Construction Of Prediction Intervals Research Articles

On the uncertainty of real estate price predictions

ABSTRACT Uncertainty quantification associated with real estate appraisal has largely been overlooked in the literature. In this paper, we address this gap by analysing the uncertainty in automated property valuations using conformal prediction, a distribution-free procedure for constructing prediction intervals with valid coverage in finite samples. Through an empirical study of property prices in the San Francisco Bay Area, we find that prediction intervals obtained using conformal quantile regression have exact coverage. In contrast, prediction intervals obtained from non-conformal quantile regressions severely undercover the data. Furthermore, we show that the intervals adapt to various characteristics of the dwellings, which is crucial given the heterogeneous nature of real estate data. Indeed, we observe that larger and older properties, those in both low and high-income neighbourhoods, as well as those on the market for less than one year are more challenging to evaluate.

Uncertainty quantification in epigenetic clocks via conformalized quantile regression.

DNA methylation (DNAm) is a chemical modification of DNA that can be influenced by various factors, including age, environment, and lifestyle. An epigenetic clock is a predictive tool that measures biological age based on DNAm levels. It can provide insights into an individual's biological age, which may differ from their chronological age. This difference, known as the epigenetic age acceleration, may indicate the state of one's health and risk for age-related diseases. Moreover, epigenetic clocks are used in studies of aging to assess the effectiveness of anti-aging interventions and to understand the underlying mechanisms of aging and disease. Various epigenetic clocks have been developed using samples from different populations, tissues, and cell types, typically by training high-dimensional linear regression models with an elastic net penalty. While these models can predict mean biological age with high precision, there is a lack of uncertainty quantification which is important for interpreting the precision of age estimations and for clinical decision-making. To understand the distribution of a biological age clock beyond its mean, we propose a general pipeline for training epigenetic clocks, based on an integration of high-dimensional quantile regression and conformal prediction, to effectively reveal population heterogeneity and construct prediction intervals. Our approach produces adaptive prediction intervals not only achieving nominal coverage but also accounting for the inherent variability across individuals. By using the data collected from 728 blood samples in 11 DNAm datasets from children, we find that our quantile regression-based prediction intervals are narrower than those derived from conventional mean regression-based epigenetic clocks. This observation demonstrates an improved statistical efficiency over the existing pipeline for training epigenetic clocks. In addition, the resulting intervals have a synchronized varying pattern to age acceleration, effectively revealing cellular evolutionary heterogeneity in age patterns in different developmental stages during individual childhoods and adolescent cohort. Our findings suggest that conformalized high-dimensional quantile regression can produce valid prediction intervals and uncover underlying population heterogeneity. Although our methodology focuses on the distribution of aging in children, it is applicable to a broader range of populations to improve understanding of epigenetic age beyond the mean. This inference-based toolbox could provide valuable insights for future applications of epigenetic interventions for age-related diseases.

Epidemiological modeling of COVID-19 data with Advanced statistical inference based on Type-II progressive censoring

This research proposes the Kavya-Manoharan Unit Exponentiated Half Logistic (KM-UEHL) distribution as a novel tool for epidemiological modeling of COVID-19 data. Specifically designed to analyze data constrained to the unit interval, the KM-UEHL distribution builds upon the unit exponentiated half logistic model, making it suitable for various data from COVID-19. The paper emphasizes the KM-UEHL distribution's adaptability by examining its density and hazard rate functions. Its effectiveness is demonstrated in handling the diverse nature of COVID-19 data through these functions. Key characteristics like moments, quantile functions, stress-strength reliability, and entropy measures are also comprehensively investigated. Furthermore, the KM-UEHL distribution is employed for forecasting future COVID-19 data under a progressive Type-II censoring scheme, which acknowledges the time-dependent nature of data collection during outbreaks. The paper presents various methods for constructing prediction intervals for future-order statistics, including maximum likelihood estimation, Bayesian inference (both point and interval estimates), and upper-order statistics approaches. The Metropolis-Hastings and Gibbs sampling procedures are combined to create the Markov chain Monte Carlo simulations because it is mathematically difficult to acquire closed-form solutions for the posterior density function in the Bayesian framework. The theoretical developments are validated with numerical simulations, and the practical applicability of the KM-UEHL distribution is showcased using real-world COVID-19 datasets.

