EG Toxicity Study

Case Background:

A study was conducted to assess the toxicity of ethylene glycol on the fetal development of mice. Developmental toxicity studies of laboratory animals play a crucial role in the testing and regulation of chemicals. Exposure to developmental toxicants typically causes a variety of adverse effects, such as fetal malformations and reduced fetal weight at term. In a typical developmental toxicity experiment, laboratory animals are assigned to increasing doses of a chemical or test substance.
Ethylene glycol (EG) is used as an anti-freezer, as a solvent in the paint and plastics industries, and in the formulation of various types of inks. In a study of laboratory mice conducted through the National Toxicology Program (NTP), EG was administered at doses of 0, 750, 1500, or 3000 mg/kg/day to 94 pregnant mice (dams) beginning just after implantation. Following sacrifice, fetal weight and evidence of malformations were recorded for each live fetus. In this study, there were two outcomes of interest - (1) fetus weight (gm); (2) evidence of malformation (present or absent). There were a total 94 litters (composed of a total of 1028 live fetuses).


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/*    Import EG Toxicity Study Data     */
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Proc IMPORT out=EG datafile= "C:\Users\Jenn\Documents\Mixed Models\Pregnant Mice EG Study\EG.xlsx"
DBMS=xlsx REPLACE; run;

title 'Preview EG Toxicity Data';
PROC PRINT data = EG (obs=10);
run;

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Model 1: Fetus Weight

Need of Specialtized Statistical Methods:

  • We expect the mice fetuses within the same dam will be more similar than between different dams (due to genetic similarities of offspring of the same mother mouse). This is due to naturally occurring clusters.
  • Since fetuses from the same dam are correlated, we can capture this as a source of variation (either through a random effect or correlation structure)

Methods Selection & Justification:

  • Account for Inter-Litter Correlation
    • We may model this with a random effect for litter, or use a compound symmetry correlation structure
    • Since we are interested in the mean structure, we plan to fit a Marginal Model (GEE) with Dose as a Fixed Effect and compound symmetry correlation structure
  • Treat Dose as Continuous or Categorical?
    • Dose as a continuous covariate allows for a range of estimates (not just at the dose levels given). However, there is a non-linear relationship present between dose and fetal weight, which would require a transformation and may hinder interpretability.
    • We did exploratory analysis to determine an appropriate transformation for dose, and found that sqrt(dose/1000) had a linear relationship with fetal weight.
    • However, we decided to treat dose as a categorical nominal variable, since it does not appear that the specific dose units (mg/kg/day) have immediate importance. Also, this also allows for easier interpretability of estimates.

Selected Model & Assumptions:

  • Marginal (GEE) Model with Compound Symmetry Correlation Structure Population-averaged approach
    • Fixed Effect - Dose (categorical)
    • Correlation within a litter is modeled through a CS correlation structure
    • We use Kenward-Roger approximation method for our degrees of freedom, since we have unequal litter sizes
  • Assumptions:
    • Fetal weight is normally distributed, and that our error terms are independent and have constant variance.
    • Fetuses within a litter have a common correlation


MODEL 1: Marginal Model (GEE): Fetal Weight at Term

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/*      MODEL1: Marginal Model (GEE): Fetal Weight at Term      */
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Proc IMPORT out=EG datafile= "C:\Users\Jenn\Documents\Mixed Models\Pregnant Mice EG Study\EG.xlsx"
DBMS=xlsx REPLACE; run;
  
PROC SORT data=EG;
 by litterID dose;
run;


title 'Marginal Model (GEE) Dose as Categorical, CS covariance structure';
PROC MIXED  data=EG empirical covtest;
CLASS litterID dose (ref="0");
MODEL Wgt = dose / solution DDFM=KR residual;
REPEATED / subject=dose(litterID) type=cs;
title 'Marginal Model: Dose (categorical) is Fixed; CS Covariance Structure';
ESTIMATE "low vs no dose" dose 1 0 0 -1 / cl alpha=0.01667;
ESTIMATE "med vs no dose" dose 0 1 0 -1 / cl alpha=0.01667; 
ESTIMATE "high vs no dose" dose 0 0 1 -1 / cl alpha=0.01667;
LSMEANS dose / cl diff pdiff;
run;


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Model 1 Conclusions:

  • Intra-Class Correlation
    • Our model defines two sources of variation: within-litter variability (0.005569) and between-litter variability (0.007018).
    • Our intra-class correlation is: p=0.00702/(0.00702+0.00557)=0.558
  • Point Estimates & Confidence Intervals
    • We have strong evidence that dose is significant, with F(3,90)=47.40, p-value<.001. This indicates that a difference in fetal weight at term exists amongst dose groups.
    • On average, we find a 0.2627mg decrease in fetal weight for 3000 mg/kg/day EG dose group compared to no EG group.
    • The negative estimates indicate that the fetal weight of mice exposed to EG are lower than the no dose group, for all dose group (750, 1500, 3000 mg/kg/day)




Model 2: Model Probability of Fetus Malformation

Need of Specialtized Statistical Methods:

  • As before, we to allow fetuses from the same dam to be correlated. We can capture this as a source of variation (either through a random effect or correlation structure).
  • Since our response is binary, (malformation present or absent), we should consider a Logistic Model, that models the probability of malformation through the logit link function.

