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 

(μcontrol – μdose1)

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

Fenoxycarb 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

# 2nd brood 50 < 2.15 (down)

octylp #2nd 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 MTTT
Significant affects of compounds tested in mysid demonstration studies included in the ISR

(including both results from Dunn’s and Dunnett’stests)

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