Probability Of Stopping Research Articles

An automated platform trial framework for A/B testing

This paper proposes a platform trial for conducting A/B tests with multiple arms and interim monitoring to investigate the impact of several factors on the expected sample size and probability of early stopping. We examined the performance of three stopping boundaries: O’Brien Fleming (OBF) stopping for either futility or difference (both), Pocock stopping for futility only, and fixed sample size design. We simulated twelve scenarios of different orders of arms based on various effect sizes, as well as considered 1 or 3 interim looks. The overall findings are summarizing in a flowchart to provide intuitive guidance for the design of the platform based on the simulation. We found that it is better to use OBF stopping for both if there is any effective variant and the trial is sufficiently powered to detect the expected effect size. If the study is underpowered to detect a difference, we recommend fixed sample size design to gather as much information as possible, however if the expected sample size is important to minimize, we recommend using Pocock boundaries with futility monitoring. Our results aimed at helping high-tech companies conduct their own studies without requiring extensive knowledge of clinical trial design and statistical methodology.

The last-success stopping problem with random observation times

AbstractSuppose N independent Bernoulli trials with success probabilities $$p_1, p_2,\ldots $$ p 1 , p 2 , … are observed sequentially at times of a mixed binomial process. The task is to maximise, by using a nonanticipating stopping strategy, the probability of stopping at the last success. The case $$p_k=1/k$$ p k = 1 / k has been studied by many authors as a version of the familiar best choice problem, where both N and the observation times are random. We consider a more general profile $$p_k=\theta /(\theta +k-1)$$ p k = θ / ( θ + k - 1 ) and assume that the prior distribution of N is negative binomial with shape parameter $$\nu $$ ν , so the arrivals occur at times of a mixed Poisson process. The setting with two parameters offers a high flexibility in understanding the nature of the optimal strategy, which we show is intrinsically related to monotonicity properties of the Gaussian hypergeometric function. Using this connection, we find that the myopic stopping strategy is optimal if and only if $$\nu \ge \theta $$ ν ≥ θ . Furthermore, we derive formulas to assess the winning probability and discuss limit forms of the problem for large N.

Holistic Sensitivity Analysis for Long-Term Energy Demand Prediction of Battery Electric Vehicles

AbstractAccurate and robust range estimation algorithms for battery electric vehicles have the potential to reduce range anxiety, increase the acceptance of lower-range vehicles, and improve the overall driving experience. However, developing such algorithms faces challenges due to the complexity of the driver-vehicle-environment system and the multitude of factors influencing a vehicle's energy demand. To address these challenges, this paper introduces a sensitivity analysis focused on driver- and environment-related factors, which are notably difficult to predict. Employing a global sensitivity analysis for factor prioritization, this study delineates and assesses the parameters and their value distributions using a validated vehicle simulation model. The co-simulation of a powertrain and an auxiliaries model enables the parameter-specific investigation of parameters related to the thermal system. The results are scenario-individual parameter rankings that show the importance of the considered factors in prediction algorithms and guide the strategy for the development of these algorithms. The acceleration behavior of the driver, often emphasized in literature, is shown to be of secondary importance to energy consumption. Moreover, factors such as air density and wind speed are identified as crucial in highway driving scenarios, whereas outside temperature and the probability of stopping at traffic lights are critical in urban settings. For validation purposes, the resulting rankings of the sensitivity study are validated by means of a convergence analysis.

Early stopping versus continued retrievals after failed recanalization: associated factors and implications for outcome

BackgroundSuccessful recanalization defined as modified Thrombolysis in Cerebral Infarction Score (mTICI) ≥2b is not achieved in 15%–20% of patients with acute ischemic stroke. This study aims to identify patient-specific factors...

Stern, Gamow, and the Shabbat Elevator Effect

Abstract In addition to being known for their other work, physicists George Gamow and Marvin Stern also published an analysis of an intriguing problem regarding their perception that although both worked on different floors, it seemed that the first elevator to arrive on their respective floors was traveling in the opposite direction of their destination. In this manuscript, a fictitious conversation occurs between the two in regards to the probability of the elevator stopping on every floor (which they term the Shabbat Effect). One claims that it is the number of elevator occupants that predominates whereas the other claims it is the number of floors in the building that predominates in giving rise to this effect. Equations for estimating the probability of the Shabbat Effect are developed and analyzed. The resulting equations show that the relationship between the number of elevator occupants and floors is surprisingly complicated. Consequently, no general rule can be given for whether the probability of the Shabbat Effect increases or decreases for an arbitrary change in the number of occupants and floors. However, it discovered that for similar changes in the number of occupants and floors, it is the number of floors that predominates in determining the probability of the elevator stopping on every floor.

