All Publications

  • Sequential allocation of vaccine to control an infectious disease. Mathematical biosciences Rao, I. J., Brandeau, M. L. 2022: 108879


    The problem of optimally allocating a limited supply of vaccine to control a communicable disease has broad applications in public health and has received renewed attention during the COVID-19 pandemic. This allocation problem is highly complex and nonlinear. Decision makers need a practical, accurate, and interpretable method to guide vaccine allocation. In this paper we develop simple analytical conditions that can guide the allocation of vaccines over time. We consider four objectives: minimize new infections, minimize deaths, minimize life years lost, or minimize quality-adjusted life years lost due to death. We consider an SIR model with interacting population groups. We approximate the model using Taylor series expansions, and develop simple analytical conditions characterizing the optimal solution to the resulting problem for a single time period. We develop a solution approach in which we allocate vaccines using the analytical conditions in each time period based on the state of the epidemic at the start of the time period. We illustrate our method with an example of COVID-19 vaccination, calibrated to epidemic data from New York State. Using numerical simulations, we show that our method achieves near-optimal results over a wide range of vaccination scenarios. Our method provides a practical, intuitive, and accurate tool for decision makers as they allocate limited vaccines over time, and highlights the need for more interpretable models over complicated black box models to aid in decision making.

    View details for DOI 10.1016/j.mbs.2022.108879

    View details for PubMedID 35843382

  • Surveillance for endemic infectious disease outbreaks: Adaptive sampling using profile likelihood estimation. Statistics in medicine Fairley, M., Rao, I. J., Brandeau, M. L., Qian, G. L., Gonsalves, G. S. 2022


    Outbreaks of an endemic infectious disease can occur when the disease is introduced into a highly susceptible subpopulation or when the disease enters a network of connected individuals. For example, significant HIV outbreaks among people who inject drugs have occurred in at least half a dozen US states in recent years. This motivates the current study: how can limited testing resources be allocated across geographic regions to rapidly detect outbreaks of an endemic infectious disease? We develop an adaptive sampling algorithm that uses profile likelihood to estimate the distribution of the number of positive tests that would occur for each location in a future time period if that location were sampled. Sampling is performed in the location with the highest estimated probability of triggering an outbreak alarm in the next time period. The alarm function is determined by a semiparametric likelihood ratio test. We compare the profile likelihood sampling (PLS) method numerically to uniform random sampling (URS) and Thompson sampling (TS). TS was worse than URS when the outbreak occurred in a location with lower initial prevalence than other locations. PLS had lower time to outbreak detection than TS in some but not all scenarios, but was always better than URS even when the outbreak occurred in a location with a lower initial prevalence than other locations. PLS provides an effective and reliable method for rapidly detecting endemic disease outbreaks that is robust to this uncertainty.

    View details for DOI 10.1002/sim.9420

    View details for PubMedID 35527474

  • Effectiveness of Policies for Addressing the US Opioid Epidemic: A Model-Based Analysis from the Stanford-Lancet Commission on the North American Opioid Crisis. Lancet Regional Health. Americas Rao, I. J., Humphreys, K., Brandeau, M. L. 2021; 3


    Background: The U.S. opioid crisis has been exacerbated by COVID-19 and the spread of synthetic opioids (e.g., fentanyl).Methods: We model the effectiveness of reduced prescribing, drug rescheduling, prescription monitoring programs (PMPs), tamper-resistant drug reformulation, excess opioid disposal, naloxone availability, syringe exchange, pharmacotherapy, and psychosocial treatment. We measure life years, quality-adjusted life years (QALYs), and opioid-related deaths over five and ten years.Findings: Under the status quo, our model predicts that approximately 547,000 opioid-related deaths will occur from 2020 to 2024 (range 441,000 - 613,000), rising to 1,220,000 (range 996,000 - 1,383,000) by 2029. Expanding naloxone availability by 30% had the largest effect, averting 25% of opioid deaths. Pharmacotherapy, syringe exchange, psychosocial treatment, and PMPs are uniformly beneficial, reducing opioid-related deaths while leading to gains in life years and QALYs. Reduced prescribing and increasing excess opioid disposal programs would reduce total deaths, but would lead to more heroin deaths in the short term. Drug rescheduling would increase total deaths over five years as some opioid users escalate to heroin, but decrease deaths over ten years. Combined interventions would lead to greater increases in life years, QALYs, and deaths averted, although in many cases the results are subadditive.Interpretation: Expanded health services for individuals with opioid use disorder combined with PMPs and reduced opioid prescribing would moderately lessen the severity of the opioid crisis over the next decade. Tragically, even with improved public policies, significant morbidity and mortality is inevitable.

