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Objectives: Liver cirrhosis (LC) can be caused by obesity, alcohol consumption, viral infection, and autoimmune disease. Early diagnosis and management of LC is important for patient quality of life. Non-invasive diagnostic methods are useful for predicting the current status and mortality risk of LC. The purpose of this study is to identify relevant diagnostic factors measured in routine laboratory test of alcohol-related liver cirrhosis (ALC) patients., Methods: This study analyzed data from 127 patients with ALC, including their laboratory test results and clinical information, including coagulation parameters, hematologic parameters, and biochemical parameters. These data were used to compare the performance of the prediction models from three machine learning algorithms including K-nearest neighbor (KNN), support vector machine (SVM), and random forest (RF)., Results: Higher Model for End-stage Liver Disease (MELD) score were associated with prothrombin time (PT) and D-dimer. Logistic and multiple linear regression analyses revealed significant factors predicting mortality in the MELD group. Machine learning approaches were used to predict death in ALC patients using some laboratory parameters associated with mortality. The prediction model based on SVM exhibited better prediction performance than others., Conclusion: PT and D-dimer were the factors that were most strongly associated with 90-day mortality, and machine learning methods can create prediction models with good predictive power., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 Elsevier B.V. All rights reserved.)

Increased vascular stiffness, fluid overload, and left ventricular diastolic dysfunction (LVDD) are common in patients with chronic kidney disease (CKD). We investigated the potential moderating effect of volume status in the relationship between arterial stiffness and left ventricular (LV) diastolic function in non-dialysis patients with stage 5 CKD. The radial augmentation index at a heart rate of 75 beats/min (rAIx75), overhydration/extracellular water (OH/ECW), and E/e´ ratio were concurrently measured in 152 consecutive patients. Each of these parameters reflects the status of vascular stiffness, fluid balance, and LV diastolic function, respectively. Hierarchical regression analysis demonstrated a significant interaction effect of OH/ECW for all patients (P = 0.015), even after controlling for confounders. In separate analyses, this interaction effect was particularly significant in women (P = 0.010), whereas its significance in patients with diabetes was marginally significant (P = 0.062). Our study suggested that fluid overload could be one of the more aggravating factors of LVDD in patients with CKD who have increased arterial stiffness. Therefore, it is advisable to conduct simultaneous assessments of vascular stiffness, fluid balance, and LV function, particularly in the specific groups mentioned earlier. Our results may serve as evidence applicable to patients with chronic heart failure., (© 2024. The Author(s).)

The Nun study is a well-known longitudinal epidemiology study of aging and dementia that recruited elderly nuns who were not yet diagnosed with dementia (i.e., incident cohort) and who had dementia prior to entry (i.e., prevalent cohort). In such a natural history of disease study, multistate modeling of the combined data from both incident and prevalent cohorts is desirable to improve the efficiency of inference. While important, the multistate modeling approaches for the combined data have been scarcely used in practice because prevalent samples do not provide the exact date of disease onset and do not represent the target population due to left-truncation. In this paper, we demonstrate how to adequately combine both incident and prevalent cohorts to examine risk factors for every possible transition in studying the natural history of dementia. We adapt a four-state nonhomogeneous Markov model to characterize all transitions between different clinical stages, including plausible reversible transitions. The estimating procedure using the combined data leads to efficiency gains for every transition compared to those from the incident cohort data only., (© 2023. The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.)

