Mean Imputation Research Articles

Statistical Evaluation of Item Nonresponse Methods Using the World Bank’s 2015 Philippines Enterprise Survey

The main objective of the study was to evaluate item nonresponse procedures through a simulation study of different nonresponse levels or missing rates. A simulation study was used to explore how each of the response rates performs under a variety of circumstances. It also investigated the performance of procedures suggested for item nonresponse under various conditions and variable trends. The imputation methods considered were the cell mean imputation, random hotdeck, nearest neighbor, and simple regression. These variables are some of the major indicators for measuring productive labor and decent work in the country. For the purpose of this study, the researcher is interested in evaluating methods for imputing missing data for the number of workers and total cost of labor per establishment from the World Bank’s 2015 Enterprise Survey for the Philippines.
 The performances of the imputation techniques for item nonresponse were evaluated in terms of bias and coefficient of variation for accuracy and precision. Based on the results, the cell-mean imputation was seen to be most appropriate for imputing missing values for the total number of workers and total cost of labor per establishment. Since the study was limited to the variables cited, it is recommended to explore other labor indicators. Moreover, exploring choice of other clustering groups is highly recommended as clustering groups have great effect in the resulting estimates of imputation estimation. It is also recommended to explore other imputation techniques like multiple regression and other parametric models for nonresponse such as the Bayes estimation method. For regression based imputation, since the study is limited only in using the cluster groupings estimation, it is highly recommended to use other possible variables that might be related to the variable of interest to verify the results of this study.

A Hybrid Modified Deep Learning Data Imputation Method for Numeric Datasets

Missing data is a major problem in terms of both machine learning and data mining methods. Like most of these methods do not work with missing data, negative results may occur on the performance of the working ones, also. Imputation is a data preprocessing method used to replace missing data with appropriate values. This study aims at developing a hybrid modified imputation method based on deep learning approach. For this purpose, we use Random Forest and Datawig deep learning imputation (called RF-DLI) methods together. Datawig is a deep learning-based library that supports missing value imputation for all types of data. RF-DLI approach includes the following steps to impute missing data. First, the importance of each attribute of the dataset is determined with Random Forest (RF). Second, the most important 50% of the attributes are selected. Finally, each missing value is imputed with datawig (DLI) using these most important attributes. The study uses six real-world datasets from different fields with 30% missing data. The imputation performance of RF-DLI is compared to KNN, MICE, and MEAN imputation approaches in terms of MAE, RMSE, and R2 evaluation metrics. The results show that in most cases, the RF-DLI approach has better imputation performance than the other techniques mentioned.

Comparing low-pass sequencing and genotyping for trait mapping in pharmacogenetics

BackgroundLow pass sequencing has been proposed as a cost-effective alternative to genotyping arrays to identify genetic variants that influence multifactorial traits in humans. For common diseases this typically has required both large sample sizes and comprehensive variant discovery. Genotyping arrays are also routinely used to perform pharmacogenetic (PGx) experiments where sample sizes are likely to be significantly smaller, but clinically relevant effect sizes likely to be larger.ResultsTo assess how low pass sequencing would compare to array based genotyping for PGx we compared a low-pass assay (in which 1x coverage or less of a target genome is sequenced) along with software for genotype imputation to standard approaches. We sequenced 79 individuals to 1x genome coverage and genotyped the same samples on the Affymetrix Axiom Biobank Precision Medicine Research Array (PMRA). We then down-sampled the sequencing data to 0.8x, 0.6x, and 0.4x coverage, and performed imputation. Both the genotype data and the sequencing data were further used to impute human leukocyte antigen (HLA) genotypes for all samples. We compared the sequencing data and the genotyping array data in terms of four metrics: overall concordance, concordance at single nucleotide polymorphisms in pharmacogenetics-related genes, concordance in imputed HLA genotypes, and imputation r2. Overall concordance between the two assays ranged from 98.2% (for 0.4x coverage sequencing) to 99.2% (for 1x coverage sequencing), with qualitatively similar numbers for the subsets of variants most important in pharmacogenetics. At common single nucleotide polymorphisms (SNPs), the mean imputation r2 from the genotyping array was 0.90, which was comparable to the imputation r2 from 0.4x coverage sequencing, while the mean imputation r2 from 1x sequencing data was 0.96.ConclusionsThese results indicate that low-pass sequencing to a depth above 0.4x coverage attains higher power for association studies when compared to the PMRA and should be considered as a competitive alternative to genotyping arrays for trait mapping in pharmacogenetics.

