We study the distribution of the maximum likelihood estimate (MLE) in high-dimensional logistic models, extending the recent results from [14] to the case where the Gaussian covariates may have an arbitrary covariance structure. We prove that in the limit of large problems holding the ratio between the number p of covariates and the sample size n constant, every finite list of MLE coordinates follows a multivariate normal distribution. Concretely, the jth coordinate βj of the MLE is asymptotically normally distributed with mean α β j and standard deviation σ /τ j ; here, β j is the value of the true regression coefficient, and τ j the standard deviation of the jth predictor conditional on all the others. The numerical parameters α > 1 and σ only depend upon the problem dimensionality p/n and the overall signal strength, and can be accurately estimated. Our results imply that the MLE's magnitude is biased upwards and that the MLE's standard deviation is greater than that predicted by classical theory. We present a series of experiments on simulated and real data showing excellent agreement with the theory.

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Hip (HD) and Elbow Dysplasia (ED) are two common complex developmental disorders of dogs. In order to decrease their prevalence and severity, the Orthopedic Foundation for Animals (OFA) has a voluntary registry of canine hip and elbow conformation certified by boarded radiologists. However, the voluntarily reports have been severely biased against exposing dogs with problems, especially at beginning period. Fluctuated by additional influential factors such as age, the published raw scores barely showed trends of improvement. In this study, we used multiple-trait mixed model to simultaneously adjust these factors and incorporate pedigree to derive Estimated Breeding Values (EBV). A total of 1,264,422 dogs from 74 breeds were evaluated for EBVs from 760,455 hip scores and 135,409 elbow scores. These EBVs have substantially recovered the reporting bias and the other influences. Clear and steady trends of genetic improvement were observed over the 40 years since 1970. The total genetic improvements were 16.4% and 1.1% of the phenotypic standard deviation for HD and ED, respectively. The incidences of dysplasia were 0.83% and 2.08%, and the heritabilities were estimated as 0.22 and 0.17 for hip and elbow scores, respectively. The genetic correlation between them was 0.12. We conclude that EBV is more effective than reporting raw phenotype. The weak genetic correlation suggested that selection based on hip scores would also slightly improve elbow scores but it is necessary to allocate effort toward improvement of elbow scores alone.

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ObjectiveTo compare the effectiveness and safety of the six interventions for neovascular glaucoma.DesignA systematic review and network meta-analysis.MethodsRandomised controlled trials and cohort studies which compared the six interventions in neovascular glaucoma were identified using the following databases searched up to 1 September 2020: PubMed, Cochrane Library, Embase and Web of Science. The quality assessment was conducted by using the Cochrane risk of bias tool and the Newcastle-Ottawa scale. The primary outcome measure was the weighted mean differences for intraocular pressure reduction. Secondary one was ORs for success rate. Outcome measures were reported with a 95% CI and p<0.05 was considered statistically significant. Network meta-analysis was performed using Stata V.15.0.ResultsTwenty-three studies involving a total of 1303 patients were included. The types of surgical treatments included Ahmed glaucoma valve (AGV) implant surgery, AGV combined with intravitreal anti-vascular endothelial growth factor (AGV +IVAV), cyclophotocoagulation (CPC), cyclocryotherapy (CCT), trabeculectomy with mitomycin (Trab(MMC)) and Trab(MMC) combined with IVAV (Trab(MMC)+IVAV). Network meta-analysis showed that in comparison with AGV, AGV +IVAV (MD=4.74, 95% CI 1.04 to 8.45) and Trab(MMC)+IVAV (MD=6.19, 95% CI 0.99 to 11.40) showed a favourable effect in intraocular pressure reduction (IOPR) 6 months after surgery. Compared with CCT, AGV (OR=−0.17, 95% CI −0.53 to −0.05), AGV +IVAV (OR=−0.10, 95% CI −3.48 to −1.19), CPC (OR=−0.12, 95% CI −0.53 to −0.05), Trab(MMC) (OR=3.54, 95% CI 1.15 to 10.91) and Trab(MMC)+IVAV (OR=5.78, 95% CI 2.29 to 14.61) showed a superior impact in success rate. The order of efficacy as best intervention ranked as follows: Trab(MMC)+IVAV (IOPR 6 months after surgery, surface under the cumulative ranking (SUCRA)=88.1), CPC (IOPR 12 months after surgery, SUCRA=81.9), AGV +IVAV (IOPR 12 months after surgery, SUCRA=79.9) and AGV +IVAV (success rate, SUCRA=92.7). Adverse events were also summarised in detail.ConclusionIn the treatment of neovascular glaucoma, AGV+IVAV and CPC were more effective in IOPR and success rate than the other four interventions. Additionally, AGV+IVAV is superior to CPC concerning the success rate in the long-term treatment. However, considering the limitations of this review, more high-quality trials, especially those surgical interventions not mentioned in this review, should be carried out in the future to further confirm the current findings.