Displaying publications 1 - 20 of 92 in total

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  1. Surendran S, Thomas E
    Am J Orthod Dentofacial Orthop, 2014 Jan;145(1):7-14.
    PMID: 24373650 DOI: 10.1016/j.ajodo.2013.09.007
    The objective of this study was to determine whether dental calcification can be used as a first-level diagnostic tool for assessment of skeletal maturity.
    Matched MeSH terms: Likelihood Functions
  2. Ting CM, Samdin SB, Salleh ShH, Omar MH, Kamarulafizam I
    PMID: 23367426 DOI: 10.1109/EMBC.2012.6347491
    This paper applies an expectation-maximization (EM) based Kalman smoother (KS) approach for single-trial event-related potential (ERP) estimation. Existing studies assume a Markov diffusion process for the dynamics of ERP parameters which is recursively estimated by optimal filtering approaches such as Kalman filter (KF). However, these studies only consider estimation of ERP state parameters while the model parameters are pre-specified using manual tuning, which is time-consuming for practical usage besides giving suboptimal estimates. We extend the KF approach by adding EM based maximum likelihood estimation of the model parameters to obtain more accurate ERP estimates automatically. We also introduce different model variants by allowing flexibility in the covariance structure of model noises. Optimal model selection is performed based on Akaike Information Criterion (AIC). The method is applied to estimation of chirp-evoked auditory brainstem responses (ABRs) for detection of wave V critical for assessment of hearing loss. Results shows that use of more complex covariances are better estimating inter-trial variability.
    Matched MeSH terms: Likelihood Functions
  3. Lim KK, Yoon SY, Mohd Taib NA, Shabaruddin FH, Dahlui M, Woo YL, et al.
    Appl Health Econ Health Policy, 2018 06;16(3):395-406.
    PMID: 29572724 DOI: 10.1007/s40258-018-0384-8
    OBJECTIVE: Previous studies showed that offering BRCA mutation testing to population subgroups at high risk of harbouring the mutation may be cost effective, yet no evidence is available for low- or middle-income countries (LMIC) and in Asia. We estimated the cost effectiveness of BRCA mutation testing in early-stage breast cancer patients with high pre-test probability of harbouring the mutation in Malaysia, an LMIC in Asia.

    METHODS: We developed a decision analytic model to estimate the lifetime costs and quality-adjusted life-years (QALYs) accrued through BRCA mutation testing or routine clinical surveillance (RCS) for a hypothetical cohort of 1000 early-stage breast cancer patients aged 40 years. In the model, patients would decide whether to accept testing and to undertake risk-reducing mastectomy, oophorectomy, tamoxifen, combinations or neither. We calculated the incremental cost-effectiveness ratio (ICER) from the health system perspective. A series of sensitivity analyses were performed.

    RESULTS: In the base case, testing generated 11.2 QALYs over the lifetime and cost US$4815 per patient whereas RCS generated 11.1 QALYs and cost US$4574 per patient. The ICER of US$2725/QALY was below the cost-effective thresholds. The ICER was sensitive to the discounting of cost, cost of BRCA mutation testing and utility of being risk-free, but the ICERs remained below the thresholds. Probabilistic sensitivity analysis showed that at a threshold of US$9500/QALY, 99.9% of simulations favoured BRCA mutation testing over RCS.

    CONCLUSIONS: Offering BRCA mutation testing to early-stage breast cancer patients identified using a locally-validated risk-assessment tool may be cost effective compared to RCS in Malaysia.

