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International Plant Protection Convention 04_TPPT_2016_Jul Examples of estimated numbers of treated pests using both direct and modified methods Agenda item: 4.2 ESTIMATING TREATED NUMBERS FROM CONTROL EMERGENCE (Prepared by Mr Mike Ormsby) BACKGROUND: [1] This paper was last discussed at the Technical Panel on Phytosanitary Treatments (TPPT) in March 2016 virtual meeting1. The TPPT pointed out that more discussion and examples should be given on how the use of this formula could affect the estimated number. The TPPT is invited to: (1) (2) (3) Review this document and provide comments; Agree with the proposed formula; Consequently, if agreement is reached, revise the “Instructions to assist NPPOs and RPPOs to assist in proper and complete treatment submissions” section 4 on “General considerations when calculating the level of efficacy achieved by a treatment schedule”. The proposed text is presented as attachment 1 of this document (black text)2. DISCUSSION: [2] The statistical issue associated with estimating treated or exposed populations from control numbers was recognised as long ago as 19493, in that “When the number of organisms treated in a dosage-mortality study is not known exactly, but is estimated from a sample, weighting must be modified.” [3] When the population of treated pests is estimated from control pest populations, the estimation must be based on a statistical analysis of the controls. Where possible, control data should not be grouped together, but should be recorded for each individual test commodity or target pest. [4] Researchers need to apply the same statistical rigour to control data as they do to treatment data. Where the infestation rate for each regulated article in the control is known, the estimated treated regulated article infestation rate would be: [5] Average per treated regulated article = µ - (STD × 1.645) [6] 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: [7] Average per treated regulated article = µ - (STD × (1+1/r)) [8] Note: r is equal to the number of control replicates used to estimate the mean (µ) and standard deviation (STD) of the control means. [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. 1 TPPT March 2016 virtual meeting report: https://www.ippc.int/static/media/files/publication/en/2016/05/Report_TPPT_2016_Mar_2016-05-03.pdf 2 Please refer to document 03_TPPT_2016_Mar of the TPPT March 2016 virtual meeting and to the meeting report. 3 Wadley F. M. (1949) Dosage-mortality cor.elation with number treated estimated from a parallel sample. Annals of Applied Biology, 36: 196–202. International Plant Protection Convention Page 1 of 5 Examples of estimated numbers of treated pests using both direct and modified methods 04_TPPT_2016_Jul (4.2) - We need an estimate of the common variance so let s2 be the pooled variance of the transformed counts about their respective means. 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). - The standard error4 of this is equal to 𝐒𝐄 × √(𝐦 + 𝐫 ). - 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 𝟏 ̅) ± (𝐒𝐄 × √(𝟏 + )). samples (𝒙 𝐫 - As we want the most conservative estimate (to have 95% confidence that we do not have any false 𝟏 ̅) − ( 𝐒𝐄 × √(𝟏 + )). negatives) we use the estimate (𝒙 𝐫 [10] The following are three examples of published treatment research that estimated treated numbers from control emergence. The examples provide a comparison of the estimated treated numbers using direct calculations from control data verses using the statistical adjustment described above. [11] Example 1: Santaballa E., Laborda R., Cerdá M. (2009) Quarantine cold treatment against Ceratitis capitata (Wiedemann) (Diptera: Tephritidae) to