Comment on "Under-reported data analysis with INAR-hidden Markov chains"

In Fernandez-Fontelo et al (Statis. Med. 2016, DOI 10.1002/sim.7026) hidden integer-valued autoregressive (INAR) processes are used to estimate reporting probabilities for various diseases. In this comment it is demonstrated that the Poisson INAR(1) model with time-homogeneous underreporting can be expressed equivalently as a completely observed INAR(inf) model with a geometric lag structure. This implies that estimated reporting probabilities depend on the assumed lag structure of the latent process.Comment: This is the pre-reviewing version of a letter published in Statistics in Medicine 38(5), 893-898: https://onlinelibrary.wiley.com/doi/full/10.1002/sim.8032 Fernandez-Fontelo et al published a reply which raises some interesting further points: https://onlinelibrary.wiley.com/doi/10.1002/sim.8033 After a 12 month embargo period the accepted version will be made available on arxi

Defining the qualitative elements of Aichi Biodiversity Target 11 with regard to the marine and coastal environment in order to strengthen global efforts for marine biodiversity conservation outlined in the United Nations Sustainable Development Goal 14

The Convention on Biological Diversity (CBD) Aichi Target 11 states that, “by 2020, at least 17 per cent of terrestrial and inland water, and 10 per cent of coastal and marine areas, especially areas of particular importance for biodiversity and ecosystem services, are conserved through effectively and equitably managed, ecologically representative and well-connected systems of protected areas and other effective area-based conservation measures, and integrated into the wider landscapes and seascapes”. There has been rapid progress to meet the quantitative goal (the 10% target). However, the qualitative aspects of Aichi target 11 are less well described. The United Nations Sustainable Development Goal (SDG) 14 to “conserve and sustainably use the oceans, seas and marine resources for sustainable development” reaffirms the quantitative element of Aichi target 11, and, through the described sub-targets, places further emphasis on the economic and social context of global development. The complexity of the language from Aichi target 11 is not mirrored in SDG 14, leading to a potential scenario where the knowledge and progress towards Aichi Target 11 will be diluted as the focus shifts to the SDGs. This paper presents current knowledge and implementation of the qualitative elements of Aichi Target 11 and highlights gaps in knowledge. We conclude that the progress made so far on describing and implementing the qualitative goals of Aichi Target 11 should be integrated into SDG 14 in order to strengthen global efforts for marine biodiversity conservation and support the broader vision for sustainable development that will “transform our world”

Estimation of adjusted rate differences using additive negative binomial regression

Rate differences are an important effect measure in biostatistics and provide an alternative perspective to rate ratios. When the data are event counts observed during an exposure period, adjusted rate differences may be estimated using an identity-link Poisson generalised linear model, also known as additive Poisson regression. A problem with this approach is that the assumption of equality of mean and variance rarely holds in real data, which often show overdispersion. An additive negative binomial model is the natural alternative to account for this, however, standard model-fitting methods are often unable to cope with the constrained parameter space arising from the non-negativity restrictions of the additive model. In this paper, we propose a novel solution to this problem using a variant of the ECME algorithm. Our method provides a reliable way to fit an additive negative binomial regression model and also permits flexible generalisations using semi-parametric regression functions. We illustrate the method using a placebo-controlled clinical trial of fenofibrate treatment in patients with type II diabetes, where the outcome is the number of laser therapy courses administered to treat diabetic retinopathy. An R package is available that implements the proposed method. Copyright c 2015 John Wiley & Sons, Ltd

ADH1B is associated with alcohol dependence and alcohol consumption in populations of European and African ancestry.

A coding variant in alcohol dehydrogenase 1B (ADH1B) (rs1229984) that leads to the replacement of Arg48 with His48 is common in Asian populations and reduces their risk for alcoholism, but because of very low allele frequencies the effects in European or African populations have been difficult to detect. We genotyped and analyzed this variant in three large European and African-American case-control studies in which alcohol dependence was defined by the Diagnostic and Statistical Manual of Mental Disorders, Fourth Edition (DSM-IV) criteria, and demonstrated a strong protective effect of the His48 variant (odds ratio (OR) 0.34, 95% confidence interval (CI) 0.24, 0.48) on alcohol dependence, with genome-wide significance (6.6 × 10(-10)). The hypothesized mechanism of action involves an increased aversive reaction to alcohol; in keeping with this hypothesis, the same allele is strongly associated with a lower maximum number of drinks in a 24-hour period (lifetime), with P=3 × 10(-13). We also tested the effects of this allele on the development of alcoholism in adolescents and young adults, and demonstrated a significantly protective effect. This variant has the strongest effect on risk for alcohol dependence compared with any other tested variant in European populations

