LAGDA

A model for the data:

, 1,2,..., ; 1,2,..., ; 1,2,...,

where is a random tank effect and is a random error component

associated with the animal.
Then , 1,2,..., ; 1,2,..., ;

var(

ijk i ij ijk ij

ij ijk

ij i ij ij y i d j t k n

y i d j t

y   

 

        

    



2 2 ) ij ij n      

So using a weighted analysis on the tank means is not valid unless tank to tank variability is equal to

zero.

# Overview of Statistical Comments for LAGDA

Presented by Mary Christman MCC Statistical Consulting

# General Points

 

## LAGDA has 3 data types

 

### Continuous, e.g. length or weight

 

### Discrete, e.g. number dead out of n individuals

 

### Ordinal categorical, e.g. severity scores for histopathology

# General Points

 

## Each of these requires distinct statistical methods for analysis

 

### Continuous

– ANOVAs assuming normality or some other specific probability distribution

 

### Discrete

- ANOVAs proportion (Binomial) or count (Poisson) distributions

 

### Ordinal categorical

– categorical data analyses such as RSCABS or cumulative logits if proportional odds model is appropriate

# Current Statistical Methods

 

## Treats both continuous and discrete data as continuous

 

### Does transformations to get normality

 

### If cannot achieve normality with a transformation the default is to go to non

- parametric tests

 

### Aside: the decision tree seems to vary by model organism as well as by laboratory within reliability studies

 

### Loss of power

 

### Not using expert knowledge of the biological system and the behavior of the endpoint

 

### According to the descriptions in the ISR and supporting documents, the methods are misapplied

 E.g. going to nonparametric ANOVA when treatment variances are unequal

# Current Statistical Methods

 

### Descriptions, and in some cases applications, of statistical methods vary among the documents provided for the LAGDA.

 

### For example, the ISR differs in description from all of the individual documents and document EPA

- HQ

- OPP

- 2013

- 0182

- 0041.pdf differs from the remaining documents.

 

### Implementation of the package varies among labs and assays, specifically the decision tree procedure is not always followed

 

### This is problematical since the choice of test can influence the overall conclusion of reliability of the test protocol.

 

### For example, if one lab uses a very liberal test and another uses a conservative test then they could draw different conclusions

.  

### This makes inter

- lab comparisons difficult without re

- analyzing the entire set of data.

# Data Driven Analyses

 

## Default approach is one where the statistical methods are based on the given dataset

 

### seems “objective” = use of the default option removes decisions from the analyst

 

### It is not objective

 

### it relies on the particular data set

– not reproducible if the experiment is re

- run with a new set of animals

 

### Problem for the type I error

 

### The stated nominal error rate is not based on a procedure that allows the individual dataset to “decide” the statistical method

# Current Statistical Methods

 

## No inter

- laboratory statistical comparison

 

### All discussion is descriptive

 

### For example, tabular description of similarities and differences in statistical results

 

### Reliance on CVs within laboratories as evidence of reliability

 Not a good measure of reliability or robustness

 

### Should perform a statistical analysis that compares across laboratories for each test substance

 

### Should compare across laboratories for control results over all tests substances

 This requires treating each lab*test substance combination as a level of a single variable

# Increasing Power

 

## The current tests are underpowered with respect to one or more of the endpoints. As a consequence there is a need to consider modifications to the current designs to increase power.

 

### The obvious first choice is to increase replication. That is not the only approach that should be considered though.

 

### Alternative is to re

- allocate organisms appropriately

 

### E.g. if a treatment level is expected to induce a large variation in endpoint values, need more exp. units in the level

 

### Using the right statistical method to analyze the data will aid in increasing power.

# Increasing Power

 

## Another concept to think about:

 

### Combining data for a more complete analysis will aid in hidden replication.

 

### For example, rather than analyzing genders separately for an endpoint, consider running a two

- way model that includes gender as an effect. The degrees of freedom associated with the error term are increased, which means that the test of the main effect of treatment has increased power.

 

### Actually this is a plea to re

- think approaches and consider more comprehensive modeling and testing approach rather than analyzing each endpoint separately for each time point (e.g. weight at 3 different time points) and gender

# Increasing Power

 

## Some more things that can be done to increase power.

 

### Thoroughly review the current data and previous studies to

 

### Identify and rank the various sources of error contributing to the uncertainty

 

### Redesign your studies to minimize the major

sources. This could include

 

### refining the protocol description

 

### changing the design by reallocating the number of individuals among tanks and treatments

# Increasing Power

 

## Finally

 

### Rethink the treatment structure, i.e. the levels of the EC used. Think about the expected form of the dose

- response curve and choose accordingly.

