Probability Interval Research Articles

Pathological response in resectable non-small cell lung cancer: a systematic literature review and meta-analysis.

Surrogate endpoints for overall survival in patients with resectable non-small cell lung cancer receiving neoadjuvant therapy are needed to provide earlier treatment outcome indicators and accelerate drug approval. This study's main objectives were to investigate the association among pathological complete response, major pathological response, event-free survival and overall survival and to determine whether treatment effects on pathological complete response and event-free survival correlate with treatment effects on overall survival. A comprehensive systematic literature review was conducted to identify neoadjuvant studies in resectable non-small cell lung cancer. Analysis at the patient level using frequentist and Bayesian random effects (hazard ratio [HR] for overall survival or event-free survival by pathological complete response or major pathological response status, yes vs no) and at the trial level using weighted least squares regressions (hazard ratio for overall survival or event-free survival vs pathological complete response, by treatment arm) were performed. In both meta-analyses, pathological complete response yielded favorable overall survival compared with no pathological complete response (frequentist, 20 studies and 6530 patients: HR = 0.49, 95% confidence interval = 0.42 to 0.57; Bayesian, 19 studies and 5988 patients: HR = 0.48, 95% probability interval = 0.43 to 0.55) and similarly for major pathological response (frequentist, 12 studies and 1193 patients: HR = 0.36, 95% confidence interval = 0.29 to 0.44; Bayesian, 11 studies and 1018 patients: HR = 0.33, 95% probability interval = 0.26 to 0.42). Across subgroups, estimates consistently showed better overall survival or event-free survival in pathological complete response or major pathological response compared with no pathological complete response or no major pathological response. Trial-level analyses showed a moderate to strong correlation between event-free survival and overall survival hazard ratios (R2 = 0.7159) but did not show a correlation between treatment effects on pathological complete response and overall survival or event-free survival. There was a strong and consistent association between pathological response and survival and a moderate to strong correlation between event-free survival and overall survival following neoadjuvant therapy for patients with resectable non-small cell lung cancer.

Epidemiological insights into paratuberculosis in camels in Saudi Arabia: Bayesian estimation of true prevalence and identification of risk factors.

Paratuberculosis, caused by Mycobacterium avium subsp. paratuberculosis (MAP), is a significant concern in the camel population of Saudi Arabia. This study aimed to provide epidemiological insights into the disease by estimating the true prevalence in camels in the Eastern Province and Riyadh, using a Bayesian estimation framework, and exploring the associated risk factors through a frequentist approach. A total of 1200 camel blood samples were collected and analyzed using an indirect ELISA method. The true herd-level prevalence was estimated at 0.7 (95% probability interval: 0.57 to 0.81), and the mean expected true animal-level prevalence was 0.17 (0.14 to 0.20). Risk factors associated with Map seropositivity were identified, including sex, breed, raising system, and production type. Females, single breed camels, and nomadic raising systems were found to have lower odds of seropositivity, while camels used for racing and show had significantly higher odds. The study's Bayesian approach, adjusting for the imperfect accuracy of MAP tests, provides a nuanced understanding of the disease's prevalence in the region. The integration of true prevalence estimates with risk factor analysis offers a comprehensive framework that can guide future policies and strategies in the fight against paratuberculosis in Saudi Arabia. The findings emphasize the importance of targeted control measures, underscoring the urgent need for interventions in Saudi Arabia's camel population. By understanding the true disease prevalence and its associated risk factors, we can enhance disease management strategies, offering valuable insights for future control and eradication efforts in the region.

On the early postclassic collapse of Plazuelas (Northern Border of Mesoamerica): Archaeomagnetic evidence based on full geomagnetic vectors

We report a detailed rock-magnetic, archaeomagnetic and absolute intensity investigation on burned in situ remains of the Plazuelas archaeological site (Northern Border of Mesoamerica). Fifty-six specimens were subjected to step-wise alternating field demagnetizations to retrieve characteristic remanence directions. All samples yielded evidence of stable, single-component magnetization carried by magnetite or Ti-poor titanomagnetite. Sixty-four specimens were selected for paleointensity experiments following the Thellier double heating technique, including remanence anisotropy correction. The archaeomagnetic dating, based on full geomagnetic vectors, was performed using the global geomagnetic models and the regional Paleosecular Variation Curves available for Mesoamerica. The most probable age intervals obtained for the burned floor of Site 1 (Casas Tapadas North) are within the interval 972AD – 744 AD. In the case of the burned floor of Site 2 (Casas Tapadas West), the ages obtained fall within 971 AD - 752 AD. In the case of the burned floor of Site 3 (South Sector), the ages obtained fall within the interval 752 AD – 969 AD. The calculation of the most probable age intervals, carried out using the Bootstrap resampling method, provided the dates of 940 ± 6 AD, 896 ± 14 AD and 883 ± 14 AD, respectively. These ages agree well with various archaeological hypotheses on the sudden collapse of Plazuelas as a result of intentional destruction, mutilation and generalized firing due to the local war and/or social unrest.