    Matched MeSH terms: Likelihood Functions
  4. Hammond D, Kin F, Prohmmo A, Kungskulniti N, Lian TY, Sharma SK, et al.
    Asia Pac J Public Health, 2008;20(3):193-203.
    PMID: 19124313 DOI: 10.1177/1010539508317572
    At present, 70% of the world's 1.1 billion smokers are in developing countries, with over 50% in Asia alone. The current study examined patterns of youth smoking in Thailand and Malaysia. Respondents were 2002 youths between the ages of 13 and 17 from Thailand (n = 1000) and Malaysia (n = 1002). Respondents were selected using a multistage cluster sampling design and surveyed between January 2005 and March 2005. Approximately 3% of youth between the ages of 13 and 17 were current smokers, with an additional 10% to 12% reporting experimental smoking. Males were between 7 and 15 times more likely to report smoking behavior than females. Less than 1% of females respondents in either country met the criteria for current smoking, and less than 5% met the criteria for experimental smoking. In contrast, more than 50% Thai males and approximately one-third of Malaysian males aged 17 met the criteria for either experimental or current smoking.
    Matched MeSH terms: Likelihood Functions
  5. Omer ME, Abu Bakar M, Adam M, Mustafa M
    Asian Pac J Cancer Prev, 2021 Apr 01;22(4):1045-1053.
    PMID: 33906295 DOI: 10.31557/APJCP.2021.22.4.1045
    OBJECTIVE: Cure rate models are survival models, commonly applied to model survival data with a cured fraction. In the existence of a cure rate, if the distribution of survival times for susceptible patients is specified, researchers usually prefer cure models to parametric models. Different distributions can be assumed for the survival times, for instance, generalized modified Weibull (GMW), exponentiated Weibull (EW), and log-beta Weibull. The purpose of this study is to select the best distribution for uncured patients' survival times by comparing the mixture cure models based on the GMW distribution and its particular cases.

    MATERIALS AND METHODS: A data set of 91 patients with high-risk acute lymphoblastic leukemia (ALL) followed for five years from 1982 to 1987 was chosen for fitting the mixture cure model. We used the maximum likelihood estimation technique via R software 3.6.2 to obtain the estimates for parameters of the proposed model in the existence of cure rate, censored data, and covariates. For the best model choice, the Akaike information criterion (AIC) was implemented.

    RESULTS: After comparing different parametric models fitted to the data, including or excluding cure fraction, without covariates, the smallest AIC values were obtained by the EW and the GMW distributions, (953.31/969.35) and (955.84/975.99), respectively. Besides, assuming a mixture cure model based on GMW with covariates, an estimated ratio between cure fractions for allogeneic and autologous bone marrow transplant groups (and its 95% confidence intervals) were 1.42972 (95% CI: 1.18614 - 1.72955).

    CONCLUSION: The results of this study reveal that the EW and the GMW distributions are the best choices for the survival times of Leukemia patients.
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    Matched MeSH terms: Likelihood Functions
  6. Kaushik SP, Vu C
    Aust N Z J Med, 2000 Apr;30(2):231-5.
    PMID: 10833116
    BACKGROUND: From European and North American data, it is recommended in the Asia Pacific consensus statement, that one week therapy with a proton pump inhibitor, amoxycillin and clarithromycin be used for Helicobacter pylori eradication, in areas of high metronidazole resistance. The efficacy of this regimen is unknown in Singapore.

    AIM: To assess the efficacy, safety and compliance of an H. pylori eradication regimen and examine clinical factors that potentially determine eradication.

    METHODS: Consecutive outpatients from a multicultural, south east Asian, population with H. pylori infection, with or without peptic ulcer, were treated with lansoprazole 30 mg, amoxycillin 1 gm, clarithromycin 500 mg, twice a day for seven days. Eradication was assessed by either rapid urease, histology or urea breath test. Compliance and side effects were recorded. The eradication rate and effect of ethnicity, age, sex, usage of alcohol, smoking and non-steroidal anti-inflammatory drugs, history of ulcer and endoscopic diagnosis on eradication were examined by univariate and multivariate analysis.

    RESULTS: Of 113 patients, the eradication rate by intention to treat was 98/113 (87%) (95% confidence interval [CI] 80-93%) and per protocol was 98/106 (92%) (95% CI 87-97%). Using Fisher's exact test, eradication was more successful in Chinese (intention to treat and per protocol respectively p=0.02 and p<0.001) compared to non-Chinese. By logistic regression analysis ethnicity was an independent factor associated with eradication success (p=0.0025). Side effects occurred in five (4.4%), resulting in cessation of treatment.

    CONCLUSIONS: This one week eradication regimen is safe and effective in south east Asians. Chinese ethnicity may be associated with a higher likelihood of eradication success.

    Matched MeSH terms: Likelihood Functions
  7. Yang Y, Li J, Yang S, Li X, Fang L, Zhong C, et al.
    BMC Evol. Biol., 2017 01 18;17(1):22.
    PMID: 28100168 DOI: 10.1186/s12862-016-0849-z
    BACKGROUND: A large-scale systematical investigation of the influence of Pleistocene climate oscillation on mangrove population dynamics could enrich our knowledge about the evolutionary history during times of historical climate change, which in turn may provide important information for their conservation.