Objectives: The comparative efficacy of microscopic tympanoplasty (MT) and endoscopic tympanoplasty (ET) has been widely studied to some extent through meta-analyses. However, most studies on learning curve comparisons between the two surgeries were performed by experienced ET surgeons. We compared the surgical outcomes of MT and ET and evaluated the difference of learning curve between ET and MT performed by a single unskilled, in both MT and ET, surgeon., Design: A total of 91 patients underwent ET and MT at a tertiary hospital. We reviewed the patients' medical records and analyzed all findings, including otoscopic pictures, pure tone audiometry (PTA) before and after surgery, and operation records. All operations were performed by a single otologist who had an experience of a year of otology fellowship at a tertiary university hospital. We compared the demographic and clinical characteristics, including age, sex, admission duration, and audiological outcomes before and after surgery. We also assessed the difference in the decrease in operation time., Results: Among 91 patients, 44 were in the ET group and 47 were in the MT group. The mean age was 51.15 years, and 37 (40.7%) were men. Eighty-two (90.1%) patients were administered local anesthesia. Graft failure was observed in 19 (20.9%) patients, and the mean postoperative follow-up duration was 66.42 days. There were no statistically significant differences in age, sex, affected side, graft failure rate, and operation time between the ET and MT groups. There was a significant improvement in air conduction hearing and air-bone gap after surgery in both groups. Bone conduction hearing did not change before and after the surgery in either group. However, the improvement in air condition and reduction in the air-bone gap did not differ between the two groups. Multivariate linear regression analysis showed that there were no significant variables that affected operation time among age, sex, operation method (ET or MT), anesthesia, graft material, and technique. The spline regression analysis showed the decrease in operative time in ET was significantly faster than MT in the period from 8th to 19th cases., Conclusions: The surgical outcomes of ET are comparable to those of MT in terms of operation time, graft uptake, and postoperative hearing results, even in surgeons who are not experienced with both MT and ET. The operation time of ET was longer than that of MT in the early phase, and the decrease in the operating time was significantly faster in ET than in MT. Both MT and ET reached a plateau in the operation time, and this plateau appeared to be similar in both surgeries., (© 2022. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.)

Background: Low bone mass is common in malnourished patients with chronic kidney disease (CKD) and can lead to a higher risk of fractures. Elderly and CKD patients have the same risk factors for protein-energy wasting, sarcopenia, and osteoporosis. Here, we investigated the association between phase angle (PhA) and bone mineral density (BMD) in dialysis-naïve patients with CKD stage 5 (CKD5) and identified a statistical relationship between PhA and age, which affects bone density. Methods: Bio-impedance spectroscopy for evaluating body composition and PhA and dual-energy X-ray absorptiometry for determining the BMD were simultaneously performed in 167 consecutive patients (mean age, 59.65 ± 13.98 years; women, 40.1%). Two-way analysis of variance (ANOVA) was conducted to assess the potential interaction effect of PhA and age on femoral neck BMD (FN-BMD). Results: Our results showed that PhA and age were independently associated with FN-BMD and T-score in multiple linear regressions analyses. A significant interaction effect of PhA and age on FN-BMD was found on two-way ANOVA ( p = 0.028). The average BMD values for the first and second tertiles of the PhA were higher in the young versus elderly group, whereas patients in the elderly group had higher BMD in the third tertiles. Conclusions: A relationship was noted between PhA and BMD in patients with advanced-stage CKD. The effect of PhA level on FN-BMD differed between elderly and young patients. Our study suggested that higher PhA levels could be a marker explaining the maintenance of good bone health in elderly patients with CKD5. Further longitudinal analyses are needed to determine whether PhA predicts the risk of CKD-MBD-related fractures during CKD progression.

Background: The incubation period of an infectious disease is defined as the elapsed time between the exposure to the pathogen and the onset of symptoms. Although both the mRNA-based and the adenoviral vector-based vaccines have shown to be effective, there have been raising concerns regarding possible decreases in vaccine effectiveness for new variants and variations in the incubation period., Methods: We conducted a unicentric observational study at the Hospital Universitari de Bellvitge, Barcelona, using a structured telephone survey performed by trained interviewers to estimate the incubation period of the SARS-CoV-2 Delta variant in a cohort of Spanish hospitalized patients. The distribution of the incubation period was estimated using the generalized odds-rate class of regression models., Results: From 406 surveyed patients, 242 provided adequate information to be included in the analysis. The median incubation period was 2.8 days (95%CI: 2.5-3.1) and no differences between vaccinated and unvaccinated patients were found. Sex and age are neither shown not to be significantly related to the COVID-19 incubation time., Conclusions: Knowing the incubation period is crucial for controlling the spread of an infectious disease: decisions on the duration of the quarantine or on the periods of active monitoring of people who have been at high risk of exposure depend on the length of the incubation period. Furthermore, its probability distribution is a key element for predicting the prevalence and the incidence of the disease., (© 2022. The Author(s).)