Sensor attack detection based on active excitation response with uncertain delays

Cyber–physical systems face the threat of sensor attacks, which can result in incorrect measurements of the physical state for the controller and lead to erroneous decisions and control instructions. To address this issue, our paper introduces a sensor attack detection method involving the active injection of excitation into the system and a comparison of actual sensor data with the expected response. First, we address challenges posed by sensing noise and uncertain delays by compensating for them and presenting a probability interval derived from the convolution of noise and delay. Second, we create an anticipated response spectrum by adjusting the probability interval within a defined time window under specific active excitation. Third, the disparity between the expected response spectrum and the actual sensor data within the time window is utilized to calculate the probability of a sensor being attacked. Finally, we evaluate the effectiveness of our method through extensive simulations in a vehicle-platoon case study.

Ramming Mechanism Based on Permanent Magnet Synchronous Linear Motor

To overcome the drawbacks of the traditional ramming mechanism, such as complicated maintenance and low reliability, an artillery ramming mechanism is proposed in this study based on the principle of a double primary tubular permanent magnet synchronous linear motor. First, a subdomain model is proposed for this mechanism, which significantly simplifies the programming difficulty by solving through coordinate transformation. In comparison to the finite element method, the analytical method considers the flux barrier and end effects, resulting in high calculation accuracy. Then, considering the uncertain factors in the machining process, an interval uncertainty optimization model considering robustness is established using the interval order and interval probability degree method, which is further solved via interval nesting optimization. Compared with the initial structure, the average thrust and thrust density of the optimized structure are increased by 32.7% and 12.4%, respectively, with almost constant thrust ripple. Finally, a prototype and control platform are developed to verify the validity of our work and superiority of the proposed structure through experiments involving electromagnetic parameters and comparative experiments.

Probabilistic load forecasting for integrated energy systems using attentive quantile regression temporal convolutional network

The burgeoning proliferation of integrated energy systems has fostered an unprecedented degree of coupling among various energy streams, thereby elevating the necessity for unified multi-energy forecasting (MEF). Prior approaches predominantly relied on independent predictions for heterogeneous load demands, overlooking the synergy embedded within the dataset. The two principal challenges in MEF are extracting the intricate coupling correlations among diverse loads and accurately capturing the inherent uncertainties associated with each type of load. This study proposes an attentive quantile regression temporal convolutional network (QTCN) as a probabilistic framework for MEF, featuring an end-to-end predictor for the probabilistic intervals of electrical, thermal, and cooling loads. This study leverages an attention layer to extract correlations between diverse loads. Subsequently, a QTCN is implemented to retain the temporal characteristics of load data and gauge the uncertainties and temporal correlations of each load type. The multi-task learning framework is deployed to facilitate simultaneous regression of various quantiles, thereby expediting the training progression of the forecasting model. The proposed model is validated using realistic load data and meteorological data from the Arizona State University metabolic system and National Oceanic and Atmospheric Administration respectively, and the results indicate superior performance and greater economic benefits compared to the baselines in existing literature.

A conformal regressor for predicting negative conversion time of Omicron patients.

In light of the situation and the characteristics of Omicron, the country has continuously optimized the rules for the prevention and control of COVID-19. The global epidemic is still spreading, and new cases of infection continue to emerge in China. To facilitate the infected person to estimate the course of virus infection, a prediction model for predicting negative conversion time is proposed in this article. The clinical features of Omicron-infected patients in Shandong Province in the first half of 2022 are retrospectively studied. These features are grouped by disease diagnosis result, clinical sign, traditional Chinese medicine symptoms, and drug use. These features are input to the eXtreme Gradient Boosting (XGBoost) model, and the output is the predicted number of negative conversion days. At the same time, XGBoost is used as the underlying algorithm of the conformal prediction (CP) framework, which can realize the probability interval estimation with a controllable error rate. The results show that the proposed model has a mean absolute error of 3.54days and has the shortest interval prediction result. This shows that the method in this paper can carry more decision-making information and help people better understand the disease and self-estimate the course of the disease to a certain extent.

