The treatment of epilepsy in younger and older adults: Demographic differences and prescribing patterns of anti-seizure medications in Canada.

OBJECTIVE: Our study describes adults in Canada between 2009 and 2013 receiving at least one antiseizure medication (ASM) at the end of a hospitalization for newly-diagnosed epilepsy, with a focus on the type of ASM prescribed, changes in drug prescriptions after one year, and how this differs between younger and older adults. METHODS: Canada-wide data from the Discharge Abstract Database and the National Prescription Drug Utilization Information System database from 2009 to 2013 were used to identify individuals hospitalized with newly-diagnosed epilepsy and prescribed an ASM at the end of this hospitalization. We classified ASMs into enzyme inducing (EIASM) and non-enzyme inducing (non-EIASM). Confidence intervals and p-values were generated using an exact binomial distribution. RESULTS: Our study sample included 10,568 adults. 61.3% (95% CI: 60.3, 62.2) of all prescriptions were for EIASMs. Among EIASMs, phenytoin was the most frequently prescribed drug in both younger (aged 18-59 years) and older subjects. Among older adults prescribed EIASMs, 53.1% (95% CI: 51.5, 54.7) were men; and for non-EIASMs, 45.2% (95% CI: 43.0%, 47.4) were men. Among the 3847 older adults initially prescribed EIASMs, 7.1% (95% CI: 6.4, 8.0) switched to non-EIASMs at one year following their hospital discharge. CONCLUSION: Non-EIASM have been available to clinicians since the 1990's but suboptimal ASMs such as phenytoin remained frequently prescribed during the period of this study. This is an especially pressing issue among older adults due to the greater risk of drug intolerability, related to metabolic changes that occur with greater age, increasing comorbidity burden, and frailty. Men were disproportionately prescribed EIASM, as compared to women who were more often prescribed non-EIASM.

Generalized Sparse Additive Models.

We present a unified framework for estimation and analysis of generalized additive models in high dimensions. The framework defines a large class of penalized regression estimators, encompassing many existing methods. An efficient computational algorithm for this class is presented that easily scales to thousands of observations and features. We prove minimax optimal convergence bounds for this class under a weak compatibility condition. In addition, we characterize the rate of convergence when this compatibility condition is not met. Finally, we also show that the optimal penalty parameters for structure and sparsity penalties in our framework are linked, allowing cross-validation to be conducted over only a single tuning parameter. We complement our theoretical results with empirical studies comparing some existing methods within this framework.

Nonparametric regression with adaptive truncation via a convex hierarchical penalty.

We consider the problem of nonparametric regression with a potentially large number of covariates. We propose a convex, penalized estimation framework that is particularly well suited to high-dimensional sparse additive models and combines the appealing features of finite basis representation and smoothing penalties. In the case of additive models, a finite basis representation provides a parsimonious representation for fitted functions but is not adaptive when component functions possess different levels of complexity. In contrast, a smoothing spline-type penalty on the component functions is adaptive but does not provide a parsimonious representation. Our proposal simultaneously achieves parsimony and adaptivity in a computationally efficient way. We demonstrate these properties through empirical studies and show that our estimator converges at the minimax rate for functions within a hierarchical class. We further establish minimax rates for a large class of sparse additive models. We also develop an efficient algorithm that scales similarly to the lasso with the number of covariates and sample size.

Convex Modeling of Interactions with Strong Heredity.

We consider the task of fitting a regression model involving interactions among a potentially large set of covariates, in which we wish to enforce strong heredity. We propose FAMILY, a very general framework for this task. Our proposal is a generalization of several existing methods, such as VANISH [Radchenko and James, 2010], hierNet [Bien et al., 2013], the all-pairs lasso, and the lasso using only main effects. It can be formulated as the solution to a convex optimization problem, which we solve using an efficient alternating directions method of multipliers (ADMM) algorithm. This algorithm has guaranteed convergence to the global optimum, can be easily specialized to any convex penalty function of interest, and allows for a straightforward extension to the setting of generalized linear models. We derive an unbiased estimator of the degrees of freedom of FAMILY, and explore its performance in a simulation study and on an HIV sequence data set.