Osteopenia, sarcopenia, and increased vascular stiffness are common in patients with chronic kidney disease-mineral bone disorder (CKD-MBD) with protein energy wasting and can lead to worse clinical outcomes. We investigated the potential moderating role of the lean tissue index (LTI) in the relationship between bone microarchitecture and vascular stiffness in dialysis naïve patients with stage 5 CKD. Bioimpedance spectroscopy for evaluating LTI, lumbar spine dual energy X-ray absorptiometry for determining the trabecular bone score (TBS), and arterial applanation tonometry measurements for the central augmentation index, at a heart rate of 75 beats/minute (cAIx75), were simultaneously performed in 117 consecutive patients. A hierarchical regression analysis was conducted to assess the moderating effect of LTI on the relationship between TBS and cAIx75 after adjusting for age and sex. The effect of the interaction between LTI and TBS on cAIx75 was statistically significant ( p = 0.030), demonstrating that the cAIx75 tends to decrease more, with the joint effect of LTI and TBS. In the separate analyses, the interaction effect was significant only in women ( p = 0.048) and the group of diabetes ( p = 0.042). Our study suggests that the evaluation of changes in body composition, bone health, and vascular stiffness needs to be performed simultaneously in patients with advanced-stage CKD. Further research in patients with different stages of CKD warranted to generalize and apply our results to patients in other stages.

Conditional independence assumption of truncation and failure times conditioning on covariates is a fundamental and common assumption in the regression analysis of left-truncated and right-censored data. Testing for this assumption is essential to ensure the correct inference on the failure time, but this has often been overlooked in the literature. With consideration of challenges caused by left truncation and right censoring, tests for this conditional independence assumption are developed in which the generalized odds ratio derived from a Cox proportional hazards model on the failure time and the concept of Kendall's tau are combined. Except for the Cox proportional hazards model, no additional model assumptions are imposed, and the distributions of the truncation time and conditioning variables are unspecified. The asymptotic properties of the test statistic are established and an easy implementation for obtaining its distribution is developed. The performance of the proposed test has been evaluated through simulation studies and two real studies.

For semi-competing risks data involving a non-terminal event and a terminal event we derive the asymptotic distributions of the event-specific win ratios under proportional hazards (PH) assumptions for the relevant cause-specific hazard functions of the non-terminal and terminal event, respectively. The win ratios converge to the respective hazard ratios under the PH assumptions and therefore are censoring-free, whether or not the censoring distributions in the two treatment arms are the same. With the asymptotic bivariate normal distributions of the win ratios, confidence intervals and testing procedures are obtained. Through extensive simulation studies and data analysis, we identified proper transformations of the win ratios that yield good control of the type one error rate for various testing procedures while maintaining competitive power. The confidence intervals also have good coverage probabilities. Furthermore, a test for the PH assumptions and a test of equal hazard ratios are developed. The new procedures are illustrated in the clinical trial Aldosterone Antagonist Therapy for Adults With Heart Failure and Preserved Systolic Function, which evaluated the effects of spironolactone in patients with heart failure and a preserved left ventricular ejection fraction., (© 2021 John Wiley & Sons Ltd. This article has been contributed to by US Government employees and their work is in the public domain in the USA.)

Acute myeloid leukemia (AML) with rearrangement of the lysine methyltransferase 2a gene (KMT2Ar) has adverse outcomes. However, reports on the prognostic impact of various translocations causing KMT2Ar are conflicting. Less is known about associated mutations and their prognostic impact. In a retrospective analysis, we identified 172 adult patients with KMT2Ar AML and compared them to 522 age-matched patients with diploid AML. KMT2Ar AML had fewer mutations, most commonly affecting RAS and FLT3 without significant impact on prognosis, except for patients with ≥2 mutations with lower overall survival (OS). KMT2Ar AML had worse outcomes compared with diploid AML when newly diagnosed and at relapse, especially following second salvage (median OS of 2.4 vs 4.8 months, P < 0.0001). Therapy-related KMT2Ar AML (t-AML) had worse outcomes compared with de novo KMT2Ar AML (median OS of 0.7 years vs 1.4 years, P < 0.0001). Allogeneic hematopoietic stem cell transplant (allo-HSCT) in first remission was associated with improved OS (5-year, 52 vs 14% for no allo-HSCT, P < 0.0001). In a multivariate analysis, translocation subtypes causing KMT2Ar did not predict survival, unlike age and allo-HSCT. In conclusion, KMT2Ar was associated with adverse outcomes regardless of translocation subtype. Therefore, AML risk stratification guidelines should include all KMT2Ar as adverse., (© 2021. The Author(s).)

