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Bridge H, Morgan KE, Frost C. Negative variance components and intercept-slope correlations greater than one in magnitude: How do such "non-regular" random intercept and slope models arise, and what should be done when they do? Stat Med 2024; 43:2747-2764. [PMID: 38695394 DOI: 10.1002/sim.10070] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2023] [Revised: 02/17/2024] [Accepted: 03/19/2024] [Indexed: 06/15/2024]
Abstract
Statistical models with random intercepts and slopes (RIAS models) are commonly used to analyze longitudinal data. Fitting such models sometimes results in negative estimates of variance components or estimates on parameter space boundaries. This can be an unlucky chance occurrence, but can also occur because certain marginal distributions are mathematically identical to those from RIAS models with negative intercept and/or slope variance components and/or intercept-slope correlations greater than one in magnitude. We term such parameters "pseudo-variances" and "pseudo-correlations," and the models "non-regular." We use eigenvalue theory to explore how and when such non-regular RIAS models arise, showing: (i) A small number of measurements, short follow-up, and large residual variance increase the parameter space for which data (with a positive semidefinite marginal variance-covariance matrix) are compatible with non-regular RIAS models. (ii) Non-regular RIAS models can arise from model misspecification, when non-linearity in fixed effects is ignored or when random effects are omitted. (iii) A non-regular RIAS model can sometimes be interpreted as a regular linear mixed model with one or more additional random effects, which may not be identifiable from the data. (iv) Particular parameterizations of non-regular RIAS models have no generality for all possible numbers of measurements over time. Because of this lack of generality, we conclude that non-regular RIAS models can only be regarded as plausible data-generating mechanisms in some situations. Nevertheless, fitting a non-regular RIAS model can be acceptable, allowing unbiased inference on fixed effects where commonly recommended alternatives such as dropping the random slope result in bias.
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Affiliation(s)
- Helen Bridge
- Alumna, London School of Hygiene and Tropical Medicine, London, UK
| | - Katy E Morgan
- Department of Medical Statistics, London School of Hygiene and Tropical Medicine, London, UK
| | - Chris Frost
- Department of Medical Statistics, London School of Hygiene and Tropical Medicine, London, UK
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Reis CLB, de Fátima Pereira Madureira M, Cunha CLR, Junior WCR, Araújo TH, Esteves A, Stuani MBS, Kirschneck C, Proff P, Matsumoto MAN, Küchler EC, Silva Barroso de Oliveira D. Testosterone suppression impacts craniofacial growth structures during puberty : An animal study. J Orofac Orthop 2023; 84:287-297. [PMID: 35147736 DOI: 10.1007/s00056-021-00373-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/25/2021] [Accepted: 10/10/2021] [Indexed: 10/19/2022]
Abstract
AIM Hormones play a crucial role in growth development; however, the impact of testosterone suppression (TS) on craniofacial growth during puberty remains inconclusive. This study aimed to evaluate the impact of TS during puberty on cephalometric measurements and histological characteristics of facial growth centers. MATERIALS AND METHODS Thirty-six heterogenic Wistar male rats were randomly allocated into experimental orchiectomy (ORX) and control (sham) groups. At an age of 23 days (prepubertal stage), orchiectomy and placebo surgery were performed. Cephalometric measurements were performed via lateral cephalograms during and after puberty. The animals were euthanized at an age of 45 days (pubertal stage) and 73 days (postpubertal stage). Histological slices of the growth centers (condyle, premaxilla, and median palatine suture) were stained with hematoxylin and eosin, and sirius red. Student's t or Mann-Whitney U tests were used to compare linear and angular cephalometric measurements across groups (α error = 5%). RESULTS Linear and angular measurements were statistically different in ORX animals (cranial bones, maxilla, and mandible) at 45 days and 73 days. Condylar histology showed a decrease in prechondroblast differentiation and a delay of mineralization in ORX animals. Vascularization of the medium palatine suture was lower in the ORX group at 45 days. Type I and III collagen fiber synthesis was lower in the ORX groups. In the premaxillary suture, collagen fibers were better organized in the sham groups. CONCLUSIONS Our results suggest that testosterone suppression affects craniofacial growth during puberty.
