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Tan WY, Hargreaves CA, Kandiah N, Hilal S. Association of Multi-Domain Factors with Cognition in the UK Biobank Study. J Prev Alzheimers Dis 2024; 11:13-21. [PMID: 38230713 DOI: 10.14283/jpad.2024.3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2024]
Abstract
BACKGROUND Dementia is a multifactorial syndrome attributable to a combination of vascular risk factors, lifestyle factors and neurodegeneration. However, little is known about the relative contribution of all these factors and their combined effects on cognition among the older population. OBJECTIVE To examine the association of four domains of risk factors (sociodemographic, vascular risk factors, neuroimaging markers, lifestyle and psychosocial factors) with cognition in older adults. DESIGN A cross-sectional study. SETTING Data was obtained from a large-scale population-based study, UK Biobank study, at the first imaging visit assessment. PARTICIPANTS Participants are citizen or permanent residents of UK, aged 60 years old and above. MEASURES Cognitive function was assessed using the general cognitive ability score (g-factor score) derived from principal components analysis estimates of six cognitive tests. Associations with cognition were examined using multivariable linear regression for each domain and in combination. RESULTS The study included 19,773 participants (mean age 68.5 ± 5.3 years SD, 9,726 (49%) male). Participants with lower cognitive scores (poorer cognition) were older, female, non-whites individuals, less educated and more socially deprived than participants with better cognitive scores. Participants with lower cognitive scores also tended to have higher vascular risk factors, lower brain volumes and more adverse lifestyle behaviours. The multivariable analysis found associations between adverse lifestyle and psychosocial factors with poorer cognition, i.e., being obese by measure of body fat percentage, having diabetes, higher white matter hyperintensity volume, increased sedentary screen time watching TV, being socially isolated and having depression were independently associated with poorer cognition. While larger hippocampal volume, having optimal sleep duration, adherence to a heathy diet, current and former alcohol drinking, increased wine consumption and sedentary screen time using a computer were associated with better cognition. CONCLUSION A combination of adverse lifestyle and psychosocial factors were independently associated with poorer cognition in older adults. Findings in this study can potentially support public health communications to promote cognitive function and independence among older adults. This research has been conducted using the UK Biobank Resource under Application Number 71022.
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Affiliation(s)
- W Y Tan
- Dr Saima Hilal, Saw Swee Hock School of Public Health, National University of Singapore, Tahir Foundation Building, 12 Science Drive 2, #10-03T, Singapore 117549,
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Wan Asyraf WZ, Ah Khan YK, Chung LW, Kee HF, Irene L, Ang CL, Choon WK, Mak CS, Tan WY, Wn Nafisah WY, Hamidon B. Malaysia Stroke Council guide on acute stroke care service during COVID-19 Pandemic. Med J Malaysia 2020; 75:311-313. [PMID: 32467554] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
On the 18th of March 2020, the Malaysia government declared a movement control order (MCO) due to the unprecedented COVID-19 pandemic. Although the majority of patients presented with respiratory-related symptoms, COVID-19 patients may present atypically with neurological manifestations and may even have an increased risk of stroke. The Malaysia Stroke Council is concerned regarding the level of care given to stroke patients during this pandemic. During the recent National Stroke Workflow Steering Committee meeting, a guide was made based on the currently available evidences to assist Malaysian physicians providing acute stroke care in the hospital setting in order to provide the best stroke care while maintaining their own safety. The guide comprises of prehospital stroke awareness, hyperacute stroke care, stroke care unit and intensive care unit admission, post-stroke rehabilitation and secondary prevention practice. We urge continuous initiative to provide the best stroke care possible and ensure adequate safety for both patients and the stroke care team.