The score-goldilocks design for phase 3 clinical trials

ABSTRACT In this paper, we propose a new Bayesian adaptive design, score-goldilocks design, which has the same algorithmic idea as goldilocks design. The score-goldilocks design leads to a uniform formula for calculating the probability of trial success for different endpoint trials by using the normal approximation. The simulation results show that the score-goldilocks design is not only very similar to the goldilocks design in terms of operating characteristics such as type 1 error, power, average sample size, probability of stop for futility, and probability of early stop for success, but also greatly saves the calculation time and improves the operation efficiency.

A Markov network approach for reproducing purchase behaviours observed in convenience stores

The convenience store industry in Japan holds immense significance, making a thorough comprehension of customer purchase behaviour invaluable for companies aiming to gain insights into their customer base. In this paper, we propose a novel application of a Markov network model to simulate purchases guided by stopping probabilities calculated from real data. Each node in the Markov network represents different product categories available for purchase. Additionally, we introduce the concept of a “driving force,” quantifying the influence of purchasing product A on the likelihood of purchasing product B, compared to random purchasing. For instance, our analysis reveals that the inclusion of nutrient bars in a purchase set leads to, on average, a 13% reduction in tobacco purchases compared to random patterns. To validate our approach, we compare the simulated macro-level purchase behaviours with real point of Sale (POS) data obtained from a prominent convenience store giant, 7-Eleven. The dataset is comprised of roughly 54 million receipts, in which we focus on the product categories existing in this dataset rather than individual products. Our model successfully replicates the purchase size distribution for 99.9% of all purchases and the purchase counts across various product categories, demonstrating its efficacy in capturing broad purchase patterns.

The Bayesian Group-Sequential Predictive Evidence Value Design for Phase II Clinical Trials with Binary Endpoints

AbstractIn clinical research, the initial efficacy of a new agent is typically assessed in a phase IIA study. Bayesian group-sequential designs are often based on predictive probability of trial success. In this paper, the novel Bayesian group-sequential predictive evidence value design is introduced, and we prove that the predictive probability approach is a special case of it. A comparison with Simon’s two-stage and competing Bayesian designs based on phase IIA cancer trials is provided. Results show that the novel design can improve operating characteristics such as the false-positive rate, probability of early stopping for futility and expected sample size of the trial. Given these advantages, the predictive evidence value design constitutes an important addition to the biostatistician’s toolbelt when planning a phase IIA trial the Bayesian way, in particular, when small sample sizes and a large probability for early termination under the null hypothesis are desired.

Optimal futility stopping boundaries for binary endpoints

BackgroundGroup sequential designs incorporating the option to stop for futility at the time point of an interim analysis can save time and resources. Thereby, the choice of the futility boundary importantly impacts the design’s resulting performance characteristics, including the power and probability to correctly or wrongly stop for futility. Several authors contributed to the topic of selecting good futility boundaries. For binary endpoints, Simon’s designs (Control Clin Trials 10:1–10, 1989) are commonly used two-stage designs for single-arm phase II studies incorporating futility stopping. However, Simon’s optimal design frequently yields an undesirably high probability of falsely declaring futility after the first stage, and in Simon’s minimax design often a high proportion of the planned sample size is already evaluated at the interim analysis leaving only limited benefit in case of an early stop.MethodsThis work focuses on the optimality criteria introduced by Schüler et al. (BMC Med Res Methodol 17:119, 2017) and extends their approach to binary endpoints in single-arm phase II studies. An algorithm for deriving optimized futility boundaries is introduced, and the performance of study designs implementing this concept of optimal futility boundaries is compared to the common Simon’s minimax and optimal designs, as well as modified versions of these designs by Kim et al. (Oncotarget 10:4255–61, 2019).ResultsThe introduced optimized futility boundaries aim to maximize the probability of correctly stopping for futility in case of small or opposite effects while also setting constraints on the time point of the interim analysis, the power loss, and the probability of stopping the study wrongly, i.e. stopping the study even though the treatment effect shows promise. Overall, the operating characteristics, such as maximum sample size and expected sample size, are comparable to those of the classical and modified Simon’s designs and sometimes better. Unlike Simon’s designs, which have binding stopping rules, the optimized futility boundaries proposed here are not adjusted to exhaust the full targeted nominal significance level and are thus still valid for non-binding applications.ConclusionsThe choice of the futility boundary and the time point of the interim analysis have a major impact on the properties of the study design. Therefore, they should be thoroughly investigated at the planning stage. The introduced method of selecting optimal futility boundaries provides a more flexible alternative to Simon’s designs with non-binding stopping rules. The probability of wrongly stopping for futility is minimized and the optimized futility boundaries don’t exhibit the unfavorable properties of an undesirably high probability of falsely declaring futility or a high proportion of the planned sample evaluated at the interim time point.