    View details for DOI 10.1016/j.lana.2021.100031

    View details for PubMedID 34790907

  • Effectiveness of Face Masks in Reducing the Spread of COVID-19: A Model-Based Analysis. Medical decision making : an international journal of the Society for Medical Decision Making Rao, I. J., Vallon, J. J., Brandeau, M. L. 2021: 272989X211019029


    BACKGROUND: The World Health Organization and US Centers for Disease Control and Prevention recommend that both infected and susceptible people wear face masks to protect against COVID-19.METHODS: We develop a dynamic disease model to assess the effectiveness of face masks in reducing the spread of COVID-19, during an initial outbreak and a later resurgence, as a function of mask effectiveness, coverage, intervention timing, and time horizon. We instantiate the model for the COVID-19 outbreak in New York, with sensitivity analyses on key natural history parameters.RESULTS: During the initial epidemic outbreak, with no social distancing, only 100% coverage of masks with high effectiveness can reduce the effective reproductive number Re below 1. During a resurgence, with lowered transmission rates due to social distancing measures, masks with medium effectiveness at 80% coverage can reduce Re below 1 but cannot do so if individuals relax social distancing efforts. Full mask coverage could significantly improve outcomes during a resurgence: with social distancing, masks with at least medium effectiveness could reduce Re below 1 and avert almost all infections, even with intervention fatigue. For coverage levels below 100%, prioritizing masks that reduce the risk of an infected individual from spreading the infection rather than the risk of a susceptible individual from getting infected yields the greatest benefit.LIMITATIONS: Data regarding COVID-19 transmission are uncertain, and empirical evidence on mask effectiveness is limited. Our analyses assume homogeneous mixing, providing an upper bound on mask effectiveness.CONCLUSIONS: Even moderately effective face masks can play a role in reducing the spread of COVID-19, particularly with full coverage, but should be combined with social distancing measures to reduce Re below 1.[Box: see text].

    View details for DOI 10.1177/0272989X211019029

    View details for PubMedID 34041970

  • Optimal allocation of limited vaccine to control an infectious disease: Simple analytical conditions. Mathematical biosciences Rao, I. J., Brandeau, M. L. 2021: 108621


    When allocating limited vaccines to control an infectious disease, policy makers frequently have goals relating to individual health benefits (e.g., reduced morbidity and mortality) as well as population-level health benefits (e.g., reduced transmission and possible disease eradication). We consider the optimal allocation of a limited supply of a preventive vaccine to control an infectious disease, and four different allocation objectives: minimize new infections, deaths, life years lost, or quality-adjusted life years (QALYs) lost due to death. We consider an SIR model with n interacting populations, and a single allocation of vaccine at time 0. We approximate the model dynamics to develop simple analytical conditions characterizing the optimal vaccine allocation for each objective. We instantiate the model for an epidemic similar to COVID-19 and consider n=2 population groups: one group (individuals under age 65) with high transmission but low mortality and the other group (individuals age 65 or older) with low transmission but high mortality. We find that it is optimal to vaccinate younger individuals to minimize new infections, whereas it is optimal to vaccinate older individuals to minimize deaths, life years lost, or QALYs lost due to death. Numerical simulations show that the allocations resulting from our conditions match those found using much more computationally expensive algorithms such as exhaustive search. Sensitivity analysis on key parameters indicates that the optimal allocation is robust to changes in parameter values. The simple conditions we develop provide a useful means of informing vaccine allocation decisions for communicable diseases.

    View details for DOI 10.1016/j.mbs.2021.108621

    View details for PubMedID 33915160

  • Optimal allocation of limited vaccine to minimize the effective reproduction number. Mathematical biosciences Rao, I. J., Brandeau, M. L. 2021: 108654


    We examine the problem of allocating a limited supply of vaccine for controlling an infectious disease with the goal of minimizing the effective reproduction number Re. We consider an SIR model with two interacting populations and develop an analytical expression that the optimal vaccine allocation must satisfy. With limited vaccine supplies, we find that an all-or-nothing approach is optimal. For certain special cases, we determine the conditions under which the optimal Re is below 1. We present an example of vaccine allocation for COVID-19 and show that it is optimal to vaccinate younger individuals before older individuals to minimize Re if less than 59% of the population can be vaccinated. The analytical conditions we develop provide a simple means of determining the optimal allocation of vaccine between two population groups to minimize Re.

