Abstract: Waiting for elective procedures has become a major health concern in both rich and poor countries. The inadequate balance between the demand for and the supply of health services negatively affects the quality of life, mortality, and government appraisal. This study presents the first mathematical framework shedding light on how much, when, and where to invest in health capacity to end waiting lists for elective surgeries. We model the healthcare system as a two-stage stochastic capacity expansion problem where government investment decisions are represented as a non-symmetric Nash bargaining solution. In particular, the model assesses the capacity requirements, optimal allocation, and corresponding financial investment per hospital, region, specialty, and year. We use the proposed approach to target Chile's elective surgical waiting lists (2021- 2031), considering patients' priorities, 10 regional health services, 24 hospitals, and 10 surgical specialties. We generate uncertain future demand scenarios using historical data (2012-2021) and 100 autoregressive integrated moving average prediction models. The results indicate that USD 3,331.677 million is necessary to end the waiting lists by 2031 and that the Nash approach provides a fair resource distribution with a 6% efficiency loss. Additionally, a smaller budget (USD 2,000 million) was identified as necessary to end the waiting lists in a longer planning horizon. Further analysis revealed the impact of investment in patient transfer and a decline in investment yield.

Abstract: The operating theater is one of the most expensive units in the hospital, representing up to 40% of the total expenses. Because of its importance, the operating room scheduling problem has been addressed from many different perspectives since the early 1960s. One of the main difficulties that
has reduced the applicability of the current results is the high variability in surgery duration, making schedule recommendations hard to implement.
In this work, we propose a time-indexed scheduling formulation to solve the operational problem. Our main contribution is that we propose the use of chance constraints related to the surgery duration's probability distribution for each surgeon to improve the scheduling performance. We show how to implement these chance constraints as linear ones in our time-indexed formulation, enhancing the performance of the resulting schedules significantly.
Through data analysis of real historical instances, we develop specific constraints that improve the schedule, reducing the need for overtime without affecting the utilization significantly. Furthermore, these constraints give the operating room manager the possibility of balancing overtime and utilization through a tunning parameter in our formulation. Finally, through simulations and the use of real instances, we report the performance for four different metrics, showing the importance of using historical data to get the right balance between the utilization and overtime.

Abstract: Acoustic features of speech are promising as objective markers for mental health monitoring. Specialized smartphone apps can gather such acoustic data without disrupting the daily activities of patients. Nonetheless, the psychiatric assessment of the patient's mental state is typically a sporadic occurrence that takes place every few months. Consequently, only a slight fraction of the acoustic data is labeled and applicable for supervised learning. The majority of the related work on mental health monitoring limits the considerations only to labeled data using a predefined ground-truth period. On the other hand, semi-supervised methods make it possible to utilize the entire dataset, exploiting the regularities in the unlabeled portion of the data to improve the predictive power of a model. To assess the applicability of semi-supervised learning approaches, we discuss selected state-of-the-art semi-supervised classifiers, namely, label spreading, label propagation, a semi-supervised support vector machine, and the self training classifier. We use real-world data obtained from a bipolar disorder patient to compare the performance of the different methods with that of baseline supervised learning methods. The experiment shows that semi-supervised learning algorithms can outperform supervised algorithms in predicting bipolar disorder episodes.