    RESULTS: In this study, phylogeography of a mangrove tree Sonneratia alba was studied by sequencing three chloroplast fragments and seven nuclear genes. A low level of genetic diversity at the population level was detected across its range, especially at the range margins, which was mainly attributed to the steep sea-level drop and associated climate fluctuations during the Pleistocene glacial periods. Extremely small effective population size (Ne) was inferred in populations from both eastern and western Malay Peninsula (44 and 396, respectively), mirroring the fragility of mangrove plants and their paucity of robustness against future climate perturbations and human activity. Two major genetic lineages of high divergence were identified in the two mangrove biodiversity centres: the Indo-Malesia and Australasia regions. The estimated splitting time between these two lineages was 3.153 million year ago (MYA), suggesting a role for pre-Pleistocene events in shaping the major diversity patterns of mangrove species. Within the Indo-Malesia region, a subdivision was implicated between the South China Sea (SCS) and the remaining area with a divergence time of 1.874 MYA, corresponding to glacial vicariance when the emerged Sunda Shelf halted genetic exchange between the western and eastern coasts of the Malay Peninsula during Pleistocene sea-level drops. Notably, genetic admixture was observed in populations at the boundary regions, especially in the two populations near the Malacca Strait, indicating secondary contact between divergent lineages during interglacial periods. These interregional genetic exchanges provided ample opportunity for the re-use of standing genetic variation, which could facilitate mangrove establishment and adaptation in new habitats, especially in the context of global climate changes.

    CONCLUSION: Phylogeogrpahic analysis in this study reveal that Pleistocene sea-level fluctuations had profound influence on population differentiation of the mangrove tree S. alba. Our study highlights the fragility of mangrove plants and offers a guide for the conservation of coastal mangrove communities experiencing ongoing changes in sea-level.

    Matched MeSH terms: Likelihood Functions
  8. Amin L, Hashim H, Mahadi Z, Ismail K
    BMC Med Res Methodol, 2018 12 05;18(1):163.
    PMID: 30518344 DOI: 10.1186/s12874-018-0619-2
    BACKGROUND: The demand in biobanking for the collection and maintenance of biological specimens and personal data from civilians to improve the prevention, diagnosis and treatment of diseases has increased notably. Despite the advancement, certain issues, specifically those related to privacy and data protection, have been critically discussed. The purposes of this study are to assess the willingness of stakeholders to participate in biobanking and to determine its predictors.

    METHODS: A survey of 469 respondents from various stakeholder groups in the Klang Valley region of Malaysia was carried out. Based on previous research, a multi-dimensional instrument measuring willingness to participate in biobanking, and its predictors, was constructed and validated. A single step Structural Equation Modelling was performed to analyse the measurements and structural model using the International Business Machines Corporation Software Package for Social Sciences, Analysis of Moment Structures (IBM SPSS Amos) version 20 with a maximum likelihood function.