    View details for DOI 10.1016/j.mbs.2021.108654

    View details for PubMedID 34216636

  • Assessment of physician training and prediction of workforce needs in paediatric cardiac intensive care in the United States. Cardiology in the young Horak, R. V., Marino, B. S., Werho, D. K., Rhodes, L. A., Costello, J. M., Cabrera, A. G., Cooper, D. S., Bai, S., Tabbutt, S., Rao, I., Scheinker, D., Shin, A. Y., Krawczeski, C. D. 2021: 1-6


    To assess the training and the future workforce needs of paediatric cardiac critical care faculty.REDCap surveys were sent May-August 2019 to medical directors and faculty at the 120 US centres participating in the Society of Thoracic Surgeons Congenital Heart Surgery Database. Faculty and directors were asked about personal training pathway and planned employment changes. Directors were additionally asked for current faculty numbers, expected job openings, presence of training programmes, and numbers of trainees. Predictive modelling of the workforce was performed using respondents' data. Patient volume was projected from US Census data and compared to projected provider availability.Sixty-six per cent (79/120) of directors and 62% (294/477) of contacted faculty responded. Most respondents had training that incorporated critical care medicine with the majority completing training beyond categorical fellowship. Younger respondents and those in dedicated cardiac ICUs were more significantly likely to have advanced training or dual fellowships in cardiology and critical care medicine. An estimated 49-63 faculty enter the workforce annually from various training pathways. Based on modelling, these faculty will likely fill current and projected open positions over the next 5 years.Paediatric cardiac critical care training has evolved, such that the majority of faculty now have dual fellowship or advanced training. The projected number of incoming faculty will likely fill open positions within the next 5 years. Institutions with existing or anticipated training programmes should be cognisant of these data and prepare graduates for an increasingly competitive market.

    View details for DOI 10.1017/S1047951121004893

    View details for PubMedID 34924098

  • Health outcomes and cost-effectiveness of diversion programs for low-level drug offenders: A model-based analysis. PLoS medicine Bernard, C. L., Rao, I. J., Robison, K. K., Brandeau, M. L. 2020; 17 (10): e1003239


    BACKGROUND: Cycles of incarceration, drug abuse, and poverty undermine ongoing public health efforts to reduce overdose deaths and the spread of infectious disease in vulnerable populations. Jail diversion programs aim to divert low-level drug offenders toward community care resources, avoiding criminal justice costs and disruptions in treatment for HIV, hepatitis C virus (HCV), and drug abuse. We sought to assess the health benefits and cost-effectiveness of a jail diversion program for low-level drug offenders.METHODS AND FINDINGS: We developed a microsimulation model, calibrated to King County, Washington, that captured the spread of HIV and HCV infections and incarceration and treatment systems as well as preexisting interventions such as needle and syringe programs and opiate agonist therapy. We considered an adult population of people who inject drugs (PWID), people who use drugs but do not inject (PWUD), men who have sex with men, and lower-risk heterosexuals. We projected discounted lifetime costs and quality-adjusted life years (QALYs) over a 10-year time horizon with and without a jail diversion program and calculated resulting incremental cost-effectiveness ratios (ICERs) from the health system and societal perspectives. We also tracked HIV and HCV infections, overdose deaths, and jail population size. Over 10 years, the program was estimated to reduce HIV and HCV incidence by 3.4% (95% CI 2.7%-4.0%) and 3.3% (95% CI 3.1%-3.4%), respectively, overdose deaths among PWID by 10.0% (95% CI 9.8%-10.8%), and jail population size by 6.3% (95% CI 5.9%-6.7%). When considering healthcare costs only, the program cost $25,500/QALY gained (95% CI $12,600-$48,600). Including savings from reduced incarceration (societal perspective) improved the ICER to $6,200/QALY gained (95% CI, cost-saving $24,300). Sensitivity analysis indicated that cost-effectiveness depends on diversion program participants accessing community programs such as needle and syringe programs, treatment for substance use disorder, and HIV and HCV treatment, as well as diversion program cost. A limitation of the analysis is data availability, as fewer data are available for diversion programs than for more established interventions aimed at people with substance use disorder. Additionally, like any model of a complex system, our model relies on simplifying assumptions: For example, we simplified pathways in the healthcare and criminal justice systems, modeled an average efficacy for substance use disorder treatment, and did not include costs associated with homelessness, unemployment, and breakdown in family structure.CONCLUSIONS: We found that diversion programs for low-level drug offenders are likely to be cost-effective, generating savings in the criminal justice system while only moderately increasing healthcare costs. Such programs can reduce incarceration and its associated costs, and also avert overdose deaths and improve quality of life for PWID, PWUD, and the broader population (through reduced HIV and HCV transmission).

