Linear and generalized linear models for the detection of QTL effects on within-subject variability

SummaryQuantitative trait loci (QTLs) may affect not only the mean of a trait but also its variability. A special aspect is the variability between multiple measured traits of genotyped animals, such as the within-litter variance of piglet birth weights. The sample variance of repeated measurements is assigned as an observation for every genotyped individual. It is shown that the conditional distribution of the non-normally distributed trait can be approximated by a gamma distribution. To detect QTL effects in the daughter design, a generalized linear model with the identity link function is applied. Suitable test statistics are constructed to test the null hypothesis H0: No QTL with effect on the within-litter variance is segregating versus HA: There is a QTL with effect on the variability of birth weight within litter. Furthermore, estimates of the QTL effect and the QTL position are introduced and discussed. The efficiency of the presented tests is compared with a test based on weighted regression. The error probability of the first type as well as the power of QTL detection are discussed and compared for the different tests.

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Posterior contraction in sparse generalized linear models

Biometrika ◽

10.1093/biomet/asaa074 ◽

2020 ◽

Author(s):

Seonghyun Jeong ◽

Subhashis Ghosal

Keyword(s):

Generalized Linear Models ◽

Bayesian Methods ◽

Generalized Linear Model ◽

Linear Models ◽

Continuous Distribution ◽

Fractional Power ◽

Regression Coefficients ◽

Link Function ◽

Convergence Properties ◽

Set Up

Summary We study posterior contraction rates in sparse high-dimensional generalized linear models using priors incorporating sparsity. A mixture of a point mass at zero and a continuous distribution is used as the prior distribution on regression coefficients. In addition to the usual posterior, the fractional posterior, which is obtained by applying Bayes theorem with a fractional power of the likelihood, is also considered. The latter allows uniformity in posterior contraction over a larger subset of the parameter space. In our set-up, the link function of the generalized linear model need not be canonical. We show that Bayesian methods achieve convergence properties analogous to lasso-type procedures. Our results can be used to derive posterior contraction rates in many generalized linear models including logistic, Poisson regression and others.

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Generalized Linear Models

10.1093/oso/9780198798170.003.0015 ◽

2021 ◽

pp. 195-208

Author(s):

Andy Hector

Keyword(s):

Regression Analysis ◽

Maximum Likelihood ◽

Generalized Linear Models ◽

Linear Models ◽

Square Root ◽

Link Function ◽

Data Transformations ◽

Normal Distributions ◽

Equal Variance ◽

The Mean

This chapter revisits a regression analysis to explore the normal least squares assumption of approximately equal variance. It also considers some of the data transformations that can be used to achieve this. A linear regression of transformed data is compared with a generalized linear-model equivalent that avoids transformation by using a link function and non-normal distributions. Generalized linear models based on maximum likelihood use a link function to model the mean (in this case a square-root link) and a variance function to model the variability (in this case the gamma distribution, where the variance increases as the square of the mean). The Box–Cox family of transformations is explained in detail.

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The Use of the Generalized Linear Model to Assess the Speed and Uniformity of Germination of Corn and Soybean Seeds

Agronomy ◽

10.3390/agronomy11030588 ◽

2021 ◽

Vol 11 (3) ◽

pp. 588

Author(s):

Deoclecio Jardim Amorim ◽

Amanda Rithieli Pereira dos Santos ◽

Gabriela Nunes da Piedade ◽

Rute Quelvia de Faria ◽

Edvaldo Aparecido Amaral da Silva ◽

...

Keyword(s):

Generalized Linear Model ◽

Linear Models ◽

Soybean Seeds ◽

Link Function ◽

Physiological Quality ◽

The Difference ◽

The Times ◽

Binomial Response

The use of seeds with high physiological quality allows rapid growth and establishment of seedlings in the field to be obtained. Therefore, the accuracy of the information obtained during the determination of the physiological quality of seeds is of great importance. The objective was to use generalized linear models, investigating which link function (Probit, Logit and Complementary log-log) is suitable to predict T50 and uniformity during germination of soybean and corn seeds. To perform the experiments, we used seeds from five commercial hybrids and/or cultivars of corn and soybean. The germination speed was calculated by counting the germinated seeds and the results were expressed in the form of proportions. Germination uniformity was calculated by the difference in the times required for germination. The best model was selected according to the criteria of the test of Deviance, AIC and BIC. The Logit model showed accurate results for most cultivars. The evaluation of germination in the form of proportions considering the assumption of binomial response is satisfactory, and the choice of the link function is dependent on the characteristics of each lot and/or species evaluated. The use of this methodology makes it possible to estimate any germination time and uniformity.

