Biased Estimates Research Articles

Is the sequence ratio an unbiased estimate of the incidence rate ratio? A simulation study.

We aimed to evaluate the conditions under which the sequence ratio (SR) obtained from a sequence symmetry analysis is an unbiased estimate of the true incidence rate ratio (IRR). We simulated cohorts of 1 million individuals who could initiate an exposure drug and experience a very rare, rare, common, or frequent outcome of interest. The outcome rate among exposed individuals was modified by a true incidence rate ratio of 0.2, 0.5, 1.0, 2.0, and 5.0. We further evaluated scenarios where the outcome was fatal and led to immediate censoring or the outcome reduced the rate of initiation of the exposure drug. We found the SR to be close to unbiased for rare, common, and frequent events, except when the true IRR was 5.0 (mean SR 4.94 and 3.74 for common and frequent events). The SR was slightly biased when the outcome was very rare. When the outcome was potentially fatal, the SR was increasingly biased with an increasing probability of death. Likewise, when the outcome reduced the probability of future exposure, the SR was upwards biased. The SR is a biased estimate of the incidence rate ratio, when the true IRR is high, the outcome has a high mortality, or when the outcome reduces the probability of future exposure.

SMALL AREA ESTIMATION WITH HIERARCHICAL BAYES FOR CROSS-SECTIONAL AND TIME SERIES SKEWED DATA

Small Area Estimation (SAE) is a method based on modeling for estimating small area parameters, that applies Linear Mixed Model (LMM) as its basic. It is conventionally solved with Empirical Best Linear Unbiased Prediction (EBLUP). The main requirement for LMM to produce high precision estimates is normally distributed. The observation unit is food crop farmer households from Sulawesi Tenggara Province to estimate food and non-food per capita expenditure at the district/city level using SAE that has been positively skewed. Applying EBLUP for positively skewed data will result less accurate estimates. Meanwhile, transformation will be potentially result biased estimates. Therefore, the problem of skewed data and small area level in this research was completed by Hierarchical Bayes (HB) on combination cross-sectional and time series under skew-normal distribution assumption. The results obtained were skew-normal SAE HB model was significantly reducing Relative Root Mean Squared Error (RRMSE) than the direct estimation. It indicates that SAE modeling is able to provide a shrinkage effect on the direct estimation results. But, there is slightly different interpretating between direct estimation and skew-normal SAE HB. It is possible because the modeling used assumption that the autocorrelation coefficient is equal to 1 or known as the random walk effect. However, in reality, Susenas is not a panel data, so unit of observation for each time period may be different. Therefore, further research should be compared it with the skew-normal or another skewed distribution that assumes the autocorrelation coefficient is unknown and should be estimated in the model.

Predicting absolute risk for a person with missing risk factors.

We compared methods to project absolute risk, the probability of experiencing the outcome of interest in a given projection interval accommodating competing risks, for a person from the target population with missing predictors. Without missing data, a perfectly calibrated model gives unbiased absolute risk estimates in a new target population, even if the predictor distribution differs from the training data. However, if predictors are missing in target population members, a reference dataset with complete data is needed to impute them and to estimate absolute risk, conditional only on the observed predictors. If the predictor distributions of the reference data and the target population differ, this approach yields biased estimates. We compared the bias and mean squared error of absolute risk predictions for seven methods that assume predictors are missing at random (MAR). Some methods imputed individual missing predictors, others imputed linear predictor combinations (risk scores). Simulations were based on real breast cancer predictor distributions and outcome data. We also analyzed a real breast cancer dataset. The largest bias for all methods resulted from different predictor distributions of the reference and target populations. No method was unbiased in this situation. Surprisingly, violating the MAR assumption did not induce severe biases. Most multiple imputation methods performed similarly and were less biased (but more variable) than a method that used a single expected risk score. Our work shows the importance of selecting predictor reference datasets similar to the target population to reduce bias of absolute risk predictions with missing risk factors.

Unified Framework for Faster Clustering via Joint Schatten p-Norm Factorization With Optimal Mean.