    View details for DOI 10.1371/journal.pmed.1003239

    View details for PubMedID 33048929

  • Target Based Care: An Intervention to Reduce Variation in Postoperative Length of Stay. The Journal of pediatrics Shin, A. Y., Rao, I. J., Bassett, H. K., Chadwick, W., Kim, J., Kipps, A. K., Komra, K., Loh, L., Maeda, K., Mafla, M., Presnell, L., Sharek, P. J., Steffen, K. M., Scheinker, D., Algaze, C. A. 2020


    OBJECTIVES: To derive care targets and evaluate the impact of displaying them at the point of care on postoperative length of stay (LOS).STUDY DESIGN: A prospective cohort study using 2 years of historical controls within a freestanding, academic children's hospital. Patients undergoing benchmark cardiac surgery between May 4, 2014 and August 15, 2016 (preintervention) and September 6, 2016 to September 30, 2018 (postintervention) were included. The intervention consisted of displaying at the point of care targets for the timing of extubation, transfer from the intensive care unit (ICU), and hospital discharge. Family satisfaction, reintubation, and readmission rates were tracked.RESULTS: The postintervention cohort consisted of 219 consecutive patients. There was a reduction in variation for ICU (difference in SD -2.56, p < 0.01), and total LOS (difference in SD -2.84, P < .001). Patients stayed on average 0.97 fewer days (p<0.001) in the ICU (median -1.01 [IQR -2.15,-0.39], 0.7 fewer days (p<0.001) on mechanical ventilation (median -0.54 [IQR -0.77,-0.50], and 1.18 fewer days (p<0.001) for the total LOS (median -2.25 [IQR -3.69,-0.15]. Log transformed multivariable linear regression demonstrated the intervention to be associated with shorter ICU LOS (beta coefficient -0.19, SE 0.059, p<0.001), total postoperative LOS (beta coefficient -0.12, SE 0.052, p=0.02), and ventilator duration (beta coefficient -0.21, SE 0.048, p<0.001). Balancing metrics did not differ after the intervention.CONCLUSIONS: Target based care is a simple, novel intervention associated with reduced variation in LOS and absolute LOS across a diverse spectrum of complex cardiac surgeries.

    View details for DOI 10.1016/j.jpeds.2020.09.017

    View details for PubMedID 32920104

  • Predicting and improving patient-level antibiotic adherence. Health care management science Rao, I. n., Shaham, A. n., Yavneh, A. n., Kahana, D. n., Ashlagi, I. n., Brandeau, M. L., Yamin, D. n. 2020


    Low adherence to prescribed medications causes substantial health and economic burden. We analyzed primary data from electronic medical records of 250,000 random patients from Israel's Maccabi Healthcare services from 2007 to 2017 to predict whether a patient will purchase a prescribed antibiotic. We developed a decision model to evaluate whether an intervention to improve purchasing adherence is warranted for the patient, considering the cost of the intervention and the cost of non-adherence. The best performing prediction model achieved an average area under the receiver operating characteristic curve (AUC) of 0.684, with 82% accuracy in detecting individuals who had less than 50% chance of purchasing a prescribed drug. Using the decision model, an adherence intervention targeted to patients whose predicted purchasing probability is below a specified threshold can increase the number of prescriptions filled while generating significant savings compared to no intervention - on the order of 6.4% savings and 4.0% more prescriptions filled for our dataset. We conclude that analysis of large-scale patient data from electronic medical records can help predict the probability that a patient will purchase a prescribed antibiotic and can provide real-time predictions to physicians, who can then counsel the patient about medication importance. More broadly, in-depth analysis of patient-level data can help shape the next generation of personalized interventions.

    View details for DOI 10.1007/s10729-020-09523-3

    View details for PubMedID 33017035

  • Cost-Effectiveness Analysis of Fenestrated Endovascular Aneurysm Repair Compared With Open Surgical Repair for Patients With Juxtarenal Abdominal Aortic Aneurysms George, E. L., Nardacci, L., Sinawang, P., Rao, I., Owens, D. K., Garcia-Toca, M. MOSBY-ELSEVIER. 2019: E244–E245