Steven J. Miller

Hallee E. Wong, Brianna C. Heggeseth, Steven J. Miller

Accurately predicting patients' risk of 30-day hospital readmission would enable hospitals to efficiently allocate resource-intensive interventions. We develop a new method, Categorical Co-Frequency Analysis (CoFA), for clustering diagnosis codes from the International Classification of Diseases (ICD) according to the similarity in relationships between covariates and readmission risk. CoFA measures the similarity between diagnoses by the frequency with which two diagnoses are split in the same direction versus split apart in random forests to predict readmission risk. Applying CoFA to de-identified data from Berkshire Medical Center, we identified three groups of diagnoses that vary in readmission risk. To evaluate CoFA, we compared readmission risk models using ICD majors and CoFA groups to a baseline model without diagnosis variables. We found substituting ICD majors for the CoFA-identified clusters simplified the model without compromising the accuracy of predictions. Fitting separate models for each ICD major and CoFA group did not improve predictions, suggesting that readmission risk may be more homogeneous that heterogeneous across diagnosis groups.

Steven J. Miller

We explore the effect of zeros at the central point on nearby zeros of elliptic curve L-functions, especially for one-parameter families of rank r over Q. By the Birch and Swinnerton Dyer Conjecture and Silverman's Specialization Theorem, for t sufficiently large the L-function of each curve E_t in the family has r zeros (called the family zeros) at the central point. We observe experimentally a repulsion of the zeros near the central point, and the repulsion increases with r. There is greater repulsion in the subset of curves of rank r+2 than in the subset of curves of rank r in a rank r family. For curves with comparable conductors, the behavior of rank 2 curves in a rank 0 one-parameter family over Q is statistically different from that of rank 2 curves from a rank 2 family. Unlike excess rank calculations, the repulsion decreases markedly as the conductors increase, and we conjecture that the r family zeros do not repel in the limit. Finally, the differences between adjacent normalized zeros near the central point are statistically independent of the repulsion, family rank and rank of the curves in the subset. Specifically, the differences between adjacent normalized zeros are statistically equal for all curves investigated with rank 0, 2 or 4 and comparable conductors from one-parameter families of rank 0 or 2 over Q.