In an infectious disease cohort study, individuals who have been infected with a pathogen are often recruited for follow up. The period between infection and the onset of symptomatic disease, referred to as the incubation period, is of interest because of its importance on disease surveillance and control. However, the incubation period is often difficult to ascertain due to the uncertainty associated with asymptomatic infection onset time. An additional complication is that the observed infected subjects are likely to have longer incubation periods due to the prevalent sampling. In this article, we demonstrate how to estimate the distribution of the incubation period with the uncertain infection onset, subject to left-truncation and right-censoring. We employ a family of sufficiently general parametric models, the generalized odds-rate class of regression models, for the underlying incubation period and its correlation with covariates. In simulation studies, we assess the finite sample performance of the model fitting and hazard function estimation. The proposed method is illustrated on data from the HIV/AIDS study on injection drug users admitted to a detoxification program in Badalona, Spain., (© 2020 John Wiley & Sons Ltd.)

Background: Poor outcomes for patients with ovarian cancer relate to dormant, drug-resistant cancer cells that survive after primary surgery and chemotherapy. Ovarian cancer (OvCa) cells persist in poorly vascularized scars on the peritoneal surface and depend on autophagy to survive nutrient deprivation. The authors have sought drugs that target autophagic cancer cells selectively to eliminate residual disease., Methods: By using unbiased small-interfering RNA (siRNA) screens, the authors observed that knockdown of anaplastic lymphoma kinase (ALK) reduced the survival of autophagic OvCa cells. Small-molecule ALK inhibitors were evaluated for their selective toxicity against autophagic OvCa cell lines and xenografts. Autophagy was induced by reexpression of GTP-binding protein Di-Ras3 (DIRAS3) or serum starvation and was evaluated with Western blot analysis, fluorescence imaging, and transmission electron microscopy. Signaling pathways required for crizotinib-induced apoptosis of autophagic cells were explored with flow cytometric analysis, Western blot analysis, short-hairpin RNA knockdown of autophagic proteins, and small-molecule inhibitors of STAT3 and BCL-2., Results: Induction of autophagy by reexpression of DIRAS3 or serum starvation in multiple OvCa cell lines significantly reduced the 50% inhibitory concentration of crizotinib and other ALK inhibitors. In 2 human OvCa xenograft models, the DIRAS3-expressing tumors treated with crizotinib had significantly decreased tumor burden and long-term survival in 67% to 79% of mice. Crizotinib treatment of autophagic cancer cells further enhanced autophagy and induced autophagy-mediated apoptosis by decreasing phosphorylated STAT3 and BCL-2 signaling., Conclusions: Crizotinib may eliminate dormant, autophagic, drug-resistant OvCa cells that remain after conventional cytoreductive surgery and combination chemotherapy. A clinical trial of ALK inhibitors as maintenance therapy after second-look operations should be seriously considered., (© 2020 American Cancer Society.)

We propose a penalized variable selection method for the Cox proportional hazards model with interval censored data. It conducts a penalized nonparametric maximum likelihood estimation with an adaptive lasso penalty, which can be implemented through a penalized EM algorithm. The method is proven to enjoy the desirable oracle property. We also extend the method to left truncated and interval censored data. Our simulation studies show that the method possesses the oracle property in samples of modest sizes and outperforms available existing approaches in many of the operating characteristics. An application to a dental caries data set illustrates the method's utility.

We propose a semiparametric multi-state frailty model to analyze clustered event-history data subject to interval censoring. The proposed model is motivated by an attempt to study the life course of dental caries at the tooth level, taking into account the multiplicity of caries states and the intra-oral clustering of observations made at periodic time points. Of particular interest is the study of the intra-oral distribution of processes leading to carious lesions, and whether this distribution varies with gender. The model assumes, in view of the covariate profile, a proportionality of the transition intensities conditional on subject-level frailties, coupled with a linear spline approximation of the log baseline intensities. The model estimation is conducted using a penalized likelihood where the smoothing parameters are estimated as reciprocal variance components under a mixed-model representation. A Bayesian method is proposed to predict tooth-level caries transition probabilities, which can be used for tailoring tooth-level caries treatment and prevention plans. Intensive simulation studies indicate that the model fitting and prediction perform reasonably well under realistic sample sizes. The practical utility of the methods is illustrated using data from a longitudinal study on oral health among children from low-income families residing in the city of Detroit, Michigan.