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Behaviour of the Monotone Single Index Model Under Repeated Measurements

Sankhya A ◽

10.1007/s13171-021-00250-7 ◽

2021 ◽

Author(s):

Fadoua Balabdaoui ◽

Cécile Durot ◽

Hanna Jankowski

Keyword(s):

Goodness Of Fit ◽

Linear Models ◽

Predictive Performance ◽

Repeated Measurements ◽

Link Function ◽

Data Set ◽

Single Index ◽

Index Model ◽

Single Index Model ◽

Leukemia Data

AbstractThe generalized linear model is an important method in the statistical toolkit. The isotonic single index model can be thought of as a further generalization whereby the link function is assumed to be monotone non-decreasing as opposed to known and fixed. Such a shape constraint is quite natural in many statistical problems, and is fulfilled by the usual generalized linear models. In this paper we consider inference in this model in the setting where repeated measurements of predictor values and associated responses are observed. This setting is encountered in medical studies and is very different from the one considered in the classical monotone single index model studied in the literature. Here, we use nonparametric maximum likelihood estimation to infer the unknown regression vector and link function. We present a detailed study of finite and asymptotic properties of this estimator and propose goodness-of-fit tests for the model. Through an extended simulation study, we show that the model has competitive predictive performance. We illustrate our estimation approach using a Leukemia data set.

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Blood neurofilament light concentration at admittance: a potential prognostic marker in COVID-19

Journal of Neurology ◽

10.1007/s00415-021-10517-6 ◽

2021 ◽

Author(s):

Anne Hege Aamodt ◽

Einar August Høgestøl ◽

Trine Haug Popperud ◽

Jan Cato Holter ◽

Anne Ma Dyrhol-Riise ◽

...

Keyword(s):

Nervous System ◽

Single Molecule ◽

Linear Models ◽

Clinical Signs ◽

Repeated Measurements ◽

Cns Injury ◽

Serum Concentrations ◽

Blood Biomarkers ◽

Neurofilament Light Chain ◽

Neurofilament Light

Abstract Objective To test the hypotheses that blood biomarkers for nervous system injury, serum concentrations of neurofilament light chain protein (NfL) and glial fibrillary acidic protein (GFAp) can serve as biomarkers for disease severity in COVID-19 patients. Methods Forty-seven inpatients with confirmed COVID-19 had blood samples drawn on admission for assessing serum biomarkers of CNS injury by Single molecule array (Simoa), NfL and GFAp. Concentrations of NfL and GFAp were analyzed in relation to symptoms, clinical signs, inflammatory biomarkers and clinical outcomes. We used multivariate linear models to test for differences in biomarker concentrations in the subgroups, accounting for confounding effects. Results In total, 21% (n = 10) of the patients were admitted to an intensive care unit, and the overall mortality rate was 13% (n = 6). Non-survivors had higher serum concentrations of NfL (p < 0.001) upon admission than patients who were discharged alive both in adjusted analyses (p = 2.6 × 10–7) and unadjusted analyses (p = 0.001). The concentrations of NfL in non-survivors increased over repeated measurements; whereas, the concentrations in survivors were stable. The GFAp concentration was also significantly higher in non-survivors than survivors (p = 0.02). Conclusion Increased concentrations of NfL and GFAp in COVID-19 patients on admission may indicate increased mortality risk. Measurement of blood biomarkers for nervous system injury can be useful to detect and monitor CNS injury in COVID-19.

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Study on Association between Height, Weight, Iodine Supplementation and Thyroid Volume

British Journal Of Nutrition ◽

10.1017/s0007114521002622 ◽

2021 ◽

pp. 1-25

Author(s):

Lanchun Liu ◽

Lixiang Liu ◽

Ming Li ◽

Yang Du ◽

Peng Liu ◽

...