Supervised machine learning for early predicting the sepsis patient: modified mean imputation and modified chi-square feature selection

Sepsis is a typical and significant emergency in medical clinics comprehensively. A creative and possible instrument for identifying sepsis stays elusive. Supervised models can identify potential clinical factors and give a more accurate prediction than the existing benchmark rule-based tools. This research aims to increase the sensitivity to accurately predict the sepsis patient. The proposed system consists of the mean imputation and chi-square technique to replace the missing features and feature selection, respectively. All datasets are fed into the chi-square technique for feature selection by measuring how expectations compare to actual observed data. The essential missing data are then replaced using the mean-imputation method by calculating the mean value of the available data. Finally, the selected features are used as an input to the supervised machine learning model for the classification of sepsis patient. The results of accuracy and processing time are obtained by using different datasets. The results show that the proposed solution achieves better classification performance in different data scenarios and different review types. The proposed solution provides a classification accuracy of 97.67% against the current accuracy of 91.12% on average. It also provides a processing time of 29.1 milliseconds against the current processing time of 32.8 milliseconds on average. The proposed system is focused on the feature selection process that is involved in the machine learning model. Finally, this study solves the issue of model overfitting with supervised machine learning.

An Exploration of Online Missing Value Imputation in Non-stationary Data Stream

Missing value imputation (MVI) is an important data preprocessing technique. In previous decades, MVI technique has been widely studied as well as most MVI approaches have been proposed by means of either statistics or machine learning techniques. However, all previous methods only focus on the static data, but ignore the imputation for the dynamic online data. It is intuitionistic that the imputation errors may be significantly increased when there exists concept drifts in the data stream. In this paper, we investigate the impact of adopting the conventional MVI methods in non-stationary data stream. Meanwhile, two slide time window-based strategies are proposed to alleviate this impact, where one is the plain average strategy, and the other is the logarithmic weighted average strategy that gradually adds the weights of instances along the time axis. Combining with the proposed strategies, three popular MVI techniques, mean imputation (MI), KNN imputation (KNNI) and the Bayesian principal component analysis imputation (BPCAI) are adopted, to indicate the effect of the strategies are irrelevant to the specific MVI technique. The experimental results on three different types' concept drift synthetic data sets and two real-world drifting data sets have presented the effectiveness and feasibility of the proposed strategies. Moreover, the impact of time window size has also been investigated for guiding the parameter settings in future practical applications.

Real-time imputation of missing predictor values improved the application of prediction models in daily practice

ObjectivesIn clinical practice, many prediction models cannot be used when predictor values are missing. We, therefore, propose and evaluate methods for real-time imputation. Study Design and SettingWe describe (i) mean imputation (where missing values are replaced by the sample mean), (ii) joint modeling imputation (JMI, where we use a multivariate normal approximation to generate patient-specific imputations), and (iii) conditional modeling imputation (CMI, where a multivariable imputation model is derived for each predictor from a population). We compared these methods in a case study evaluating the root mean squared error (RMSE) and coverage of the 95% confidence intervals (i.e., the proportion of confidence intervals that contain the true predictor value) of imputed predictor values. Results–RMSE was lowest when adopting JMI or CMI, although imputation of individual predictors did not always lead to substantial improvements as compared to mean imputation. JMI and CMI appeared particularly useful when the values of multiple predictors of the model were missing. Coverage reached the nominal level (i.e., 95%) for both CMI and JMI. ConclusionMultiple imputations using either CMI or JMI is recommended when dealing with missing predictor values in real-time settings.