Performance Study of Prediction Intervals with Random Forest for Poverty Data Analysis

Introduction/Main Objectives: Determine the prediction interval with for analyzing poverty data at the Regency/City level in Indonesia. Background Problems: Poverty will be a topic in various discussion and debates in the future. Novelty: This study’s methods for constructed prediction intervals are LM, Quant, SPI, HDR, and CHDR. This method can improve the prediction interval performance with Random Forests. Research Methods: The method for building forests and obtaining BOP in this study is CART with the LS splitting rule. Finding/Results: The results of this study are that the best method for one replication is HDR with 500 trees. The best method for 100 repetitions is LM. Based on hypothesis testing, there is sufficient evidence to say no difference between the LM, SPI, Quant, HDR, and CHDR methods for 100 replications at a 5% significance level.

Distribution-Free Prediction Intervals Under Covariate Shift, With an Application to Causal Inference

Owing to its appealing distribution-free feature, conformal inference has become a popular tool for constructing prediction intervals with a desired coverage rate. In scenarios involving covariate shift, where the shift function needs to be estimated from data, many existing methods resort to data-splitting techniques. However, these approaches often lead to wider intervals and less reliable coverage rates, especially when dealing with finite sample sizes. To address these challenges, we propose methods based on a pivotal quantity derived under a parametric working model and employ a resampling-based framework to approximate its distribution. The resampling-based approach can produce prediction intervals with a desired coverage rate without splitting the data and can be easily applied to causal inference settings where a shift in the covariate distribution can occur between treatment and control arms. Additionally, the proposed approaches enjoy a double robustness property and are adaptable to different prediction tasks. Our extensive numerical experiments demonstrate that, compared to existing methods, the proposed novel approaches can produce substantially shorter conformal prediction intervals with lower variability in the interval lengths while maintaining promising coverage rates and advantages in versatile usage. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

SpatialWavePredict: a tutorial-based primer and toolbox for forecasting growth trajectories using the ensemble spatial wave sub-epidemic modeling framework

BackgroundDynamical mathematical models defined by a system of differential equations are typically not easily accessible to non-experts. However, forecasts based on these types of models can help gain insights into the mechanisms driving the process and may outcompete simpler phenomenological growth models. Here we introduce a friendly toolbox, SpatialWavePredict, to characterize and forecast the spatial wave sub-epidemic model, which captures diverse wave dynamics by aggregating multiple asynchronous growth processes and has outperformed simpler phenomenological growth models in short-term forecasts of various infectious diseases outbreaks including SARS, Ebola, and the early waves of the COVID-19 pandemic in the US.ResultsThis tutorial-based primer introduces and illustrates a user-friendly MATLAB toolbox for fitting and forecasting time-series trajectories using an ensemble spatial wave sub-epidemic model based on ordinary differential equations. Scientists, policymakers, and students can use the toolbox to conduct real-time short-term forecasts. The five-parameter epidemic wave model in the toolbox aggregates linked overlapping sub-epidemics and captures a rich spectrum of epidemic wave dynamics, including oscillatory wave behavior and plateaus. An ensemble strategy aims to improve forecasting performance by combining the resulting top-ranked models. The toolbox provides a tutorial for forecasting time-series trajectories, including the full uncertainty distribution derived through parametric bootstrapping, which is needed to construct prediction intervals and evaluate their accuracy. Functions are available to assess forecasting performance, estimation methods, error structures in the data, and forecasting horizons. The toolbox also includes functions to quantify forecasting performance using metrics that evaluate point and distributional forecasts, including the weighted interval score.ConclusionsWe have developed the first comprehensive toolbox to characterize and forecast time-series data using an ensemble spatial wave sub-epidemic wave model. As an epidemic situation or contagion occurs, the tools presented in this tutorial can facilitate policymakers to guide the implementation of containment strategies and assess the impact of control interventions. We demonstrate the functionality of the toolbox with examples, including a tutorial video, and is illustrated using daily data on the COVID-19 pandemic in the USA.

Quantile control via random forest

This paper studies robust inference procedure for treatment effects in panel data with flexible relationship across units via the random forest method. The key contribution of this paper is twofold. First, we propose a direct construction of prediction intervals for the treatment effect by exploiting the information of the joint distribution of the cross-sectional units using random forest. In particular, we propose a Quantile Control Method (QCM) using the Quantile Random Forest (QRF) to accommodate flexible cross-sectional structure as well as high dimensionality. Second, we establish the asymptotic consistency of QRF under the panel/time series setup with high dimensionality, which is of theoretical interest on its own right. In addition, Monte Carlo simulations are conducted and show that prediction intervals via the QCM have excellent coverage probability for the treatment effects comparing to existing methods in the literature, and are robust to heteroskedasticity, autocorrelation, and various types of model misspecifications. Finally, an empirical application to study the effect of the economic integration between Hong Kong and mainland China on Hong Kong’s economy is conducted to highlight the potential of the proposed method.

