Dissertations / Theses on the topic 'Parametric survival models'
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Hemming, Karla. "Parametric dynamic survival models." Thesis, University of Warwick, 2000. http://wrap.warwick.ac.uk/73391/.
Full textGong, Zhaojing. "Parametric Potential-Outcome Survival Models for Causal Inference." Thesis, University of Canterbury. Mathematics and Statistics, 2008. http://hdl.handle.net/10092/1803.
Full textNwi-Mozu, Isaac. "Robustness of Semi-Parametric Survival Model: Simulation Studies and Application to Clinical Data." Digital Commons @ East Tennessee State University, 2019. https://dc.etsu.edu/etd/3618.
Full textTahir, Muhammad-Ramzan. "On validation of parametric models applied in survival analysis and reliability." Thesis, Bordeaux 1, 2012. http://www.theses.fr/2012BOR14547/document.
Full textThis is an increasing importance in survival analysis and reliability to select a suitable basic model for further inquiries of the data. Little deviation in basic model can cause serious problems in final results. The presence of censoring and accelerated stresses make this task more difficult. Chi-square type goodness of fit tests are most commonly used for model selection. Many modifications in chi-square tests have been proposed by various researcher. The first aim of the thesis is to present a goodness of fit test for wide rage of parametric models (shape-scale families) commonly used in survival analysis, social sciences, engineering, public health and demography, in presence of right censoring. We give the explicit forms of the quadratic form of the test statistic (NRR test) for various models and apply the test on real data. We develop a computer program in R-language for all models. A separate section is dedicated for the test in demography. We focus on the Birnbaum-Saunders (BS) distribution for goodness of fit test for parametric AFT-model and analysis of redundant system.The other purpose of the thesis is to give the analysis of redundant system. To ensure high reliability of the main components of the systems, standby units are used. The main component is replaced by the standby unit automatically, if it fails. The standby unit can be in warm, hot, or cold state. We give the procedure of one main and (n-1) standby units placed in hot state, and give the detailed analysis of one main and one standby unit using BS parametric family. We use Sedyakin's physical principal and the approach of accelerated failure time model for the analysis of redundant system. This approach is different from the traditional ones in the literature but difficulties in calculations. We calculate the reliability of the system in terms of distribution function (unreliability function) and asymptotic confidence interval
Läuter, Henning. "Estimation in partly parametric additive Cox models." Universität Potsdam, 2003. http://opus.kobv.de/ubp/volltexte/2011/5150/.
Full textAbdel, Hamid Hisham. "Flexible parametric survival models with time-dependent covariates for right censored data." Thesis, University of Southampton, 2012. https://eprints.soton.ac.uk/360380/.
Full textMasiulaitytė, Inga. "Regression and degradation models in reliability theory and survival analysis." Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2010. http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2010~D_20100527_134956-15325.
Full textDaktaro disertacijos tyrimo objektai yra rezervuotos sistemos ir degradaciniai modeliai. Norint užtikrinti svarbių sistemos elementų aukštą patikimumą, naudojami jų rezerviniai elementai, kurie gali būti įjungiami sugedus šiems pagrindiniams elementams. Rezerviniai elementai gali funkcionuoti skirtinguose režimuose: „karštame“, „šaltame“ arba „šiltame“. Disertacijoje yra nagrinėjamos sistemos su „šiltai“ rezervuotais elementais. Darbe suformuluojama rezervinio elemento „sklandaus įjungimo“ hipotezė ir konstruojami statistiniai kriterijai šiai hipotezei tikrinti. Nagrinėjami neparametrinio ir parametrinio taškinio bei intervalinio vertinimo uždaviniai. Disertacijoje nagrinėjami pakankamai bendri degradacijos modeliai, kurie aprašo elementų gedimų intensyvumą kaip funkciją kiek naudojamų apkrovų, tiek ir degradacijos lygio, kuri savo ruožtu modeliuojama naudojant stochastinius procesus.
Čabla, Adam. "Odhady v analýze přežívání." Master's thesis, Vysoká škola ekonomická v Praze, 2009. http://www.nusl.cz/ntk/nusl-17134.