Comparison of estimation and prediction methods for a zero-inflated geometric INAR(1) process with random coefficients

This study explores zero-inflated count time series models used to analyze data sets with characteristics such as overdispersion, excess zeros, and autocorrelation. Specifically, we investigate the ZIGINAR RC ( 1 ) process, a first-order stationary integer-valued autoregressive model with random coefficients and a zero-inflated geometric marginal distribution. Our focus is on examining various estimation and prediction techniques for this model. We employ estimation methods, including Whittle, Taper Spectral Whittle, Maximum Empirical Likelihood, and Sieve Bootstrap estimators for parameter estimation. Additionally, we propose forecasting approaches, such as median, Bayesian, and Sieve Bootstrap methods, to predict future values of the series. We assess the performance of these methods through simulation studies and real-world data analysis, finding that all methods perform well, providing 95% highest predicted probability intervals that encompass the observed data. While Bayesian and Bootstrap methods require more time for execution, their superior predictive accuracy justifies their use in forecasting.

Projected Colorectal Cancer Incidence and Mortality Based on Observed Adherence to Colonoscopy and Sequential Stool-Based Screening.

Modeling supporting recommendations for colonoscopy and stool-based colorectal cancer (CRC) screening tests assumes 100% sequential participant adherence. The impact of observed adherence on the long-term effectiveness of screening is unknown. We evaluated the effectiveness of a program of screening colonoscopy every 10 years vs annual high-sensitivity guaiac-based fecal occult blood testing (HSgFOBT) using observed sequential adherence data. The MIcrosimulation SCreening ANalysis (MISCAN) model used observed sequential screening adherence, HSgFOBT positivity, and diagnostic colonoscopy adherence in HSgFOBT-positive individuals from the National Colonoscopy Study (single-screening colonoscopy vs ≥4 HSgFOBT sequential rounds). We compared CRC incidence and mortality over 15 years with no screening or 10 yearly screening colonoscopy vs annual HSgFOBT with 100% and differential observed adherence from the trial. Without screening, simulated incidence and mortality over 15 years were 20.9 (95% probability interval 15.8-26.9) and 6.9 (5.0-9.2) per 1,000 participants, respectively. In the case of 100% adherence, only screening colonoscopy was predicted to result in lower incidence; however, both tests lowered simulated mortality to a similar level (2.1 [1.6-2.9] for screening colonoscopy and 2.5 [1.8-3.4] for HSgFOBT). Observed adherence for screening colonoscopy (83.6%) was higher than observed sequential HSgFOBT adherence (73.1% first round; 49.1% by round 4), resulting in lower simulated incidence and mortality for screening colonoscopy (14.4 [10.8-18.5] and 2.9 [2.1-3.9], respectively) than HSgFOBT (20.8 [15.8-28.1] and 3.9 [2.9-5.4], respectively), despite a 91% adherence to diagnostic colonoscopy with FOBT positivity. The relative risk of CRC mortality for screening colonoscopy vs HSgFOBT was 0.75 (95% probability interval 0.68-0.80). Findings were similar in sensitivity analyses with alternative assumptions for repeat colonoscopy, test performance, risk, age, and projection horizon. Where sequential adherence to stool-based screening is suboptimal and colonoscopy is accessible and acceptable-as observed in the national colonoscopy study, microsimulation, comparative effectiveness, screening recommendations.

Carbon price interval prediction method based on probability density recurrence network and interval multi-layer perceptron

Low-carbon development is an inevitable choice under global climate change, and carbon markets have emerged accordingly. Carbon price forecasting is a crucial aspect of research on carbon-reduction strategies. Traditional forecasting methods are mostly focused on point-valued time series and contain limited information, which causes point forecasting to lose volatility information. Such limitations highlight the importance of proposing a precise interval-valued time series prediction system. To address this issue, we propose a carbon price interval forecasting framework based on a probability density recurrence network and interval multi-layer perceptron (MLPI) from the perspective of uncertainty in the presence of carbon price fluctuations. First, we convert the original data into a probability density sequence using kernel density estimation and then build the network. To extract valid information and exclude abnormal data in the carbon price sample data, we clean the data using network topology and link prediction theory; then, the MLPI model is used for interval forecasting. To verify the forecasting performance of this method, we conduct an empirical analysis using real interval-valued carbon futures price data from the EU carbon market and compare its forecasting precision with other models under the same conditions. The results show that the proposed carbon price interval prediction framework is superior to traditional methods in terms of forecasting precision.

