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International Plant Protection Convention
Estimating Treated Numbers from Control Emergence
04_TPPT_2016_Mar
Agenda item: 04
ESTIMATING TREATED NUMBERS FROM CONTROL EMERGENCE
(Prepared by Mr Mike Ormsby)
BACKGROUND
This paper was first submitted to the Technical Panel on Phytosanitary Treatments (TPPT) in September
20151 as a discussion paper to clarify the validity of this method of estimating efficacy from research
results.
A supporting document (05_TPPT_2016_Mar)2 is provided.
The TPPT is invited to:
(1)
review this paper and provide comments
(2)
agree whether to include or not in the TPPT working procedures
Introduction
[1]
This paper has been prepared to explain the statistical basis for the use of the formulas in calculating
treatment efficacy from the results of research that estimated treated numbers form control emergence.
Proposal
[2]
That the following formula be used to estimate treatment efficacy under the specified circumstances:
[3]
Where the infestation rate for each regulated article in the control is known but the infestation rate in
treated articles is unknown, the estimated treated article infestation rate would be:
[4]
Conservative average per treated regulated article = 𝝁 − (𝐒𝐓𝐃 × 𝟏. 𝟔𝟒𝟓)
[5]
Where the control infestation rate is based on the mean of grouped commodities, as the number of
controls increases so does the level of confidence in the estimation of the population mean. A suitable
formula for estimating the average number of exposed pests per treated regulated article would therefore
be:
[6]
̅ − (SE × √(𝟏 + ))
Conservative average per treated regulated article = 𝒙
𝐫
[7]
̅) of the controls and the
Note: r is equal to the number of control replicates used to estimate the mean (𝒙
standard error (SE) of the mean.
𝟏
Background
[8]
When the population of treated pests is estimated from control pest populations, the estimation must be
based on a statistical analysis of the controls, and the control data should not be grouped together but
should be recorded for each individual test commodity or target pest.
[9]
The formula for determining the average per treated regulated article based on the mean of grouped
control commodities has been derived as follows:
- Let Ti be the transformed counts for the treated portions and Cj be the transformed counts for the
control portions and let Ta and Ca be the averages of these.
[10]
1
Link to TPPT September 2015 meeting report: https://www.ippc.int/en/publications/81833/
05_TPPT_2016_Mar: McBride et al., 2014. Assessing environmentally significant effects: a better strength-ofevidence than a single P value?
2
International Plant Protection Convention
Page 1 of 2
International Plant Protection Convention
Estimating Treated Numbers from Control Emergence
04_TPPT_2016_Mar
Agenda item: 04
[11]
- We need an estimate of the common variance so let s2 be the pooled variance of the transformed
counts about their respective means.
[12]
- The common variance (s2) is obtained from an analysis of variance of the transformed counts
𝟏
𝟏
or 𝐬𝟐 × (𝐦 + 𝐫 ) where m equals the number of treated samples (T) and r equals the number of
control samples (C).
[13]
- The standard error3 of this is equal to 𝐒𝐄 × √(𝐦 + 𝐫 ).
[14]
- In the case where there is just 1 treated sample (m=1), we get a standard error of
𝟏
𝟏
𝟏
𝐒𝐄 × √(𝟏 + )
𝐫
- The average per treated regulated article can therefore be estimated as the mean of the control
[15]
𝟏
̅) ± (𝐒𝐄 × √(𝟏 + )).
samples (𝒙
𝐫
- As we want the most conservative estimate (to have 95% confidence that we do not have any
[16]
𝟏
̅) − ( 𝐒𝐄 × √(𝟏 + )).
false negatives) we use the estimate (𝒙
𝐫
3
McBride G., Cole R G., Westbrooke I. & Jowett I. (2014) Assessing environmentally significant effects: a better
strength-of-evidence than a single P value? Environ Monit Assess 186: 2729–2740
International Plant Protection Convention
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