PEMANFAATAN METODE WEIGHTED K-NEAREST NEIGHBOR IMPUTATION (WEIGHTED KNNI) UNTUK MENGATASI MISSING DATA

Pada tahun 2020, hampir semua negara di dunia menghadapi wabah COVID-19, termasuk Indonesia. Salah satu dampak yang terjadi karena adanya pandemi COVID-19 adalah terhambatnya kegiatan statistik, seperti tertundanya atau berhentinya pelaksanaan pengumpulan data survei dan sensus serta pengumpulan data lainnya. Sementara itu, untuk memenuhi permintaan dan kebutuhan data selama masa pandemi COVID-19, badan statistik nasional harus tetap melakukan pengumpulan data dan menyediakan data statistik. Oleh sebab itu, badan statistik nasional harus melakukan adaptasi untuk kegiatan proses sensus dan survei yang dilakukan, seperti mencari mode pengumpulan data alternatif, mengurangi ukuran sampel, memodifikasi desain sampel, mengurangi item pertanyaan di kuesioner, atau lainnya. Berdasarkan uraian tersebut, adaptasi kegiatan pengumpulan data sensus/survei yang dilakukan pada masa pandemi COVID-19 akan berpengaruh pada kualitas data yang dihasilkan. Salah satunya adanya missing data. Untuk mengatasi masalah missing data, salah satu metode yang dapat digunakan adalah imputasi data. Salah satu jenis metode imputasi berbasis machine learning yang sering digunakan adalah Weighted K-Nearest Neighbor Imputation (Weighted KNNI). Metode Weighted KNNI memiliki akurasi yang lebih baik dibandingkan kedua metode imputasi lainnya (Unweighted KNNI dan Mean Imputation) pada tiap persentase missing data baik akurasi dari sisi RMSE maupun akurasi dari sisi MAPE. Berdasarkan hasil tersebut yang dilihat dari akurasinya, metode Weighted KNNI dapat digunakan sebagai salah satu solusi untuk menangani ketidaklengkapan data pada masa pandemi COVID19 sekarang ini.

Improved Mean Shift Algorithm for Maximizing Clustering Accuracy

Clustering is a machine learning method that can group similar data points. Mean Shift (MS) is a fixed window-based clustering algorithm, which calculates the number of clusters automatically but cannot guarantee the convergence of the algorithm. The main drawback of the Mean Shift Algorithm is that the algorithm requires to set a stopping criterion (threshold point) otherwise all clusters move towards one cluster and fixed bandwidth is used here. It cannot define the upper bound of iteration numbers and need to set the iteration numbers. This paper proposed a new Mean Shift Algorithm, called Improved Mean Shift (IMS) algorithm, which overcomes the all defined pitfalls of Mean Shift Algorithm. The IMS process KD-tree data structure was used to sort the dataset and all data points as initial cluster centroids without a random selection of initial centroids. In each iteration, it shifts the variable bandwidth sliding window to the actual data point nearest to the mean using k-nearest neighbours (kNN) algorithm and finds the number of clusters automatically. Also, this paper handles the missing values using Mean Imputation (MI). The IMS algorithm produces better results than the Mean Shift Algorithm on both synthetic and real datasets.

Fuzzy C-mean Missing Data Imputation for Analogy-based Effort Estimation

The accuracy of effort estimation in one of the major factors in the success or failure of software projects. Analogy-Based Estimation (ABE) is a widely accepted estimation model since its flow human nature in selecting analogies similar in nature to the target project. The accuracy of prediction in ABE model in strongly associated with the quality of the dataset since it depends on previous completed projects for estimation. Missing Data (MD) is one of major challenges in software engineering datasets. Several missing data imputation techniques have been investigated by researchers in ABE model. Identification of the most similar donor values from the completed software projects dataset for imputation is a challenging issue in existing missing data techniques adopted for ABE model. In this study, Fuzzy C-Mean Imputation (FCMI), Mean Imputation (MI) and K-Nearest Neighbor Imputation (KNNI) are investigated to impute missing values in Desharnais dataset under different missing data percentages (Desh-Miss1, Desh-Miss2) for ABE model. FCMI-ABE technique is proposed in this study. Evaluation comparison among MI, KNNI, and (ABE-FCMI) is conducted for ABE model to identify the suitable MD imputation method. The results suggest that the use of (ABE-FCMI), rather than MI and KNNI, imputes more reliable values to incomplete software projects in the missing datasets. It was also found that the proposed imputation method significantly improves software development effort prediction of ABE model.

Missing Data in Asset Pricing Panels

Missing data for return predictors is a common problem in cross sectional asset pricing studies. Most papers do not explicitly discuss how they treat missing data but conventional treatments focus on complete cases for all predictors or impute the unconditional mean for the missing predictor. Both methods have undesirable properties - they are either inefficient or lead to biased estimators and incorrect inference. We propose a simple and computationally attractive alternative approach using conditional mean imputations and weighted least squares. This method allows us to use all sample points with observed returns, it results in valid inference, and it can be applied in non-linear and high-dimensional settings. We map our estimator into a GMM framework to study its relative efficiency and find that it performs almost as well as the efficient but computationally costly GMM estimator in many cases. We apply our procedure to a large panel of return predictors and find that it leads to improved out-of-sample predictability.

