Simple or complex statistical models: Non-traditional regression models with intuitive interpretations

Abstract

The evolution of statistical modelling has historically been constrained by the practical limitations of computation; early statistical modelling favoured models which could feasibly be estimated. As increased mathematical complexity often implies more intricate computation, statistical models have grown both mathematically and computationally more complex. However, paradoxically, sometimes conceptually simpler models present more computational challenges than complex ones, and these have historically been neglected. In the case of binary responses, logistic regression models are the gold standard; covariates are modelled additively on the log-odds scale. In the case of time-to-event responses, the Cox proportional hazards regression model has additivity on the log-hazard rate scale. Both of these methods are computationally convenient, and yet the scales on which covariates are modelled are far from intuitive. We demonstrate the use of alternative models which are computationally more complex, yet feasible, but in which modelling is on a more interpretable scale. In the case of binary responses, a more intuitive alternative is log-binomial regression, in which modelling is on the log-relative risk scale. In the case of time-to-event responses, distributional regression enables modelling on the time scale. While logistic regression and proportional hazards regression qualitatively both deliver the same conclusions as the alternative models, log-binomial and distributional regression provide more interpretable coefficients, which are readily estimated.