Mean Imputation Research Articles

Dental caries incidence and associated factors in young adults.

To assess the caries incidence from late adolescence to early adulthood and to identify the factors associated with caries incidence. This is a secondary analysis of longitudinal caries data of young adults aged 17-23 from the Iowa Fluoride Study cohort. The inclusion criteria required completion of dental exams at both ages 17 and 23 and having cumulative exposure (AUC) variables data for at least 8 out of the 11 time periods between ages 17 and 23. Mean imputation was used to handle the missing explanatory variable data. Multiple linear regressions were conducted using a generalized linear model to assess the effects of sociodemographic and behavioral/dietary variables on the age 17-23 adjusted cavitated caries (D2+ MFS) increment (AdjCI17-23 ). Multicollinearity was assessed using the variance inflation factor (VIF) and the final model was selected based on the Akaike Information Criterion (AIC) using backward selection and the net effects calculated. The mean AdjCI17-23 was 2.08 (SD = 4.02). The net effects (main effect plus interactions) of higher composite socioeconomic status, higher combined daily fluoride intake, higher frequency of milk intake, lower amount of sugar-sweetened beverages intake, and lower age 17 dental caries counts were associated with lower mean AdjCI17-23 . The incidence of caries from age 17 to 23 in this study was low. This study suggests and reinforces the need to continue to advocate for caries preventive strategies such as fluoride use, encouraging milk intake, and reducing sugar-sweetened beverage intakes.

Novel Logarithmic Imputation Methods Under Ranked Set Sampling

ABSTRACT The data we encounter in real life often contain missing values. In sampling methods, missing value imputation is done with different methods. This article proposes novel logarithmic type imputation methods for estimating the population mean in the presence of missing data under ranked set sampling (RSS). According to the determined theoretical results, the proposed imputation methods are found to be the most efficient in comparison to popularly known imputation methods like mean imputation, Al-Omari and Bouza (2014) imputation methods, Sohail et al. (2018) imputation methods, and Bhushan and Pandey (2016) type imputation methods utilizing RSS. Apart from this, a simulation study has been accomplished utilizing artificially drawn symmetric and asymmetric populations. The outcomes are encountered to be rather satisfactory, showing improvement over all existing imputation methods.

On the efficiency of modified regression-type mean imputation scheme under two-phase sampling

Human-based surveys such as medical and social science surveys are often characterized by non-response or missing observations. In this study, a new class of regression-type mean imputation method that uses X̄n as an estimate of X̄ was suggested. Using partial derivative approach, the MSEs of the class of estimators presented were derived up to first order approximation under two cases. Case I: when the secondary sample S2 of size n(n<n1) is a subset of preliminary sample S1[S2 ⸦ S1] , and Case II: is when secondary sample S2 is a subset of universal set ΩN . Conditions for which the new estimator was more efficient than the other estimators studied were derived. The results of numerical examples through simulations revealed that the suggested class of estimators is more efficient.

A novel data gaps filling method for solar PV output forecasting

This study proposes a modified gaps filling method, expanding the column mean imputation method and evaluated using randomly generated missing values comprising 5%, 10%, 15%, and 20% of the original data on power output. The XGBoost algorithm was implemented as a forecasting model using the original and processed datasets and two sources of solar radiation data, namely, Shortwave Radiation (SWR) from Advanced Himawari Imager 8 (AHI-8) and Surface Solar Radiation Downward (SSRD) from ERA5 global reanalysis data. The accuracy of the two sets of forecasted power output was evaluated using Root Mean Square Error (RMSE) and Mean Absolute Error (MAE). Results show that by applying the proposed gap filling method and using SWR in forecasting solar photovoltaic (PV) output, the improvement in the RMSE and MAE values range from 12.52% to 24.30% and from 21.10% to 31.31%, respectively. Meanwhile, using SSRD, the improvement in the RMSE values range from 14.01% to 28.54% and MAE values from 22.39% to 35.53%. To further evaluate the accuracy of the proposed gap-filling method, the proposed method could be validated using different datasets and other forecasting methods. Future studies could also consider applying the said method to datasets with data gaps higher than 20%.

