The coefficient of determinationR²quantifies the proportion of variance explained by a statistical model and is an important summary statistic of biological interest. However, estimatingR²for generalized linear mixed models (GLMMs) remains challenging. We have previously introduced a version ofR²that we called for Poisson and binomial GLMMs, but not for other distributional families. Similarly, we earlier discussed how to estimate intra-class correlation coefficients (ICCs) using Poisson and binomial GLMMs. In this paper, we generalize our methods to all other non-Gaussian distributions, in particular to negative binomial and gamma distributions that are commonly used for modelling biological data. While expanding our approach, we highlight two useful concepts for biologists, Jensen's inequality and the delta method, both of which help us in understanding the properties of GLMMs. Jensen's inequality has important implications for biologically meaningful interpretation of GLMMs, whereas the delta method allows a general derivation of variance associated with non-Gaussian distributions. We also discuss some special considerations for binomial GLMMs with binary or proportion data. We illustrate the implementation of our extension by worked examples from the field of ecology and evolution in theRenvironment. However, our method can be used across disciplines and regardless of statistical environments.

Summary: Nakagawa & Schielzeth extended the widely used goodness‐of‐fit statistic R² to apply to generalized linear mixed models (GLMMs). However, their R²_GLMM method is restricted to models with the simplest random effects structure, known as random intercepts models. It is not applicable to another common random effects structure, random slopes models. I show that R²_GLMM can be extended to random slopes models using a simple formula that is straightforward to implement in statistical software. This extension substantially widens the potential application of R²_GLMM.

Jose Florez, Claudia Langenberg, Erik Ingelsson, Inga Prokopenko, Inês Barroso and colleagues perform large-scale association analyses using the Metabochip to gain further insights into the genetic architecture of glucose regulation. They identify 38 new loci influencing 1 or more glycemic traits and show that many of these loci also modify risk of type 2 diabetes. Through genome-wide association meta-analyses of up to 133,010 individuals of European ancestry without diabetes, including individuals newly genotyped using the Metabochip, we have increased the number of confirmed loci influencing glycemic traits to 53, of which 33 also increase type 2 diabetes risk (q < 0.05). Loci influencing fasting insulin concentration showed association with lipid levels and fat distribution, suggesting impact on insulin resistance. Gene-based analyses identified further biologically plausible loci, suggesting that additional loci beyond those reaching genome-wide significance are likely to represent real associations. This conclusion is supported by an excess of directionally consistent and nominally significant signals between discovery and follow-up studies. Functional analysis of these newly discovered loci will further improve our understanding of glycemic control.

Statins increase the risk of new-onset type 2 diabetes mellitus. We aimed to assess whether this increase in risk is a consequence of inhibition of 3-hydroxy-3-methylglutaryl-CoA reductase (HMGCR), the intended drug target. We used single nucleotide polymorphisms in the HMGCR gene, rs17238484 (for the main analysis) and rs12916 (for a subsidiary analysis) as proxies for HMGCR inhibition by statins. We examined associations of these variants with plasma lipid, glucose, and insulin concentrations; bodyweight; waist circumference; and prevalent and incident type 2 diabetes. Study-specific effect estimates per copy of each LDL-lowering allele were pooled by meta-analysis. These findings were compared with a meta-analysis of new-onset type 2 diabetes and bodyweight change data from randomised trials of statin drugs. The effects of statins in each randomised trial were assessed using meta-analysis. Data were available for up to 223 463 individuals from 43 genetic studies. Each additional rs17238484-G allele was associated with a mean 0·06 mmol/L (95% CI 0·05-0·07) lower LDL cholesterol and higher body weight (0·30 kg, 0·18-0·43), waist circumference (0·32 cm, 0·16-0·47), plasma insulin concentration (1·62%, 0·53-2·72), and plasma glucose concentration (0·23%, 0·02-0·44). The rs12916 SNP had similar effects on LDL cholesterol, bodyweight, and waist circumference. The rs17238484-G allele seemed to be associated with higher risk of type 2 diabetes (odds ratio [OR] per allele 1·02, 95% CI 1·00-1·05); the rs12916-T allele association was consistent (1·06, 1·03-1·09). In 129 170 individuals in randomised trials, statins lowered LDL cholesterol by 0·92 mmol/L (95% CI 0·18-1·67) at 1-year of follow-up, increased bodyweight by 0·24 kg (95% CI 0·10-0·38 in all trials; 0·33 kg, 95% CI 0·24-0·42 in placebo or standard care controlled trials and -0·15 kg, 95% CI -0·39 to 0·08 in intensive-dose vs moderate-dose trials) at a mean of 4·2 years (range 1·9-6·7) of follow-up, and increased the odds of new-onset type 2 diabetes (OR 1·12, 95% CI 1·06-1·18 in all trials; 1·11, 95% CI 1·03-1·20 in placebo or standard care controlled trials and 1·12, 95% CI 1·04-1·22 in intensive-dose vs moderate dose trials). The increased risk of type 2 diabetes noted with statins is at least partially explained by HMGCR inhibition. The funding sources are cited at the end of the paper.

Significance: When multiple pathogens cocirculate this can lead to competitive or cooperative forms of pathogen–pathogen interactions. It is believed that such interactions occur among cold and flu viruses, perhaps through broad-acting immunity, resulting in interlinked epidemiological patterns of infection. However, to date, quantitative evidence has been limited. We analyzed a large collection of diagnostic reports collected over multiple years for 11 respiratory viruses. Our analyses provide strong statistical support for the existence of interactions among respiratory viruses. Using computer simulations, we found that very short-lived interferences may explain why common cold infections are less frequent during flu seasons. Improved understanding of how the epidemiology of viral infections is interlinked can help improve disease forecasting and evaluation of disease control interventions.