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Affiliation(s)
- W Z Wan Asyraf
- Pusat Perubatan Universiti Kebangsaan Malaysia, Department of Medicine, Malaysia.
| | - Y K Ah Khan
- University Putra Malaysia, Faculty of Medicine and Health Sciences, Department of Medicine, Selangor, Malaysia
| | - L W Chung
- Hospital Umum Sarawak, Kuching, Sarawak, Malaysia
| | - H F Kee
- University Putra Malaysia, Faculty of Medicine and Health Sciences, Department of Medicine, Selangor, Malaysia
| | - L Irene
- Hospital Seberang Jaya, Pulau Pinang, Malaysia
| | - C L Ang
- Hospital Pantai Ipoh, Perak, Malaysia
| | - W K Choon
- Hospital Pantai Pulau Pinang, Malaysia
| | - C S Mak
- Hospital Gleneagles Kuala Lumpur, Malaysia
| | - W Y Tan
- Thomson Hospital, Kuala Lumpur, Malaysia
| | - W Y Wn Nafisah
- Pusat Perubatan Universiti Kebangsaan Malaysia, Department of Medicine, Malaysia
| | - B Hamidon
- University Putra Malaysia, Faculty of Medicine and Health Sciences, Department of Medicine, Selangor, Malaysia
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Wong YH, Tan WY, Tan CP, Long K, Nyam KL. Cytotoxic activity of kenaf (Hibiscus cannabinus L.) seed extract and oil against human cancer cell lines. Asian Pac J Trop Biomed 2014; 4:S510-5. [PMID: 25183141 DOI: 10.12980/apjtb.4.2014c1090] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2014] [Accepted: 03/20/2014] [Indexed: 01/01/2023] Open
Abstract
OBJECTIVE To examine the cytotoxic properties of both the kenaf (Hibiscus cannabinus L.) seed extract and kenaf seed oil on human cervical cancer, human breast cancer, human colon cancer and human lung cancer cell lines. METHODS The in vitro cytotoxic activity of the kenaf (Hibiscus cannabinus L.) seed extract and kenaf seed oil on human cancer cell lines was evaluated by using 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide and sulforhodamine B assays. Cell morphological changes were observed by using an inverted light microscope. RESULTS The kenaf seed extract (KSE) exhibited a lower IC50 than kenaf seed oil (KSO) in all of the cancer cell lines. Morphological alterations in the cell lines after KSE and KSO treatment were observed. KSE and KSO possessed effective cytotoxic activities against all the cell lines been selected. CONCLUSIONS KSE and KSO could be potential sources of natural anti-cancer agents. Further investigations on using kenaf seeds for anti-proliferative properties are warranted.
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Affiliation(s)
- Yu Hua Wong
- Department of Food Science and Nutrition, Faculty of Applied Sciences, UCSI University, 56000 Kuala Lumpur, Malaysia
| | - Wai Yan Tan
- Department of Food Science and Nutrition, Faculty of Applied Sciences, UCSI University, 56000 Kuala Lumpur, Malaysia
| | - Chin Ping Tan
- Department of Food Technology, Faculty of Food Science and Technology,Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia
| | - Kamariah Long
- Malaysian Agricultural Research & Development Institute (MARDI) PO Box 12301, 50774 Kuala Lumpur, Malaysia
| | - Kar Lin Nyam
- Department of Food Science and Nutrition, Faculty of Applied Sciences, UCSI University, 56000 Kuala Lumpur, Malaysia
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Abstract
By using the state space model (Kalman filter model) of the HIV epidemic, in this paper we have developed a general Bayesian procedure to estimate simultaneously the HIV infection distribution, the HIV incubation distribution, the numbers of susceptible people, infective people and AIDS cases. The basic approach is to use the Gibbs sampling method combined with the weighted bootstrap method. We have applied this method to the San Francisco AIDS incidence data from January 1981 to December 1992. The results show clearly that both the probability density function of the HIV infection and the probability density function of the HIV incubation are curves with two peaks. The results of the HIV infection distribution are clearly consistent with the finding by Tan et al. [W.Y. Tan, S.C. Tang, S.R. Lee, Estimation of HIV seroconversion and effects of age in San Francisco homosexual populations, J. Appl. Stat. 25 (1998) 85]. The results of HIV incubation distribution seem to confirm the staged model used by Satten and Longini [G. Satten, I. Longini, Markov chain with measurement error: estimating the 'true' course of marker of the progression of human immunodeficiency virus disease, Appl. Stat. 45 (1996) 275].
