Relation of Incident Type 1 Diabetes to Recent COVID-19 Infection: Cohort Study Using e-Health Record Linkage in Scotland.

OBJECTIVE: Studies using claims databases reported that severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection >30 days earlier was associated with an increase in the incidence of type 1 diabetes. Using exact dates of diabetes diagnosis from the national register in Scotland linked to virology laboratory data, we sought to replicate this finding. RESEARCH DESIGN AND METHODS: A cohort of 1,849,411 individuals aged <35 years without diabetes, including all those in Scotland who subsequently tested positive for SARS-CoV-2, was followed from 1 March 2020 to 22 November 2021. Incident type 1 diabetes was ascertained from the national registry. Using Cox regression, we tested the association of time-updated infection with incident diabetes. Trends in incidence of type 1 diabetes in the population from 2015 through 2021 were also estimated in a generalized additive model. RESULTS: There were 365,080 individuals who had at least one detected SARS-CoV-2 infection during follow-up and 1,074 who developed type 1 diabetes. The rate ratio for incident type 1 diabetes associated with first positive test for SARS-CoV-2 (reference category: no previous infection) was 0.86 (95% CI 0.62, 1.21) for infection >30 days earlier and 2.62 (95% CI 1.81, 3.78) for infection in the previous 30 days. However, negative and positive SARS-CoV-2 tests were more frequent in the days surrounding diabetes presentation. In those aged 0-14 years, incidence of type 1 diabetes during 2020-2021 was 20% higher than the 7-year average. CONCLUSIONS: Type 1 diabetes incidence in children increased during the pandemic. However, the cohort analysis suggests that SARS-CoV-2 infection itself was not the cause of this increase.

Rejoinder to the discussions of "Spatial+: A novel approach to spatial confounding".

In this rejoinder, we set out some of the main points that we took from the discussions of our paper "Spatial+: A novel approach to spatial confounding." The comments provided by the discussants include excellent questions and suggestions for extensions and improvements to spatial+. The discussions also highlight the growing interest in understanding spatial confounding, underpinned by the many recent contributions to the literature on this topic.

Spatial+: A novel approach to spatial confounding.

In spatial regression models, collinearity between covariates and spatial effects can lead to significant bias in effect estimates. This problem, known as spatial confounding, is encountered modeling forestry data to assess the effect of temperature on tree health. Reliable inference is difficult as results depend on whether or not spatial effects are included in the model. We propose a novel approach, spatial+, for dealing with spatial confounding when the covariate of interest is spatially dependent but not fully determined by spatial location. Using a thin plate spline model formulation we see that, in this case, the bias in covariate effect estimates is a direct result of spatial smoothing. Spatial+ reduces the sensitivity of the estimates to smoothing by replacing the covariates by their residuals after spatial dependence has been regressed away. Through asymptotic analysis we show that spatial+ avoids the bias problems of the spatial model. This is also demonstrated in a simulation study. Spatial+ is straightforward to implement using existing software and, as the response variable is the same as that of the spatial model, standard model selection criteria can be used for comparisons. A major advantage of the method is also that it extends to models with non-Gaussian response distributions. Finally, while our results are derived in a thin plate spline setting, the spatial+ methodology transfers easily to other spatial model formulations.

Inferring UK COVID-19 fatal infection trajectories from daily mortality data: Were infections already in decline before the UK lockdowns?

The number of new infections per day is a key quantity for effective epidemic management. It can be estimated relatively directly by testing of random population samples. Without such direct epidemiological measurement, other approaches are required to infer whether the number of new cases is likely to be increasing or decreasing: for example, estimating the pathogen-effective reproduction number, R, using data gathered from the clinical response to the disease. For coronavirus disease 2019 (Covid-19/SARS-Cov-2), such R estimation is heavily dependent on modelling assumptions, because the available clinical case data are opportunistic observational data subject to severe temporal confounding. Given this difficulty, it is useful to retrospectively reconstruct the time course of infections from the least compromised available data, using minimal prior assumptions. A Bayesian inverse problem approach applied to UK data on first-wave Covid-19 deaths and the disease duration distribution suggests that fatal infections were in decline before full UK lockdown (24 March 2020), and that fatal infections in Sweden started to decline only a day or two later. An analysis of UK data using the model of Flaxman et al. gives the same result under relaxation of its prior assumptions on R, suggesting an enhanced role for non-pharmaceutical interventions short of full lockdown in the UK context. Similar patterns appear to have occurred in the subsequent two lockdowns.

Was R < 1 before the English lockdowns? On modelling mechanistic detail, causality and inference about Covid-19.

