Zachary J. Smith

Background: Essential tremor (ET) is a common movement disorder that affects the upper limbs in vital activities of daily living. Few studies have examined the impact of tremor severity on caregiving intensity. Methods: Clinic-based data were collected in the United States (US) from March 2021 to August 2021 through the Adelphi ET Disease Specific Programme (DSP). Linked data between physician and care partner/patient pairs were used to evaluate care partner-reported weekly hours of patient care. Tremor severity was assessed with the Essential Tremor Rating Assessment Scale (TETRAS) Performance and Activities of Daily Living subscales. Pearson chi-square, correlation and multivariate regression analyses were conducted to examine the relationships between tremor severity and hours of care partner assistance. Results: A quarter of 960 individuals with ET required care partners. Most care partners were spouses (61%), but other family members or friends also served as care partners. About 23% of care partners reported giving constant care, defined as 112 hours per week or more, while the remainder of care partners reported caregiving time averaging 24.5 hours per week. The probability of needing a care partner was significantly associated with tremor severity, and the association between care partner need and tremor severity was moderate (bivariate r = 0.32–0.37) and not substantially impacted by the inclusion of additional covariates (age, sex, race, comorbidity, relationship with patient, and living with patient). Discussion: Roughly 25% of patients with ET have care partner needs, and the number of care partner hours provided is correlated with tremor severity. Therefore, treatments that ameliorate tremor severity have the potential to reduce caregiving intensity in ET.

Background: Essential tremor (ET) affects nearly 7 million people in the United States and consists of upper limb tremor that can affect activities of daily living, including activities related to work. Research examining the effect of ET on work productivity is limited and there are no studies using validated work productivity instruments. Methods: Clinic-based data were collected between March 2021 and August 2021 from US physicians participating in the Adelphi ET Disease Specific Programme (DSP). Patients were evaluated with the Essential Tremor Rating Assessment Scale (TETRAS), Quality of Life in Essential Tremor (QUEST) questionnaire, and the Work Productivity and Activity Impairment (WPAI) questionnaire. Statistical associations between tremor severity and work productivity were examined. Results: A total of 1,003 ET patients were identified, and 420 patients completed the WPAI questionnaire and were included in this study. Activity impairment was independently associated with tremor severity, adjusting for age, full-time vs. part-time employment, household income, depression, and anxiety. Of those who were employed (n = 165), 133 (80.6%) were employed full-time, and 141 (85.5%) had some level of work impairment. Work impairment was also independently associated with tremor severity, adjusting for the same covariates. Among those patients for whom QUEST responses were available, 47% (64/135) of patients with ET working full-time and 88% (36/41) of those working part-time reported that tremor interfered with work. Discussion: Work impairment is significantly correlated with tremor severity. Although a minority of patients in this clinic-based cohort were identified as employed, nearly all reported a negative impact on work performance.

Background: Essential tremor (ET) is a disabling syndrome consisting of tremor, primarily in the upper limbs. We assessed the correlation of The Essential Tremor Rating Assessment Scale (TETRAS) Performance Item 4 ratings of upper limb tremor with the TETRAS activities of daily living (ADL) subscale and with 2 quality of life (QoL) scales. Methods: This noninterventional, cross-sectional, point-in-time survey of neurologists(n = 60), primary care physicians (n = 38), and their patients with ET (n = 1,003) used real-world data collected through the Adelphi ET Disease Specific Programme™. Physician-reported measures (TETRAS Performance Item 4 and TETRAS ADL total) and patient-reported QoL measures (generic EuroQol-5 Dimension 5 Level [EQ-5D-5 L] and ET-specific Quality of Life in Essential Tremor Questionnaire (QUEST)) were assessed with bivariate and multivariable analyses. Sensitivity analyses were also conducted. Results: The bivariate association between TETRAS Performance Item 4 score and TETRAS ADL total score was high (Pearson r = 0.761, P < 0.001). The bivariate associations between TETRAS Performance Item 4 score and EQ-5D-5 L index score (r = –0.410, P < 0.001) and between TETRAS ADL total score and EQ-5D-5 L index score (r = –0.543, P < 0.001) were moderate. The bivariate associations between TETRAS Performance Item 4 score and QUEST total score (r = 0.457, P < 0.001), and between TETRAS ADL total score and QUEST total score (r = 0.630, P < 0.001) were also moderate. These associations were unaltered by the inclusion of covariates. Discussion: This study showed that greater tremor severity (TETRAS Performance Item 4) was positively correlated with ADL impairment (TETRAS ADL) and negatively associated with QoL (EQ-5D-5 L and QUEST). TETRAS Performance Item 4 score is a robust predictor of TETRAS ADL total score, and TETRAS Performance Item 4 and TETRAS ADL total scores were robust predictors of the 2 QoL scales. The results demonstrate the value of TETRAS scores as valid endpoints for future clinical trials. Highlights This real-world study assessed TETRAS scores as predictors of impaired QoL in ET. TETRAS Performance Item 4 and ADL were associated with EQ-5D-5 L and QUEST. TETRAS scores may serve as valid endpoints for future clinical trials.

We present a mathematical modeling framework for roster construction of a Major League Soccer (MLS) expansion team. The model seeks to construct the best squad feasible under league salary rules, while balancing present value, potential value, and future cap flexibility. Player acquisition decisions, as well as allocation of salary, targeted allocation money (TAM), general allocation money (GAM), and designated player slots, are determined simultaneously by a mixed-integer programming model. We demonstrate the model’s functionality in constructing a hypothetical expansion roster and propose a number of extensions.

This paper establishes a new relationship between proper scoring rules and convex risk measures. Specifically, we demonstrate that the entropy function associated with any weighted scoring rule is equal to the maximum value of an optimization problem where an investor maximizes a concave certainty equivalent (the negation of a convex risk measure). Using this connection, we construct two classes of proper weighted scoring rules with associated entropy functions based on ϕ-divergences. These rules are generalizations of the weighted power and weighted pseudospherical rules.

In this paper, we develop strictly proper scoring rules that may be used to evaluate the accuracy of a sequence of probabilistic forecasts. In practice, when forecasts are submitted for multiple uncertainties, competing forecasts are ranked by their cumulative or average score. Alternatively, one could score the implied joint distributions. We demonstrate that these measures of forecast accuracy disagree under some commonly used rules. Furthermore, and most importantly, we show that forecast rankings can depend on the selected scoring procedure. In other words, under some scoring rules, the relative ranking of probabilistic forecasts does not depend solely on the information content of those forecasts and the observed outcome. Instead, the relative ranking of forecasts is a function of the process by which those forecasts are evaluated. As an alternative, we describe additive and strongly additive strictly proper scoring rules, which have the property that the score for the joint distribution is equal to a sum of scores for the associated marginal and conditional distributions. We give methods for constructing additive rules and demonstrate that the logarithmic score is the only strongly additive rule. Finally, we connect the additive properties of scoring rules with analogous properties for a general class of entropy measures.