Keyword(s):

Iodine Deficiency ◽

Linear Models ◽

Thyroid Volume ◽

Salt Iodization ◽

Iodine Supplementation ◽

Random Pairing ◽

Level Data ◽

The Mean ◽

Salt Iodine ◽

The Difference

Abstract The policy of Universal Salt Iodization (USI) could reduce population’s thyroid volume (TVOL) in iodine deficiency areas. Conversely, the improved growth and developmental status of children might increase the TVOL accordingly. Whether the decreased TVOL by USI conceals the increase effect of height and weight on TVOL is unclear. The aim of this study was to analyse the association between height, weight, iodine supplementation and TVOL. Five national Iodine Deficiency Disorder surveys were matched into four pairs according to the purpose of analysis. County-level data of both detected by paired surveys were incorporated, 1: 1 random pairing method was used to match counties or individuals. The difference of TVOL between different height, weight, different iodine supplementation measures groups and the association between TVOL and them were studied. The mean height and weight of children aged 8-10 years increased from 129.9cm and 26.9kg in 2002 to 136.2cm and 32.1kg in 2019; while the median TVOL decreased from 3.10ml to 2.61ml. Iodine supplementation measures can affect TVOL; after exclude iodine effects, the median TVOL was increased with the height and weight. On the other side, after excluding the influence of height and weight, the median TVOL remained decreased. Only age, weight and salt iodine were significant associated with TVOL in multiple linear models. Development of height and weight in children is the evidence of improved nutrition. The decreased TVOL caused by iodized salt measures conceals the increase effect of height and weight on TVOL. Age, weight, and salt iodine affect TVOL significantly.

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Kidney function decline is associated with an accelerated increase in plasma homocysteine in older adults: a longitudinal study

British Journal Of Nutrition ◽

10.1017/s0007114521001690 ◽

2021 ◽

pp. 1-21

Author(s):

Hui Zhang ◽

Yi Li ◽

Meng Hao ◽

Xiaoyan Jiang ◽

Jiucun Wang ◽

...

Keyword(s):

Kidney Function ◽

Repeated Measurements ◽

Baseline Survey ◽

Mixed Effect ◽

Pronounced Increase ◽

Crude Model ◽

The Mean ◽

Kidney Function Decline ◽

Over Time

Abstract Background: Few studies have been conducted to investigate the association of kidney function decline with the trajectories of homocysteine (Hcy) over time, using repeated measurements. We aimed to investigate the association of kidney function with changes in plasma Hcy levels over time. Methods: Data were collected from the Rugao Longevity and Ageing Study. In detail, plasma Hcy and creatinine levels were measured in both waves (waves 2, 3 and 4) during the 3.5-year follow-up (N = 1135). Wave 2 was regarded as the baseline survey. The estimated glomerular filtration rate (eGFR) was calculated based on creatinine. Subjects were categorized into four groups according to quartiles of eGFR at baseline. Linear mixed-effect models were used to investigate the association of eGFR with subsequent plasma Hcy levels. Results: The mean eGFR at baseline was 90.84 (11.42) mL/min/1.73 m2. The mean plasma Hcy level was 14.09 (6.82) at baseline and increased to 16.28 (8.27) and 17.36 (10.39) μmol/L during follow-ups. In the crude model, the interaction between time and eGFR at baseline was significant (β = −0.02, 95% CI: −0.02 to −0.01, p = 0.002). After adjusting for confounding factors, a significant relationship remained (β = −0.02, 95% CI: −0.02 to −0.01, p = 0.003), suggesting that kidney function decline at baseline was associated with a faster increase in Hcy levels. Conclusion: Kidney function decline is associated with a more pronounced increase in plasma Hcy levels. Further studies with longer follow-up periods and larger sample sizes are needed to validate our findings.

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OBESITY AND SELF-REPORTED OUTCOME AFTER MINIMALLY INVASIVE LUMBAR SPINAL FUSION SURGERY

Neurosurgery ◽

10.1227/01.neu.0000313626.23194.3f ◽

2008 ◽

Vol 63 (5) ◽

pp. 956-960 ◽

Cited By ~ 70

Author(s):

David S. Rosen ◽

Sherise D. Ferguson ◽

Alfred T. Ogden ◽

Dezheng Huo ◽

Richard G. Fessler

Keyword(s):