Early detection of ovarian cancer promises to reduce mortality. While serum CA125 can detect more than 60% of patients with early stage (I-II) disease, greater sensitivity might be observed with a panel of biomarkers. Ten protein antigens and 12 autoantibody biomarkers were measured in sera from 76 patients with early stage (I-II), 44 patients with late stage (III-IV) ovarian cancer and 200 healthy participants in the normal risk ovarian cancer screening study. A four-biomarker panel (CA125, osteopontin (OPN), macrophage inhibitory factor (MIF), and anti-IL-8 autoantibodies) detected 82% of early stage cancers compared to 65% with CA125 alone. In early stage subjects the area under the receiver operating characteristic curve (AUC) for the panel (0.985) was significantly greater ( p < 0.001) than the AUC for CA125 alone (0.885). Assaying an independent validation set of sera from 71 early stage ovarian cancer patients, 45 late stage patients and 131 healthy women, AUC in early stage disease was improved from 0.947 with CA125 alone to 0.974 with the four-biomarker panel ( p = 0.015). Consequently, OPN, MIF and IL-8 autoantibodies can be used in combination with CA125 to distinguish ovarian cancer patients from healthy controls with high sensitivity. Osteopontin appears to be a robust biomarker that deserves further evaluation in combination with CA125.

Preparing the skin of rodents for surgery often involves multiple applications of antiseptic agents. However, fewer applications may achieve the same antiseptic outcome. We evaluated the antimicrobial efficacy and effects on intraoperative body temperature of various surgical scrub agents, including novel waterless alcohol-based (WAB) options. Prior to ventral laparotomy, female C57BL/6 mice were treated with 0.9% saline (control); 70% ethanol; 10% povidone-iodine alternated with saline or 70% ethanol; 2% chlorhexidine digluconate alternated with saline or 70% ethanol; or 1 of 3 WAB products-commercial surgical scrub A, commercial surgical scrub B, or a common commercial hand sanitizer. Core temperatures were recorded, and aerobic culture swabs were collected from the surgical site at multiple time points. Intraoperative temperature trajectories for animals treated with scrub B, 10% povidone-iodine with saline, or hand sanitizer did not differ from saline (control). Temperature trajectories of mice treated with other scrub agents did differ significantly from saline. Bacteria were not detected at the operative site after 3 scrubs of 70% ethanol or 10% povidone-iodine alternated with ethanol, 2 scrubs of scrub A or B, 1 scrub of hand sanitizer, and both 1 and 3 scrubs of 2% chlorhexidine alternated with ethanol. Scrub B and 2% chlorhexidine-ethanol demonstrated prolonged antibacterial efficacy. Histology of corresponding haired skin sections revealed no differences in postoperative healing between groups, and no postoperative infections occurred. These results indicate that various novel WAB disinfectants, particularly scrub B (61% ethanol and 1% chlorhexidine gluconate), mitigate intraoperative temperature effects associated with several traditional agents and combinations. Furthermore, reduction of skin bacterial load without adverse effects on healing was seen with fewer than triplicate applications of most tested agents. Ultimately effective skin preparation can be achieved by using only 1 or 2 applications of scrub, thus rendering the triplicate skin-prep method unnecessary in laboratory mice.

The genetic code sectored via tRNA charging errors, and the code progressed toward closure and universality because of evolution of aminoacyl-tRNA synthetase (aaRS) fidelity and translational fidelity mechanisms. Class I and class II aaRS folds are identified as homologs. From sequence alignments, a structurally conserved Zn-binding domain common to class I and class II aaRS was identified. A model for the class I and class II aaRS alternate folding pathways is posited. Five mechanisms toward code closure are highlighted: 1) aaRS proofreading to remove mischarged amino acids from tRNA; 2) accurate aaRS active site specification of amino acid substrates; 3) aaRS-tRNA anticodon recognition; 4) conformational coupling proofreading of the anticodon-codon interaction; and 5) deamination of tRNA wobble adenine to inosine. In tRNA anticodons there is strong wobble sequence preference that results in a broader spectrum of contacts to synonymous mRNA codon wobble bases. Adenine is excluded from the anticodon wobble position of tRNA unless it is modified to inosine. Uracil is generally preferred to cytosine in the tRNA anticodon wobble position. Because of wobble ambiguity when tRNA reads mRNA, the maximal coding capacity of the three nucleotide code read by tRNA is 31 amino acids + stops.