Deep Learning Imputation for Asymmetric and Incomplete Likert-Type Items

Asymmetric Likert-type items in research studies can present several challenges in data analysis, particularly concerning missing data. These items are often characterized by a skewed scaling, where either there is no neutral response option or an unequal number of possible positive and negative responses. The use of conventional techniques, such as discriminant analysis or logistic regression imputation, for handling missing data in asymmetric items may result in significant bias. It is also recommended to exercise caution when employing alternative strategies, such as listwise deletion or mean imputation, because these methods rely on assumptions that are often unrealistic in surveys and rating scales. This article explores the potential of implementing a deep learning-based imputation method. Additionally, we provide access to deep learning-based imputation to a broader group of researchers without requiring advanced machine learning training. We apply the methodology to the Wilmington Street Participatory Action Research Health Project.

Multinomial Logistic Factor Regression for Multi-source Functional Block-wise Missing Data.

Multi-source functional block-wise missing data arise more commonly in medical care recently with the rapid development of big data and medical technology, hence there is an urgent need to develop efficient dimension reduction to extract important information for classification under such data. However, most existing methods for classification problems consider high-dimensional data as covariates. In the paper, we propose a novel multinomial imputed-factor Logistic regression model with multi-source functional block-wise missing data as covariates. Our main contribution is to establishing two multinomial factor regression models by using the imputed multi-source functional principal component scores and imputed canonical scores as covariates, respectively, where the missing factors are imputed by both the conditional mean imputation and the multiple block-wise imputation approaches. Specifically, the univariate FPCA is carried out for the observable data of each data source firstly to obtain the univariate principal component scores and the eigenfunctions. Then, the block-wise missing univariate principal component scores instead of the block-wise missing functional data are imputed by the conditional mean imputation method and the multiple block-wise imputation method, respectively. After that, based on the imputed univariate factors, the multi-source principal component scores are constructed by using the relationship between the multi-source principal component scores and the univariate principal component scores; and at the same time, the canonical scores are obtained by the multiple-set canonial correlation analysis. Finally, the multinomial imputed-factor Logistic regression model is established with the multi-source principal component scores or the canonical scores as factors. Numerical simulations and real data analysis on ADNI data show the proposed method works well.

English

Researchers and data analysts commonly experience with missing data in their field of studies. It is necessary to handle missing data properly to obtain better and more reliable outcomes of any research. The objective of this research is to evaluate different imputation techniques for handling missing observations in weather data. For this purpose weather data of daily rainfall maximum temperature (Tmax) and minimum temperature (Tmin) of 23 stations of Pakistan were taken from Pakistan Metrological department from 1981 to 2020. There are total 14610 observation of each variable and each variable have different number of missing observations at different stations. For the estimation of missing observation at each station mean imputation k nearest neighbors (KNN) imputation predictive mean matching (PMM) imputation and sample imputation techniques are used. Among different imputation techniques the technique which provides minimum root mean square error (RMSE) is selected and used to estimate the missing observations at each station. The result shows that the selection of imputation method is different for each station and mainly depends upon the size of missing observation in the data. For rainfall data the KNN technique is the most appropriate while for Tmax and Tmin the mean imputation technique is recommended for the estimation of missing observation in the data as compared to other methods.

The Contributions of Human Capital to the Philippine GDP Per Capita

The Philippines suffered from learning loss due to school closures induced by the COVID-19 pandemic. The effects of the pandemic did not only anticipate in one direction as it posed a domino effect from one sector to another. Investing in human capital would help the country bounce back from such a loss (Sultana et al., 2022), yet it always costs a real expense (Brewer, Hentschke & Reide, 2010). To reduce the cost associated with education, the government must also boost employment (Atalay, 2015). With that, this paper aims to investigate the effects of human capital indicators determined by the World Economic Forum on Philippine GDP per capita from 1981 to 2020 for Education, from 2000 to 2020 for Health and Employment, and from 1998 to 2020 for Enabling Environment using Ordinary Least Squares Method. The findings revealed that seven sub-variables have positive effects on GDP per capita—Tertiary Enrolment Rates; Life Expectancy and Water, Sanitation, and Hygiene; Capacity for Innovation and Scientific-Technical Journal Articles; Mobile Users and Internet Users. While the rest have negative effects—Primary Enrolment Rate; Fertility Rate; Labor Force Participation; Social Mobility. The results suggest that the government prioritizes Enabling Environment and Health as these sectors need more assistance. Keywords: Contribution, Human Capital, Philippine, GDP Per Capita, Multiple Regression, EViews, Mean Imputation, Log Transformation