Full textIslam, Sarwar. "Development of flexible parametric models for competing risks and tools to facilitate in the understanding and communication of cancer survival." Thesis, University of Leicester, 2018. http://hdl.handle.net/2381/42864.
Full textHoglin, Phillip J. "Survival analysis and accession optimization of prior enlisted United States Marine Corps officers." Thesis, Monterey, California. Naval Postgraduate School, 2004. http://hdl.handle.net/10945/1673.
Full textThe purpose of this thesis is to firstly analyze the determinants on the survival of United States Marine Corps Officers, and secondly, to develop the methodology to optimize the accessions of prior and non-prior enlisted officers. Using data from the Marine Corps Officer Accession Career file (MCCOAC), the Cox Proportional Hazards Model is used to estimate the effects of officer characteristics on their survival as a commissioned officer in the USMC. A Markov model for career transition is combined with fiscal data to determine the optimum number of prior and non-prior enlisted officers under the constraints of force structure and budget. The findings indicate that prior enlisted officers have a better survival rate than their non-prior enlisted counterparts. Additionally, officers who are married, commissioned through MECEP, graduate in the top third of their TBS class, and are assigned to a combat support MOS have a better survival rate than officers who are unmarried, commissioned through USNA, graduate in the middle third of their TBS class, and are assigned to either combat or combat service support MOS. The findings also indicate that the optimum number of prior enlisted officer accessions may be considerably lower than recent trends and may differ across MOS. Based on the findings; it is recommended that prior enlisted officer accession figures be reviewed.
Major, Australian Army
Santos, Marcos Antonio de Lima. "Taxas de SobrevivÃncia de Participantes de Fundos de PensÃo Vinculados ao Setor ElÃtrico Nacional." Universidade Federal do CearÃ, 2011. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=6675.
Full textEsta dissertaÃÃo tem por objetivo calcular as taxas de sobrevivÃncia dos participantes de Fundos de PensÃo do setor elÃtrico nacional, bem como encontrar o modelo paramÃtrico de sobrevivÃncia que melhor represente os dados em estudo. Para desenvolvimento do trabalho utilizamos dados de 14 entidades com informaÃÃes de participantes ativos e aposentados, com exceÃÃo dos invÃlidos, referentes ao perÃodo de 2001 a 2009, totalizando um nÃmero total de 100.000 vidas analisadas. Para calcular as taxas brutas de sobrevivÃncia, utilizamos o mÃtodo indireto, descrito em Ferreira (1985). ApÃs o cÃlculo das taxas originais, efetuamos o processo de suavizaÃÃo por mÃdias mÃveis, visando corrigir as flutuaÃÃes indesejadas obtidas na curva bruta de sobrevivÃncia. Mesmo apÃs o processo de suavizaÃÃo, optamos por restringir o estudo Ãs idades dentro do intervalo de 25 a 85 anos, dado o baixo nÃmero de Ãbitos e expostos nas idades supramencionadas. A partir da curva suavizada, aplicamos os modelos paramÃtricos de sobrevivÃncia de Gompertz, Gompertz-Makeham, Thiele e Helingman-Pollard, para testar o melhor ajuste da equaÃÃo. Os resultados mostraram que nenhum dos modelos paramÃtricos analisados se mostrou com robustez estatÃstica suficiente para se proceder a uma anÃlise preditiva com confiabilidade aceitÃvel.
This paper aims to calculate the survival rates of the participants of the Pension Funds electricity sector as well as finding the parametric survival model that best represents the data in the study. For development work we used data from 14 organizations with information of participants and retirees, with the exception of the disabled, for the period 2001 to 2009, amounting to a total of 100,000 lives analyzed. To calculate the crude rates of survival using the indirect method described in Ferreira (1985). After calculation of the original rates, we make the process of smoothing by moving averages in order to correct the unwanted fluctuations in the curve obtained crude survival. Even after the smoothing process, we chose to restrict the study to age within the range of 25 to 85 years, given the low number of deaths at ages above and exposed. From the smooth curve we apply the parametric models of survival Gompertz, Gompertz-Makeham, Thiele and Helingman-Pollard, to test the best fit of the equation. The results showed that none of the models proved to be analyzed with parametric statistical robust enough to conduct a predictive analysis with acceptable reliability.