Groundwater Exploration in Carbonate Reservoirs Using Borehole Investigations: A Case Study from South Dobrogea, Romania

The Late Jurassic–Early Cretaceous (J3–K1) transboundary aquifer is the most important groundwater body in southern–southeastern Romania, shared with Bulgaria and hosted in karstic–fractured carbonates. We conducted an integrated evaluation of this aquifer by analyzing three 700 m deep groundwater exploration–exploitation boreholes, which intercepted it in the Cernavodă area (South Dobrogea region). The evaluation was based on geophysical wireline logging, drilling information, and borehole production tests. A K-means clustering of the logging data was performed for lithology typing, formation boundaries identification, and the delineation of probable producing intervals associated with secondary porosity development. Petrophysical interpretation was carried out via depth-constrained (zonal) inversion, using multimineral models, the estimated formation boundaries, and variable uncertainties for the main input logs. The optimal interpretation models were correlated with borehole testing results to gain insight into the hydrogeological properties of the aquifer complex. The fractured–vuggy interval with the highest water-producing potential was identified in the lower section of the J3-age Rasova Formation (639–700 m depth), comprising mainly undolomitized limestones. A southeast-to-northwest trend of increasing productivity of the boreholes, correlated with an increasing lateral dolomitization intensity within the Rasova Formation, suggests a highly heterogeneous character of the aquifer. The differences in productivity are due not only to local porosity variations but also to various degrees of pore space connectivity that are related to the amount of fracturing or karstification. The novel findings of this study have important practical implications for the optimal placement, design, and drilling program of future groundwater exploitation boreholes in the Cernavodă area and neighboring sectors.

Diversification of crop rotations and soil carbon balance: impact assessment based on national-scale monitoring data

A successful crop rotation choice is key to the profitability and sustainability of farm management and may simultaneously have an impact on soil organic carbon (SOC) content. In this study, we estimated how changes in crop rotations affected SOC balance in Finland between 2009 and 2018, using geospatial data and Bayesian modeling. The area designated for perennial-dominated and diverse cereal rotations increased over the study period. Perennial grassland rotation was found to have a positive impact on SOC balance, while rotations dominated by annual crops did not differ in their impacts on SOC content. At the national scale, changes in Finnish crop rotations resulted in an estimated annual mitigation of the loss of SOC content by 1336 Mg C year−1 in mineral soils and reduced the carbon dioxide emissions of organic soils by 10,475 Mg C year−1. The combined effect of these two contributions is 11,811 Mg C year−1, with an 80% probability interval of (−6600; 30,300) Mg C year−1. While the overall impact of changes in crop rotations on SOC is relatively small, a continued change to more diverse and perennial-dominated crop rotations may have other agronomic and environmental benefits, e.g. on resilience and biodiversity.

Bayesian Modelling of a Standard House Configuration Model to Analyze Housing Feature Impacts in Newly Developed Suburbs without Historical Sales

There is a recent trend of entire new suburbs being designed and built to solve the housing crisis all around the world. The aim of this study is to anticipate the value of housing features in newly developed suburbs using a Bayesian approach. We present the Standard House Configuration Model, where housing feature impacts are analyzed relative to the configuration of a standard house for easy interpretation. The benefit of using a Bayesian approach is that we describe housing feature impacts with highest density intervals, which more closely resemble the intuitive understanding of probability intervals than statistical confidence intervals. Our case study on newly developed suburbs in Auckland, New Zealand, demonstrates that the posterior distributions from our model effectively capture the complex relationship between housing features and sale price (R2 value of 93%). The proposed model is cross-validated on four recently developed suburbs in Auckland. For comparable suburbs, our model is able to make reasonably accurate price predictions without using any historical sale records from the target suburb. This indicates that the insights into housing feature impacts are applicable to other new suburbs still in the planning stage and, therefore, have the potential to support future suburb developments.