Construct Validity of the Questionnaire Quality From the Patients Perspective Adapted for Surgical Prostate Cancer Patients.

Patient-reported experience measures (PREMs) are important to capture the patients’ voice. No such measure is routinely used for evaluation after robotic-assisted radical prostatectomy for prostate cancer. The aim of this study was to adapt the short version of the PREM questionnaire quality from the patients’ perspective (QPP), and assess the construct validity of this version. Quality from the patients’ perspective assesses 4 dimensions of quality of care. Involving discussion with user representatives, the QPP short version was adapted by adding 7 context-specific questions based on items from the Expanded Prostate Cancer Index Composite for Clinical Practice. This short version was answered on smartphone or tablet by 265 patients. We used exploratory factor analysis to assess dimensionality. For comparison with previous publications of the QPP, the analysis was repeated after mean imputation of missing values. The factor analysis identified 7 factors among the 30 analyzed items included in the analysis, explaining 64.9% of the variance. After imputation of missing, 2 factors explained 48.6% of the variance. None of these analysis captured the 4 dimensions of the QPP.

K-means clustering for the analysis of incomplete business data

Missing values can significantly reduce the accuracy and availability of business data. Usually, when clustering incomplete data, the data with missing values are deleted, and only the complete data are analyzed. However, this often leads to significant loss or deviation of information. This paper mainly studies how to use unsupervised machine learning techniques to deal with missing values. The combination of imputation method and clustering technology forms a new method to deal with missing values, which is helpful to overcome the problem of missing data. We propose a strategy based on the combination of K-means, big data K-means, p-k-means, and mean imputation method, singular value decomposition imputation method, k-nearest neighbor imputation method. By comparing the performance of nine methods in different business data sets. The experimental analysis was carried out on four benchmark data sets. The effectiveness of K-means clustering and imputation methods is verified on different data sets, and the results also have a certain application prospect.

Real-time imputation of missing predictor values in clinical practice.

Use of prediction models is widely recommended by clinical guidelines, but usually requires complete information on all predictors, which is not always available in daily practice. We aim to describe two methods for real-time handling of missing predictor values when using prediction models in practice. We compare the widely used method of mean imputation (M-imp) to a method that personalizes the imputations by taking advantage of the observed patient characteristics. These characteristics may include both prediction model variables and other characteristics (auxiliary variables). The method was implemented using imputation from a joint multivariate normal model of the patient characteristics (joint modelling imputation; JMI). Data from two different cardiovascular cohorts with cardiovascular predictors and outcome were used to evaluate the real-time imputation methods. We quantified the prediction model's overall performance [mean squared error (MSE) of linear predictor], discrimination (c-index), calibration (intercept and slope), and net benefit (decision curve analysis). When compared with mean imputation, JMI substantially improved the MSE (0.10 vs. 0.13), c-index (0.70 vs. 0.68), and calibration (calibration-in-the-large: 0.04 vs. 0.06; calibration slope: 1.01 vs. 0.92), especially when incorporating auxiliary variables. When the imputation method was based on an external cohort, calibration deteriorated, but discrimination remained similar. We recommend JMI with auxiliary variables for real-time imputation of missing values, and to update imputation models when implementing them in new settings or (sub)populations.

Missing-Data Handling Methods for Lifelogs-Based Wellness Index Estimation: Comparative Analysis With Panel Data.