Constructing prediction intervals to explore uncertainty based on deep neural networks

The conventional approaches to constructing Prediction Intervals (PIs) always follow the principle of ‘high coverage and narrow width’. However, the deviation information has been largely neglected, making the PIs unsatisfactory. For high-risk forecasting tasks, the cost of forecast failure may be prohibitive. To address this, this work introduces a multi-objective loss function that includes Prediction Interval Accumulation Deviation (PIAD) within the Lower Upper Bound Estimation (LUBE) framework. The proposed model can achieve the goal of ‘high coverage, narrow width, and small bias’ in PIs, thus minimizing costs even in cases of prediction failure. A salient feature of the LUBE framework is its ability to discern uncertainty without explicit uncertainty labels, where the data uncertainty and model uncertainty are learned by Deep Neural Networks (DNN) and a model ensemble, respectively. The validity of the proposed method is demonstrated through its application to the prediction of carbon prices in China. Compared with conventional uncertainty quantification methods, the improved interval optimization method can achieve narrower PI widths.

Forecasting retail fuel demand in Chinese gasoline stations: a structural (double) damped trend approach

Forecasting retail fuel demand represents a crucial task for petrol companies. Indeed, the accurate prediction of demand allows improving the management of gasoline stations as well as the whole oil supply chain process. This paper provides a time series forecasting model, defined as double damped trend model, that allows efficiently forecasting the daily retail fuel demand. We propose a flexible state-space approach that encompasses several exponential smoothing alternatives. This model was first considered for the case when a single source of error drives the dynamics of the process. However, little attention was given to the case where multiple sources of errors drive its dynamics, the so-called structural approach. In this paper we focus on this case by providing closed-form results that allows simplify its likelihood estimation as well as the construction of prediction intervals. Moreover, using data for more than 400 gasoline stations in China, we show that our approach outperforms standard benchmarks in predicting both the amount of customer’s demand and prediction intervals, for different types of fuels. These results make our approach appealing for petrol companies.

Constructing prediction intervals for circuit board fault detection: A neural network approach using VI Curve

AbstractThe accuracy and reliability of circuit board fault detection are significantly influenced by the uncertainty inherent in the VI curve. Here, an ensemble neural network is proposed, which combines the neural network‐based prediction interval and ensemble approaches, to improve the accuracy of fault detection using the VI curve. First, a loss function with multiple objectives is formulated by integrating curve fitting and prediction interval. The aim is to achieve the curve fitting between current and voltage while simultaneously determining the optimal upper and lower bounds of the prediction interval. Second, an ensemble approach is employed to reduce model uncertainty and derive the ultimate current predictions and intervals. These predictions and intervals are then used in a comparative approach to automatically detect faults in circuit boards. Finally, the effectiveness of the proposed algorithm in improving the accuracy of fault detection is verified on experimental circuit boards.

Selective conformal inference with false coverage-statement rate control

SUMMARY Conformal inference is a popular tool for constructing prediction intervals. We consider here the scenario of post-selection/selective conformal inference, that is, prediction intervals are reported only for individuals selected from unlabelled test data. To account for multiplicity, we develop a general split conformal framework to construct selective prediction intervals with the false coverage-statement rate control. We first investigate the false coverage rate–adjusted method of Benjamini & Yekutieli (2005) in the present setting, and show that it is able to achieve false coverage-statement rate control, but yields uniformly inflated prediction intervals. We then propose a novel solution to the problem called selective conditional conformal prediction. Our method performs selection procedures on both the calibration set and test set, and then constructs conformal prediction intervals for the selected test candidates with the aid of the conditional empirical distribution obtained by the post-selection calibration set. When the selection rule is exchangeable, we show that our proposed method can exactly control the false coverage-statement rate in a model-free and distribution-free guarantee. For nonexchangeable selection procedures involving the calibration set, we provide non-asymptotic bounds for the false coverage-statement rate under mild distributional assumptions. Numerical results confirm the effectiveness and robustness of our method under false coverage-statement rate control and show that it achieves more narrowed prediction intervals over existing methods across various settings.

