring datasets (e.g. large sample sizes but variable sampling frequency), and

 

# apply the approach to estimate the upper centiles of atrazine historical monitoring data from surface water Community Water Systems (CWS) as a case study.

3

# Outline

 

# Description of atrazine historical data sets

 

# Methods

 

# Analysis weights

 

# Effective sample size requirements

 

# Centile estimates and confidence intervals (CI’s)

 

# Simulation study

 

# Results

 

# Discussion and conclusions

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# Description of Data Sets

 

# National Safe Drinking Water Act (SDWA) monitoring data set

 

# Nationwide program

 

# Data for case study between 1993 and 2008

 

# 50,081 atrazine measurements for finished (drinking) water from 4404 surface water CWS

 

# Samples were typically scheduled quarterly

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# Description of Data Sets

 

# Regional (Midwest corn belt) high sampling frequency data set (VMP/AMP)

 

# Combined data of Syngenta Voluntary Monitoring Program (VMP),1993

- 2002; and Atrazine Monitoring Program (AMP), 2003

- 2009 used for the case study

 

## Primarily Midwest Corn belt. CWS selection based on atrazine SDWA monitoring history;

 

## Weekly sampling typically from May through July (VMP) and April through July (AMP); biweekly other months;

 

## Finished and raw (source) water samples from more than 130 CWS with total over 46,000 measurements.

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### Method Evaluation by Simulation Data sets and

represented statistic (sub) population of data Analysis weights Effective sample size Centile estimates and C.I.s 

# Methods

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# Methods

 

# Analysis weights

 

# Number of days an individual sample “represents”.

 

## Time

- interval weights One half the time to the previous measurement and one half the time to the next measurement.

 

## Probability weights
Inverse of a known and non

- zero probability a day is sampled.

 

## Stratified systematic sampling Constant number of days between sampling events within a
stratum.

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# Methods

 

# Sample size requirements (For details: Mosquin et al., J. Environ. Qual., 2012 )

 

## Tolerance intervals (Hahn and Meeker, 1991)

 

## Relative Standard Error (RSE)

 

## Woodruff interval skewness criterion

 

# Effective sample size It is a sample size of a data set with monitoring design that is equivalent to simple random sampling. It equals the sample size of non simple random sampling discounted (i.e. divided) by a sampling design effect.

 

# Centile estimates and Woodruff confidence intervals

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# Methods

 

# Simulation to evaluate method performance on less frequent monitoring

 

# “True” monitoring data populations (computer generated/not true monitoring data)

 

## Artificial 50 or 500 site

- years

 

## 365

- d values per site

- year generated as log

- normal random variables with seasonality.

 

## Two annual mean scenarios: 1) constant; 2) normally variable.

 

# 4 samples per site

- year, 10,000 replications

 

# 1 random sample each in Jan

- Apr, May

- Jun, Jul

Aug, and Sep

- Dec.

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# Methods

# Results

 

# Requisite sample size by tolerance interval method

Smallest effective sample size for the probability of containing the 100q

- th centile with a confidence level of 100(1

- ) (Ref.: Hahn and Meeker, 1991)

Confidence Level Centile ( )

90.0% 95.0% 97.5% 99.0% 99.9%

80.0% 16 32 64 161 1609
90.0% 22 45 91 230 2302
95.0% 29 59 119 299 2995
97.5% 36 72 146 368 3688
99.0% 44 90 182 459 4603
99.9% 66 135 273 688 6905

12 For example, with effective sample size of 59, 299, 2995, there is 95% confidence that the existing monitored data contain the 95 th , 99 th and 99.9 th centile concentrations, respectively.

# Results

 

# Requisite sample size by Relative Standard Error

Smallest effective sample size such that RSE of the estimate of a population proportion will be no more than a pre

- specified upper bound. 10% RSE= accurate estimates; 30% RSE = moderately precise estimates, and RSE of 50% or more = minimal precision.