To enhance the effectiveness and efficiency of subspace clustering in visual tasks, this work introduces a novel approach that automatically eliminates the optimal mean, which is embedded in the subspace clustering framework of low-rank representation (LRR) methods, along with the computationally factored formulation of Schatten p -norm. By addressing the issues related to meaningful computations involved in some LRR methods and overcoming biased estimation of the low-rank solver, we propose faster nonconvex subspace clustering methods through joint Schatten p -norm factorization with optimal mean (JS p NFOM), forming a unified framework for enhancing performance while reducing time consumption. The proposed approach employs tractable and scalable factor techniques, which effectively address the disadvantages of higher computational complexity, particularly when dealing with large-scale coefficient matrices. The resulting nonconvex minimization problems are reformulated and further iteratively optimized by multivariate weighting algorithms, eliminating the need for singular value decomposition (SVD) computations in the developed iteration procedures. Moreover, each subproblem can be guaranteed to obtain the closed-form solver, respectively. The theoretical analyses of convergence properties and computational complexity further support the applicability of the proposed methods in real-world scenarios. Finally, comprehensive experimental results demonstrate the effectiveness and efficiency of the proposed nonconvex clustering approaches compared to existing state-of-the-art methods on several publicly available databases. The demonstrated improvements highlight the practical significance of our work in subspace clustering tasks for visual data analysis. The source code for the proposed algorithms is publicly accessible at https://github.com/ZhangHengMin/TRANSUFFC.

A Bayesian Approach for Lifetime Modeling and Prediction with Multi-Type Group-Shared Missing Covariates

In the field of reliability engineering, covariate information shared among product units within a specific group (e.g., a manufacturing batch, an operating region), such as operating conditions and design settings, exerts substantial influence on product lifetime prediction. The covariates shared within each group may be missing due to sensing limitations and data privacy issues. The missing covariates shared within the same group commonly encompass a variety of attribute types, such as discrete types, continuous types, or mixed types. Existing studies have mainly considered single-type missing covariates at the individual level, and they have failed to thoroughly investigate the influence of multi-type group-shared missing covariates. Ignoring the multi-type group-shared missing covariates may result in biased estimates and inaccurate predictions of product lifetime, subsequently leading to suboptimal maintenance decisions with increased costs. To account for the influence of the group-shared missing covariates with different structures, a new flexible lifetime model with multi-type group-shared latent heterogeneity is proposed. We further develop a Bayesian estimation algorithm with data augmentation that jointly quantifies the influence of both observed and multi-type group-shared missing covariates on lifetime prediction. A tripartite method is then developed to examine the existence, identify the correct type, and quantify the influence of group-shared missing covariates. To demonstrate the effectiveness of the proposed approach, a comprehensive simulation study is carried out. A real case study involving tensile testing of molding material units is conducted to validate the proposed approach and demonstrate its practical applicability.

Using the global randomization test as a Mendelian randomization falsification test for the exclusion restriction assumption.

Mendelian randomization may give biased causal estimates if the instrument affects the outcome not solely via the exposure of interest (violating the exclusion restriction assumption). We demonstrate use of a global randomization test as a falsification test for the exclusion restriction assumption. Using simulations, we explored the statistical power of the randomization test to detect an association between a genetic instrument and a covariate set due to (a) selection bias or (b) horizontal pleiotropy, compared to three approaches examining associations with individual covariates: (i) Bonferroni correction for the number of covariates, (ii) correction for the effective number of independent covariates, and (iii) an r2 permutation-based approach. We conducted proof-of-principle analyses in UK Biobank, using CRP as the exposure and coronary heart disease (CHD) as the outcome. In simulations, power of the randomization test was higher than the other approaches for detecting selection bias when the correlation between the covariates was low (r2 < 0.1), and at least as powerful as the other approaches across all simulated horizontal pleiotropy scenarios. In our applied example, we found strong evidence of selection bias using all approaches (e.g., global randomization test p < 0.002). We identified 51 of the 58 CRP genetic variants as horizontally pleiotropic, and estimated effects of CRP on CHD attenuated somewhat to the null when excluding these from the genetic risk score (OR = 0.96 [95% CI: 0.92, 1.00] versus 0.97 [95% CI: 0.90, 1.05] per 1-unit higher log CRP levels). The global randomization test can be a useful addition to the MR researcher's toolkit.

