From: Manibusan, Mary

To: Matten, Sharlene Subject: Fw: Answers to the clarification questions from the SAP (Tier 2)

Date: Wednesday, June 26, 2013 2:40:25 PM

Mary Manibusan, Director (202) 564-2827

From: Flynn, Kevin

Sent: Wednesday, June 26, 2013 2:37:36 PM

To: Manibusan, Mary Subject: Answers to the clarification questions from the SAP (Tier 2)

The responses to the clarification questions from the SAP from the statistician involved in both the MMT/MRT and LAGDA data analysis are below. I believe his responses answer the questions from the SAP. For further clarity and context, the LAGDA data was indeed analyzed as understood by the

SAP. Therefore, the response below is mostly germane to the MMT. As a point of clarification, the SAS code was not altered in the re-analysis, rather the data from the LAGDA was properly formated to reflect weighted replicate means that were then inputted into StatCHARRMS. On the other hand, the MMT data was inputted directly into a separate module of StatCHARRMS named somewhat confusingly "Repeated Measures" (see Response to question 2A below) and the StatCHARRMS program analyzed the data as described below.

This afternoon, Drs. Mary Christman and Dallas Johnson, asked EPA to clarify the 1-way ANOVA and the repeated measures 2-way ANOVAs as used in the Medaka multigeneration test (MMT) and Larval amphibian growth and development assay (LAGDA).

1) In the 1-way ANOVA corrected code, does the correction for MMT:

a) Use the mean value for all individuals in a tank and the weights proportional to sample size as was done to calculate the mean for the tank in the LAGDA? Or

b) Use individual observations as the experimental units and add a random effect for the tank within treatment and include denominator degrees of freedom adjusted according to the Kenward-Roger (KR) (or Satterthwaite) method? or

c) Something else?

Response for question 1 The repeated measures ANOVA module within StatCharms is designed to runspecific macros depending on the nature of the data. In particular if time (and generation) only has one level within the data set a mixed effects procedure (proc mixed) is ran with fixed effects for the model defaulting to the treatment and the random effects defaulting to replicate within treatment. This is how the analysis in the errata for the MMT was performed.

2) In the repeated measures ANOVA for MMT, the fixed effects are treatment and time, BUT that alone does not account for the repeated observations on the same experimental unit. a) How were repeated observations handled? That is what is the covariance among the error terms?

Response for question 2 A: Repeated measures ANOVA in StatChaRRms is a misnomer. The program actual uses mixed effect models to performs the analysis. If time has multiple levels within the data set the program still uses the uses mixed procedure but uses Time, Treatment and the Time-Treatment interaction as fixed effects. The random effects are replicate within the time-treatment interaction and are 'grouped' (using the SAS group option) by Time.

b) How were repeated observations handled if a non-parametric ANOVA was performed because of lack of normality?

Response for question 2 B: If the residuals are found to be non-normal the program rank transforms each observation (within a generation for each generation) by rank using the rank procedure with the blom option and using the (transformed) mean when ties occur. The program then proceeds as normal on the transformed data.

3) If the residuals show normality, but unequal variances among treatments, was a usual ANOVA and KR method or a nonparametric ANOVA done?

For question 3:This depends on the module. The module used for LAGDA will use a TamhaneDunnett test for post hoc comparisons, when the residuals are normal but there is unequal variances amongst treatments. The module used for the MMT treats a failure to pass the Levenes test like a failure to pass the Shapiro Wilks test. This means if both tests cannot be satisfied by a transformation the module will rank transform the data and proceed as described in the paragraph above for response 2 B.

Kevin Flynn USEPA/ORD/NHEERL/MED

218-529-5120