Analysis on Probability Mass Function and Probability Density Function

Probability Mass Function (PMF) and Probability Density Function (PDF) are fundamental concepts in probability theory and statistics that play a crucial role in describing the probability distribution of random variables. This abstract provides a comprehensive overview of these concepts, highlighting their definitions, characteristics, and applications. The Probability Mass Function is a concept primarily associated with discrete random variables. It defines the probability of a specific outcome occurring. The PMF assigns probabilities to individual values in the sample space, providing a clear picture of the likelihood of each possible outcome. Commonly denoted as P(X=x), where X is the random variable and x is a specific value, the PMF must satisfy two essential properties: non-negativity and the sum of probabilities over all possible outcomes equals one. On the other hand, the Probability Density Function is a concept applied to continuous random variables. Unlike the PMF, which deals with specific values, the PDF deals with ranges of values. The PDF represents the probability that a continuous random variable falls within a given interval. Denoted as f(x), it is essential to note that the probability of any specific point is zero, and instead, probabilities are defined for intervals. The area under the PDF curve over a given interval corresponds to the probability of the random variable falling within that interval. Understanding the differences and similarities between PMF and PDF is crucial for statistical analysis. While PMF is discrete and deals with specific values, PDF is continuous and provides probabilities for intervals. Both functions are integral to the calculation of various statistical measures, including expected values, variance, and standard deviation. This abstract concludes with a discussion of practical applications in diverse fields, such as finance, engineering, and natural sciences, where a deep understanding of PMF and PDF is essential for making informed decisions and drawing meaningful conclusions from data. The integration of these concepts into statistical models and analyses enhances the accuracy and reliability of predictions, making PMF and PDF indispensable tools in the field of probability and statistics

On Neutrosophic Truncation

Neutrosophic have found their place in neutrosophic studies due to the prevalence of indeterminacy in the world. We present the novel notion of neutrosophic truncated distribution, which is highly significant in analyzing events that involve the exclusion of certain data from the original dataset, particularly where there is a presence of indeterminacy in data. Unsure or ambiguous information, which is disregarded in classical logic, is incorporated within neutrosophic logic due to its focus on both certain and uncertain data. In this paper, the approach of neutrosophic truncation, and truncated distribution of neutrosophic random variable have been introduced, in addition to deriving some of its properties. And other cases discussed neutrosophic truncation depends on the neutrosophic probability function, a classical probability function, and studies neutrosophic probability and neutrosophic interval together. It studies the neutrosophic left truncated and neutrosophic right truncated. Some illustrative examples and statistical properties such as the cumulative function, the moment generating function, the order statistic, and the rth moment are presented.

The method of dispersion analysis of droplets using mini droplet cards for resource-saving agricultural technologies

The article protection of agricultural crops and gardens from various diseases and pests, chemical feeding of crops, fight against weeds, defoliation processes, traditional dispersion analysis of highly dispersed droplets formed by resource-efficient and high-performance sprayers, determination of the distribution pattern of drops in a dynamic line for a long time in order to simplify this process, to save time spent on computational work, it is proposed to use templated miniature drop cards for dispersion analysis. Mathematical-statistical analysis was performed on the basis of the collected dynamic series of tiny drop cards. In this case, the arithmetic mean value of the indicators, the mean square deviation, the coefficient of variation, the shift values for the dynamic series, the differential function of the probability of each interval for the Weibull distribution law in assessing the reliability level of highly dispersed drops, the theoretical distribution R(xi) and the expected theoretical distribution of drops in the interval (mi) probability is determined. Empirical and theoretical graphs of the Weibull distribution law are presented.

A Nomogram Model Containing Genetic Polymorphisms to Predict Risk of Pulmonary Embolism in Pregnant Women.

Pulmonary embolism (PE), the most serious presentation of venous thromboembolism (VTE), is associated with a high rate of mortality and expense. Clinical studies on pregnant women with PE are scarce. The aim of this study was to analyze the clinical impact of fibrinolytic enzyme activation inhibitor-1 (PAI-1) 4G/5G genetic polymorphisms, methylenetetrahydrofolate reductase (MTHFR) rs1801131 (A1298C) and rs1801133 (C677T) genetic polymorphisms, and establish a predictive model for pregnant women. Between September 2022 and August 2023, 53 pregnant women with PE were enrolled. Using the propensity score matching method, 106 consecutive pregnant women without VTE were 1:2 matched. The relevant patient data were collected, and the susceptibility genes for PE were detected to determine genetic polymorphisms, and PE susceptibility in pregnant women, as well as to develop predictive models. Our study showed that 4G/4G homozygous mutations increased the risk of pregnant PE fourfold (OR = 4.46, 95% CI = 1.59-12.50, P = 0.004), whereas the 4G allele mutation increased the risk twofold (OR = 2.33, 95% CI = 1.35-4.04, P = 0.002). A nomogram was established to predict the risk of pregnant women with PE by four predictive features including PAI-1 genetic polymorphisms, international normalized ratio (INR), antithrombin-III (AT-III) activity, and platelet count (PLT). The area under the curve (AUC) of the nomogram was 0.821 (0.744-0.898). The AUC of the internal validation group was 0.822 (0.674-0.971). Decision curve analysis revealed that the nomogram has a higher net benefit in the following threshold: probability interval of ≥15%. The PAI-1 4G/4G genotype is an independent risk factor for pregnant women with PE; furthermore, the presence of the 4G allele can increase the risk of PE. The study established a nomogram to predict the risk of PE in pregnant women.