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Affiliation(s)
- W Y Tan
- Department of Mathematical Sciences, The University of Memphis, 335 Winfield Dunn, Memphis, TN 38152, USA.
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Abstract
In this paper we have extended the model of HIV pathogenesis under treatment by anti-viral drugs given by Perelson et al. [A.S. Perelson et al., Science 271 (1999) 1582] to a stochastic model. By using this stochastic model as the stochastic system model, we have developed a state space model for the HIV pathogenesis under treatment by anti-viral drugs. In this state space model, the observation model is a statistical model based on the observed numbers of RNA virus copies over different times. For this model we have developed procedures for estimating and predicting the numbers of infectious free HIV and non-infectious free HIV as well as the numbers of different types of T cells through extended Kalman filter method. As an illustration, we have applied the method of this paper to the data of patient Nos. 104, 105 and 107 given by Perelson et al. [A.S. Perelson et al., Science 271 (1999) 1582] under treatment by Ritonavir. For these individuals, it is shown that within two weeks since treatment, most of the free HIV are non-infectious, indicating the usefulness of the treatment. Furthermore, the Kalman filter method revealed a much stronger effect of the treatment within the first 10 to 20 h than that predicted by the deterministic model.
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Affiliation(s)
- W Y Tan
- Department of Mathematical Sciences, University of Memphis, TN 38152, USA.
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Abstract
In this paper we have developed a state space model for the HIV epidemic in homosexual populations which have been divided into subpopulations according to sexual activity levels. In this model, the stochastic dynamic system model is the stochastic model of the HIV epidemic in terms of the chain multinomial model whereas the observation model is a statistical model based on the observed AIDS incidences. This model is applied to the San Francisco homosexual population for estimating the numbers of susceptible people, infective people and AIDS cases and for estimating the probabilities of HIV transmission from infective people to susceptible people given sexual contacts. The results show that the estimated numbers of AIDS incidence trace closely the observed numbers indicating the usefulness of the model. It is observed that the estimated numbers of latent people show multimodal curves and that HIV infection takes place during the primary stage and very late stage. The results have further shown that there are significant differences between the observed AIDS incidences and the estimates by the embedded deterministic model. These results indicate that using the embedded deterministic model to estimate the HIV-infected people and to predict future AIDS cases can be very misleading in some cases.
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Affiliation(s)
- W Y Tan
- Department of Mathematical Sciences, University of Memphis, TN 38152, USA.
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Abstract
In this paper, we develop a stochastic model for the interaction between CD4+ T cells and the human immunodeficiency virus (HIV) virus by taking into account the basic biological mechanism as described in [1-4]. We studied this stochastic model through extensive Monte Carlo simulations. Our results show that, in some cases, there is a positive probability that the virus will be eliminated by the process. We have also shown that, at the earlier stage of the infection, the probability distributions of the CD4+ T cells and free HIV are skewed; however, these distributions will eventually converge to the Gaussian distributions after several years. A real-data example is given to illustrate the application of our model.