export clementine mandarins to Japan. Bol. San. Veg. Plagas 35: 501-512 Mandarins 2°C/16 days Confirmatory Controls - MedFly TREATMENT UNIT (r) No. FRUIT / TRAY No. Pupae 1st Count TOTAL # PUPAE AVERAGE / FRUIT 1 294 4527 4527 15.40 2 286 4118 4118 14.40 3 302 4167 4167 13.80 Total 882 12,812 12,812 14.53 14.53 ± 0.93 = 13.60 0 0 Mean (± SE x (SQR(1+1/r)) = Number Tested Fruit = 2,202 Estimated Number of Treated FF (95% confidence) = 29,940 Estimated Number of Treated FF (unadjusted) = 31,995 4 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 Page 2 of 5 International Plant Protection Convention 04_TPPT_2016_Jul (4.2) Examples of estimated numbers of treated pests using both direct and modified methods [12] Example 2: De Lima, C.P.F., Jessup, A.J., Cruickshank, L., Walsh, C.J. & Mansfield, E.R. (2007) Cold disinfestation of citrus (Citrus spp.) for Mediterranean fruit fly (Ceratitis capitata) and Queensland fruit fly (Bactrocera tryoni) (Diptera: Tephritidae). New Zealand Journal of Crop and Horticultural Science, 35: 39–50. Valencia orange 2°C Confirmatory Controls No. Pupae TREATMENT UNIT (r) No. FRUIT / TRAY 1st sieve 2/5/00 1 1200 2 TOTAL # PUPAE AVERAGE/ FRUIT 45,918 45,918 38.27 1200 47,724 47,724 39.77 3 1200 47,799 47,799 39.83 Total 3600 141,441 141,441 39.3 39.3 ± 1.0 = 38.3 2nd sieve 9/5/00 0 Mean (± SE * SQR(1+1/r)) = Number Tested Fruit = Valencia orange Estimated Number of Treated FF (95% confidence) = 137,752 Estimated Number of Treated FF (unadjusted) = 141,441 3°C Confirmatory Controls No. Pupae TREATMENT UNIT (r) No. FRUIT / TRAY 1st sieve 2/5/00 1 1200 2 TOTAL # PUPAE AVERAGE/ FRUIT 50,283 50,283 41.90 1200 44,943 44,943 37.45 3 1200 47,358 47,358 39.47 Total 3600 142,584 142,584 39.6 39.6 ± 2.6 = 37.0 2nd sieve 9/5/00 0 Mean (± SE * SQR(1+1/r)) = Number Tested Fruit = Naval orange 3,600 Estimated Number of Treated FF (95% confidence) = 133,321 Estimated Number of Treated FF (unadjusted) = 142,584 2°C Confirmatory Controls No. Pupae TREATMENT UNIT (r) No. FRUIT / TRAY 1st sieve 2/5/00 1 1200 2 TOTAL # PUPAE AVERAGE/ FRUIT 54,012 54,012 45.01 1200 54,327 54,327 45.27 3 1200 57,555 57,555 47.96 Total 3600 165,894 165,894 46.1 46.1 ± 1.9 = 44.2 2nd sieve 9/5/00 0 Mean (± SE * SQR(1+1/r)) = Number Tested Fruit = [13] 3,600 3,600 Estimated Number of Treated FF (95% confidence) = 159,101 Estimated Number of Treated FF (unadjusted) = 165,894 Example 3: Summer-fruit data (Australian report) Rep1 1°C International Plant Protection Convention Confirmatory Controls - Qfly Page 3 of 5 Examples of estimated numbers of treated pests using both direct and modified methods 04_TPPT_2016_Jul (4.2) No. Pupae TREATMENT UNIT No. FRUIT / TRAY 1st sieve 09/04/07 2nd sieve 16/04/07 3rd sieve 23/04/07 1 15 1279 5 2 15 570 3 15 4 Totals TOTAL # PUPAE AVERAGE / FRUIT 0 1284 85.60 41 0 611 40.73 1519 86 0 1605 107.00 15 1670 143 0 1813 120.87 60 5,038 275 0 5,313 88.55 39.16 = 49.39 Average (± SE x (SQR(1+1/r)) = 88.55 ± Number Tested Fruit = Rep2 1°C TREATMENT UNIT No.FRUIT / TRAY 1 274 Estimated Number of Treated FF (95% confidence) = 13,534 Estimated Number of Treated FF (unadjusted) = 24,262 Confirmatory Controls - Qfly No. Pupae TOTAL # PUPAE AVERAGE / FRUIT 0 1146 114.60 132 0 1007 100.70 945 128 0 1073 107.30 10 776 114 0 890 89.00 5 10 954 346 0 1300 130.00 6 10 1198 103 0 1301 130.10 Total 60 5681 1036 0 6717 111.95 17.66 = 94.29 1st sieve 23/04/07 2nd sieve 30/04/07 3rd sieve 07/05/07 10 933 213 2 10 875 3 10 4 Average (± SE x (SQR(1+1/r)) = 111.95 ± Number Tested Fruit = Combined Rep1 and Rep2 Estimated Number of Treated FF (95% confidence) = 28,286 Estimated Number of Treated FF (unadjusted) = 33,585 Confirmatory Controls – Qfly (1°C) Total Number of Tested Fruit = Page 4 of 