Joshi, Kabita. "Finding the Cutpoint of a Continuous Covariate in a Parametric Survival Analysis Model." VCU Scholars Compass, 2016. http://scholarscompass.vcu.edu/etd/4428.
Full textRace, Jonathan Andrew. "Semi-parametric Survival Analysis via Dirichlet Process Mixtures of the First Hitting Time Model." The Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu157357742741077.
Full textTran, Xuan Quang. "Les modèles de régression dynamique et leurs applications en analyse de survie et fiabilité." Thesis, Bordeaux, 2014. http://www.theses.fr/2014BORD0147/document.
Full textThis thesis was designed to explore the dynamic regression models, assessing the sta-tistical inference for the survival and reliability data analysis. These dynamic regressionmodels that we have been considered including the parametric proportional hazards andaccelerated failure time models contain the possibly time-dependent covariates. We dis-cussed the following problems in this thesis.At first, we presented a generalized chi-squared test statisticsY2nthat is a convenient tofit the survival and reliability data analysis in presence of three cases: complete, censoredand censored with covariates. We described in detail the theory and the mechanism to usedofY2ntest statistic in the survival and reliability data analysis. Next, we considered theflexible parametric models, evaluating the statistical significance of them by usingY2nandlog-likelihood test statistics. These parametric models include the accelerated failure time(AFT) and a proportional hazards (PH) models based on the Hypertabastic distribution.These two models are proposed to investigate the distribution of the survival and reliabilitydata in comparison with some other parametric models. The simulation studies were de-signed, to demonstrate the asymptotically normally distributed of the maximum likelihood estimators of Hypertabastic’s parameter, to validate of the asymptotically property of Y2n test statistic for Hypertabastic distribution when the right censoring probability equal 0% and 20%.n the last chapter, we applied those two parametric models above to three scenes ofthe real-life data. The first one was done the data set given by Freireich et al. on thecomparison of two treatment groups with additional information about log white blood cellcount, to test the ability of a therapy to prolong the remission times of the acute leukemiapatients. It showed that Hypertabastic AFT model is an accurate model for this dataset.The second one was done on the brain tumour study with malignant glioma patients, givenby Sauerbrei & Schumacher. It showed that the best model is Hypertabastic PH onadding five significance covariates. The third application was done on the data set given by Semenova & Bitukov on the survival times of the multiple myeloma patients. We did not propose an exactly model for this dataset. Because of that was an existing oneintersection of survival times. We, therefore, suggest fitting other dynamic model as SimpleCross-Effect model for this dataset
Devamitta, Perera Muditha V. "Statistical Analysis and Modeling of Ovarian and Breast Cancer." Scholar Commons, 2017. https://scholarcommons.usf.edu/etd/7395.
Full textQuerin, Giorgia. "Unravelling the tangle of motor neuron diseases : insights from neuroimaging and neurophysiology Spinal cord multi-parametric magnetic resonance imaging for survival prediction in amyotrophic lateral sclerosis Multimodal spinal cord MRI offers accurate diagnostic classification in ALS The spinal and cerebral profile of adult spinal-muscular atrophy: a multimodal imaging study The motor unit number index (MUNIX) profile of patients with adult spinal muscular atrophy Presymptomatic longitudinal cord pathology in c9orf72 mutation carriers: longitudinal neuroimaging study." Thesis, Sorbonne université, 2019. http://www.theses.fr/2019SORUS329.