Abstract: The appointment scheduling problem (ASP) studies how to manage patient arrivals to a healthcare system to improve system performance. An important challenge occurs when some patients may not show up for an appointment. Although the ASP is well studied in the literature, the vast majority of the existing work does not consider the well-observed phenomenon that patient no-show is influenced by the appointment time, the usual decision variable in the ASP. This paper studies the ASP with random service time (exogenous uncertainty) with known distribution and patient decision-dependent no-show behavior (endogenous uncertainty). This problem belongs to the class of stochastic optimization with decision-dependent uncertainties. Such problems are notoriously difficult as they are typically nonconvex. We propose a stochastic projected gradient path (SPGP) method to solve the problem, which requires the development of a gradient estimator of the objective function-a nontrivial task, as the literature on gradient-based optimization algorithms for problems with decision-dependent uncertainty is very scarce and unsuitable for our model. Our method can solve the ASP problem under arbitrarily smooth show-up probability functions. We present solutions under different patterns of no-show behavior and demonstrate that breaking the assumption of constant show-up probability substantially changes the scheduling solutions. We conduct numerical experiments in a variety of settings to compare our results with those obtained with a distributionally robust optimization method developed in the literature. The cost reduction obtained with our method, which we call the value of distribution information, can be interpreted as how much the system performance can be improved by knowing the distribution of the service times, compared to not knowing it. We observe that the value of distribution information is up to 31% of the baseline cost, and that such value is higher when the system is crowded or/and the waiting time cost is relatively high.
Summary of Contribution: This paper studies an appointment scheduling problem under time-dependent patient no-show behavior, a situation commonly observed in practice. The problem belongs to the class of stochastic optimization problems with decision-dependent uncertainties in the operations research literature. Such problems are notoriously difficult to solve as a result of the lack of convexity, and the present case requires different techniques because of the presence of continuous distributions for the service times. A stochastic projected gradient path method, which includes the development of specialized techniques to estimate the gradient of the objective function, is proposed to solve the problem. For problems with a similar structure, the algorithm can be applied once the gradient estimator of the objective function is obtained. Extensive numerical studies are presented to demonstrate the quality of the solutions, the importance of modeling time-dependent no-shows in appointment scheduling, and the value of using distribution information about the service times.

Abstract: In recent years, highly effective treatments for hepatitis C virus (HCV) have become available. However, high prices of new treatments call for a careful policy evaluation when considering economic constraints. Although the current medical advice is to administer the new therapies to all patients, economic and capacity constraints require an efficient allocation of these scarce resources. We use stochastic dynamic programming to determine the optimal policy for prescribing the new treatment based on the age and disease progression of the patient. We show that, in a simplified version of the model, new drugs should be administered to patients at a given level of fibrosis if they are within prespecified age limits; otherwise, a conservative approach of closely monitoring the evolution of the patient should be followed. We use a cohort of Spanish patients to study the optimal policy regarding costs and health indicators. For this purpose, we compare the performance of the optimal policy against a liberal policy of treating all sick patients. In this analysis, we achieve similar results in terms of the number of transplants, HCV-related deaths, and quality of adjusted life years, with a significant reduction in overall expenditure. Furthermore, the budget required during the first year of implementation when using the proposed methodology is only 12% of that when administering the treatment to all patients at once. Finally, we propose a method to prioritize patients when there is a shortage (surplus) in the annual budget constraint and, therefore, some recommended treatments must be postponed (added).

Abstract: Puberty is a complex developmental process that varies considerably among individuals and populations. Genetic factors explain a large proportion of the variability of several pubertal traits. Recent genome-wide association studies (GWAS) have identified hundreds of variants involved in traits that result from body growth, like adult height. However, they do not capture many genetic loci involved in growth changes over distinct growth phases. Further, such GWAS have been mostly performed in Europeans, but we do not know how these findings relate to other continental populations. In this study, we analyzed the genetic basis of three pubertal traits; namely, peak height velocity (PV), age at PV (APV) and height at APV (HAPV). We analyzed a cohort of 904 admixed Chilean children and adolescents with European and Mapuche Native American ancestries. Height was measured on roughly a 6-month basis from childhood to adolescence between 2006 and 2019. We predict that the difference in HAPV between an European and a Mapuche adolescent is 4.3 cm higher in the European (P = 0.042) and APV is 0.73 years later for the European compared with the Mapuche adolescent on average (P = 0.023). Further, by performing a GWAS on 774, 433 single-nucleotide polymorphisms, we identified a genetic signal harboring 3 linked variants significantly associated with PV in boys (P < 5 x 10(-8)). This signal has never been associated with growth-related traits.