BackgroundA lifelogs-based wellness index (LWI) is a function for calculating wellness scores based on health behavior lifelogs (eg, daily walking steps and sleep times collected via a smartwatch). A wellness score intuitively shows the users of smart wellness services the overall condition of their health behaviors. LWI development includes estimation (ie, estimating coefficients in LWI with data). A panel data set comprising health behavior lifelogs allows LWI estimation to control for unobserved variables, thereby resulting in less bias. However, these data sets typically have missing data due to events that occur in daily life (eg, smart devices stop collecting data when batteries are depleted), which can introduce biases into LWI coefficients. Thus, the appropriate choice of method to handle missing data is important for reducing biases in LWI estimations with panel data. However, there is a lack of research in this area.ObjectiveThis study aims to identify a suitable missing-data handling method for LWI estimation with panel data.MethodsListwise deletion, mean imputation, expectation maximization–based multiple imputation, predictive-mean matching–based multiple imputation, k-nearest neighbors–based imputation, and low-rank approximation–based imputation were comparatively evaluated by simulating an existing case of LWI development. A panel data set comprising health behavior lifelogs of 41 college students over 4 weeks was transformed into a reference data set without any missing data. Then, 200 simulated data sets were generated by randomly introducing missing data at proportions from 1% to 80%. The missing-data handling methods were each applied to transform the simulated data sets into complete data sets, and coefficients in a linear LWI were estimated for each complete data set. For each proportion for each method, a bias measure was calculated by comparing the estimated coefficient values with values estimated from the reference data set.ResultsMethods performed differently depending on the proportion of missing data. For 1% to 30% proportions, low-rank approximation–based imputation, predictive-mean matching–based multiple imputation, and expectation maximization–based multiple imputation were superior. For 31% to 60% proportions, low-rank approximation–based imputation and predictive-mean matching–based multiple imputation performed best. For over 60% proportions, only low-rank approximation–based imputation performed acceptably.ConclusionsLow-rank approximation–based imputation was the best of the 6 data-handling methods regardless of the proportion of missing data. This superiority is generalizable to other panel data sets comprising health behavior lifelogs given their verified low-rank nature, for which low-rank approximation–based imputation is known to perform effectively. This result will guide missing-data handling in reducing coefficient biases in new development cases of linear LWIs with panel data.

Multiple imputation and direct estimation for qPCR data with non-detects

BackgroundQuantitative real-time PCR (qPCR) is one of the most widely used methods to measure gene expression. An important aspect of qPCR data that has been largely ignored is the presence of non-detects: reactions failing to exceed the quantification threshold and therefore lacking a measurement of expression. While most current software replaces these non-detects with a value representing the limit of detection, this introduces substantial bias in the estimation of both absolute and differential expression. Single imputation procedures, while an improvement on previously used methods, underestimate residual variance, which can lead to anti-conservative inference.ResultsWe propose to treat non-detects as non-random missing data, model the missing data mechanism, and use this model to impute missing values or obtain direct estimates of model parameters. To account for the uncertainty inherent in the imputation, we propose a multiple imputation procedure, which provides a set of plausible values for each non-detect. We assess the proposed methods via simulation studies and demonstrate the applicability of these methods to three experimental data sets. We compare our methods to mean imputation, single imputation, and a penalized EM algorithm incorporating non-random missingness (PEMM). The developed methods are implemented in the R/Bioconductor package nondetects.ConclusionsThe statistical methods introduced here reduce discrepancies in gene expression values derived from qPCR experiments in the presence of non-detects, providing increased confidence in downstream analyses.

Leveraging random assignment to impute missing covariates in causal studies

ABSTRACT Baseline covariates in randomized experiments are often used in the estimation of treatment effects, for example, when estimating treatment effects within covariate-defined subgroups. In practice, however, covariate values may be missing for some data subjects. To handle missing values, analysts can use imputation methods to create completed datasets, from which they can estimate treatment effects. Common imputation methods include mean imputation, single imputation via regression, and multiple imputation. For each of these methods, we investigate the benefits of leveraging randomized treatment assignment in the imputation routines, that is, making use of the fact that the true covariate distributions are the same across treatment arms. We do so using simulation studies that compare the quality of inferences when we respect or disregard the randomization. We consider this question for imputation routines implemented using covariates only, and imputation routines implemented using the outcome variable. In either case, accounting for randomization offers only small gains in accuracy for our simulation scenarios. Our results also shed light on the performances of these different procedures for imputing missing covariates in randomized experiments when one seeks to estimate heterogeneous treatment effects.

Dimension-reduced semiparametric estimation of distribution functions and quantiles with nonignorable nonresponse

To estimate distribution functions and quantiles of a response variable when the data having nonignorable nonresponse and the dimension of covariate is not low, this article assumes that the propensity follows a general semiparametric model, but the distribution of the response variable and related covariates is unspecified. To address the identifiability problem, an instrumental covariate, which is related to the response variable but unrelated to the propensity given the response variable and other covariates, is used to construct sufficient instrumental estimating equations. Three different semiparametric estimation methods are developed based on inverse probability weighting, mean imputation, and augmented inverse probability weighting. Furthermore to improve the efficiency and alleviate the curse of dimensionality, the sufficient dimension reduction technique is employed to produce efficient kernel estimation, and a class of dimension-reduced estimators for distribution functions and quantiles is proposed. Consistency and asymptotic normality of the proposed estimators are established. It can be shown that these estimators are asymptotically equivalent. The finite-sample performance of the estimators is studied through simulation, and an application to HIV-CD4 data set is also presented.