Building Better Theories: Prediction Intervals as a Tool for Theory Testing and Improvement

The precision with which a theory predicts behavior speaks both to the quality of that theory and to its potential utility in real-world applications. Unfortunately, predictive precision is frequently overlooked when evaluating theories in social psychology. Here we call attention to the benefits of placing more emphasis on predictive precision. We define what we mean by predictive precision, consider its role in theory evaluation from a philosophy of science perspective, and suggest a method for quantifying it: by constructing prediction intervals. A prediction interval is the range of values within which an empirical observation (e.g., a sample mean) is expected to fall some specified percentage (e.g., 95%) of the time. The size of a prediction interval reflects the degree of fluctuation in the empirical observations expected by theory, and so the precision of its prediction. Prediction intervals are useful because they simplify theory testing and provide a metric by which theory improvement—and so scientific progress—can be gauged. Prediction intervals are easily created when theories are expressed formally as agent-based models. We illustrate the process of creating and using prediction intervals in three detailed examples, each involving a different agent-based model concerned with the behavior of small interacting groups.

GrowthPredict: A toolbox and tutorial-based primer for fitting and forecasting growth trajectories using phenomenological growth models

Simple dynamic modeling tools can help generate real-time short-term forecasts with quantified uncertainty of the trajectory of diverse growth processes unfolding in nature and society, including disease outbreaks. An easy-to-use and flexible toolbox for this purpose is lacking. This tutorial-based primer introduces and illustrates GrowthPredict, a user-friendly MATLAB toolbox for fitting and forecasting time-series trajectories using phenomenological dynamic growth models based on ordinary differential equations. This toolbox is accessible to a broad audience, including students training in mathematical biology, applied statistics, and infectious disease modeling, as well as researchers and policymakers who need to conduct short-term forecasts in real-time. The models included in the toolbox capture exponential and sub-exponential growth patterns that typically follow a rising pattern followed by a decline phase, a common feature of contagion processes. Models include the 1-parameter exponential growth model and the 2-parameter generalized-growth model, which have proven useful in characterizing and forecasting the ascending phase of epidemic outbreaks. It also includes the 2-parameter Gompertz model, the 3-parameter generalized logistic-growth model, and the 3-parameter Richards model, which have demonstrated competitive performance in forecasting single peak outbreaks. We provide detailed guidance on forecasting time-series trajectories and available software (https://github.com/gchowell/forecasting_growthmodels), including the full uncertainty distribution derived through parametric bootstrapping, which is needed to construct prediction intervals and evaluate their accuracy. Functions are available to assess forecasting performance across different models, estimation methods, error structures in the data, and forecasting horizons. The toolbox also includes functions to quantify forecasting performance using metrics that evaluate point and distributional forecasts, including the weighted interval score. This tutorial and toolbox can be broadly applied to characterizing and forecasting time-series data using simple phenomenological growth models. As a contagion process takes off, the tools presented in this tutorial can help create forecasts to guide policy regarding implementing control strategies and assess the impact of interventions. The toolbox functionality is demonstrated through various examples, including a tutorial video, and the examples use publicly available data on the monkeypox (mpox) epidemic in the USA.

IMPROVING ACCURACY OF PREDICTION INTERVALS OF HOUSEHOLD INCOME USING QUANTILE REGRESSION FOREST AND SELECTION OF EXPLANATORY VARIABLES

Quantile regression forest (QRF) is a non-parametric method for estimating the distribution function of response by using the random forest algorithm and constructing conditional quantile prediction intervals. However, if the explanatory factors (covariates) are highly correlated, the quantile regression forest's performance will decrease, resulting in low accuracy of prediction intervals for the outcome variable. The selection of explanatory variables in quantile regression forest is investigated and addressed in this paper, using several selection scenarios that consist of the full model, forward selection, LASSO, ridge regression, and random forest to improve the accuracy of household income data prediction. This data was obtained from National Labour Force Survey in 2021. The results indicate that the random forest method outperforms other methods for explanatory selection utilizing RMSE metrics. With regard to the criteria of average coverage value just above the 95% target and statistical test results, the RF-QRF and Forward-QRF methods outperform the QRF, LASSO-QRF, and Ridge-QRF methods for constructing prediction intervals.

