It is standard practice for covariates to enter a parametric model through a single distributional parameter of interest, for example, the scale parameter in many standard survival models. Indeed, the well-known proportional hazards model is of this kind. In this article, we discuss a more general approach whereby covariates enter the model through more than one distributional parameter simultaneously (e.g., scale and shape parameters). We refer to this practice as "multi-parameter regression" (MPR) modeling and explore its use in a survival analysis context. We find that multi-parameter regression leads to more flexible models which can offer greater insight into the underlying data generating process. To illustrate the concept, we consider the two-parameter Weibull model which leads to time-dependent hazard ratios, thus relaxing the typical proportional hazards assumption and motivating a new test of proportionality. A novel variable selection strategy is introduced for such multi-parameter regression models. It accounts for the correlation arising between the estimated regression coefficients in two or more linear predictors-a feature which has not been considered by other authors in similar settings. The methods discussed have been implemented in the mpr package in R.

Summary We introduce a general, flexible, parametric survival modelling framework which encompasses key shapes of hazard functions (constant; increasing; decreasing; up then down; down then up) and various common survival distributions (log‐logistic; Burr type XII; Weibull; Gompertz) and includes defective distributions (cure models). This generality is achieved by using four distributional parameters: two scale‐type parameters—one of which relates to accelerated failure time (AFT) modelling; the other to proportional hazards (PH) modelling—and two shape parameters. Furthermore, we advocate ‘multiparameter regression’ whereby more than one distributional parameter depends on covariates—rather than the usual convention of having a single covariate‐dependent (scale) parameter. This general formulation unifies the most popular survival models, enabling us to consider the practical value of possible modelling choices. In particular, we suggest introducing covariates through just one or other of the two scale parameters (covering AFT and PH models), and through a ‘power’ shape parameter (covering more complex non‐AFT or non‐PH effects); the other shape parameter remains covariate independent and handles automatic selection of the baseline distribution. We explore inferential issues and compare with alternative models through various simulation studies, with particular focus on evidence concerning the need, or otherwise, to include both AFT and PH parameters. We illustrate the efficacy of our modelling framework by using data from lung cancer, melanoma and kidney function studies. Censoring is accommodated throughout.

Background: Elevation of serum uric acid (SUA) is associated with increased mortality; however, controversy exists regarding the nature of the relationship and differences between men and women. We explored relationships of SUA levels with all-cause mortality in a large cohort of patients within the Irish health system. Methods: A retrospective cohort study of 26,525 participants was conducted using data from the National Kidney Disease Surveillance System. SUA was modelled in increments of 59.48 µmol/L (1 mg/dL), Cox's proportional hazards model estimated hazard ratios (HRs) and 95% Confidence Intervals (CI), median lifetimes were also computed separately for men and women. Mortality patterns were further explored using penalised splines. Results: There were 1,288 (4.9%) deaths over a median follow-up of 5.1 years. In men, the risk of mortality was greatest for the lowest (<238 µmol/L) and highest (>535 µmol/L) categories and HR 2.52 (1.87-3.29) respectively]; the corresponding median lifetimes for men were reduced by 9.5 and 11.7 years respectively compared to the referent. In women, mortality risks were elevated for SUA >416 mol/L [HR 1.69 (1.13-2.47) and beyond; the corresponding median lifetime for women were reduced by 5.9 years compared to the referent. Spline analysis revealed a U-shaped association between SUA and mortality in men, while for women, the pattern of association was J-shaped. Conclusion: Mortality patterns attributed to SUA differ between men and women. Optimal survival was associated with SUA concentrations of 304-454 µmol/L for men and < 409 µmol/L for women.

Shared opinions are an important feature in the formation of social groups. In this paper, we use the Axelrod model of cultural dissemination to represent opinion-based groups. In the Axelrod model, each agent has a set of features which each holds one of a set of nominally related traits. Survey data has a similar structure, where each participant answers each of a set of items with responses from a fixed list. We present an alternative method of displaying the Axelrod model by representing it as a bipartite graph, i.e., participants and their responses as separate nodes. This allows us to see which feature-trait combinations are selected in the final state. This visualisation is particularly useful when representing survey data as it illustrates the co-evolution of attitudes and opinion-based groups in Axelrod's model of cultural diffusion. We also present a modification to the Axelrod model. A standard finding of the Axelrod model with many features is for all agents to fully agree in one cluster. We introduce an agreement threshold and allow nodes to interact only with those neighbours who are within this threshold (i.e., those with similar opinions) rather than those with any opinion. This method reliably yields a large number of clusters for small agreement thresholds and, importantly, does not limit to single cluster when the number of features grows large. This potentially provides a method for modelling opinion-based groups where as opinions are added, the number of clusters increase.

Strategies adopted globally to mitigate the threat of COVID–19 have primarily involved lockdown measures with substantial economic and social costs with varying degrees of success. Morbidity patterns of COVID–19 variants have a strong association with age, while restrictive lockdown measures have association with negative mental health outcomes in some age groups. Reduced economic prospects may also afflict some age cohorts more than others. Motivated by this, we propose a model to describe COVID–19 community spread incorporating the role of age-specific social interactions. Through a flexible parameterisation of an age-structured deterministic Susceptible Exposed Infectious Removed (SEIR) model, we provide a means for characterising different forms of lockdown which may impact specific age groups differently. Social interactions are represented through age group to age group contact matrices, which can be trained using available data and are thus locally adapted. This framework is easy to interpret and suitable for describing counterfactual scenarios, which could assist policy makers with regard to minimising morbidity balanced with the costs of prospective suppression strategies. Our work originates from an Irish context and we use disease monitoring data from February 29th 2020 to January 31st 2021 gathered by Irish governmental agencies. We demonstrate how Irish lockdown scenarios can be constructed using the proposed model formulation and show results of retrospective fitting to incidence rates and forward planning with relevant “what if / instead of” lockdown counterfactuals. Uncertainty quantification for the predictive approaches is described. Our formulation is agnostic to a specific locale, in that lockdown strategies in other regions can be straightforwardly encoded using this model.