Sea turtle density surface models along the United States Atlantic coast

Spatially explicit estimates of marine species distribution and abundance are required to quantify potential impacts from human activities such as military training and testing, fisheries interactions, and offshore energy development. There are 4 protected species of sea turtle (loggerhead, green, Kemp’s ridley, and leatherback) commonly found along the east coast of the USA, our study area, and which require impact assessments. Data from 7 different survey organizations were used to create density surface models for the 4 sea turtle species utilizing 1.2 million km of line-transect surveys. A substantial portion (29.7%) of available sightings were not identified to the species level. Not including these sightings would underestimate density, so a conditional random forest model was used to assign unidentified sightings to species. Higher densities of loggerhead, green, and Kemp’s ridley sea turtles were predicted south of the Outer Banks in cool months, transitioning northwards in late spring to occupy seasonal neritic habitats. The highest leatherback densities were predicted off the coasts of Georgia and Florida. Leatherbacks were also predicted throughout offshore areas. The predicted distribution patterns generally matched satellite tracking and strandings data, indicating the models reproduced established seasonal movements. Surveys rarely detect sea turtles smaller than 40 cm, so these age classes are not represented. The models are the first for the study area to apply availability bias estimates developed in or near the study area and attempt to classify unidentified sightings to the species level, providing an updated, critical tool for conservation management along the eastern seaboard.

High-resolution regional gravity field modeling in data-challenging regions for the realization of geopotential-based height systems

Modern height systems are based on the combination of satellite positioning and gravity field models of high resolution. However, in many regions, especially developing or newly industrializing countries, there is no (reliable) regional gravity model at all, due to challenges such as limited data availability, unknown/low data quality, and missing metadata. This paper addresses this issue in a case study of Colombia, where eight decades of historical terrestrial and airborne gravity measurements are available but widely contain systematic errors, outliers, and biases. Correspondingly, processing strategies and structures are proposed and applied to validate and improve the quality of old gravity datasets. A novel method is developed based on spherical radial basis functions (SRBFs) for estimating biases, which are found in different airborne surveys with values exceeding 40 mGal. The validity of this bias estimation method is demonstrated both by a simulation test and by the evaluation of the airborne data in comparison to the SATOP (SAtellite-TOPography) model, which merges the satellite-only global gravity model GOCO06s with the Earth2014 topography model. The terrestrial and airborne data are then combined with a global gravity model (GGM), ultra-high-resolution topography models, as well as altimetry-derived gravity anomalies from DTU21GRA for the offshore areas. The results are presented in terms of height anomalies (QGeoidCOL2023), and they are thoroughly validated using GPS/leveling data both in the absolute and relative manner. The standard deviation in comparison to the GPS/leveling data after applying a correction surface to account for the datum inconsistencies amounts to 15.76 cm, which is 27% smaller compared to the mean standard deviation value given by five recent high-resolution GGMs, and 36% smaller than the one delivered by the latest South American quasi-geoid model QGEOID2021. The relative validation results show that QGeoidCOL2023 performs better, i.e., delivers lower RMS errors than the GGMs and QGEOID2021 in all the baseline length groups. These results indicate the validity and benefits of the developed methods and procedures, which can be used for other data-challenging areas to facilitate the realization of geopotential-based height systems.Graphical

Robust best linear weighted estimator with missing covariates in survival analysis.

Missing data in covariates can result in biased estimates and loss of power to detect associations. We consider Cox regression in which some covariates are subject to missing. The inverse probability weighted approach is often applied to regression analysis with missing covariates. Inverse probability weighted estimators typically are less efficient than likelihood-based estimators, but in general are more robust against model misspecification. In this article, we propose a robust best linear weighted estimator for Cox regression with missing covariates. Our proposed estimator is the projection of the simple inverse probability weighted estimator onto the orthogonal complement of the score space based on a working regression model of the observed data. The efficiency gain is from the use of the association between the survival outcome variable and the available covariates, which is the working regression model. The asymptotic distribution is derived, and the finite sample performance of the proposed estimator is examined via extensive simulation studies. The methods are applied to a colorectal cancer study to assess the association of the microsatellite instability status with colorectal cancer-specific mortality.

Impact-Aware Foot Motion Reconstruction and Ramp/Stair Detection Using One Foot-Mounted Inertial Measurement Unit.