    RESULTS: Malaysian stakeholders in the Klang Valley were found to be cautious of biobanks. Although they perceived the biobanks as moderately beneficial (mean score of 4.65) and were moderately willing to participate in biobanking (mean score of 4.10), they professed moderate concern about data and specimen protection issues (mean score of 4.33). Willingness to participate in biobanking was predominantly determined by four direct predictors: specific application-linked perceptions of their benefits (β = 0.35, p 
    Matched MeSH terms: Likelihood Functions
  9. Esa R, Ong AL, Humphris G, Freeman R
    BMC Oral Health, 2014;14:19.
    PMID: 24621226 DOI: 10.1186/1472-6831-14-19
    To investigate the role of geography (place of residence) as a moderator in the relationship between dental caries disease and treatment experience and dental fear in 16-year-olds living in Malaysia.
    Matched MeSH terms: Likelihood Functions
  10. Tin-Oo MM, Saddki N, Hassan N
    BMC Oral Health, 2011;11:6.
    PMID: 21342536 DOI: 10.1186/1472-6831-11-6
    We assessed factors influencing patients' satisfaction with their dental appearance and the treatments they desired to improve dental aesthetics.
    Matched MeSH terms: Likelihood Functions
  11. Nadarajah K, Omar NS, Rosli MM, Shin Tze O
    Biomed Res Int, 2014;2014:434257.
    PMID: 25258710 DOI: 10.1155/2014/434257
    Two field isolates of Rhizoctonia solani were isolated from infected paddy plants in Malaysia. These isolates were verified via ITS-rDNA analysis that yielded ~720 bp products of the ITS1-5.8S-ITS4 region, respectively. The sequenced products showed insertion and substitution incidences which may result in strain diversity and possible variation in disease severity. These strains showed some regional and host-specific relatedness via Maximum Likelihood and further phylogenetic analysis via Maximum Parsimony showed that these strains were closely related to R. solani AG1-1A (with 99-100% identity). Subsequent to strain verification and analysis, these isolates were used in the screening of twenty rice varieties for tolerance or resistance to sheath blight via mycelial plug method where both isolates (1801 and 1802) showed resistance or moderate resistance to Teqing, TETEP, and Jasmine 85. Isolate 1802 was more virulent based on the disease severity index values. This study also showed that the mycelial plug techniques were efficient in providing uniform inoculum and humidity for screening. In addition this study shows that the disease severity index is a better mode of scoring for resistance compared to lesion length. These findings will provide a solid basis for our future breeding and screening activities at the institution.
    Matched MeSH terms: Likelihood Functions
  12. Trimarsanto H, Amato R, Pearson RD, Sutanto E, Noviyanti R, Trianty L, et al.
    Commun Biol, 2022 Dec 23;5(1):1411.
    PMID: 36564617 DOI: 10.1038/s42003-022-04352-2
    Traditionally, patient travel history has been used to distinguish imported from autochthonous malaria cases, but the dormant liver stages of Plasmodium vivax confound this approach. Molecular tools offer an alternative method to identify, and map imported cases. Using machine learning approaches incorporating hierarchical fixation index and decision tree analyses applied to 799 P. vivax genomes from 21 countries, we identified 33-SNP, 50-SNP and 55-SNP barcodes (GEO33, GEO50 and GEO55), with high capacity to predict the infection's country of origin. The Matthews correlation coefficient (MCC) for an existing, commonly applied 38-SNP barcode (BR38) exceeded 0.80 in 62% countries. The GEO panels outperformed BR38, with median MCCs > 0.80 in 90% countries at GEO33, and 95% at GEO50 and GEO55. An online, open-access, likelihood-based classifier framework was established to support data analysis (vivaxGEN-geo). The SNP selection and classifier methods can be readily amended for other use cases to support malaria control programs.
    Matched MeSH terms: Likelihood Functions
  13. Guure CB, Ibrahim NA, Adam MB
    Comput Math Methods Med, 2013;2013:849520.
    PMID: 23476718 DOI: 10.1155/2013/849520
    Interval-censored data consist of adjacent inspection times that surround an unknown failure time. We have in this paper reviewed the classical approach which is maximum likelihood in estimating the Weibull parameters with interval-censored data. We have also considered the Bayesian approach in estimating the Weibull parameters with interval-censored data under three loss functions. This study became necessary because of the limited discussion in the literature, if at all, with regard to estimating the Weibull parameters with interval-censored data using Bayesian. A simulation study is carried out to compare the performances of the methods. A real data application is also illustrated. It has been observed from the study that the Bayesian estimator is preferred to the classical maximum likelihood estimator for both the scale and shape parameters.
    Matched MeSH terms: Likelihood Functions
  14. Jani J, Mustapha ZA, Ling CK, Hui ASM, Teo R, Ahmed K
    Data Brief, 2020 Dec;33:106388.
    PMID: 33102655 DOI: 10.1016/j.dib.2020.106388