Covariate adjustment in Bayesian adaptive randomized controlled trials.

In conventional randomized controlled trials, adjustment for baseline values of covariates known to be at least moderately associated with the outcome increases the power of the trial. Recent work has shown a particular benefit for more flexible frequentist designs, such as information adaptive and adaptive multi-arm designs. However, covariate adjustment has not been characterized within the more flexible Bayesian adaptive designs, despite their growing popularity. We focus on a subclass of these which allow for early stopping at an interim analysis given evidence of treatment superiority. We consider both collapsible and non-collapsible estimands and show how to obtain posterior samples of marginal estimands from adjusted analyses. We describe several estimands for three common outcome types. We perform a simulation study to assess the impact of covariate adjustment using a variety of adjustment models in several different scenarios. This is followed by a real-world application of the compared approaches to a COVID-19 trial with a binary endpoint. For all scenarios, it is shown that covariate adjustment increases power and the probability of stopping the trials early, and decreases the expected sample sizes as compared to unadjusted analyses.

Adalimumab Biosimilar in Pediatric Inflammatory Bowel Disease: A Retrospective Study from the Sicilian Network for Inflammatory Bowel Disease (SN-IBD)

Background: The utilization of anti-tumor necrosis factor-α (anti-TNF-α) biosimilars in inflammatory bowel disease (IBD) is constantly increasing. However, pediatric data are limited. This study aimed to assess the effectiveness and safety of adalimumab biosimilar (ADL-BioS) in pediatric IBD patients. Methods: All consecutive pediatric IBD patients from the Sicilian Network for Inflammatory Bowel Disease cohort treated with ADL-BioS from 2019 to 2021 were recruited. Remission at weeks 14 and 52, treatment persistence, and adverse events were the endpoints of this study. Factors associated with clinical remission and treatment persistence were examined. Results: There were 41 patients in total. Nine (22%) patients were switched from the reference product to ADL-BioS. Two patients had multiple switches. Eleven months was the median follow-up period. Clinical remission was attained by 70.7% and 72.0% of patients on weeks 14 and 52, respectively. Four (9.8%) adverse events occurred (10.1/100 person-year). Treatment persistence was 85.4% at 1 and 2 years. Patients with a longer duration of disease had a higher probability of stopping their treatment (p = 0.036). Conclusions: This is the first real-world study that particularly addresses the use of ADL-BioS in pediatric IBD. With high rates of treatment persistence and a low frequency of non-serious side effects, ADL-BioS seems to be effective.

A Bayesian adaptive design approach for stepped-wedge cluster randomized trials.

The Bayesian group sequential design has been applied widely in clinical studies, especially in Phase II and III studies. It allows early termination based on accumulating interim data. However, to date, there lacks development in its application to stepped-wedge cluster randomized trials, which are gaining popularity in pragmatic trials conducted by clinical and health care delivery researchers. We propose a Bayesian adaptive design approach for stepped-wedge cluster randomized trials, which makes adaptive decisions based on the predictive probability of declaring the intervention effective at the end of study given interim data. The Bayesian models and the algorithms for posterior inference and trial conduct are presented. We present how to determine design parameters through extensive simulations to achieve desired operational characteristics. We further evaluate how various design factors, such as the number of steps, cluster size, random variability in cluster size, and correlation structures, impact trial properties, including power, type I error, and the probability of early stopping. An application example is presented. This study presents the incorporation of Bayesian adaptive strategies into stepped-wedge cluster randomized trials design. The proposed approach provides the flexibility to stop the trial early if substantial evidence of efficacy or futility is observed, improving the flexibility and efficiency of stepped-wedge cluster randomized trials.