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Affiliation(s)
- Caio Luiz Bitencourt Reis
- Department of Pediatric Dentistry, School of Dentistry of Ribeirão Preto, University of São Paulo, Ribeirão Preto, São Paulo, Brazil
- Department of Clinic and Surgery, School of Dentistry, Federal University of Alfenas, Rua Gabriel Monteiro da Silva, 700, Centro, Alfenas, Minas Gerais, 37130-001, Alfenas, Brazil
| | - Magali de Fátima Pereira Madureira
- Department of Clinic and Surgery, School of Dentistry, Federal University of Alfenas, Rua Gabriel Monteiro da Silva, 700, Centro, Alfenas, Minas Gerais, 37130-001, Alfenas, Brazil
| | - Caio Luis Rocha Cunha
- Department of Clinic and Surgery, School of Dentistry, Federal University of Alfenas, Rua Gabriel Monteiro da Silva, 700, Centro, Alfenas, Minas Gerais, 37130-001, Alfenas, Brazil
| | - Wagner Costa Rossi Junior
- Institute of Biomedical Sciences, Department of Anatomy, Federal University of Alfenas, Alfenas, Brazil
| | - Tomaz Henrique Araújo
- Institute of Biomedical Sciences, Department Structural Biology, Federal University of Alfenas, Alfenas, Brazil
| | - Alessandra Esteves
- Institute of Biomedical Sciences, Department of Anatomy, Federal University of Alfenas, Alfenas, Brazil
| | - Maria Bernadete Sasso Stuani
- Department of Pediatric Dentistry, School of Dentistry of Ribeirão Preto, University of São Paulo, Ribeirão Preto, São Paulo, Brazil
| | - Christian Kirschneck
- Department of Orthodontics, University Medical Centre of Regensburg, Regensburg, Germany
| | - Peter Proff
- Department of Orthodontics, University Medical Centre of Regensburg, Regensburg, Germany
| | - Mírian Aiko Nakane Matsumoto
- Department of Pediatric Dentistry, School of Dentistry of Ribeirão Preto, University of São Paulo, Ribeirão Preto, São Paulo, Brazil
| | - Erika Calvano Küchler
- Department of Pediatric Dentistry, School of Dentistry of Ribeirão Preto, University of São Paulo, Ribeirão Preto, São Paulo, Brazil
- Department of Orthodontics, University Medical Centre of Regensburg, Regensburg, Germany
| | - Daniela Silva Barroso de Oliveira
- Department of Clinic and Surgery, School of Dentistry, Federal University of Alfenas, Rua Gabriel Monteiro da Silva, 700, Centro, Alfenas, Minas Gerais, 37130-001, Alfenas, Brazil.
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Powder KE, Albertson RC. Cichlid fishes as a model to understand normal and clinical craniofacial variation. Dev Biol 2016; 415:338-346. [PMID: 26719128 PMCID: PMC4914429 DOI: 10.1016/j.ydbio.2015.12.018] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2015] [Revised: 12/14/2015] [Accepted: 12/21/2015] [Indexed: 01/26/2023]
Abstract
We have made great strides towards understanding the etiology of craniofacial disorders, especially for 'simple' Mendelian traits. However, the facial skeleton is a complex trait, and the full spectrum of genetic, developmental, and environmental factors that contribute to its final geometry remain unresolved. Forward genetic screens are constrained with respect to complex traits due to the types of genes and alleles commonly identified, developmental pleiotropy, and limited information about the impact of environmental interactions. Here, we discuss how studies in an evolutionary model - African cichlid fishes - can complement traditional approaches to understand the genetic and developmental origins of complex shape. Cichlids exhibit an unparalleled range of natural craniofacial morphologies that model normal human variation, and in certain instances mimic human facial dysmorphologies. Moreover, the evolutionary history and genomic architecture of cichlids make them an ideal system to identify the genetic basis of these phenotypes via quantitative trait loci (QTL) mapping and population genomics. Given the molecular conservation of developmental genes and pathways, insights from cichlids are applicable to human facial variation and disease. We review recent work in this system, which has identified lbh as a novel regulator of neural crest cell migration, determined the Wnt and Hedgehog pathways mediate species-specific bone morphologies, and examined how plastic responses to diet modulate adult facial shapes. These studies have not only revealed new roles for existing pathways in craniofacial development, but have identified new genes and mechanisms involved in shaping the craniofacial skeleton. In all, we suggest that combining work in traditional laboratory and evolutionary models offers significant potential to provide a more complete and comprehensive picture of the myriad factors that are involved in the development of complex traits.
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Affiliation(s)
- Kara E Powder
- Department of Biology, University of Massachusetts Amherst, 221 Morrill Science Center South, 611 North Pleasant Street, Amherst, MA 01003, USA.
| | - R Craig Albertson
- Department of Biology, University of Massachusetts Amherst, 221 Morrill Science Center South, 611 North Pleasant Street, Amherst, MA 01003, USA.