Motion reconstruction using wearable sensors enables broad opportunities for gait analysis outside laboratory environments. Inertial Measurement Unit (IMU)-based foot trajectory reconstruction is an essential component of estimating the foot motion and user position required for any related biomechanics metrics. However, limitations remain in the reconstruction quality due to well-known sensor noise and drift issues, and in some cases, limited sensor bandwidth and range. In this work, to reduce drift in the height direction and handle the impulsive velocity error at heel strike, we enhanced the integration reconstruction with a novel kinematic model that partitions integration velocity errors into estimates of acceleration bias and heel strike vertical velocity error. Using this model, we achieve reduced height drift in reconstruction and simultaneously accomplish reliable terrain determination among level ground, ramps, and stairs. The reconstruction performance of the proposed method is compared against the widely used Error State Kalman Filter-based Pedestrian Dead Reckoning and integration-based foot-IMU motion reconstruction method with 15 trials from six subjects, including one prosthesis user. The mean height errors per stride are 0.03±0.08 cm on level ground, 0.95±0.37 cm on ramps, and 1.27±1.22 cm on stairs. The proposed method can determine the terrain types accurately by thresholding on the model output and demonstrates great reconstruction improvement in level-ground walking and moderate improvement on ramps and stairs.

Digital Mapping of Soil Particle Size Fractions in the Loess Plateau, China, Using Environmental Variables and Multivariate Random Forest

Soil particle size fractions (PSFs) are important properties for understanding the physical and chemical processes in soil systems. Knowledge about the distribution of soil PSFs is critical for sustainable soil management. Although log-ratio transformations have been widely applied to soil PSFs prediction, the statistical distribution of original data and the transformed data given by log-ratio transformations is different, resulting in biased estimates of soil PSFs. Therefore, multivariate random forest (MRF) was utilized for the simultaneous prediction of soil PSFs, as it is able to capture dependencies and internal relations among the three components. Specifically, 243 soil samples collected across the Loess Plateau were used. Meanwhile, Landsat data, terrain attributes, and climatic variables were employed as environmental variables for spatial prediction of soil PSFs. The results depicted that MRF gave satisfactory soil PSF prediction performance, where the R2 values were 0.62, 0.53, and 0.73 for sand, silt, and clay, respectively. Among the environmental variables, nighttime land surface temperature (LST_N) presented the highest importance in predicting soil PSFs in the Loess Plateau, China. Maps of soil PSFs and texture were generated at a 30 m resolution, which can be utilized as alternative data for soil erosion management and ecosystem conservation.

Local mitigation of higher-order ionospheric effects in DFMC SBAS and system performance evaluation

Dual-frequency multi-constellation (DFMC) satellite-based augmentation system (SBAS) is a new SBAS standard for aeronautical navigation systems. It supports aircraft navigation from the enroute to approach phases via the L1 and L5 frequencies (1575.42 and 1176.45 MHz). Although the ionosphere-free (IF) combination in the DFMC SBAS operation removes the first-order ionospheric delays in the pseudorange measurement, remaining terms including the satellite-clock offset errors and higher-order ionospheric (HOI) delays are still unaccounted for. The DFMC SBAS accuracy and integrity can be affected by the HOI effects, especially during severe ionospheric disturbances. In this work, we present the local DFMC SBAS corrections with and without the mitigation of HOI delays. We first estimate the HOI delay terms using the received pseudorange followed by separate satellite and receiver bias estimations based on the minimum sum-variance technique. The integrity terms can then be obtained. The performances of DFMC SBAS using the global navigation satellite system (GNSS) data including GPS, Galileo, and QZSS are evaluated using obtained GNSS data at stations in Thailand on the ionospheric quiet and disturbed days. The results show that with the HOI mitigation, the vertical positioning errors (VPE) on the quiet and disturbed days can be improved by 12% and 9%, whereas the vertical protection levels (VPL) are improved by 16% and 21%, respectively. In addition, we perform a preliminary assessment of DFMC SBAS based on the International Civil Aviation Organization (ICAO) requirements of two categories: Localizer Performance with Vertical guidance (LPV-200) and Category I precision approach (CAT-I) showing promising results.

Multilevel modeling in single-case studies with zero-inflated and overdispersed count data.

