Statistical modeling with litter as a random effect in mixed models to manage "intralitter likeness".

"Intralitter likeness," the possibility that the shared genetic and/or maternal environment in multiparous species causes strong similarity for outcome variables in littermates, violates a core statistical assumption, that of observation independence, when littermate outcomes are analyzed. Intralitter likeness has been of major concern to investigators for several decades. Despite consensus and guidance, many research reports in the rodent literature continue to ignore intralitter likeness. A historical review of the literature revealed that the long-preferred solution was to include litter as an effect in statistical models. Limitations in software development and computing capacity prior to 1990, however, appear to have led researchers and guidance authorities to endorse instead the method of using one value per litter. Here, the history of discussions regarding intralitter likeness in developmental neurotoxicological research is reviewed; growing knowledge regarding the biological bases and significance of intralitter likeness is discussed; principles underlying the use of litter as a random effect in mixed models are presented; statistical examples are provided illustrating the advantages and critical importance of including litter as a random effect in mixed models; and results using all data points (all pups from all litters) with litter as a random effect, are compared to results based on random selections of representative littermates. Mixed models with litter included as a random effect have distinct advantages for the analysis of clustered data. Modern computing capacity provides ready accessibility to mixed models for all researchers. Accessibility however does not preclude the need for appropriate expertise and consultation in the use of mixed (hierarchical) models.

[1]  J. Casellas.  Inbred mouse strains and genetic stability: a review. , 2011, Animal : an international journal of animal bioscience.

[2]  C. Eisenhart.  The assumptions underlying the analysis of variance. , 1947, Biometrics.

[3]  J. Vandenbergh,et al.  Intrauterine position effects , 2002, Neuroscience & Biobehavioral Reviews.

[4]  J. Haseman,et al.  Selection of appropriate experimental units in teratology , 1974 .

[5]  C. Sobin,et al.  Olfactory recognition memory is disrupted in young mice with chronic low-level lead exposure. , 2015, Toxicology letters.

[6]  C. Sobin,et al.  Microglial disruption in young mice with early chronic lead exposure. , 2013, Toxicology letters.

[7]  Brady T. West,et al.  Linear Mixed Models: A Practical Guide Using Statistical Software , 2006 .

[8]  vom Saal.  TRIENNIAL REPRODUCTION SYMPOSIUM: Environmental programming of reproduction during fetal life: Effects of intrauterine position and the endocrine disrupting chemical bisphenol A. , 2016 .

[9]  E. Zorrilla,et al.  Multiparous species present problems (and possibilities) to developmentalists. , 1997, Developmental psychobiology.

[10]  B Giraudeau,et al.  Negative values of the intraclass correlation coefficient are not theoretically possible. , 1996, Journal of clinical epidemiology.

[11]  B. Pearce,et al.  Principles and pitfalls in the analysis of prenatal treatment effects in multiparous species. , 1992, Neurotoxicology and teratology.

[12]  C. Sobin,et al.  Early chronic low-level Pb exposure alters global exploratory behaviors but does not impair spatial and object memory retrieval in an object-in-place task in pre-adolescent C57BL/6J mice. , 2017, Neurotoxicology and teratology.

[13]  D. Resnik.  Statistics, ethics, and research: An agenda for education and reform , 2000 .

[14]  M. Brumley,et al.  Responsiveness of rat fetuses to sibling motor activity: Communication in utero? , 2018, Developmental psychobiology.

[15]  M. Festing.  Design and statistical methods in studies using animal models of development. , 2006, ILAR journal.

[16]  B. A. Becker.  Commentary: The statistics of teratology. , 1974, Teratology.

[17]  L. Matzel,et al.  The impact of environmental interventions among mouse siblings on the heritability and malleability of general cognitive ability , 2018, Philosophical Transactions of the Royal Society B: Biological Sciences.

[18]  C. Sobin,et al.  Early chronic lead exposure reduces exploratory activity in young C57BL/6J mice , 2015, Journal of applied toxicology : JAT.

[19]  N. Vargesson.  Thalidomide‐induced teratogenesis: History and mechanisms , 2015, Birth defects research. Part C, Embryo today : reviews.

[20]  B C Allen,et al.  Dose-response assessments for developmental toxicity. IV. Benchmark doses for fetal weight changes. , 1995, Fundamental and applied toxicology : official journal of the Society of Toxicology.

[21]  T. Bale,et al.  Driving the Next Generation: Paternal Lifetime Experiences Transmitted via Extracellular Vesicles and Their Small RNA Cargo , 2019, Biological Psychiatry.