RSE upper

bound, True Population Percentage

10.0% 5.0% 2.5% 1.0% 0.1%

50% 37 77 157 397 3997
40% 57 119 244 619 6244
30% 101 212 434 1101 11101
20% 226 476 976 2476 24976
10% 901 1901 3901 9901 99901

13 For example, at moderate precision (30% RSE), the required smallest effective sample size is 212, 1101, and 11101, for the 95 th , 99 th , and 99.9 th centile estimates, respectively. i.e., 99 th centile

# Results

 

# Requisite sample size by Woodruff interval skewness criterion

Smallest effective sample size according to skewness of the binomial distribution used in the Woodruff confidence interval determination. Under simple random sampling, two

- sided confidence intervals obtained for the Woodruff method are expected to have reasonable coverage provided that the binomial distribution associated with the centile does not have excessive skew.

14 For example, an effective sample size of 69, 389, and 3989 would provide a good coverage of the true population of 95 th , 99 th , and the 99.9 th centiles
, respectively, by the Woodruff confidence intervals.

# Results

 

# Simulation study

 

## Coverage Percent intervals containing the true target quantity

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### True value /2 zone /2 zone 10,000 simulations and CI’s

# Results

 

# Simulation study

 

### Probability weights: estimates very close to true value and CI coverage around 95% except the 99.9 th 

### centile of 50 site

- year set.

 

### Time

- interval weights: estimates slightly larger than true value and one

sided coverage close to 95% or better except the 99.9 th 

### centile of 50 site

year set.

Number Site

- Years Centile True Average of

Population Probability Weights Time

- interval Weights

Estimated

Centile Coverage Two

sided (%) Estimated Centile Coverage
Two

- sided (%) Coverage One

- sided (%)

50 (total 200 samples) 0.90 1.62 1.58 96 1.80 89 100
0.95 2.44 2.39 97 2.68 92 100
0.99 5.09 4.92 92 5.40 90 93
0.999 10.01 9.24 24 9.40 24 24
500 (total 2000 samples) 0.90 1.62 1.59 94 1.81 30 100
0.95 2.44 2.41 95 2.71 52 100
0.99 5.09 5.19 96 5.73 83 100
0.999 10.01 11.60 92 12.52 90 93

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# Results

 

# Atrazine data sets

 

# Unequal weighting effects and estimated effective sample sizes

Dataset Water Sample

Type Number of CWS Years Number of Atrazine
Measurements Design
Effect Effective Sample Size

SDWA Finished 4,404 1993

- 2008 50,081 4.11 12,166

VMP/AMP Finished 220 1993

- 2009 48,532 2.62 18,538

Raw 228 1993

- 2009 46,491 2.76 16,828

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# Results

 

# Estimated centiles and their Woodruff confidence intervals for raw and finished water atrazine measurements (ppb).

18 * Numbers in parentheses are one

- sided 95% confidence interval.

# Discussion and Conclusions

 

## Atrazine SDWA, and VMP/AMP datasets have more than140,000 measurements in over 4400 CWS during the period 1993 to 2009, on which this case study is based.

 

## Based on the Woodruff criterion method, minimum effective sample sizes to estimate confidence intervals for the 95th, 99th, and 99.9th centiles were 69, 389, and 3989, respectively. A simulation exercise showed these numbers to be conservative in the determined sample sizes.

 

## With effective sample sizes greater than values shown in the tolerance interval table, it can be stated, for example, that “there is 95% confidence that the existing monitored data include the 99 th 

## centile analyte concentration”.

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# Discussion and Conclusions

 

## Combined with requisite sample sizes, the proposed survey sampling method is useful for estimating quantities from monitoring programs where there is a large amount of data but limited data per site

- year to estimate upper centiles of interest at a site

- year level.

 

## Existing monitoring data from a range of sources (e.g. government, company and academia), assuming the underlining data population is understood, can together be used to greatly improve the understanding of the likely distribution of residues in water and these estimates can provide valuable reality checks for model output in regulatory assessment.

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# End of slides

Thank you!