5 300 574 Total Estimated Number of Treated FF (95% confidence) = 41,820 Total Estimated Number of Treated FF (unadjusted) = 57,847 International Plant Protection Convention ATTACHMENT 1 04_TPPT_2016_Jul (4.2) ATTACHMENT 1: INSTRUCTIONS TO ASSIST NPPOS AND RPPOS IN PROPER AND COMPLETE TREATMENT SUBMISSIONS [14] 4. General considerations when calculating the level of efficacy achieved by a treatment schedule The panel has recommended a number of principles that should be apply when calculating the efficacy achieved by a treatment schedule at the 95% confidence level, based on the total number of target pests treated. Further information on the calculation of the level of efficacy is provided in a publication by Couey and Chew (1986). These principles include: - Percentage mortality of treated target pests should be adjusted for mortality in the control by the following formula: Ya = 100% - [(X – Y)/X](100%), where Ya is the adjusted percentage surviving in the treated cohort, X is the percentage surviving in the control and Y is the percentage surviving in the treated cohort (Abbott 1925). - Greater than expected response levels in controls may indicate a target pest population under stress that may be more susceptible to the treatment than a natural population. If control response is high, evidence should be provided that either indicates pest susceptibility to the treatment is no greater than normal populations or that high control response reflects normal conditions; - Sample sizes and repetitions should be sufficient to account both for natural variation and achieve significant regressions when extrapolating treatment efficacy. A small number of treatment repetitions can, on analysis, result in statistical errors giving meaningless conclusions (if the SD at 95% is greater than the mean, the lower (worst case) result may be a negative dose e.g. 10 ± 12 gives a range from -2 to 22). - When the population of treated pests is estimated from control pest populations, the estimation must be based on a statistical analysis of the controls, control data should not be grouped together, but should be recorded for each individual test commodity or target pest. Pseudo-replication5 should be avoided or minimized, as much as possible; - 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: Average per treated regulated article = μ - (STD × 1.645) - 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: ̅ − (SE × √𝟏 + (𝟏 ÷ 𝒓)) Average per treated regulated article = 𝒙 ̅) of the controls Note: r is equal to the number of control replicates used to estimate the mean (𝒙 and the standard error (SE) of the mean. 5 Pseudo-replication is used to test for treatment effects with data from experiments where either treatments are not replicated (though samples may be) or replicates are not statistically independent. The error described by this term arises when treatments are assigned to units that are sub-sampled and the treatment F-ratio in an analysis of variance (ANOVA) table is formed with respect to the residual mean square rather than with respect to the among unit mean square. The F-ratio relative to the within unit mean square is vulnerable to the confounding of treatment and unit effects, especially when unit number is small (e.g. four tank units, two tanks treated, two not treated, several subsamples per tank). The error is avoided by forming the F-ratio relative to the among unit mean square in the ANOVA table (tank MS in the example above). Pseudo-replication, as originally defined, is a special case of inadequate specification of random factors where both random and fixed factors are present: http://en.wikipedia.org/wiki/Pseudoreplication International Plant Protection Convention Page 5 of 5