COMPARISON OF SIMPLE MISSING DATA IMPUTATION TECHNIQUES FOR NUMERICAL AND CATEGORICAL DATASETS

Almost every dataset has missing data. The common reasons are sensor error, equipment malfunction, human error, or translation loss. We study the efficacy of statistical (mean, median, mode) and machine learning based (k-nearest neighbors) imputation methods in accurately imputing missing data in numerical datasets with data missing not at random (MNAR) and data missing completely at random (MCAR) as well as categorical datasets. Imputed datasets are used to make prediction on the test set and Mean squared error (MSE) in prediction is used as the measure of performance of the imputation. Mean absolute difference between the original and imputed data is also observed. When the data is MCAR, kNN imputation results in lowest MSE for all datasets, making it the most accurate method. When less than 20% of data is missing, mean and median imputations are effective in regression problems. kNN imputation is better at 20% missingness and significantly better when 50% or more data is missing. For the kNN method, k = 5 gives better results than k=3 but k=10 gives similar results to k=5. For MNAR datasets, statistical methods result in similar or lower MSE compared to kNN imputation when less than 25% of instances have a missing feature. For higher missing levels, kNN imputation is superior. Given enough data points without missing features, deleting the instances with missing data may be a better choice at lower missingness levels. For categorical data imputation, kNN and Mode imputation are both effective.

Analyzing the Effect of Imputation on Classification Performance under MCAR and MAR Missing Mechanisms

Many datasets in statistical analyses contain missing values. As omitting observations containing missing entries may lead to information loss or greatly reduce the sample size, imputation is usually preferable. However, imputation can also introduce bias and impact the quality and validity of subsequent analysis. Focusing on binary classification problems, we analyzed how missing value imputation under MCAR as well as MAR missingness with different missing patterns affects the predictive performance of subsequent classification. To this end, we compared imputation methods such as several MICE variants, missForest, Hot Deck as well as mean imputation with regard to the classification performance achieved with commonly used classifiers such as Random Forest, Extreme Gradient Boosting, Support Vector Machine and regularized logistic regression. Our simulation results showed that Random Forest based imputation (i.e., MICE Random Forest and missForest) performed particularly well in most scenarios studied. In addition to these two methods, simple mean imputation also proved to be useful, especially when many features (covariates) contained missing values.

Bootstrap Based Diagnostics for Survival Regression Model with Interval and Right-Censored Data

This research proposes a new approach based on the bias-corrected bootstrap harmonic mean and random imputation technique to obtain the adjusted residuals (Hboot) when a survival model is fit to right- and interval-censored data with covariates. Following that, the model adequacy and influence diagnostics based on these adjusted residuals, case deletion diagnostics, and the normal curvature are discussed. Simulation studies were conducted to assess the performance of the parameter estimate and compare the performances of the traditional Cox-Snell (CS), modified Cox-Snell (MCS) and Hboot at various censoring proportions (cp) and samples sizes ($n$) using the log-logistic and extreme minimum value regression models with right- and interval-censored data. The results clearly indicated that Hboot outperformed other residuals at all levels of cp and $n$, for both models. The proposed methods are then illustrated using real data set from the COM breast cancer data. The results indicate that the proposed methods work well to address model adequacy and identify potentially influential observations in the data set.

Potable Water Quality Prediction Using Artificial Intelligence and Machine Learning Algorithms for Better Sustainability

Water is one of the most important resources for human life and health. Global climate change, industrialization and urbanization pose serious dangers to existing water resources. Water quality has traditionally been predicted by expensive, time-consuming laboratory and statistical analysis. However, machine learning algorithms can be applied to determine the water quality index in real time efficiently and quickly. With this motivation, a dataset obtained from the Kaggle website was used to classify water quality in this research. Some features were found to be empty in the data set. Traditional methods (drop, mean imputation) and regression method were applied for null values. After the null values were completed, RF, Adaboost and XGBoost were applied for binary classification. Gridsearch and Randomsearch methods have been applied in hyper parameter optimization. Among all the algorithms used, the SXH hybrid method created with the Support Vector Regression (SVR) and XGBoost methods showed the best classification performance with 99.4% accuracy and F1-score. Comparison of our results with previous similar studies showed that our SVR XGboost Hybrid (SXH) model had the best performance ratio (Accuracy, F1-score). The performance of our proposed model is proof that hybrid machine learning methods can provide an innovative perspective on potable water quality.