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Affiliation(s)
- W Y Tan
- Department of Mathematical Sciences, University of Memphis, Tennessee 38152, USA
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Gail MH, Tan WY, Pee D, Goedert JJ. Survival after AIDS diagnosis in a cohort of hemophilia patients. Multicenter Hemophilia Cohort Study. J Acquir Immune Defic Syndr Hum Retrovirol 1997; 15:363-9. [PMID: 9342256 DOI: 10.1097/00042560-199708150-00006] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
Abstract
We studied factors affecting survival after the diagnosis of AIDS in a cohort of 1253 patients with hemophilia. The nature of the AIDS-defining condition was found to be as important as age at seroconversion and CD4+ lymphocyte level in predicting survival. A multivariate analysis yielded estimates of median survival for groups defined by age at seroconversion (0 through 15, 16 through 69), CD4+ lymphocyte count (<100 cells/microl versus > or = 100 cells/microl), and 10 AIDS-defining disease groups. Estimates of median survival after a single AIDS-defining condition ranged from 3 to 51 months, depending on the diseases. Median survival after a second AIDS-defining condition was about 1.5- to 2.0-fold shorter than after an initial, isolated AIDS-defining condition. HIV-related neurologic disease (i.e., AIDS dementia complex or multifocal leukoencephalopathy) was a notable exception. It correlated with the shortest estimates of median survival (3 to 9 months), and this poor prognosis was no worse for patients who had a second AIDS-defining condition. The results of this analysis were consistent in most respects with other published analyses of factors affecting survival. These findings may be useful in the clinical care of persons with AIDS and in estimating the number of persons alive who have had a particular AIDS-defining disease.
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Affiliation(s)
- M H Gail
- Biostatistics Branch, National Cancer Institute, Bethesda, Maryland 20892-7368, U.S.A
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Abstract
By using a two stage model of carcinogenesis, we generated Monte Carlo studies to assess the efficiency and robustness of the 3-poly test for animal carcinogenicity experiments. The Monte Carlo results indicate that the 3-poly test is quite powerful for detecting the carcinogenic effects of complete carcinogens, moderate promoters, and initiators with moderate or large effect, but, in some cases, it is less powerful for weak initiators or weak promoters. As expected, the 3-poly test is insensitive to the toxicity of many agents.
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Affiliation(s)
- W Y Tan
- Department of Mathematical Sciences, University of Memphis, TN 38152, USA
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Abstract
In this paper we use a general stochastic model to characterize the HIV incubation distributions. We generate some Monte Carlo data under different conditions and compare the fitting of HIV incubation distributions by some well known parametric models and some non-parametric methods. The parametric models include most of those that have appeared in the literature. The non-parametric methods include the Kaplan--Meier method, the EMS method, the spline approximation and the Bacchetti method. The comparison criteria are the chi-square statistic, the residual sum of squares, the AIC and the BIC. We show that the non-parametric methods, especially the EMS method, provide excellent fits in almost all cases; for the parametric models, the generalized log-logistic distributions with three and with four parameters fit better than other parametric models.
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Affiliation(s)
- W Y Tan
- Department of Mathematical Sciences, University of Memphis, TN 38152, USA
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Abstract
In this paper we use a stochastic model for the HIV epidemic in homosexual populations to characterize the HIV infection and seroconversion. Using computer generated data, we compare the fitting of infection distributions and of seroconversion distributions by different parametric models as well as by nonparametric methods. The nonparametric methods include the Kaplan-Meier method, EMS method, Bacchetti's method, and the spline approximation. The parametric models include most of the models which have been used in the literature. The comparison criteria are the chi-square statistic, the AIC (Akaike Information Criterion) and the residual sums of squares. The numerical results suggest that for the proportional mixing pattern, the EMS method, the spline method, Bacchetti's method, and the generalized log-logistic distributions with three and with four parameters provide better fitting for the infection and the seroconversion distributions in most cases. For the restricted mixing patterns, the EMS method, the spline method, Bacchetti's method, and some mixtures of distributions provide close fitting to the infection and the seroconversion distributions.