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de Mello WG, de Morais SRL, Dornelles RCM, Kagohara Elias LL, Antunes-Rodrigues J, Bedran de Castro JC. Effects of neonatal castration and androgenization on sexual dimorphism in bone, leptin and corticosterone secretion. Bone 2012; 50:893-900. [PMID: 22210233 DOI: 10.1016/j.bone.2011.12.009] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 06/08/2011] [Revised: 12/12/2011] [Accepted: 12/14/2011] [Indexed: 11/22/2022]
Abstract
This study investigated the role of neonatal sex steroids in rats on sexual dimorphism in bone, as well as on leptin and corticosterone concentrations throughout the lifespan. Castration of males and androgenization of females were used as models to investigate the role of sex steroids shortly after birth. Newborn Wistar rats were divided into four groups, two male groups and two female groups. Male pups were cryoanesthetized and submitted to castration or sham-operation procedures within 24 h after birth. Female pups received a subcutaneous dose of testosterone propionate (100 μg) or vehicle. Rats were euthanized at 20, 40, or 120 postnatal days. Body weight was also measured at 20, 40, and 120 days of age, and blood samples and femurs were collected. The length and thickness of the femurs were measured and the areal bone mineral density (areal BMD) was determined by dual-energy X-ray absorptiometry (DEXA). Biomechanical three-point bending testing was used to evaluate bone breaking strength, energy to fracture, and extrinsic stiffness. Blood samples were submitted to a biochemical assay to estimate calcium, phosphorus, alkaline phosphatase, leptin, and corticosterone levels. Weight gain, areal BMD and bone biomechanical properties increased rapidly with respect to age in all groups. In control animals, skeletal sexual dimorphism, leptin concentration, and dimorphic corticosterone concentration patterns were evident after puberty. However, androgen treatment induced changes in growth, areal BMD, and bone mass properties in neonatal animals. In addition, neonatally-castrated males had bone development and mechanical properties similar to those of control females. These results suggest that the exposure to neonatal androgens may represent at least one covariate that mediates dimorphic variation in leptin and corticosterone secretions. The study indicates that manipulation of the androgen environment during the critical period of sexual differentiation of the brain causes long-lasting changes in bone development, as well as serum leptin and corticosterone concentrations. In addition, this study provides useful models for the investigation of bone disorders induced by hypothalamic hypogonadism.
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Affiliation(s)
- Wagner Garcez de Mello
- Multicentric Graduate Studies Program in Physiological Sciences, Brazilian Physiological Society/Univ. Estadual Paulista, SP, Brazil
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Smith EP, Specker B, Korach KS. Recent experimental and clinical findings in the skeleton associated with loss of estrogen hormone or estrogen receptor activity. J Steroid Biochem Mol Biol 2010; 118:264-72. [PMID: 19900547 PMCID: PMC4782142 DOI: 10.1016/j.jsbmb.2009.10.016] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 09/08/2009] [Revised: 10/25/2009] [Accepted: 10/30/2009] [Indexed: 10/20/2022]
Abstract
Studies on rodent models and rare human disorders of estrogen production or response have revealed an increased complexity of the actions of estrogen on bone. ERalpha disruption in human males results in delayed epiphyseal maturation, tall stature, trabecular thinning, marked cortical thinning, genu valgum and significantly reduced cortical vBMD, but trabecular number is preserved and there is normal to increased periosteal expansion. Aromatase deficiency results overall in a similar phenotype, although less is known about skeletal architecture. Importantly, estrogen replacement in these individuals, even if provided late in the third decade, may normalize aBMD. Less certain is whether there is complete recovery of normal skeletal architecture and strength. Rodent models, in general, are consistent with the human phenotype but are confounded by inherent differences between mouse and human physiology and issues regarding the completeness of the different knock-out lines. Both human and rodent studies suggest that residual effects of estrogen through ERbeta, truncated ERalpha forms or nonclassical estrogen receptors might account for different phenotypes in the hERKO man, aromatase deficient subjects and rodents. Importantly, androgen, particularly by preserving trabecular number and augmenting both periosteal and epiphyseal growth, also has significant actions on bone.
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Affiliation(s)
- Eric P Smith
- Department of Internal Medicine, Division of Endocrinology, Diabetes and Metabolism, University of Cincinnati College of Medicine, Cincinnati, OH 45267, USA.