We advocate for a tRNA- rather than an mRNA-centric model for evolution of the genetic code. The mechanism for evolution of cloverleaf tRNA provides a root sequence for radiation of tRNAs and suggests a simplified understanding of code evolution. To analyze code sectoring, rooted tRNAomes were compared for several archaeal and one bacterial species. Rooting of tRNAome trees reveals conserved structures, indicating how the code was shaped during evolution and suggesting a model for evolution of a LUCA tRNAome tree. We propose the polyglycine hypothesis that the initial product of the genetic code may have been short chain polyglycine to stabilize protocells. In order to describe how anticodons were allotted in evolution, the sectoring-degeneracy hypothesis is proposed. Based on sectoring, a simple stepwise model is developed, in which the code sectors from a 1→4→8→∼16 letter code. At initial stages of code evolution, we posit strong positive selection for wobble base ambiguity, supporting convergence to 4-codon sectors and ∼16 letters. In a later stage, ∼5-6 letters, including stops, were added through innovating at the anticodon wobble position. In archaea and bacteria, tRNA wobble adenine is negatively selected, shrinking the maximum size of the primordial genetic code to 48 anticodons. Because 64 codons are recognized in mRNA, tRNA-mRNA coevolution requires tRNA wobble position ambiguity leading to degeneracy of the code.

Cloverleaf tRNA with a 75 nucleotide (nt) core is posited to have evolved from ligation of three 31 nt minihelices followed by symmetric internal deletions of 9 nt within ligated acceptor stems. Statistical tests strongly support the model. Although the tRNA anticodon loop and T loop are homologs, their U-turns have been treated as distinct motifs. An appropriate comparison, however, shows that intercalation of D loop G19 between T loop bases 4 and 5 causes elevation of T loop base 5 and flipping of T loop bases 6 and 7 out of the 7 nt loop. In the anticodon loop, by contrast, loop bases 3-7 stack tightly to form a stiff connection to mRNA. Furthermore, we identify ancient repeat sequences of 3 (GCG), 5 (UAGCC) and 17 nt (∼CCGGGUUCAAAACCCGG) that comprise 75 out of 75 nts of the tRNA cloverleaf core. To present a sufficiently stiff 3-nt anticodon, a 7-nt anticodon loop was necessary with a U-turn between loop positions 2 and 3. Cloverleaf tRNA, therefore, was a radical evolutionary innovation essential for the 3-nt code. Conservation of GCG and UAGCC repeat sequences indicates that cloverleaf tRNA is at the interface between a strange RNA repeat world and the first evolution of molecules that fold to assume biologic functions. We posit that cloverleaf tRNA was the molecular archetype around which translation systems evolved.

Background: Mass spectrometry (MS) data are often generated from various biological or chemical experiments and there may exist outlying observations, which are extreme due to technical reasons. The determination of outlying observations is important in the analysis of replicated MS data because elaborate pre-processing is essential for successful analysis with reliable results and manual outlier detection as one of pre-processing steps is time-consuming. The heterogeneity of variability and low replication are often obstacles to successful analysis, including outlier detection. Existing approaches, which assume constant variability, can generate many false positives (outliers) and/or false negatives (non-outliers). Thus, a more powerful and accurate approach is needed to account for the heterogeneity of variability and low replication., Findings: We proposed an outlier detection algorithm using projection and quantile regression in MS data from multiple experiments. The performance of the algorithm and program was demonstrated by using both simulated and real-life data. The projection approach with linear, nonlinear, or nonparametric quantile regression was appropriate in heterogeneous high-throughput data with low replication., Conclusion: Various quantile regression approaches combined with projection were proposed for detecting outliers. The choice among linear, nonlinear, and nonparametric regressions is dependent on the degree of heterogeneity of the data. The proposed approach was illustrated with MS data with two or more replicates.