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Stellen Li

Publications and source records attributed to Stellen Li.

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Accounting for Heavy Censoring in Evaluating the Risk Stratification Abilities of Existing Models for Time to Diagnosis of Huntington Disease

Huntington disease (HD) is a neurodegenerative disease with progressively worsening symptoms. Accurately modeling time to HD diagnosis is essential for clinical trial design. Langbehn's model, the CAG-Age Product (CAP) model, the Prognostic Index Normed (PIN) model, and the Multivariate Risk Score (MRS) model have all been proposed for this task. However, these models may yield conflicting predictions and few studies have systematically compared their performance. Further, those that have could be misleading due to testing the models on the same data used to train them and failing to account for high rates of right censoring (80%+) in performance metrics. We discuss the theoretical foundations of these models, offering intuitive comparisons about their practical feasibility. We externally validate their risk stratification abilities using data from the ENROLL-HD study and two censoring-appropriate performance metrics, guiding model selection for HD clinical trial design. As these models were developed in HD studies that ended more than a decade ago, we compared their predictive performance using published parameters versus updated ones (re-estimated using ENROLL-HD). We show how these models can be used to estimate sample sizes for an HD clinical trial. Based on either metric and using published or updated parameters, the MRS model, which incorporates the most covariates, performed best. However, the simpler PIN model offered similarly good performance while requiring fewer variables, many of which would require patients to undergo additional tests. In illustrating an HD clinical trial design, we defined an optimal threshold based on model performance metrics to determine which patients are more likely to be diagnosed. Sample size calculations using an optimal threshold based on metrics that did not account for censoring, as in previous studies, are shown to lead to underpowered trials.

stat.AP

Polyhedra with hexagonal and triangular faces and three faces around each vertex

We analyze polyhedra composed of hexagons and triangles with three faces around each vertex, and their 3-regular planar graphs of edges and vertices, which we call "trihexes". Trihexes are analogous to fullerenes, which are 3-regular planar graphs whose faces are all hexagons and pentagons. Every trihex can be represented as the quotient of a hexagonal tiling of the plane under a group of isometries generated by $180^\circ$ rotations. Every trihex can also be described with either one or three "signatures": triples of numbers $(s, b, f)$ that describe the arrangement of the rotocenters of these rotations. Simple arithmetic rules relate the three signatures that describe the same trihex. We obtain a bijection between trihexes and equivalence classes of signatures as defined by these rules. Labeling trihexes with signatures allows us to put bounds on the number of trihexes for a given number vertices $v$ in terms of the prime factorization of $v$ and to prove a conjecture concerning trihexes that have no "belts" of hexagons.

math.CO