[22]  William M. Stanish,et al.  Estimation of the Intraclass Correlation Coefficient for the Analysis of Covariance Model , 1983 .

[23]  E. Howard,et al.  Statistical procedure in developmental studies on species with multiple offspring. , 1973, Developmental psychobiology.

[24]  Ziyad Mahfoud,et al.  What Is an Intracluster Correlation Coefficient? Crucial Concepts for Primary Care Researchers , 2004, The Annals of Family Medicine.

[25]  G Molenberghs,et al.  Statistical Methods for Developmental Toxicity: Analysis of Clustered Multivariate Binary Data , 1999, Annals of the New York Academy of Sciences.

[26]  Stanley E Lazic,et al.  Improving basic and translational science by accounting for litter-to-litter variation in animal models , 2013, BMC Neuroscience.

[27]  Nicola Iovino,et al.  Functions and mechanisms of epigenetic inheritance in animals , 2018, Nature Reviews Molecular Cell Biology.

[28]  H. Kalter.  Editorial: Choice of the number of sampling units in teratology. , 1974, Teratology.

[29]  Ks Joseph,et al.  Temporal trends in the frequency of twins and higher-order multiple births in Canada and the United States , 2012, BMC Pregnancy and Childbirth.

[30]  C W Hughes,et al.  Outcome of early experience studies as affected by between-litter variance. , 1979, The Journal of nutrition.

[31]  Matthijs Verhage,et al.  Multilevel analysis quantifies variation in the experimental effect while optimizing power and preventing false positives , 2015, BMC Neuroscience.

[32]  R. Müller,et al.  A critical discussion of intraclass correlation coefficients. , 1994, Statistics in medicine.

[33]  L. Ryan.  The use of generalized estimating equations for risk assessment in developmental toxicity. , 1992, Risk analysis : an official publication of the Society for Risk Analysis.

[34]  M. D. Hogan,et al.  Selection of the experimental unit in teratology studies. , 1975, Teratology.

[35]  C. Sobin,et al.  Early chronic low-level lead exposure produces glomerular hypertrophy in young C57BL/6J mice. , 2014, Toxicology letters.

[36]  V. Moser,et al.  Statistical issues and techniques appropriate for developmental neurotoxicity testing: a report from the ILSI Research Foundation/Risk Science Institute expert working group on neurodevelopmental endpoints. , 2008, Neurotoxicology and teratology.

[37]  C. Sobin,et al.  Early Chronic Low-Level Lead Exposure Reduced C-C Chemokine Receptor 7 in Hippocampal Microglia. , 2019, Toxicology letters.

[38]  Joel A Dubin,et al.  Advantages of mixed effects models over traditional ANOVA models in developmental studies: a worked example in a mouse model of fetal alcohol syndrome. , 2007, Developmental psychobiology.

[39]  M. G. Dhar,et al.  Blood flow in the uterine loop artery and loop vein is bidirectional in the mouse: Implications for transport of steroids between fetuses , 1992, Physiology & Behavior.

[40]  A. Satorra,et al.  Complex Sample Data in Structural Equation Modeling , 1995 .

[41]  Ben Lehner,et al.  Intergenerational and transgenerational epigenetic inheritance in animals , 2019, Nature Cell Biology.

[42]  Donald R. Williams,et al.  Between-litter variation in developmental studies of hormones and behavior: Inflated false positives and diminished power , 2017, Frontiers in Neuroendocrinology.

[43]  C. Mactutus,et al.  Polytocus focus: Uterine position effect is dependent upon horn size , 2015, International Journal of Developmental Neuroscience.

[44]  D. Janszen,et al.  Effect of different sampling designs on outcome of endocrine disruptor studies. , 2000, Reproductive toxicology.

[45]  Judith D. Singer,et al.  Using SAS PROC MIXED to Fit Multilevel Models, Hierarchical Models, and Individual Growth Models , 1998 .

[46]  B C Allen,et al.  Dose-response assessment for developmental toxicity. III. Statistical models. , 1994, Fundamental and applied toxicology : official journal of the Society of Toxicology.

[47]  M. Kramer,et al.  GENERALIZED LINEAR MIXED MODELS , 2012 .

[48]  Laura N. Vandenberg,et al.  To Cull or Not To Cull? Considerations for Studies of Endocrine-Disrupting Chemicals. , 2016, Endocrinology.

[49]  Zhe Feng,et al.  A general introduction to adjustment for multiple comparisons. , 2017, Journal of thoracic disease.