Mind the Large Gap: Novel Algorithm Using Seasonal Decomposition and Elastic Net Regression to Impute Large Intervals of Missing Data in Air Quality Data

Air quality data sets are widely used in numerous analyses. Missing values are ubiquitous in air quality data sets as the data are collected through sensors. Recovery of missing data is a challenging task in the data preprocessing stage. This task becomes more challenging in time series data as time is an implicit variable that cannot be ignored. Even though existing methods to deal with missing data in time series perform well in situations where the percentage of missing values is relatively low and the gap size is small, their performances are reasonably lower when it comes to large gaps. This paper presents a novel algorithm based on seasonal decomposition and elastic net regression to impute large gaps of time series data when there exist correlated variables. This method outperforms several other existing univariate approaches namely Kalman smoothing on ARIMA models, Kalman smoothing on structural time series models, linear interpolation, and mean imputation in imputing large gaps. However, this is applicable only when there exists one or more correlated variables with the time series with large gaps.

Healthcare costs of congenital cytomegalovirus (cCMV) disease in infants during the first two years of life: a retrospective German claims database analysis

BackgroundCongenital cytomegalovirus (cCMV) infection can cause severe neurological damage, growth retardation, hearing loss, and microcephaly in infants. We aimed at assessing healthcare costs of infants with recorded cCMV diagnosis in an administrative claims database in the first 2 years of life.MethodsWe conducted a retrospective, controlled cohort study using German claims data from the Institute for Applied Health Research Berlin (InGef) database. Incremental healthcare costs during the first and second year of life were assessed by matching (1:60) infants with cCMV diagnoses ≤ 90 days after birth (cCMV90 cohort) to infants without cCMV diagnosis (“representative” controls) and infants with cCMV diagnoses ≤ 21 days after birth plus specific symptoms (cCMV21-S) to infants without cCMV and any ICD-10-GM records (besides Z00-Z99) until 4th preventive health check-up (“healthy” controls). Due to missing data, mean imputation was applied for aids and remedies costs.ResultsWe identified 54 and 24 infants born 2014–2018 for the cCMV90 and cCMV21-S cohorts, respectively. During the first year, mean (median) healthcare costs were significantly higher in cCMV90 cases vs. “representative” controls (€22,737 (€9759) vs. €3091 (€863), p < 0.001), with 87.2% inpatient costs. Healthcare costs for cCMV21-S cases compared to “healthy” controls were €34,498 (€20,924) vs. €680 (€569), p < 0.001. Differences decreased for both comparisons in the second year but remained statistically significant.ConclusionscCMV comprises a considerable economic burden for the German healthcare system (€19,646 to €33,818 higher mean costs for infants with recorded cCMV diagnosis in the first year of life). Attempts should be made to reduce this burden.

Local mean imputation for handling missing value to provide more accurate facies classification

The search for oil and gas reserves is an ongoing challenge. The possibility of oil and natural gas reserves running out in Indonesia in less than 25 years must also be considered by the industry. Unfortunately, the process of exploration and development of hydrocarbon fields still has its challenges, one of which is knowing the characteristics of hydrocarbon reservoirs. One of these characteristics that should be analyzed is rock facies. This could be done by using core data, well logs, analog studies, and others. However, this method is very expensive and time-consuming. Currently, the machine learning approach is the most popular solution for the classification of rock facies. However, a common issue with this method is the missing values due to recording errors in the field. Meanwhile, a machine learning system requires accurate data to form a good model. Therefore, we propose the use of a simple imputation method to solve the local mean imputation method by considering the uniqueness of each class before performing the imputation process. We also implemented several popular boosting methods in machine learning such as comparing Extreme Gradient Boosting and Light Gradient Boosting with several machine learning algorithms that are often used in solving facies classification problems such as Random Forest, Decision Tree, Support Vector Machine, and K-Nearest Neighbor. According to our results, the Local Mean imputation method improved the model's performance, where the perceived increase was between 1-10% and the model with the best performance was generated by the Random Forest method.