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Affiliation(s)
- W Y Tan
- Department of Mathematical Sciences, University of Memphis, Tennessee
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Abstract
Recently there has been increased interest in considering factorial designs for randomized clinical trials when one wishes to study two or more treatments. Such designs may offer impressive gains in efficiency compared with a series of trials studying one treatment at a time. This is especially true when the treatments do not interact with one another. If interactions are of special interest, factorial designs provide one sensible approach for studying them, but larger sample sizes would be required because tests for interactions have lower power than those for main effects. In trials designed to test putative agents for preventing cancer, interactions may be of less interest so that fractions of higher-order factorial designs might be appropriate. Sometimes it may not be reasonable, interesting, feasible, or ethical to study all treatment combinations required in a complete or fractional factorial design, yet one may want to preserve some of the factorial structure to increase efficiency and to aid understanding. For such situations, incomplete factorial designs are proposed. Although not all of the advantages of full factorial designs are preserved, such designs may provide reasonable compromises for certain situations.
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Affiliation(s)
- D P Byar
- National Cancer Institute, Bethesda, Maryland 20892
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Abstract
In this paper we develop a stochastic model for the HIV epidemic in a homosexual population and use the model to characterize the HIV infection distribution and seroconversion distribution. Through computer-generated infection distributions and seroconversion distributions, we assess the effects of various risk factors on these distributions. The fitting of some data sets generated by computer suggests that the three-parameter generalized log-logistic distribution should be assumed as the infection distribution for the proposed stochastic model of HIV epidemics.
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Affiliation(s)
- W Y Tan
- Department of Mathematical Sciences, Memphis State University, Tennessee
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Abstract
The back-calculation method has been used to estimate the number of HIV infections from AIDS incidence data in a particular population. We present an extension of back calculation that provides estimates of the numbers of HIV infectives in different stages of infection. We model the staging process with a time-dependent Markov process that partitions the HIV infectious period into the following progressive stages and/or substages: stage 1, infected but antibody negative; substages 2-3; antibody positive but asymptomatic; substages 4-6, pre-AIDS symptoms and/or abnormal haematologic indicator, stage 7, clinical AIDS. We also model an eight stage, decreased due to AIDS. The model allows for time-dependent treatment effects that slow the rate of progression in substages 4-7. We use the estimated AIDS incubation period distribution for the Markov model in back calculation from AIDS incidence data to estimate the total number of HIV infections and the parameters of the infection probability distribution. We then use these estimates in the Markov model to estimate the stage-specific numbers of HIV infections over the course of the epidemic in the population under study. Example calculations employ data for epidemic in San Francisco City, Clinic Cohort.
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Affiliation(s)
- I M Longini
- Division of Biostatistics, School of Public Health, Emory University, Atlanta, GA 30322
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Abstract
This paper presents a mixed model of carcinogenesis and derives the incidence functions and the first four cumulants of the number of tumors. The model is then fitted to some retinoblastoma data from the SEER (Surveillance Epidemiology End Results) project of the National Cancer Institute for the years 1973-1982. In all the cases presented, the estimated incidence functions appear to fit the observed incidence curves quite well, suggesting the usefulness of the model.
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Affiliation(s)
- W Y Tan
- Department of Mathematical Sciences, Memphis State University, Tennessee 38152
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Tan WY, Brown CC. Cancer chemotherapy with immunostimulation: a nonhomogeneous stochastic model for drug resistance. I. One drug case. Math Biosci 1989; 97:145-60. [PMID: 2520208 DOI: 10.1016/0025-5564(89)90002-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Abstract
In this paper we develop a nonhomogeneous stochastic model for drug resistance in chemotherapy that permits killing resistant cells with immunostimulation. The probability distribution of the number of resistant tumor cells, the probability of no resistant tumor cells, and the expected value and cumulants of the number of resistant tumor cells are derived under very general conditions. The application of these results is illustrated with some numerical examples.
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Abstract
In this paper we propose a stochastic model for the AIDS spread in a homosexual population. The probability generating function (PGF) of the numbers of latent persons, infective persons and AIDS cases is derived. By using the PGF, it is shown that the expected numbers and variances and covariances of these persons satisfy some ordinary differential equations. These equations have been solved numerically to assess effects of various factors on AIDS spread.