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Bianchi MS, Catalano PN, Bonaventura MM, Silveyra P, Bettler B, Libertun C, Lux-Lantos VAR. Effect of androgens on sexual differentiation of pituitary gamma-aminobutyric acid receptor subunit GABA(B) expression. Neuroendocrinology 2004; 80:129-42. [PMID: 15591793 DOI: 10.1159/000082527] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 04/26/2004] [Accepted: 09/23/2004] [Indexed: 12/28/2022]
Abstract
Previous work demonstrated a sexually dimorphic ontogenic expression of gamma-aminobutyric acid receptors (GABA(B)R) in rat pituitary. As sex steroids determine sex-specific expression patterns, we now studied the effect of sex hormones on pituitary GABA(B)R expression. GABA(B)R subunits, measured by Western blot and by semi-quantitative RT-PCR and luteinizing hormone (LH), follicle-stimulating hormone (FSH) and testosterone measured by RIA were determined in two experimental designs: First experimental design: 8- and 15-day-old females (8F, 15F); 8F and 15F treated with 100 mug testosterone propionate (TP) on day 1 of life (8F100TP, 15F100TP), 8- and 15-day-old males (8M, 15M) and 8M and 15M castrated on day 1 (8MC, 15MC). Second experimental design: 8-day-old female and male animals: 8F, 8F100TP, 8F treated with 1 mug/day TP on days 1-4 (8F1TP), 8F treated with the androgen antagonist Flutamide (Flut: 2.5 mg/100 g BW of pregnant mother on days E17-E23) (8F-Flut), 8M, 8MC, 8M treated with Flut as above (8M-Flut) and 8MC-Flut. In these animals, in addition, GABA, glutamate, aspartate and taurine were measured by HPLC in hypothalami and cortex. In the first set of experiments, GABA(B1)R mRNA/protein expression was higher in 8F than in 15F, 8M or 15M. In 8F100TP, GABA(B1)R mRNA/protein decreased to male levels. TP treatment did not alter GABA(B1)R expression in 15F. There was no difference in GABA(B1)R expression between 8M and 15M and neonatal castration did not modify its expression. In the second set of experiments, TP (1 mug) or Flut did not modify GABA(B1)R in 8F, while 100 microg TP continued to decrease GABA(B1)R expression. In 8M, Flut, alone or with castration, increased GABA(B1)R mRNA/protein expression to 8F. Hypothalamic GABA content followed the same pattern as pituitary GABA(B)R expression in 8-day-old animals, suggesting a cross-regulation. With regard to hormonal levels, 100 microg, but not 1 microg TP altered gonadotropins at 8 days, although both treatments effectively androgenized females as evidenced by lack of cycling. We conclude that androgens, acting pre- and postnatally, decrease pituitary GABA(B)R subunit expression.
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Affiliation(s)
- María S Bianchi
- Instituto de Biología y Medicina Experimental-CONICET, University of Buenos Aires, Buenos Aires, Argentina
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Rogers RS, Graziottin TM, Lin CS, Kan YW, Lue TF. Intracavernosal vascular endothelial growth factor (VEGF) injection and adeno-associated virus-mediated VEGF gene therapy prevent and reverse venogenic erectile dysfunction in rats. Int J Impot Res 2003; 15:26-37. [PMID: 12605238 DOI: 10.1038/sj.ijir.3900943] [Citation(s) in RCA: 137] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Penile veno-occlusive dysfunction (venogenic erectile dysfunction) is a common cause of erectile dysfunction (ED). We investigated whether vascular endothelial growth factor (VEGF) can be used to prevent and reverse venogenic ED in a rat model. Pharmacological cavernosometry was developed and validated using adult male rats with either arteriogenic or venogenic ED. Castrated animals were treated with intracavernous VEGF as either a recombinant protein (C+VEGF) or adeno-associated virus (AAV)-mediated VEGF gene therapy (C+VEGF gene) in an attempt to prevent the development of venogenic ED. Other animal groups received testosterone replacement (C+testosterone) or intracavernous AAV-LacZ gene (C+LacZ). Animals with documented venogenic ED were treated with intracavernous VEGF in an attempt to reverse their ED. Functional analysis (pharmacological infusion cavernosometry) was performed following treatment. Penile specimens were harvested for immunohistochemistry and electron microscopic evaluation. Castrated rats showed a decrease in papaverine-induced intracavernous pressure and an increase in maintenance and drop rates during pharmacological cavernosometry. These changes were prevented by systemic testosterone and intracavernous VEGF or AAV-VEGF therapy. Moreover, intracavernous VEGF was able to reverse the venogenic ED produced by castration. The quantity of penile smooth muscle detected by alpha actin staining decreased after castration but not in the C+T, C+VEGF, or C+VEGF gene groups. Transmission electron microscopy revealed atrophy of penile smooth muscle cells and nerves in the castrated rats. In VEGF-treated rats, regeneration of smooth muscle and nerves as well as endothelial cell hypertrophy and hyperplasia were the prominent features. In our animal model, systemic testosterone replacement or intracavernous VEGF (protein and VEGF gene) prevented the veno-occlusive dysfunction in castrated animals. In rats with established venous leakage, VEGF treatment reversed the cavernosometric findings of leakage. Intracavernous injection of either VEGF protein or VEGF gene may be a preferred therapy to preserve erectile function in patients in whom testosterone therapy is contraindicated.
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Affiliation(s)
- R S Rogers
- Knuppe Molecular Urology Laboratory, Department of Urology, University of California School of Medicine, 94143, USA
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