Seamless phase 2/3 design for trials with multiple co-primary endpoints using Bayesian predictive power

Seamless phase 2/3 design has become increasingly popular in clinical trials with a single endpoint. Trials that define success based on the achievement of all co-primary endpoints (CPEs) encounter the challenge of inflated type 2 error rates, often leading to an overly large sample size. To tackle this challenge, we introduced a seamless phase 2/3 design strategy that employs Bayesian predictive power (BPP) for futility monitoring and sample size re-estimation at interim analysis. The correlations among multiple CPEs are incorporated using a Dirichlet-multinomial distribution. An alternative approach based on conditional power (CP) was also discussed for comparison. A seamless phase 2/3 vaccine trial employing four binary endpoints under the non-inferior hypothesis serves as an example. Our results spotlight that, in scenarios with relatively small phase 2 sample sizes (e.g., 50 or 100 subjects), the BPP approach either outperforms or matches the CP approach in terms of overall power. Particularly, with n1 = 50 and ρ = 0, BPP showcases an overall power advantage over CP by as much as 8.54%. Furthermore, when the phase 2 stage enrolled more subjects (e.g., 150 or 200), especially with a phase 2 sample size of 200 and ρ = 0, the BPP approach evidences a peak difference of 5.76% in early stop probability over the CP approach, emphasizing its better efficiency in terminating futile trials. It’s noteworthy that both BPP and CP methodologies maintained type 1 error rates under 2.5%. In conclusion, the integration of the Dirichlet-Multinominal model with the BPP approach offers improvement in certain scenarios over the CP approach for seamless phase 2/3 trials with multiple CPEs.

Ending child labour: does conditional cash transfer matter? Evidence from Indonesia

Purpose This study aims to investigate the extent to which the Indonesian conditional cash transfer (CCT), known as the Family Hope Program (FHP), impacts the probability of children engaging in labour activities.Design/methodology/approach This study utilizes data from the Indonesian Family Life Survey in 2014, focussing on periods following the implementation of the FHP. To estimate the impact of FHP on child labour in Indonesia, the authors employ a propensity score matching strategy to balance the characteristics observed between the participant and non-participant groups.Findings The estimates show that FHP has no statistical impact on child labour across all matching techniques. This implies that receiving the CCT does not always help poor households decrease the probability of stopping their children from participating in labour activities.Social implications The conditions applied to the beneficiaries, which only require children to attend school without requiring them to stop working, may not effectively address the issue of child labour. The current structure and design of the FHP need to be re-evaluated and improved to effectively combat child labour.Originality/value Despite numerous studies examining the impact of CCT on child labour which remains inconclusive in Indonesia, this study contributes to the existing literature by considering children participating in labour activities across all types of work without focussing on specific education levels or regions.Peer reviewThe peer review history for this article is available at: https://publons.com/publon/10.1108/IJSE-07-2023-0580

FDI flows and sudden stops in small open economies

Why are balance of payments crises, characterized by Sudden Stops of capital inflows, more frequent in emerging economies than advanced economies? This paper argues that differences in the composition of the financial account flows explain 30 percent of the gap in the probability of a crisis. I document that although advanced economies have, on average, zero net foreign direct investment (FDI), they have sufficient FDI outflows to act as buffer savings during financial distress. To quantify the effect of this FDI channel on the probability of a crisis, I propose a small open economy model with a loan-to-value collateral constraint and FDI vulnerable to government confiscation risk. The calibrated model suggests that if an emerging economy increases its capital-to-GDP ratio and eliminates government confiscation risk, it would reduce the probability of a Sudden Stop from 2.9 to 2.7 percent, while simultaneously increasing its debt-to-GDP ratio from 47 to 65 percent.

Информационная инфраструктура, обеспечивающая своевременное обнаружение мезомасштабных конвективных комплексов

The results of the development of an information infrastructure that provides timely detection of mesoscale convective complexes (MCC) are described, automatic procedures that implement the basic functionality of this infrastructure are described. Along with the detection of MCC, the described procedures allow us to identify zones of deep convection, i.e. such MCC that develop according to the scenario of "daytime storms", i.e. intense thunderstorms, squalls and tornadoes. Information infrastructure, provides integration of satellite microwave radiometric sensing data of geostationary observations in the visible and IR range. This integration is designed to ensure the restoration of atmospheric temperature and humidity profiles in the conditions of emergency atmospheric situations caused by the MCC. The methodological feature of the developed approach is to minimize the probability of stopping the data analysis system when access to individual sources of a priori information is terminated. This technique is based on the use of an automatic system of adaptation to changes in access conditions and the application of the results of model forecasts of the development of atmospheric processes.