Enhancing Predictive Modeling in Kuala Lumpur Real Estate: A Comprehensive Data Preprocessing and Feature Engineering Approach

The real estate market in Kuala Lumpur exhibits complex dynamics influenced by various factors. This paper presents a comprehensive approach to enhance the prediction of real estate prices in Kuala Lumpur utilizing a dataset of 49,416 records with advanced data preprocessing techniques, exploratory data analysis (EDA), and predictive modeling. Initially, the dataset undergoes rigorous preprocessing including handling missing values through property type-specific mean imputation, label encoding categorical variables, and standardization to ensure uniformity and compatibility for analysis. Subsequently, EDA techniques are employed to gain insights into the dataset's characteristics and relationships among variables. To improve model performance and interpretability, feature selection is performed based on Mutual Information (MI) score and correlation metrics. This aids in identifying the most relevant features for predicting real estate prices in Kuala Lumpur. Additionally, feature engineering techniques are applied to create two new features that capture nuanced aspects of the real estate market. The predictive modeling phase employs a Linear Regression algorithm to forecast real estate prices. Leveraging the preprocessed data and optimized feature set, the model aims to accurately predict property prices based on available features. The linear regression model offers interpretability, enabling stakeholders to understand the driving factors behind price variations. Through a rigorous methodology encompassing data preprocessing, exploratory analysis, feature selection, engineering, and predictive modeling, this study contributes to enhancing the accuracy and interpretability of real estate price prediction in Kuala Lumpurthat applies advanced machine learning methods. The findings offer valuable insights for real estate investors, policymakers, and stakeholders to make informed decisions in this dynamic market landscape.

Interpretable generalized neural additive models for mortality prediction of COVID-19 hospitalized patients in Hamadan, Iran

BackgroundThe high number of COVID-19 deaths is a serious threat to the world. Demographic and clinical biomarkers are significantly associated with the mortality risk of this disease. This study aimed to implement Generalized Neural Additive Model (GNAM) as an interpretable machine learning method to predict the COVID-19 mortality of patients.MethodsThis cohort study included 2181 COVID-19 patients admitted from February 2020 to July 2021 in Sina and Besat hospitals in Hamadan, west of Iran. A total of 22 baseline features including patients' demographic information and clinical biomarkers were collected. Four strategies including removing missing values, mean, K-Nearest Neighbor (KNN), and Multivariate Imputation by Chained Equations (MICE) imputation methods were used to deal with missing data. Firstly, the important features for predicting binary outcome (1: death, 0: recovery) were selected using the Random Forest (RF) method. Also, synthetic minority over-sampling technique (SMOTE) method was used for handling imbalanced data. Next, considering the selected features, the predictive performance of GNAM for predicting mortality outcome was compared with logistic regression, RF, generalized additive model (GAMs), gradient boosting decision tree (GBDT), and deep neural networks (DNNs) classification models. Each model trained on fifty different subsets of a train-test dataset to ensure a model performance. The average accuracy, F1-score and area under the curve (AUC) evaluation indices were used for comparison of the predictive performance of the models.ResultsOut of the 2181 COVID-19 patients, 624 died during hospitalization and 1557 recovered. The missing rate was 3 percent for each patient. The mean age of dead patients (71.17 ± 14.44 years) was statistically significant higher than recovered patients (58.25 ± 16.52 years). Based on RF, 10 features with the highest relative importance were selected as the best influential features; including blood urea nitrogen (BUN), lymphocytes (Lym), age, blood sugar (BS), serum glutamic-oxaloacetic transaminase (SGOT), monocytes (Mono), blood creatinine (CR), neutrophils (NUT), alkaline phosphatase (ALP) and hematocrit (HCT). The results of predictive performance comparisons showed GNAM with the mean accuracy, F1-score, and mean AUC in the test dataset of 0.847, 0.691, and 0.774, respectively, had the best performance. The smooth function graphs learned from the GNAM were descending for the Lym and ascending for the other important features.ConclusionsInterpretable GNAM can perform well in predicting the mortality of COVID-19 patients. Therefore, the use of such a reliable model can help physicians to prioritize some important demographic and clinical biomarkers by identifying the effective features and the type of predictive trend in disease progression.

Evaluating the Effects of Missing Data Handling Methods on Scale Linking Accuracy.