    In 2019, 10 million new cases of tuberculosis have been reported worldwide. Our data reports genetic analyses of a Mycobacterium tuberculosis strain SBH321 isolated from a 31-year-old female with pulmonary tuberculosis. The genomic DNA of the strain was extracted from pure culture and subjected to sequencing using Illumina platform. M. tuberculosis strain SBH321 consists of 4,374,895 bp with G+C content of 65.59%. The comparative analysis by SNP-based phylogenetic analysis using maximum-likelihood method showed that our strain belonging to sublineage of the Ural family of Europe-America-Africa lineage (Lineage 4) and clustered with M. tuberculosis strain OFXR-4 from Taiwan. The whole genome sequence is deposited at DDBJ/ENA/GenBank under the accession WCJH00000000 (SRR10230353).
    Matched MeSH terms: Likelihood Functions
  15. Jani J, Mustapha ZA, Jamal NB, Stanis CS, Ling CK, Avoi R, et al.
    Data Brief, 2019 Oct;26:104445.
    PMID: 31534995 DOI: 10.1016/j.dib.2019.104445
    A Mycobacterium tuberculosis strain SBH162 was isolated from a 49-year-old male with pulmonary tuberculosis. GeneXpert MDR/RIF identified the strain as rifampicin-resistant M. tuberculosis. The whole genome sequencing was performed using Illumina HiSeq 4000 system to further investigate and verify the mutation sites of the strain through genetic analyses namely variant calling using bioinformatics tools. The de novo assembly of genome generated 100 contigs with N50 of 156,381bp. The whole genome size was 4,343,911 bp with G + C content of 65.58% and consisted of 4,306 predicted genes. The mutation site, S450L, for rifampicin resistance was detected in the rpoB gene. Based on the phylogenetic analysis using the Maximum Likelihood method, the strain was identified as belonging to the Europe America Africa lineage (Lineage 4). The genome dataset has been deposited at DDBJ/ENA/GenBank under the accession number SMOE00000000.
    Matched MeSH terms: Likelihood Functions
  16. Md Yusof NF, Ramli NA, Yahaya AS, Sansuddin N, Ghazali NA, Al Madhoun W
    Environ Monit Assess, 2010 Apr;163(1-4):655-67.
    PMID: 19365611 DOI: 10.1007/s10661-009-0866-0
    There are many factors that influence PM(10) concentration in the atmosphere. This paper will look at the PM(10) concentration in relation with the wet season (north east monsoon) and dry season (south west monsoon) in Seberang Perai, Malaysia from the year 2000 to 2004. It is expected that PM(10) will reach the peak during south west monsoon as the weather during this season becomes dry and this study has proved that the highest PM(10) concentrations in 2000 to 2004 were recorded in this monsoon. Two probability distributions using Weibull and lognormal were used to model the PM(10) concentration. The best model used for prediction was selected based on performance indicators. Lognormal distribution represents the data better than Weibull distribution model for 2000, 2001, and 2002. However, for 2003 and 2004, Weibull distribution represents better than the lognormal distribution. The proposed distributions were successfully used for estimation of exceedences and predicting the return periods of the sequence year.
    Matched MeSH terms: Likelihood Functions
  17. Solarin SA, Al-Mulali U, Ozturk I
    Environ Sci Pollut Res Int, 2018 Nov;25(31):30949-30961.
    PMID: 30182312 DOI: 10.1007/s11356-018-3060-5
    We investigate the role of military expenditure on emission in USA during the period 1960-2015. To achieve the objectives of this study, two measures of military expenditure are utilised, while several timeseries models are constructed with the gross domestic product (GDP) per capita, population, energy consumption per capita, non-renewable energy consumption per capita, renewable energy consumption per capita, urbanisation, trade openness and financial development serving as additional determinants of air pollution. We also use ecological indicator as an alternative measure of pollution. Moreover, different timeseries methods are utilised including a likelihood-based approach with two structural breaks. The output of this research concluded that all the variables are cointegrated. It is found that military expenditure has mixed impact on CO2 emissions. Real GDP per capita, energy consumption per capita, non-renewable energy consumption per capita, population and urbanisation increase CO2 emissions per capita in the long-run, while renewable energy consumption, financial development and trade openness reduce it. There is also evidence for the mixed role of military expenditure, when ecological footprint is utilised as the environmental degradation index. From the output of this research, few policy recommendations are offered for the examined country.
    Matched MeSH terms: Likelihood Functions
  18. Foo SK, Cubbidge RP, Heitmar R
    Eur J Ophthalmol, 2021 Jul;31(4):1870-1876.
    PMID: 32468855 DOI: 10.1177/1120672120926455
    BACKGROUND: Numerous fast threshold strategies have been developed in perimetry which use maximum likelihood approaches to estimate the threshold. A recent approach to threshold estimation has been developed estimating the threshold from a limited number of test points which further reduces examination time. This strategy, SPARK, has not been compared to the SITA strategy. The aim of this study was to compare SPARK with SITA in a normal cohort to evaluate within and between strategy agreement in threshold estimates.