Methods Selection & Justification:

  • Account for Inter-Litter Correlation
    • We may model this with a random effect for litter, or use a compound symmetry correlation structure
    • Since we are interested in the mean structure, we plan to fit a Marginal Generalized Linear Model (GLM) with logit link. Here, Dose as a Fixed Effect, and we use a compound symmetry correlation structure
  • Treat Dose as Continuous or Categorical?
    • Dose as a continuous covariate allows for a range of probability estimates (not just at the dose levels given). However, there is a non-linear relationship present between dose and the probability of malformation, which would require a transformation and may hinder interpretability.
    • As before, we plan to treat dose as a categorical nominal variable, since it does not appear that the dose units (mg/kg/day) have immediate importance, and this also allows for easier interpretability of estimates.

Selected Model & Assumptions:

  • Marginal (GLM) Logistic Model with Compound Symmetry Correlation Structure
    • Population-averaged approach
    • Fixed Effect - Dose (categorical)
    • Correlation within a litter is modeled through a CS correlation structure
    • Uses a working covariance structure that is robust to misspecification, and parameter estimates are computed according to an empirical “sandwich” estimator.
  • Assumptions:
    • Malformations follows a Binomial distribution
    • Fetuses within a litter have a common correlation


MODEL 2: Marginal Logistic Regression Model: Probability of Malformation

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/*      MODEL2: Marginal Logistic Regression Model: Probability of Malformation     */
/**********************************************************************************/

Proc IMPORT out=EG datafile= "C:\Users\Jenn\Documents\Mixed Models\Pregnant Mice EG Study\EG.xlsx"
DBMS=xlsx REPLACE; run;
  
title 'Marginal Model: Dose is Fixed; CS Covariance Structure';
PROC GENMOD data=EG descending plots=all;
CLASS litterID dose (ref="0");
MODEL Malform = dose / dist=binomial type3;
REPEATED subject=litterID / type=cs corrw covb CORRB;
ESTIMATE "OR Low vs No Dose" dose 1 0 0 -1 / exp;
ESTIMATE "OR Med vs No Dose" dose 0 1 0 -1 / exp;
ESTIMATE "OR High vs No Dose" dose 0 0 1 -1 / exp;
ESTIMATE "OR Med vs Low Dose" dose -1 1 0 0 / exp;
ESTIMATE "OR High vs Low Dose" dose -1 0 1 0 / exp;
ESTIMATE "OR High vs Medium Dose" dose 0 -1 1 /exp;
LSMEANS dose / cl diff pdiff or;
ESTIMATE "Prob of Malform for No Dose" int 1 dose 0 0 0 1 / exp;
ESTIMATE "Prob of Malform for Low Dose" int 1 dose 1 0 0 0 / exp;
ESTIMATE "Prob of Malform for Med Dose" int 1 dose 0 1 0 0 / exp;
ESTIMATE "Prob of Malform for High Dose" int 1 dose 0 0 1 0 / exp;
OUTPUT out=new3 P=PRED L=LOWER U=UPPER;
run;

symbol1 i = join v=circle l=32  c = black;
symbol2 i = join v=star l=32  c = black;
symbol3 i = join v=star l=32  c = black;
PROC GPLOT data=new3;
PLOT PRED*dose LOWER*dose UPPER*dose / overlay;
title 'Estimated Logistic Curve from our Marginal Model';
run;


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Model 2 Conclusions:

  • Probability of Malformation
    • We have strong evidence that dose is significant, with Chi-Squared test=42.30, p-value<.001. This indicates that a difference in probability of malformation exists amongst dose groups.
    • The estimated probability of malformation for a fetus at term from a litter receiving the highest EG dose (3000 mg/kg/day) is 56.9%
    • Notice that our estimated probability of malformation is larger for higher EG dose levels, with larger variability at higher dose levels.
  • Odds Ratios
    • Notice a significant difference exists between all dose levels at alpha =0.05 except between high (3000 mg/kg/day) and medium (1500 mg/kg/day).
    • For the 750 mg/kg/day litters, the odds of malformation at term are 38.7 times more often than the odds for the no dose litters.
    • Thus, we see that exposure to EG results in a higher probability of fetus malformations