An ELISA test using a circulating Mycobacterium bovis peptide for detecting bovine tuberculosis in dairy cattle.

This study aimed to determine the sensitivity (Se) and specificity (Sp) of a circulating pathogen-specific biomarker (polyketide synthetase 5, Pks5)-based enzyme-linked immunosorbent assay (ELISA) independently or in conjunction with a caudal fold tuberculin (CFT) test for bovine tuberculosis (bTB) screening in dairy cattle. We enrolled 987 dairy cows from 34 herds in Chiang Mai province, Thailand. A conditionally independent Bayesian model with a single population was inferred from the test results. The percentage of positive results for the Pks5-ELISA using 0.4 OD cutoff test and CFT test were 9.0% (89/987) and 10.5% (104/987), respectively. The median of posterior estimates of Se for the Pks5-ELISA test was 90.2% (95% posterior probability interval [PPI] = 76.6-97.4%), while the estimated Sp was slightly higher (median = 92.9, 95% PPI = 91.0-94.5%). The median estimated Se of the CFT test was 85.9% (95% PPI = 72.4-94.6%), while the estimated Sp was higher, with a median of 90.7% (95% PPI = 88.7-92.5%). The posterior estimate for true disease prevalence was 2.4% (95% PPI = 1.2-3.9%). The Pks5-ELISA test yielded characteristics at or above the acceptable standards for bTB detection. Therefore, the pathogen-specific biomarker, Pks5, is a potential detection system for bTB screening and may be applied as an ancillary test together with the currently applied standard method (CFT test) to reinforce the bTB control and eradication programs.

Credal Valuation Networks for Machine Reasoning Under Uncertainty

Contemporary undertakings provide limitless opportunities for widespread application of machine reasoning and artificial intelligence in situations characterised by uncertainty, hostility and sheer volume of data. The paper develops a valuation network as a graphical system for higher-level fusion and reasoning under uncertainty in support of the human operators. Valuations, which are mathematical representation of (uncertain) knowledge and collected data, are expressed as credal sets, defined as coherent interval probabilities in the framework of imprecise probability theory. The basic operations with such credal sets, combination and marginalisation, are defined to satisfy the axioms of a valuation algebra. A practical implementation of the credal valuation network is discussed and its utility demonstrated on a small scale example.

An extended Bayesian semi-mechanistic dose-finding design for phase I oncology trials using pharmacokinetic and pharmacodynamic information.

We propose a model-based, semi-mechanistic dose-finding (SDF) design for phase I oncology trials that incorporates pharmacokinetic/pharmacodynamic (PK/PD) information when modeling the dose-toxicity relationship. This design is motivated by a phase Ib/II clinical trial of anti-CD20/CD3 T cell therapy in non-Hodgkin lymphoma patients; it extends a recently proposed SDF model framework by incorporating measurements of a PD biomarker relevant to the primary dose-limiting toxicity (DLT). We propose joint Bayesian modeling of the PK, PD, and DLT outcomes. Our extensive simulation studies show that on average the proposed design outperforms some common phase I trial designs, including modified toxicity probability interval (mTPI) and Bayesian optimal interval (BOIN) designs, the continual reassessment method (CRM), as well as an SDF design assuming a latent PD biomarker (SDF-woPD), in terms of the percentage of correct selection of maximum tolerated dose (MTD) and average number of patients allocated to MTD, under a variety of dose-toxicity scenarios. When the working PK model and the class of link function between the cumulative PD effect and DLT probability is correctly specified, the proposed design also yields better estimated dose-toxicity curves than CRM and SDF-woPD. Our sensitivity analyses suggest that the design's performance is reasonably robust to prior specification for the parameter in the link function, as well as misspecification of the PK model and class of the link function.