Pitfalls of using the risk ratio in meta‐analysis

For meta-analysis of studies that report outcomes as binomial proportions, the most popular measure of effect is the odds ratio (OR), usually analyzed as log(OR). Many meta-analyses use the risk ratio (RR) and its logarithm, because of its simpler interpretation. Although log(OR) and log(RR) are both unbounded, use of log(RR) must ensure that estimates are compatible with study-level event rates in the interval (0, 1). These complications pose a particular challenge for random-effects models, both in applications and in generating data for simulations. As background we review the conventional random-effects model and then binomial generalized linear mixed models (GLMMs) with the logit link function, which do not have these complications. We then focus on log-binomial models and explore implications of using them; theoretical calculations and simulation show evidence of biases. The main competitors to the binomial GLMMs use the beta-binomial (BB) distribution, either in BB regression or by maximizing a BB likelihood; a simulation produces mixed results. Two examples and an examination of Cochrane meta-analyses that used RR suggest bias in the results from the conventional inverse-variance-weighted approach. Finally, we comment on other measures of effect that have range restrictions, including risk difference, and outline further research

On the Legendre differential equation with uncertainties at the regular-singular point 1: Lp random power series solution and approximation of its statistical moments

"This is the peer reviewed version of the following article: Calatayud, J, Cortés, J-;C, Jornet, M. On the Legendre differential equation with uncertainties at the regular-singular point 1: Lp random power series solution and approximation of its statistical moments. Comp and Math Methods. 2019; 1:e1045. https://doi.org/10.1002/cmm4.1045 , which has been published in final form at https://doi.org/10.1002/cmm4.1045. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving."[EN] In this paper, we construct two linearly independent response processes to the random Legendre differential equation on (-1,1)U(1,3), consisting of Lp(omega) convergent random power series around the regular¿singular point 1. A theorem on the existence and uniqueness of Lp(omega) solution to the random Legendre differential equation on the intervals (-1,1) and (1,3) is obtained. The hypotheses assumed are simple: initial conditions in Lp(omega) and random input A in L infinite(omega) (this is equivalent to A having absolute moments that grow at most exponentially). Thus, this paper extends the deterministic theory to a random framework. Uncertainty quantification for the solution stochastic process is performed by truncating the random series and taking limits in Lp(omega). In the numerical experiments, we approximate its expectation and variance for certain forms of the differential equation. The reliability of our approach is compared with Monte Carlo simulations and generalized polynomial chaos expansions.Spanish Ministerio de Economía y Competitividad, Grant/Award Number: MTM2017-89664-P; Programa de Ayudas de Investigación y Desarrollo; Universitat Politècnica de ValènciaCalatayud-Gregori, J.; Cortés, J.; Jornet-Sanz, M. (2019). On the Legendre differential equation with uncertainties at the regular-singular point 1: Lp random power series solution and approximation of its statistical moments. Computational and Mathematical Methods. 1(4):1-12. https://doi.org/10.1002/cmm4.1045S11214Calbo, G., Cortés, J.-C., Jódar, L., & Villafuerte, L. (2011). Solving the random Legendre differential equation: Mean square power series solution and its statistical functions. Computers & Mathematics with Applications, 61(9), 2782-2792. doi:10.1016/j.camwa.2011.03.045Villafuerte, L., Braumann, C. A., Cortés, J.-C., & Jódar, L. (2010). Random differential operational calculus: Theory and applications. Computers & Mathematics with Applications, 59(1), 115-125. doi:10.1016/j.camwa.2009.08.061Wong, E., & Hajek, B. (1985). Stochastic Processes in Engineering Systems. Springer Texts in Electrical Engineering. doi:10.1007/978-1-4612-5060-9Nouri, K., & Ranjbar, H. (2014). Mean Square Convergence of the Numerical Solution of Random Differential Equations. Mediterranean Journal of Mathematics, 12(3), 1123-1140. doi:10.1007/s00009-014-0452-8Lupulescu, V., O’Regan, D., & ur Rahman, G. (2014). Existence results for random fractional differential equations. Opuscula Mathematica, 34(4), 813. doi:10.7494/opmath.2014.34.4.813Villafuerte, L., & Chen-Charpentier, B. M. (2012). A random differential transform method: Theory and applications. Applied Mathematics Letters, 25(10), 1490-1494. doi:10.1016/j.aml.2011.12.033Licea, J. A., Villafuerte, L., & Chen-Charpentier, B. M. (2013). Analytic and numerical solutions of a Riccati differential equation with random coefficients. Journal of Computational and Applied Mathematics, 239, 208-219. doi:10.1016/j.cam.2012.09.040Lang, S. (1997). Undergraduate Analysis. Undergraduate Texts in Mathematics. doi:10.1007/978-1-4757-2698-5Cortés, J.-C., Romero, J.-V., Roselló, M.-D., Santonja, F.-J., & Villanueva, R.-J. (2013). Solving Continuous Models with Dependent Uncertainty: A Computational Approach. Abstract and Applied Analysis, 2013, 1-10. doi:10.1155/2013/983839Calatayud, J., Cortés, J. C., Jornet, M., & Villanueva, R. J. (2018). Computational uncertainty quantification for random time-discrete epidemiological models using adaptive gPC. Mathematical Methods in the Applied Sciences, 41(18), 9618-9627. doi:10.1002/mma.531