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Affiliation(s)
- W Y Tan
- Department of Mathematical Sciences, Memphis State University, Tennessee 38152
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Chu KC, Brown CC, Tarone RE, Tan WY. Differentiating among proposed mechanisms for tumor promotion in mouse skin with the use of the multievent model for cancer. J Natl Cancer Inst 1987; 79:789-96. [PMID: 3116311] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023] Open
Abstract
Numerous mechanisms for tumor promotion in mouse skin have been recently proposed. These include the multistage, genetic view of Slaga, Furstenberger, and Marks; the multistage, genetic and/or epigenetic view of Parkinson; and the two-stage view of Yuspa and Hennings. With the use of the multievent model, a mathematical model for cancer that can incorporate cell proliferation phenomena, these tumor promotion mechanisms were modeled mathematically. It was found that the models had different predictions about the incidence of papillomas in initiator-promoter-initiator experiments and the incidence of carcinomas in initiator-promoter experiments with varying periods of tumor promotion. Upon analysis, existing data were shown to be in agreement with the Yuspa and Hennings two-stage model. The analysis also supported the view, formulated by Scribner and co-workers, that different types of initiated cells were created, some capable of transformation to carcinomas and some not. Phenomena determined by use of benign tumors as the end point may need to be demonstrated with the use of the carcinoma as the end point, prior to the acceptance of these phenomena being applicable to the human carcinogenic process.
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Affiliation(s)
- K C Chu
- Early Detection Branch, National Cancer Institute, Bethesda, MD 20892
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Tan WY, Singh KP. Assessing the effects of metabolism of environmental agents on cancer tumor development by a two-stage model of carcinogenesis. Environ Health Perspect 1987; 74:203-210. [PMID: 3691427 PMCID: PMC1474501 DOI: 10.1289/ehp.8774203] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
By combining the Michaelis-Menten kinetics of metabolism with the two-stage model of Moolgavkar and Knudson (1981) and the extended two-stage model of carcinogenesis proposed by Tan and Gastardo (1985), this paper proceeds to investigate the effects of metabolism of carcinogens on cancer tumor development. It is shown that the nonlinear kinetics of metabolism of carcinogens affect the dose-response relationship mainly through the mutation rates. If the initiator is affected by metabolism, then the metabolism of promoters has very little or negligible effects of the expected incidences and the number of tumors.
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Affiliation(s)
- W Y Tan
- Department of Mathematical Sciences, Memphis State University, TN 38152
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Tan WY, Wu XQ, Zong LF. [Clinical analysis of 20 patients with liquefied petroleum gas burns]. Zhonghua Wai Ke Za Zhi 1986; 24:365-6, 383. [PMID: 3816438] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [MESH Headings] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
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Tan WY. [Analysis of 131 cases of rabies]. Zhonghua Liu Xing Bing Xue Za Zhi 1982; 3:230-2. [PMID: 7185459] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [MESH Headings] [Subscribe] [Scholar Register] [Indexed: 01/23/2023]
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Abstract
"Consider a two organs system for which one of the two organs must function for the individual to survive. This paper derives the survival probability distributions under more general situations by adopting [the] Markov process approach, thus providing extensions of results given in Gross, Clark and Liu (1971) and Kodlin (1967). The results obtained are then extended to a k-organs system."
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Tan WY. On the absorption probabilities and absorption times of finite homogeneous birth-death processes. Biometrics 1976; 32:745-52. [PMID: 1009223] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [MESH Headings] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
Abstract
This paper provides some formulas for the absorption probabilities, the mean absorption times and the variances of first absorption times in finite homogeneous absorbing birth-death processes. The results are then applied to a genetic model of Moran [1958] for computing the absorption probability densities, the mean absorption times and the variances of first absorption times. Specifically, it is shown that the probability distribution of the first absorption time is the matrix analog of exponential distribution or a mixture of exponential distributions if the transition matrix is diagonable.
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