Count outcomes are frequently encountered in single-case experimental designs (SCEDs). Generalized linear mixed models (GLMMs) have shown promise in handling overdispersed count data. However, the presence of excessive zeros in the baseline phase of SCEDs introduces a more complex issue known as zero-inflation, often overlooked by researchers. This study aimed to deal with zero-inflated and overdispersed count data within a multiple-baseline design (MBD) in single-case studies. It examined the performance of various GLMMs (Poisson, negative binomial [NB], zero-inflated Poisson [ZIP], and zero-inflated negative binomial [ZINB] models) in estimating treatment effects and generating inferential statistics. Additionally, a real example was used to demonstrate the analysis of zero-inflated and overdispersed count data. The simulation results indicated that the ZINB model provided accurate estimates for treatment effects, while the other three models yielded biased estimates. The inferential statistics obtained from the ZINB model were reliable when the baseline rate was low. However, when the data were overdispersed but not zero-inflated, both the ZINB and ZIP models exhibited poor performance in accurately estimating treatment effects. These findings contribute to our understanding of using GLMMs to handle zero-inflated and overdispersed count data in SCEDs. The implications, limitations, and future research directions are also discussed.

Use of Residuals and Rank Product in Detection of Outlier in Survival Analysis with Crimean-Congo Hemorrhagic Fever Data

Purpose: Survival analysis is a statistical method used in many fields, especially in the field of health. It involves modeling the relationship between the survival time of individuals after a treatment or procedure and the event called response. The presence of outliers in the data may cause biased parameter estimations of the established models. Also, this situation causes the proportional hazards assumption to be violated especially in Cox regression analysis. Outlier(s) are identified with the help of residuals, Bootstrap Hypothesis test and Rank product test. Method: In R.4.0.3 software, outlier(s) are determined on a clinical dataset by the Schoenfeld residual, Martingale residual, Deviance residual method and Bootstrap Hypothesis test (BHT) based on Concordance index, and Rank product test. Results: After the cox regression established by the backward stepwise and robust cox regression, it was observed that the established models did not fit. So, the outlier(s) determined by the methods mentioned. Conclusion: It was decided that only one observation could be excluded from the study. As in the survival data, in many data types, outliers can be detected and further analyzes can be applied by using the methods mentioned.

Wavelet-based information theory in quantitative assessment of AFM images’ quality

The quantitative assessment of the image quality produced by atomic force microscopy (AFM) is an ongoing and challenging task. In our study, we demonstrate Shannon’s application of information theory for measuring image quality. Specifically, we propose quantifying the loss of image information due to the various distortion processes by exploring the relationship between image information based on the information channel capacity (ICC), spectral image representation, and visual quality. Since the ideal image is unavailable, the power and noise spectrum, the critical input information for the image quality evaluation, must be robustly estimated in the proposed method. The classical, most popular Welch method for spectral estimation uses an average of several windowed periodograms and can produce biased spectrum estimates. Therefore, in our work, we discuss an alternative technique based on the wavelet transform that can be applied to solve this challenging problem, specifically in the case of noisy, uncertain AFM measurements. Finally, we validate the performance of the enhanced ICC-wavelet-based algorithm with noisy measurement AFM data.

The mind in the machine: Estimating mind perception's effect on user satisfaction with voice-based conversational agents

Given the interest in imbuing voice-based conversational agents with humanlike features, understanding how this affects user satisfaction is ultimately important for business performance. Mind perception theory explains how ascribing the mental capacity for agency and experience to artificial intelligence shapes subsequent user attitudes. Hence, we estimate the effect of mind perception on satisfaction in users with high/low innovativeness using data from text-based online reviews, which better reflect actual usage than traditional surveys. Methodologically, where numerous controls affect the cause and outcome variables in a model, traditional machine learning methods produce biased estimates. We overcome this by deploying Double/Debiased Machine Learning (combined with text analytics). Results show that user satisfaction is increased by two forms of perceived experience: directed at moral agents, or moral patients. Perceived agency, however, has no significant influence. The increase in satisfaction from both types of perceived experience is stronger among users with high (vs. low) innovativeness.

