Robust methods for heteroskedastic regression

THI Modulation of Genetic and Non-genetic Variance Components for Carcass Traits in Hanwoo Cattle

The phenotype of carcass traits in beef cattle are affected by random genetic and non-genetic effects, which both can be modulated by an environmental variable such as Temperature-Humidity Index (THI), a key environmental factor in cattle production. In this study, a multivariate reaction norm model (MRNM) was used to assess if the random genetic and non-genetic (i.e., residual) effects of carcass weight (CW), back fat thickness (BFT), eye muscle area (EMA), and marbling score (MS) were modulated by THI, using 9,318 Hanwoo steers (N = 8,964) and cows (N = 354) that were genotyped on the Illumina Bovine SNP50 BeadChip (50K). THI was measured based on the period of 15–45 days before slaughter. Both the correlation and the interaction between THI and random genetic and non-genetic effects were accounted for in the model. In the analyses, it was shown that the genetic effects of EMA and the non-genetic effects of CW and MS were significantly modulated by THI. No significant THI modulation of such effects was found for BFT. These results highlight the relevance of THI changes for the genetic and non-genetic variation of CW, EMA, and MS in Hanwoo beef cattle. Importantly, heritability estimates for CW, EMA, and MS from additive models without considering THI interactions were underestimated. Moreover, the significance of interaction can be biased if not properly accounting for the correlation between THI and genetic and non-genetic effects. Thus, we argue that the estimation of genetic parameters should be based on appropriate models to avoid any potential bias of estimates. Our finding should serve as a basis for future studies aiming at revealing genotype by environment interaction in estimation and genomic prediction of breeding values.

Quantification of Visual Field Variability in Glaucoma: Implications for Visual Field Prediction and Modeling

Purpose

To quantify visual field (VF) variability as a function of threshold sensitivity and location, and to compare weighted pointwise linear regression (PLR) with unweighted PLR and pointwise exponential regression (PER) for data fit and prediction ability.

Methods

Two datasets were used for this retrospective study. The first was used to characterize and estimate VF variability, and included a total of 4,747 eyes of 3,095 glaucoma patients with six or more VFs and 3 years or more of follow-up. After performing PER for each series, standard deviation of residuals was quantified for each decibel of sensitivity as a measure of variability. A separate dataset was used to test and compare unweighted PLR, weighted PLR, and PER for data fit and prediction, and included 261 eyes of 176 primary open-angle glaucoma patients with 10 or more VFs and 6 years or more of follow-up.

Results

The degree of variability changed as a function of threshold sensitivity with a zenith and a nadir at 33 and 11 dB, respectively. Variability decreased with eccentricity and was higher in the central 10° (P < 0.001). Differences among the methods for data fit were negligible. PER was the best model to predict future sensitivity values in the mid term and long term.

Conclusions

VF variability increases with the severity of glaucoma damage and decreases with eccentricity. Weighted linear regression neither improves model fit nor prediction. PER exhibited the best prediction ability, which is likely related to the nonlinear nature of long-term glaucomatous perimetric decay.

Translational Relevance

This study suggests that taking into account heteroscedasticity has no advantage in VF modeling.