Detail is a double edged sword in epidemiological modelling. The inclusion of mechanistic detail in models of highly complex systems has the potential to increase realism, but it also increases the number of modelling assumptions, which become harder to check as their possible interactions multiply. In a major study of the Covid-19 epidemic in England, Knock et al. (2020) fit an age structured SEIR model with added health service compartments to data on deaths, hospitalization and test results from Covid-19 in seven English regions for the period March to December 2020. The simplest version of the model has 684 states per region. One main conclusion is that only full lockdowns brought the pathogen reproduction number, R, below one, with R ≫ 1 in all regions on the eve of March 2020 lockdown. We critically evaluate the Knock et al. epidemiological model, and the semi-causal conclusions made using it, based on an independent reimplementation of the model designed to allow relaxation of some of its strong assumptions. In particular, Knock et al. model the effect on transmission of both non-pharmaceutical interventions and other effects, such as weather, using a piecewise linear function, b(t), with 12 breakpoints at selected government announcement or intervention dates. We replace this representation by a smoothing spline with time varying smoothness, thereby allowing the form of b(t) to be substantially more data driven, and we check that the corresponding smoothness assumption is not driving our results. We also reset the mean incubation time and time from first symptoms to hospitalisation, used in the model, to values implied by the papers cited by Knock et al. as the source of these quantities. We conclude that there is no sound basis for using the Knock et al. model and their analysis to make counterfactual statements about the number of deaths that would have occurred with different lockdown timings. However, if fits of this epidemiological model structure are viewed as a reasonable basis for inference about the time course of incidence and R, then without very strong modelling assumptions, the pathogen reproduction number was probably below one, and incidence in substantial decline, some days before either of the first two English national lockdowns. This result coincides with that obtained by more direct attempts to reconstruct incidence. Of course it does not imply that lockdowns had no effect, but it does suggest that other non-pharmaceutical interventions (NPIs) may have been much more effective than Knock et al. imply, and that full lockdowns were probably not the cause of R dropping below one.

Analyzing the Time Course of Pupillometric Data.

This article provides a tutorial for analyzing pupillometric data. Pupil dilation has become increasingly popular in psychological and psycholinguistic research as a measure to trace language processing. However, there is no general consensus about procedures to analyze the data, with most studies analyzing extracted features from the pupil dilation data instead of analyzing the pupil dilation trajectories directly. Recent studies have started to apply nonlinear regression and other methods to analyze the pupil dilation trajectories directly, utilizing all available information in the continuously measured signal. This article applies a nonlinear regression analysis, generalized additive mixed modeling, and illustrates how to analyze the full-time course of the pupil dilation signal. The regression analysis is particularly suited for analyzing pupil dilation in the fields of psychological and psycholinguistic research because generalized additive mixed models can include complex nonlinear interactions for investigating the effects of properties of stimuli (e.g., formant frequency) or participants (e.g., working memory score) on the pupil dilation signal. To account for the variation due to participants and items, nonlinear random effects can be included. However, one of the challenges for analyzing time series data is dealing with the autocorrelation in the residuals, which is rather extreme for the pupillary signal. On the basis of simulations, we explain potential causes of this extreme autocorrelation, and on the basis of the experimental data, we show how to reduce their adverse effects, allowing a much more coherent interpretation of pupillary data than possible with feature-based techniques.

A generalized Fellner-Schall method for smoothing parameter optimization with application to Tweedie location, scale and shape models.

We consider the optimization of smoothing parameters and variance components in models with a regular log likelihood subject to quadratic penalization of the model coefficients, via a generalization of the method of Fellner (1986) and Schall (1991). In particular: (i) we generalize the original method to the case of penalties that are linear in several smoothing parameters, thereby covering the important cases of tensor product and adaptive smoothers; (ii) we show why the method's steps increase the restricted marginal likelihood of the model, that it tends to converge faster than the EM algorithm, or obvious accelerations of this, and investigate its relation to Newton optimization; (iii) we generalize the method to any Fisher regular likelihood. The method represents a considerable simplification over existing methods of estimating smoothing parameters in the context of regular likelihoods, without sacrificing generality: for example, it is only necessary to compute with the same first and second derivatives of the log-likelihood required for coefficient estimation, and not with the third or fourth order derivatives required by alternative approaches. Examples are provided which would have been impossible or impractical with pre-existing Fellner-Schall methods, along with an example of a Tweedie location, scale and shape model which would be a challenge for alternative methods, and a sparse additive modeling example where the method facilitates computational efficiency gains of several orders of magnitude. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Common femoral vein thrombosis caused by a metal-on-metal hip arthroplasty-related pseudotumor.

We present a case of a pseudotumor causing a deep femoral vein thrombosis 16 months after undergoing a metal-on-metal total hip arthroplasty. There is increasing concern over the effect of metal ions that are produced by wear in metal-on-metal hip arthroplasty systems. Recently, a number of articles have reported the development of an inflammatory pseudotumor causing a number of different problems early on in the lifespan of the implant necessitating revision surgery. This case reports the first presentation of a pseudotumor causing a serious venous thrombosis due to pressure effect and indicates further possible evidence for caution when considering metal-on-metal bearing hip arthroplasty.