Comparison of common multiple imputation approaches: An application of logistic regression with an interaction

Background Multiple imputation is often used to reduce bias and gain efficiency when there is missing data. The most appropriate imputation method depends on the model the analyst is interested in fitting. We consolidate and compare the performance and ease of use for several commonly implemented imputation approaches. Methods Using 1000 simulations, each with 10,000 observations, under six data-generating mechanisms (DGM), we investigate the performance of four methods: (i) ’passive imputation’, (ii) ’just another variable’ (JAV), (iii) ’stratify-impute-append’ (SIA), and (iv) ’substantive model compatible fully conditional specification’ (SMCFCS). The application of each method is shown in an empirical example using England-based cancer registry data. Results SMCFCS and SIA showed the least biased estimate of the coefficients for the fully, and partially, observed variable and the interaction term. SMCFCS and SIA showed good coverage and low relative error for all DGMs. SMCFCS had a large bias when there was a low prevalence of the fully observed variable in the interaction. SIA performed poorly when the fully observed variable in the interaction had a continuous underlying form. Conclusion SMCFCS and SIA give consistent estimation and either can be used in most analyses. SMCFCS performed better than SIA when the fully observed variable in the interaction had an underlying continuous form. Researchers should be cautious when using SMCFCS when there is a low prevalence of the fully observed variable in the interaction.

BDS-3 six-frequency precise point positioning: effects of receiver-dependent inter-frequency clock bias and multi-frequency contributions

We find that there is time-varying bias at the receiver in BDS-3 multi-frequency phase observations, which will lead to receiver-dependent inter-frequency clock bias (RIFCB) and damage the rigor of BDS-3 multi-frequency precise point positioning (PPP) model. A unified RIFCB correction method compatible with uncombined and ionospheric-free combined PPP models using any BDS-3 frequencies is proposed. The contributions of multi-frequency integration to BDS-3 static and kinematic PPP performance are evaluated. The results indicate that the RIFCB amplitude can reach 1 dm. If the RIFCB correction is ignored, the phase observation residuals present a systematic bias. RIFCB has potential effects on precise time transfer, ionospheric monitoring, and fractional cycle bias estimation. Experimental results show that the long-term frequency stability of time transfer can be improved by correcting RIFCB. The joint use of all BDS-3 six-frequency signals can significantly shorten the convergence time, and the positioning accuracy can also be slightly improved.

Airborne imagery does not preclude detectability issues in estimating bird colony size

Aerial images obtained by drones are increasingly used for ecological research such as wildlife monitoring. Yet detectability issues resulting from animal activity or visibility are rarely considered, although these may lead to biased population size and trend estimates. In this study, we investigated detectability in a census of Malagasy pond heron Ardeola idae colonies on the island of Mayotte. We conducted repeated drone flights over breeding colonies in mangrove habitats during two breeding seasons. We then identified individuals and nests in the images and fitted closed capture-recapture models on nest-detection histories. We observed seasonal variation in the relative abundance of individuals, and intra-daily variation in the relative abundance of individuals—especially immature birds—affecting the availability of nests for detection. The detection probability of nests estimated by capture–recapture varied between 0.58 and 0.74 depending on flyover days and decreased 25% from early to late morning. A simulation showed that three flyovers are necessary to detect a 5–6% decline in colonies of 50 to 200 nests. These results indicate that the detectability of nests of forest-canopy breeding species from airborne imagery can vary over space and time; we recommend the use of capture-recapture methods to control for this bias.

Exploring the variations of the pancreatic ductal system: a systematic review and meta-analysis of observational studies.

The exocrine part of the pancreas has a duct system called the pancreatic ductal system (PDS). Its mechanism of development is complex, and any reorganization during early embryogenesis can give rise to anatomical variants. The aim of this study is to collect, classify, and analyze published evidence on the importance of anatomical variants of the PDS, addressing gaps in our understanding of such variations. The MEDLINE, Web of Science, Embase, and Google Scholar databases were searched to identify publications relevant to this review. R studio with meta-package was used for data extraction, risk of bias estimation, and statistical analysis. A total of 64 studies out of 1,778 proved suitable for this review and metanalysis. The meta-analysis computed the prevalence of normal variants of the PDS (92% of 10,514 subjects). Type 3 variants and "descending" subtypes of the main pancreatic duct (MPD) predominated in the pooled samples. The mean lengths of the MPD and accessory pancreatic duct (APD) were 16.53 cm and 3.36 cm, respectively. The mean diameters of the MPD at the head and the APD were 3.43 mm and 1.69 mm, respectively. The APD was present in only 41% of samples, and the long type predominated. The pancreatic ductal anatomy is highly variable, and the incorrect identification of variants may be challenging for surgeons during ductal anastomosis with gut, failure to which may often cause ductal obstruction or pseudocysts formation.