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Alternatives to evaluate the effect of Life Stage and Varieties on Cold Treatment: Confidence intervals and Odds- Ratio measure

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Objetive Harmonize procedures for comparing life stage tolerances and the effect of varieties / species. Answer the question: Which lethal dose levels will be used to determine MTLS?

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Dose-Response Models This model are used for bioassay results The aim is to describe the probability (proportion or percentage) of “sucess” (i.e. control, mortality, survival) as a function of the dose (exposure time, temperature, etc) Three commonly used models: Probit model Logit model Complementary log-log (clog-log) model

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Link function for models The link function is a transformation of the response in order to linearize the realtion between response (p) and dose (x) or logarithm of dose ModelLink functionModel ecuation Probit Logit Clog-log

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Model selection Selection can be done using any goodness of fit statistic: -2 log (maximum likelihood) Pearson χ 2 Pseudo R 2 AIC Selection should be performed in each different bioassay Replications should be including in the analysis (replications normally improve the fit)

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Probit model First use in binomial data was in 1934 (Bliss) For nearly 40 years employment tables and interpolations to convert percentages or proportions of controlled individuals, obtaining graphics where it was expected to have a more or less linear relationship between dose and probit Probit analysis can be done by eye, through hand calculations, or by using a statistical program (SAS,SPSS, R, S, S-Plus, EPA (IBM), TOXSTAT, ToxCalc, Stephan program). Most common outcome of a dose-response experiment in which probit analysis is used is the LC50/LD50/LT50 and its respective intervals.

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Estimated LD50 using Probit softwares

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Little et al, 1998. Environmental Toxicology and Risk Assessment

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Estimated LD50 confidence intervals using Probit softwares

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Origins of differences Control Treatment (Dose=0): included or not in the analysis. Mortality: corrected or not? Parameters estimation: least squares methods or maximum likelihood? Confidence intervals: how are calculate?

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Corrected mortality Data will be corrected if there is more than 10% mortality in the control (???). Corrected mortality:

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Confidence Intervals

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Egg StageFirst and Second Larvae StageThird Larvae Stage DoseSizeLiveDoseSizeLiveDoseSizeLive 028026404202690280262 128020634201344280253 22801414420755280220 3280645420327280127 42803174204102807 7 0104200122800 102800124200142800 1228001442000280242 14280004202564280237 02802633420595280232 12802084420447280128 2280150542037102801 3 60742025122800 4 31104200142800 7 01242000280242 1028001442004280239 12280004202595280236 1428003420767280138 0280263442074102803 1 208542054122800 2 134742011142800 3 65104200 428022124200 72800144200 102800 122800 142800

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Best Model Selection StageModelInterceptDoseAICLD50SE (LD50) Egg Probit-1.48760.704381.332.1120.0364 Logit-2.52611.201183.082.1030.0363 clog-log-1.96270.7213101.222.2120.0417 First and Second Larvae Stage Probit-0.630.3328160.091.8930.1531 Logit-1.35940.634171.992.1440.1279 clog-log-0.72590.2651154.71.3550.205 Third Larvae Stage Probit-4.89990.6963106.517.0370.0511 Logit-9.06641.2914109.677.0210.0492 clog-log-6.07440.7703146.447.4010.0573

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Logit model Logit is another form of transforming binomial data into linearity and is very similar to probit. In general, if response vs. dose data are not normally distributed, Finney suggests using the logit over the probit transformation (Finney, 1952).

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Odds Indicates how likely it is a success to occur in respect to not happen:

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Odds Ratio If the CI is under 1, there is less probability of success in (x+1) respect to x If the CI contains 1, there is no diference in the probability of success in (x+1) respect to x If the CI is above 1, there is more probability of success in (x+1) with respect to x

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Multiple Logistic Model If define “o” for eggs and “1” for larvae (first and second stage).

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Odds Ratio This can also be used for varieties!!!

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GRA 6020 Multivariate Statistics; The Linear Probability model and The Logit Model (Probit) Ulf H. Olsson Professor of Statistics.

GRA 6020 Multivariate Statistics; The Linear Probability model and The Logit Model (Probit) Ulf H. Olsson Professor of Statistics.

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