    METHODS: A total of 83 normal subjects each underwent two visual field examinations with SITA and SPARK on two separate occasions on a randomly selected eye. The eye examined and the order of strategy examined first was randomised but remained constant over the two perimetry visits.

    RESULTS: Visual field examination with SPARK Precision was on average 33% faster than SITA Standard. A positive correlation between group mean sensitivities of SITA Standard and SPARK Precision (rho = 0.713, p 

    Matched MeSH terms: Likelihood Functions
  19. Quek SP, Davies SJ, Itino T, Pierce NE
    Evolution, 2004 Mar;58(3):554-70.
    PMID: 15119439
    We investigate the evolution of host association in a cryptic complex of mutualistic Crematogaster (Decacrema) ants that inhabits and defends Macaranga trees in Southeast Asia. Previous phylogenetic studies based on limited samplings of Decacrema present conflicting reconstructions of the evolutionary history of the association, inferring both cospeciation and the predominance of host shifts. We use cytochrome oxidase I (COI) to reconstruct phylogenetic relationships in a comprehensive sampling of the Decacrema inhabitants of Macaranga. Using a published Macaranga phylogeny, we test whether the ants and plants have cospeciated. The COI phylogeny reveals 10 well-supported lineages and an absence of cospeciation. Host shifts, however, have been constrained by stem traits that are themselves correlated with Macaranga phylogeny. Earlier lineages of Decacrema exclusively inhabit waxy stems, a basal state in the Pachystemon clade within Macaranga, whereas younger species of Pachystemon, characterized by nonwaxy stems, are inhabited only by younger lineages of Decacrema. Despite the absence of cospeciation, the correlated succession of stem texture in both phylogenies suggests that Decacrema and Pachystemon have diversified in association, or codiversified. Subsequent to the colonization of the Pachystemon clade, Decacrema expanded onto a second clade within Macaranga, inducing the development of myrmecophytism in the Pruinosae group. Confinement to the aseasonal wet climate zone of western Malesia suggests myrmecophytic Macaranga are no older than the wet forest community in Southeast Asia, estimated to be about 20 million years old (early Miocene). Our calculation of COI divergence rates from several published arthropod studies that relied on tenable calibrations indicates a generally conserved rate of approximately 1.5% per million years. Applying this rate to a rate-smoothed Bayesian chronogram of the ants, the Decacrema from Macaranga are inferred to be at least 12 million years old (mid-Miocene). However, using the extremes of rate variation in COI produces an age as recent as 6 million years. Our inferred timeline based on 1.5% per million years concurs with independent biogeographical events in the region reconstructed from palynological data, thus suggesting that the evolutionary histories of Decacrema and their Pachystemon hosts have been contemporaneous since the mid-Miocene. The evolution of myrmecophytism enabled Macaranga to radiate into enemy-free space, while the ants' diversification has been shaped by stem traits, host specialization, and geographic factors. We discuss the possibility that the ancient and exclusive association between Decacrema and Macaranga was facilitated by an impoverished diversity of myrmecophytes and phytoecious (obligately plant inhabiting) ants in the region.
    Matched MeSH terms: Likelihood Functions
  20. Nayak VC, Rastogi P, Kanchan T, Yoganarasimha K, Kumar GP, Menezes RG
    Forensic Sci Int, 2010 Apr 15;197(1-3):67-9.
    PMID: 20071110 DOI: 10.1016/j.forsciint.2009.12.055
    The fingerprints are very typical for a human being. The present study was undertaken to study the gender differences in fingerprint ridge density in Chinese and Malaysian population. The study done on 200 subjects (100 males and 100 females) of Chinese origin and 100 subjects (50 males and 50 females) of Malaysian origin revealed that significant gender differences occur in the finger ridge density. Fingerprint mean ridge density of 12 ridges/25 mm(2) or less is found to be more likely to be of males and a mean ridge count of more the 13 ridges/25 mm(2) is more likely of female origin in Chinese subjects. Fingerprint mean ridge density of 11 ridges/25 mm(2) or less is found to be more likely to be of males and a mean ridge count of more the 13 ridges/25 mm(2) is more likely of female origin in Malaysian subjects.
    Matched MeSH terms: Likelihood Functions
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