Minimally Invasive ◽

Linear Models ◽

Short Form ◽

Length Of Hospital Stay ◽

Fusion Surgery ◽

Body Habitus ◽

Short Form 36 ◽

Spinal Fusion Surgery ◽

The Mean ◽

Lumbar Spinal

Abstract OBJECTIVE Many patients undergoing lumbar spine fusion are overweight or obese. The relationship between body habitus and outcome after lumbar spine fusion surgery is not well defined. METHODS We analyzed a prospectively maintained database of self-reported pain and quality of life measures, including Visual Analog Scale pain score, Short Form 36, and Oswestry Disability Index. We selected patients undergoing minimally invasive transforaminal lumbar interbody fusion between September 2002 and June 2006 at a single institution. We used linear regression models and mixed-effects linear models to examine the relationships between body habitus and self-reported outcomes. RESULTS The analysis identified 110 patients meeting the study criteria, with a median follow-up period of 14.8 months. The mean age was 56 years, mean height was 169 cm, and mean weight was 82.2 kg. The mean body mass index (BMI) was 28.7 kg/m2; 31% of patients were overweight (BMI, 25–29.9), and 32% of patients were obese (BMI, >30). Linear regression analysis did not identify a correlation between weight or BMI and pre- and postsurgery changes in any of the outcome measures. The significant findings observed in the mixed-effects linear models were that the changing patterns of Short Form 36 Body Pain subscale and Short Form 36 Vitality subscale varied significantly by category of BMI (P = 0.01 and P = 0.002, respectively), but not significantly if continuous BMI was used (P = 0.53 and P = 0.46, respectively). BMI correlated marginally with estimated blood loss (P = 0.08), but not operative time, length of hospital stay, or complications. CONCLUSION Among this cohort of minimally invasive lumbar fusion patients, body habitus measured by BMI, weight, or height did not have a significant relationship with most self-reported outcome measures, operative time, length of hospital stay, or complications. Obesity should not be considered a contraindication to minimally invasive lumbar spinal fusion surgery.

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A modified sonographic technique for assessment of gastric emptying of liquid

Acta Radiologica ◽

10.1080/j.1600-0455.2003.00055.x ◽

2003 ◽

Vol 44 (3) ◽

pp. 340-342 ◽

Cited By ~ 4

Author(s):

J. F. Pedersen

Keyword(s):

Gastric Emptying ◽

Repeated Measurements ◽

Intraindividual Variation ◽

Ultrasound Technique ◽

Liquid Meal ◽

Ultrasound Monitoring ◽

Gastric Emptying Time ◽

The Mean ◽

Antral Area ◽

Emptying Time

Purpose: Ultrasound scanning is replacing scintigraphy in studies of gastric emptying of liquid, but both have considerable day-to-day variability. This study describes a modified ultrasound technique for assessing gastric emptying of liquid, and evaluates the inter- and intraindividual variation in emptying time. Material and Methods: On different days, each of 12 healthy volunteers had meals of 350 ml broth. The antral area was measured at sonography 5 times before the meal as a baseline, and every 1–4 min after the meal. The time until the antral area had decreased to 150% of baseline (T150) was determined and used as surrogate expression of gastric emptying time. Results: The mean T150 for a broth meal was 12.6 min (range 5–21) and 13.5 min (6–23) (first and second meal, respectively). The standard deviation of the differences between the 12 pairs of repeated measurements was 3.1 min and the coefficient of variation was 24%. Conclusion: Ultrasound monitoring of antral size after a liquid meal is a well suited method for assessing gastric emptying of liquid.

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On the Wave Spectrum Generated by Tropical Heating

Journal of the Atmospheric Sciences ◽

10.1175/2011jas3718.1 ◽

2011 ◽

Vol 68 (9) ◽

pp. 2042-2060 ◽

Cited By ~ 9

Author(s):

David A. Ortland ◽

M. Joan Alexander ◽

Alison W. Grimsdell

Keyword(s):

Linear Models ◽

Nonlinear Models ◽

Wave Spectrum ◽

Convective Heating ◽

Temperature Structure ◽

Mean Flow ◽

Quasi Biennial Oscillation ◽

Wave Response ◽

Zonal Wavenumber ◽

The Mean

Abstract Convective heating profiles are computed from one month of rainfall rate and cloud-top height measurements using global Tropical Rainfall Measuring Mission and infrared cloud-top products. Estimates of the tropical wave response to this heating and the mean flow forcing by the waves are calculated using linear and nonlinear models. With a spectral resolution up to zonal wavenumber 80 and frequency up to 4 cpd, the model produces 50%–70% of the zonal wind acceleration required to drive a quasi-biennial oscillation (QBO). The sensitivity of the wave spectrum to the assumed shape of the heating profile, to the mean wind and temperature structure of the tropical troposphere, and to the type of model used is also examined. The redness of the heating spectrum implies that the heating strongly projects onto Hough modes with small equivalent depth. Nonlinear models produce wave flux significantly smaller than linear models due to what appear to be dynamical processes that limit the wave amplitude. Both nonlinearity and mean winds in the lower stratosphere are effective in reducing the Rossby wave response to heating relative to the response in a linear model for a mean state at rest.

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