Multi‐stage stochastic dual dynamic programming to low‐carbon economic dispatch for power systems with flexible carbon capture and storage devices

AbstractThe carbon capture and storage (CCS) technique gains much attention due to its role in reducing CO2 emissions. By introducing flexible CCS devices into conventional power plants, the low‐carbon economic operation of the power system can be achieved. However, the uncertainty of renewable energy makes it hard to obtain an optimal operation policy. First, the detailed model of CCS consisting of bypass venting stacks, solvent storage tanks, absorber, and stripper is described. Then, a low‐carbon economic dispatch model of the power system with CCS is proposed to minimize the total operation and renewable energy abandonment penalty costs. Next, the problem is reformulated as multi‐stage stochastic programming, and the stochastic dual dynamic programming (SDDP) method is applied to relieve the computation burden. To control the probability of stopping the algorithm prematurely, a new stopping criterion based on a two‐sided hypothesis test is proposed. Finally, the effectiveness of the proposed model and the new stopping criterion is demonstrated by case studies on a practical power system.

Effect of mitochondrial circulation on mitochondrial age density distribution.

Recent publications report that although the mitochondria population in an axon can be quickly replaced by a combination of retrograde and anterograde axonal transport (often within less than 24 hours), the axon contains much older mitochondria. This suggests that not all mitochondria that reach the soma are degraded and that some are recirculating back into the axon. To explain this, we developed a model that simulates mitochondria distribution when a portion of mitochondria that return to the soma are redirected back to the axon rather than being destroyed in somatic lysosomes. Utilizing the developed model, we studied how the percentage of returning mitochondria affects the mean age and age density distributions of mitochondria at different distances from the soma. We also investigated whether turning off the mitochondrial anchoring switch can reduce the mean age of mitochondria. For this purpose, we studied the effect of reducing the value of a parameter that characterizes the probability of mitochondria transition to the stationary (anchored) state. The reduction in mitochondria mean age observed when the anchoring probability is reduced suggests that some injured neurons may be saved if the percentage of stationary mitochondria is decreased. The replacement of possibly damaged stationary mitochondria with newly synthesized ones may restore the energy supply in an injured axon. We also performed a sensitivity study of the mean age of stationary mitochondria to the parameter that determines what portion of mitochondria re-enter the axon and the parameter that determines the probability of mitochondria transition to the stationary state. The sensitivity of the mean age of stationary mitochondria to the mitochondria stopping probability increases linearly with the number of compartments in the axon. High stopping probability in long axons can significantly increase mitochondrial age.

Optimization of headway and bus stop spacing for low demand bus routes

ABSTRACT We propose a methodology for optimization of service headway and stop spacing along a low-demand bus route that minimizes operator and user costs. This study develops analytical cost models that are representative of low-demand routes by using negative binomial distribution for passenger demand for boarding and alighting pattern to estimate the probability of stopping and both random and planned arrival of passengers are considered to estimate the waiting time. Pareto optimal solutions obtained using multi-objective evolutionary algorithm, NSGA-II indicate that optimal values of headway and stop spacing are underestimated if optimized based on assumptions typical of high-demand routes which is passenger demand for boarding and alighting at bus stops randomly following a Poisson process. With the aid of the study methodology, transit planners will be able to improve the service utilization and passenger accessibility along an under-performing low demand routes by recommending minimal modifications to the existing route and bus schedule.

Multi-Modal Interaction-Aware Motion Prediction at Unsignalized Intersections

Autonomous vehicle technologies have evolved quickly over the last few years, with safety being one of the key requirements for their full deployment. However, ensuring their safety while navigating through highly interactive and complex scenarios remains a critical challenge. To tackle this problem, intention estimation and motion prediction are fundamental. In this work, a method to infer the intentions, based on a Dynamic Bayesian Network (DBN), and predict the motion, using Markov Chains, of the nearby vehicles at unsignalized intersections is proposed. This approach considers all possible corridors of the surrounding traffic participants and takes into account their interactions to infer the probabilities of stopping or crossing the intersection, as well as the probability of being in each of the possible navigable corridors. To achieve this, the DBN is used to model the relationships between the observed states and the unobserved intentions of the nearby agents. The Markov Chain model, obtained from a kinematic model, is used to predict the future motions of the vehicles, taking into account their current state, their inferred intentions, and the uncertainty associated with the prediction. The resulting multi-modal motion predictions are sent to the ego vehicle to navigate through the scene. The proposed method is evaluated in 6 real situations extracted from publicly available datasets and is compared with a model-based and a learn-based baseline models. The results showed that the proposed method outperformed both baselines in terms of accuracy considering the metrics ADE and FDE.