 

### Has any thought been given to the effect of differences in time to metamorphosis (determines final sample date) on the amount of exposure of the larvae and juveniles to the test substances?

# Other Points

 

## Clarity of the protocol

 

### What is the experimental unit for analysis for each endpoint

 

### Description of storing data but little description of data preparation for statistical analysis

 

### Identification of the measurement unit (larva, tank?) and what constitutes the replicate for data analysis

 

### Problem with identification of the appropriate replicate in StatCHARRMS

 

### Inconsistency of application of the statistical methods is partly due to the short description provided

# Other Points

 

## Statistical methods are incorrectly described/applied in some cases

 

### E.g. mentioning a test for comparing 2 means as an alternative to the omnibus test that all treatments means are equal

 

### E.g. Stating that a trend test should be performed if the data show a possible trend

 

### E.g. Using the tank median from the Kaplan

- Meier estimator as the derived variable for tank time to event for analysis in an ANOVA

– ignores the variability of the estimate

 

### Lack of recognition of nested structure of the experimental design (animals within tanks, tanks within treatments)

# Other Points

 

## Randomization

 

### how are male

- female pairs chosen for egg production at first stage?

 

### Another example is “prior to egg placement in test chambers, impartially selected groups of 25 eggs”

 

### Are the eggs a mixture from different parents?

# Power Analyses for Sample Size

 

### Power analyses should be geared toward identifying the required sample sizes needed to detect a biologically relevant difference between means

 

### Based on the test that will actually be performed after data collection

 

### Using the right measure of standard deviation

 

### E.g. in a t

- test of 2 means, use the common standard deviation of each population assuming homogeneity

 

### E.g. in a 1

- way ANOVA with homogeneous variances use the square root of MSE, the estimate of error variance

 

### Using the right measure for the type I error rate

 

### If ONLY 1 t

- test then use the stated α

 

### If doing multiple comparisons with adjustments for multiplicity, use a modified test

- wise α * 

### that controls the family

- wise α = 0.05

# Test of difference of 2 means ( μ control 

# – μ dose1 

# )

o 

## How big a sample size/group is needed when

o 

### α = 0.05

o 

### power = β = 0.80

o 

### s = 10

o 

### Difference between means is 10 = (20

– 30)

o 

### Assume approximate normality and common variance

o 

### T

- test of difference

o 

## N/group = 17

## Test of difference of 2 means in a 1

- way ANOVA

chemical Sensitive endpoint F0 F1

3,5DCP Total offspring/female 200 ug /L (down) 7.2 L (Down)

Time to molt 22 (up) > 490

Fenoxy carb 14d length 2.3 ug /L (down) NA
Total offspring/female 4.9 (down) 2.5 (up)
Fipronil Time to molt <1 >16

7d length <1 >16

Ketoconazole 7d weight <2.15 >33.7

# 2 nd brood 50 < 2.15 (down)

octylp #2 nd brood 4.1 >17.9
# reproducing females 41 >17.9

Lindane 14d length 327 ng /L(down)

--- Total offspring

---- 159

vinclozolin 14d length 8.2 (up)

--- Termination length

--- 24.8 (up diagonal)

survival 600 (down diag ) 200 (down)

Day to first brood 119 (up diag ) 24.8 (up) Most sensitive endpoints for the MTTTSignificant affects of compounds tested in mysid demonstration studies included in the ISR (including both results from Dunn’s and Dunnett’s tests)

Reproduction Growth and Development Survival Most Sensitive

Compounds tested F0 F1 F0 F1 F0 F1 F0 F1 F0=F1

Atrazine #

3,5

- dichlorophenol x x x x

Fenoxycarb* x x x x

Fipronil* x x x x x

Flutamide* x NA x NA x

Ketoconazole x x x x

Lindane x x x

4

- tert

- Octylphenol* x x x

Perfluorodecanoic acid x x

Prochloraz* x NA x NA x

Prochloraz x x x x * = Low replicate numbers remaining in F1 generation in one or more treatments [ na ] = Not assessed due to limited number of offspring. # = No effects measured