Statistical inference for noisy nonlinear ecological dynamic systems.

Chaotic ecological dynamic systems defy conventional statistical analysis. Systems with near-chaotic dynamics are little better. Such systems are almost invariably driven by endogenous dynamic processes plus demographic and environmental process noise, and are only observable with error. Their sensitivity to history means that minute changes in the driving noise realization, or the system parameters, will cause drastic changes in the system trajectory. This sensitivity is inherited and amplified by the joint probability density of the observable data and the process noise, rendering it useless as the basis for obtaining measures of statistical fit. Because the joint density is the basis for the fit measures used by all conventional statistical methods, this is a major theoretical shortcoming. The inability to make well-founded statistical inferences about biological dynamic models in the chaotic and near-chaotic regimes, other than on an ad hoc basis, leaves dynamic theory without the methods of quantitative validation that are essential tools in the rest of biological science. Here I show that this impasse can be resolved in a simple and general manner, using a method that requires only the ability to simulate the observed data on a system from the dynamic model about which inferences are required. The raw data series are reduced to phase-insensitive summary statistics, quantifying local dynamic structure and the distribution of observations. Simulation is used to obtain the mean and the covariance matrix of the statistics, given model parameters, allowing the construction of a 'synthetic likelihood' that assesses model fit. This likelihood can be explored using a straightforward Markov chain Monte Carlo sampler, but one further post-processing step returns pure likelihood-based inference. I apply the method to establish the dynamic nature of the fluctuations in Nicholson's classic blowfly experiments.

The effects of group size, leaf size, and density on the performance of a leaf-mining moth.

1. The effects of two factors, leaf size and group size, on the performance of the Tupelo leafminer, Antispila nysaefoliella (Lepidoptera: Heliozelidae), were examined by fitting growth models to mine expansion data using nonlinear mixed-effects models. 2. The rate of mine expansion served as a proxy for larval performance because of its correlation with both feeding activity and growth rate and is also the means by which a larva achieves its final mine size (or total consumption). 3. Leaf size was used as a measure of resource availability, and was expected to reduce the impact of resource competition and enhance larval performance. 4. In contrast to the unidirectional effects expected for leaf size (i.e. more resources should enhance performance), the direction for the effects of group size was expected to depend on the mechanism(s) driving the effect. For example, if there is resource competition among larvae in a group, then this could increase the feeding rates of some larvae or reduce the total consumption of others. However, if leaf mining induces host plant chemical defences, then larger groups might elicit a greater defensive response by the host plant (at the leaf), and hence, be characterized by reduced feeding and growth rates. 5. To investigate these interactions, two growth models, the Gompertz model and a modified version of the von Bertalanffy growth equation, were fitted to time series of the sizes of individual leaf mines using nonlinear mixed-effects models. Linear and nonlinear associations of each factor (group size or leaf size) with model parameters were then evaluated using a hierarchical testing procedure by determining: (i) whether inclusion of the factor produced a better-fit model, and (ii) if it did, the form of that relationship (i.e. linear or nonlinear). 6. Three patterns were detected with these analyses. (i) Leaf size had a significant positive, linear relationship with mine expansion rate. (ii) Group size had a significant quadratic relationship with mine expansion rate. (iii) The effects of leaf and group size on the maximum mine size were opposite to those found with growth rate.

Low-rank scale-invariant tensor product smooths for generalized additive mixed models.

A general method for constructing low-rank tensor product smooths for use as components of generalized additive models or generalized additive mixed models is presented. A penalized regression approach is adopted in which tensor product smooths of several variables are constructed from smooths of each variable separately, these "marginal" smooths being represented using a low-rank basis with an associated quadratic wiggliness penalty. The smooths offer several advantages: (i) they have one wiggliness penalty per covariate and are hence invariant to linear rescaling of covariates, making them useful when there is no "natural" way to scale covariates relative to each other; (ii) they have a useful tuneable range of smoothness, unlike single-penalty tensor product smooths that are scale invariant; (iii) the relatively low rank of the smooths means that they are computationally efficient; (iv) the penalties on the smooths are easily interpretable in terms of function shape; (v) the smooths can be generated completely automatically from any marginal smoothing bases and associated quadratic penalties, giving the modeler considerable flexibility to choose the basis penalty combination most appropriate to each modeling task; and (vi) the smooths can easily be written as components of a standard linear or generalized linear mixed model, allowing them to be used as components of the rich family of such models implemented in standard software, and to take advantage of the efficient and stable computational methods that have been developed for such models. A small simulation study shows that the methods can compare favorably with recently developed smoothing spline ANOVA methods.