Imputation methods for addressing missing data in short-term monitoring of air pollutants

Background: Monitoring of environmental contaminants is a critical part of exposure sciences and epidemiological research. Missing data are often encountered when performing short-term monitoring (<24hr) of air pollutants with real-time monitors, especially in resource-limited areas. Approaches for handling consecutive periods of missing and incomplete data in this context remain unclear. Our aim is to evaluate existing imputation methods for handling missing data for real-time monitors operating for short durations.Methods: In a current field-study, real-time particulate monitors were placed outside of 20 households for 24-hours. Missing data was simulated at four consecutive periods of missingness (20%, 40%, 60%, 80%). Univariate (Mean, Median, Last Observation Carried Forward, Kalman Filter, Random, Markov) and multivariate time-series (Predictive Mean Matching, Row Mean Method) methods were used to impute missing concentrations, and performance was evaluated using five error metrics (Absolute Bias, Percent Absolute Error in Means, R2 Coefficient of Determination, Root Mean Square Error, Mean Absolute Error). Results: Univariate methods of Markov, random, and mean imputations performed best, yielding 24-hour mean concentrations with low error and high R2 values across all levels of missingness. When evaluating error metrics minute-by-minute, Kalman Filters, median, and Markov methods performed well at low levels of missingness (20-40%). However, at higher levels of missingness (60-80%), Markov, random, median, and mean imputation performed best on average. Multivariate imputation methods performed worst across all levels of missingness. Conclusion: Epidemiological studies often report pollutant concentration in relationship to their potential health effect by averaging minute or hourly concentrations over 24-hours. However, when more than 25% of data is missing, daily average pollutant concentrations cannot be reliably computed. Univariate imputation may provide a reasonable solution to addressing missing data for short-term monitoring of air pollutants. Further efforts are needed to evaluate imputation methods that are generalizable across a diverse range of study environments.

Investigation of the Effect of Missing Data Handling Methods on Measurement Invariance of Multi-Dimensional Structures

The purpose of this study was to compare the missing data handling methods on measurement invariance of multi-dimensional structures. For this purpose, data of 10857 students who participated in PISA 2015 administration from Turkey and Singapore and fully responded to the items related to affective characteristics of science literacy was used. Data with different percentages of missing data (5%, 10%, and 20% missing data) were generated from the complete data set with missing completely at random (MCAR) mechanism. In all data sets, missing data was completed with listwise deletion (LD), serial mean imputation (SMI), regression imputation (RI), expectation maximization (EM), and multiple imputation (MI) methods. Measurement invariance of the construct being measured between countries on completed data sets was investigated with multiple-group confirmatory factor analysis (MG-CFA). Findings from each dataset were compared with reference values. In the results of the study, RI and MI methods in the data set with 5% missing, EM method in the data set with 10% missing, and MI method in the data set with 20% missing gave the more similar results to the reference values than the other methods.

Direct estimation of the area under the receiver operating characteristic curve with verification biased data.

In medical diagnostic studies, verification of the true disease status might be partially missing based on results of diagnostic tests and other characteristics of subjects. Because estimates of area under the ROC curve (AUC) based on partially validated subjects are usually biased, it is usually necessary to estimate AUC from a bias-corrected ROC curve. In this article, various direct estimation methods of the AUC based on hybrid imputation [full imputations and mean score imputation (MSI)], inverse probability weighting, and the semiparametric efficient (SPE) approach are proposed and compared in the presence of verification bias when the test result is continuous under the assumption that the true disease status, if missing, is missing at random. Simulation results show that the proposed estimators are accurate for the biased sampling if the disease and verification models are correctly specified. The SPE and MSI based estimators perform well even under the misspecified disease/verification models. Numerical studies are performed to compare the finite sample performance of the proposed approaches with existing methods. A real dataset of neonatal hearing screening study is analyzed.