Point and interval prediction for significant wave height based on LSTM-GRU and KDE

Accurate wave height prediction is significant for wave power generation, maritime traffic, and disaster prevention and reduction. This paper proposes a novel point and interval prediction framework based on deep learning methods for wave height prediction. First, multidimensional and multisource datasets are preprocessed. Subsequently, a feature selection process is executed to remove superfluous features. Third, a hybrid model that combines long short-term memory (LSTM) and a gated recurrent unit (GRU) is used to predict wave height. This model uses multivariate features that are positively correlated with wave height as input data. Finally, kernel density estimation (KDE) is leveraged to estimate the probability density distribution of the prediction errors generated the wave height prediction interval. The proposed LSTM-GRU-KDE forecasting framework is compared with benchmark models to verify its practicability. The LSTM-GRU model with multiple feature inputs has lower root mean square error and mean absolute error values and a higher coefficient of determination in predicting hourly wave height for all buoy stations compared to those of LSTM with multiple feature inputs and LSTM-GRU with a single feature input. Moreover, by the coverage width-based criterion, KDE (box) stands out as a superior choice among interval forecasting methods, offering a higher degree of reliability when constructing prediction intervals.

Studying the evolutions, differences, and water security impacts of water demands under shared socioeconomic pathways: A SEMs-bootstrap-ANN approach applied to Sichuan Province

In this study, a SEMs-bootstrap-ANN method was presented for constructing prediction intervals (PIs) of water demand under shared socioeconomic pathways (SSPs). The primary objective was to examine the evolution, disparities, and impacts on water security. Initially, a bootstrap algorithm and an artificial neural network (ANN) were combined to form a bootstrap-ANN model, which determined the centres and widths of the PIs at a specified significance level by estimating the distributions of prediction values and errors. The water demand factors in SSPs were projected using socioeconomic models like Cobb-Douglas, based on the narratives of the International Institute for Applied Systems Analysis (IIASA). By incorporating these factors into the bootstrap-ANN model, the study obtained the temporal changes of water demand PIs in SSPs, while quantifying the differences and water security implications using the interval difference index (IDI) and surface water exploration index (SWEI). The case study focused on Sichuan province, and the model performance was evaluated via the evaluation indices and cross-validation. The results demonstrated five key findings.Firstly, the proposed method showed a greater PICP of 0.985, slightly larger PIRAW of 9.83%, and higher MAIS than other methods in the historical dataset, indicating a small disadvantage in width in return for better accuracy and overall performance.Secondly, the reliability of the results in the SSP period was supported by the PIRAWs (mostly within 15%), the cross errors (approximately 5%), and their performance in 2021 (the PIs in SSP2 almost covered all true values).Thirdly, the total water demands in all SSPs within Sichuan Province exhibited a consistent upward trajectory, with SSP5 displaying the highest increase of 44–63% compared to current water usage.Fourthly, among the four SSPs, the most substantial disparities were observed between SSP5 and SSP3, reaching a maximum difference of 32%. Conversely, the disparities between SSP2 and SSP1 fluctuated around zero, transitioning from negative to positive trends. Notably, from an environmental perspective, SSP1 was considered preferable to SSP2.Lastly, the SWEIs, which reflected water security conditions in Sichuan Province under the four SSPs, ranked in the following order: SSP3, SSP1, SSP2, and SSP5, indicating a progressively worsening situation. Despite not reaching stress thresholds even during dry years until 2100, the water security conditions could deteriorate by 28–46% compared to historical extremes and by 3–16% compared to extended extremes in dry years.