For large-scale assessments, data are often collected with missing responses. Despite the wide use of item response theory (IRT) in many testing programs, however, the existing literature offers little insight into the effectiveness of various approaches to handling missing responses in the context of scale linking. Scale linking is commonly used in large-scale assessments to maintain scale comparability over multiple forms of a test. Under a common-item nonequivalent group design (CINEG), missing data that occur to common items potentially influence the linking coefficients and, consequently, may affect scale comparability, test validity, and reliability. The objective of this study was to evaluate the effect of six missing data handling approaches, including listwise deletion (LWD), treating missing data as incorrect responses (IN), corrected item mean imputation (CM), imputing with a response function (RF), multiple imputation (MI), and full information likelihood information (FIML), on IRT scale linking accuracy when missing data occur to common items. Under a set of simulation conditions, the relative performance of the six missing data treatment methods under two missing mechanisms was explored. Results showed that RF, MI, and FIML produced less errors for conducting scale linking whereas LWD was associated with the most errors regardless of various testing conditions.

Classification of breast cancer recurrence based on imputed data: a simulation study

Several studies have been conducted to classify various real life events but few are in medical fields; particularly about breast recurrence under statistical techniques. To our knowledge, there is no reported comparison of statistical classification accuracy and classifiers’ discriminative ability on breast cancer recurrence in presence of imputed missing data. Therefore, this article aims to fill this analysis gap by comparing the performance of binary classifiers (logistic regression, linear and quadratic discriminant analysis) using several datasets resulted from imputation process using various simulation conditions. Our study aids the knowledge about how classifiers’ accuracy and discriminative ability in classifying a binary outcome variable are affected by the presence of imputed numerical missing data. We simulated incomplete datasets with 15, 30, 45 and 60% of missingness under Missing At Random (MAR) and Missing Completely At Random (MCAR) mechanisms. Mean imputation, hot deck, k-nearest neighbour, multiple imputations via chained equation, expected-maximisation, and predictive mean matching were used to impute incomplete datasets. For each classifier, correct classification accuracy and area under the Receiver Operating Characteristic (ROC) curves under MAR and MCAR mechanisms were compared. The linear discriminant classifier attained the highest classification accuracy (73.9%) based on mean-imputed data at 45% of missing data under MCAR mechanism. As a classifier, the logistic regression based on predictive mean matching imputed-data yields the greatest areas under ROC curves (0.6418) at 30% missingness while k-nearest neighbour tops the value (0.6428) at 60% of missing data under MCAR mechanism.

PP92 Should Missing Data Be Multiply Imputed Prior To Longitudinal Linear Mixed-Model Analyses In Trial-Based Economic Evaluations?

IntroductionFor the analysis of clinical effects, multiple imputation (MI) of missing data was shown to be unnecessary when using longitudinal linear mixed-models (LLM). It remains unclear whether this also applies to cost estimates from trial-based economic evaluations, that are generally right-skewed. Therefore, this study aimed to assess whether MI is required prior to LLM when analyzing longitudinal cost-effectiveness data.MethodsTwo-thousand complete datasets were simulated containing five time points. Incomplete datasets were generated with 10 percent, 25 percent, and 50 percent missing data in costs and effects, assuming a Missing At Random (MAR) mechanism. Statistical performance of six different methodological strategies was compared in terms of empirical bias (EB), root-mean-squared error (RMSE), and coverage rate (CR). Six strategies were compared: (i) LLM (LLM), (ii) MI prior to LLM (MI-LLM), (iii) mean imputation prior to LLM (M-LLM), (iv) complete-case analysis prior to seemingly unrelated regression (CCA-SUR), (v) MI prior to SUR (MI-SUR), and (vi) mean imputation prior to SUR (M-SUR). To evaluate the impact on the probability of cost-effectiveness at different willingness-to-pay [WTPs] thresholds, cost-effectiveness analyses were performed by applying the six strategies to two empirical datasets with 9% and 50% of missing data, respectively.ResultsFor costs and effects, LLM, MI-LLM, and MI-SUR performed better than M-LLM, CCA-SUR, and M-SUR, as indicated by smaller EBs and RMSEs, as well as CRs closer to the nominal levels of 0.95. However, even though LLM, MI-LLM, and MI-SUR performed equally well for effects, MI-LLM and MI-SUR were found to perform better than LLM for costs at 10 percent and 25 percent missing data. At 50 percent missing data, all strategies resulted in relatively high EBs and RMSEs for costs. In both empirical datasets, LLM, MI-LLM, and MI-SUR all resulted in similar probabilities of cost-effectiveness at different WTPs.ConclusionsWhen opting for using LLM for analyzing trial-based economic evaluation data, researchers are advised to multiply impute missing values first. Otherwise, MI-SUR may also be used.