Optimization-Based Prediction Uncertainty Qualification of Climatic Parameters

Abstract Point predictions of hydroclimatic processes through nonlinear modeling tools are associated with uncertainty. The main goal of this research was to construct prediction intervals (PIs) for nonlinear artificial neural network (ANN)-based models of evaporation and the standardized precipitation index (SPI). These are two critical indicators for climate for four stations in Iran (i.e., Tabriz, Urmia, Ardabil, and Ahvaz) to qualify their predicted uncertainty values (UVs). We used classical techniques of bootstrap (BS), mean variance estimation (MVE), and Delta, as well as an optimization-based method of lower upper bound estimation (LUBE), to construct and compare the PIs. The wavelet-based denoising method was also adopted to denoise input data, enhancing the modeling performance. The obtained results indicate the ability of the BS and LUBE methods to estimate the uncertainty bound. The Delta method mostly failed to find the desired coverage due to its narrow PIs. On the other hand, the MVE method, due to its wide bound, did not convey valuable information about uncertainty. According to the obtained results, denoising the input vector could enhance the PI quality in the modeling of the SPI by up to 76%. It was more prominent than reducing the UV for evaporation models, which was observed the most at the Ardabil station, up to 30%. The inherently more random nature of drought than the evaporation process was interpreted as the cause of this reaction. From the results, Urmia station seems the riskiest regarding drought ventures. Significance Statement The point predictions of evaporation and precipitation (in the form of SPI) are subject to uncertainty. The best way is to provide an area with the highest contingency as a prediction interval. The reduction in the width of such an interval leads to increased confidence in explaining and predicting these processes. We investigated different methods and found that by utilizing the optimization-based method for denoised inputs, uncertainty values of the output were conveyed better. Additionally, we concluded that the more random the process, the greater its uncertainty. A primary sense of the drought risk was made from the uncertainty perspective.

Robust Adaptive Rescaled Lncosh Neural Network Regression Toward Time-Series Forecasting

In time series forecasting with outliers and random noise, parameter estimation in a neural network via minimizing the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{2}$</tex-math> </inline-formula> loss is unreliable. Therefore, an adaptive rescaled lncosh loss function is proposed in this article to handle time series modeling with outliers and random noise. It overcomes the limitation of the single distribution of traditional loss functions and can switch among <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{1}$</tex-math> </inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{2}$</tex-math> </inline-formula> , and the Huber losses. A tuning parameter in the loss function is estimated by using a “working” likelihood approach according to estimated residuals. From the proposed loss function, a robust adaptive rescaled lncosh neural network (RARLNN) regression model is developed for highly accurate predictions. In the training phase of the model, an iterative learning procedure is presented to estimate the tuning parameter and train the neural network in iterations. A new prediction interval construction method is also developed based on quantile theory. The proposed RARLNN model is applied to two groups of wind speed forecasting tasks. The results show that the proposed RARLNN model is more conducive to enhancing forecasting accuracy and stability from the perspectives of noise distribution and outliers.

Ensemble water quality forecasting based on decomposition, sub-model selection, and adaptive interval

The prediction of effluent quality for wastewater treatment plants (WWTPs) has caused widespread concern due to its essential role in ensuring water quality standards and reducing energy consumption. However, the complex nonlinearity of WWTPs leads to difficulties in forecasting and less attention to forecast uncertainty. A novel ensemble water quality forecasting (EWQF) system is proposed that incorporates data preprocessing, point prediction and interval prediction. The system provides an accurate prediction of effluent quality and analyses this uncertainty, for enabling feed-forward control of WWTPs. Specifically, the original water quality data is decomposed into subsequences containing more information and less noise based on improved variational modal decomposition (IVMD). The optimal sub-model for each sub-series is selected from six prediction models based on the sub-model selection strategy, and the point prediction results for water quality are obtained by combining the prediction results of the sub-models. Robust and reliable prediction interval construction based on adaptive kernel density estimation. The results demonstrate that the EWQF achieves optimal point prediction results (R2 = 0.955). The EWQF interval prediction achieves the optimal coverage width criterion (CWC) for different confidence intervals and decision objectives. These results demonstrate that EWQF systems can perform excellent point and interval prediction.

Improved methods to construct prediction intervals for network meta-analysis.

Network meta-analysis has played an important role in evidence-based medicine for assessing the comparative effectiveness of multiple available treatments. The prediction interval has been one of the standard outputs in recent network meta-analysis as an effective measure that enables simultaneous assessment of uncertainties in treatment effects and heterogeneity among studies. To construct the prediction interval, a large-sample approximating method based on the t-distribution has generally been applied in practice; however, recent studies have shown that similar t-approximation methods for conventional pairwise meta-analyses can substantially underestimate the uncertainty under realistic situations. In this article, we performed simulation studies to assess the validity of the current standard method for network meta-analysis, and we show that its validity can also be violated under realistic situations. To address the invalidity issue, we developed two new methods to construct more accurate prediction intervals through bootstrap and Kenward-Roger-type adjustment. In simulation experiments, the two proposed methods exhibited better coverage performance and generally provided wider prediction intervals than the ordinary t-approximation. We also developed an R package, PINMA (https://cran.r-project.org/web/packages/PINMA/), to perform the proposed methods using simple commands. We illustrate the effectiveness of the proposed methods through applications to two real network meta-analyses.