Full textMotor neuron diseases (MNDs) are characterized by dysfunction and loss of ventral horn MNs in the spinal grey matter (GM). Nevertheless, different MNDs such as amyotrophic lateral sclerosis (ALS) and spinal muscular atrophy (SMA) present with specific clinical presentations. Magnetic resonance imaging (MRI) is the most powerful approach at the brain and spinal cord (SC) level to extract quantitative data on degeneration. At the same time, neurophysiological techniques including motor unit number index (MUNIX) could represent a useful tool to map MN loss. The objective of this project was to combine SC and brain MRI with MUNIX to better characterize degeneration in MNDs, with the aim of identifying possible markers of disease progression. In ALS patients, we showed that SC MRI parameters improve diagnostic and prognostic prediction. Secondly, we longitudinally analyzed a wide population of pre-symptomatic carriers of the c9orf72 mutation, detecting early and progressive cervical WM degeneration. Finally, we considered a cohort of SMN1-related adult SMA patients who underwent a SC and brain MRI protocol combined with MUNIX. We detected isolated cervical GM atrophy not associated with WM pathology. After 24 months observation time, significant MUNIX modifications were demonstrated, suggesting that neurophysiological techniques could be an effective biomarker of disease progression
Chan, Yiu Ming. "Statistical Analysis and Modeling of Prostate Cancer." Scholar Commons, 2013. http://scholarcommons.usf.edu/etd/4806.
Full textGonçalves, José Henrique Dias. "Estimação de Modelos de sobrevivência para tempos entre a prestação e a cobrança de serviços de regulação." Master's thesis, Instituto Superior de Economia e Gestão, 2010. http://hdl.handle.net/10400.5/2149.
Full textNo presente estudo, foram aplicados vários modelos para estimar a função de sobrevivência relativa aos tempos decorridos entre a prestação de um serviço e a sua cobrança. O estudo envolveu dados experimentais, obtidos através da base de dados dos Órgãos de Comunicação Social notificados para pagar a Taxa de Regulação e Supervisão à Entidade Reguladora para a Comunicação Social. Antes de proceder à estimação dos modelos propostos, foi introduzida uma análise detalhada dos dados, baseada em estatísticas descritivas e cruzamentos de variáveis. Ao nível da estimação, considerou-se os seguintes modelos: 1) Kaplan-Meier; 2) Modelo de Cox com hazard proporcional; 3) Exponencial; 4) Weibull; 5) Log-Logístico. Numa última fase, foi feita uma análise de resíduos utilizando a metodologia de Cox-Snell. Os resultados permitem concluir que as variáveis Valor a pagar e Ano têm um contributo importante na explicação do tempo entre a prestação de um serviço de regulação e a sua cobrança.
Diamoutene, Abdoulaye. "Contribution de la Théorie des Valeurs Extrêmes à la gestion et à la santé des systèmes." Thesis, Toulouse, INPT, 2018. http://www.theses.fr/2018INPT0139/document.
Full textThe operation of a system in general may at any time be affected by an unforeseen incident. When this incident has major consequences on the system integrity and the quality of system products, then it is said to be in the context of extreme events. Thus, increasingly researchers have a particular interest in modeling such events with studies on the reliability of systems and the prediction of the different risks that can hinder the proper functioning of a system. This thesis takes place in this very perspective. We use Extreme Value Theory (EVT) and extreme order statistics as a decision support tool in modeling and risk management in industry and aviation. Specifically, we model the surface roughness of machined parts and the reliability of the associated cutting tool with the extreme order statistics. We also did a modeling using the "Peaks-Over Threshold, POT" approach to make predictions about the potential victims in the American General Aviation (AGA) following extreme accidents. In addition, the modeling of systems subjected to environmental factors or covariates is most often carried out by proportional hazard models based on the hazard function. In proportional hazard models, the baseline risk function is typically Weibull distribution, which is a monotonic function. The analysis of the operation of some systems like the cutting tool in the industry has shown that a system can deteriorated on one phase and improving on the next phase. Hence, some modifications have been made in the Weibull distribution in order to have non-monotonic basic risk functions, more specifically, the increasing-decreasing risk function. Despite these changes, taking into account extreme operating conditions and overestimating risks are problematics. We have therefore proposed from Gumbel's standard distribution, an increasingdecreasing risk function to take into account extreme conditions, and established mathematical proofs. Furthermore, an example of the application in the field of industry was proposed. This thesis is organized in four chapters and to this must be added a general introduction and a general conclusion. In the first chapter, we recall some basic notions about the Extreme Values Theory. The second chapter focuses on the basic concepts of survival analysis, particularly those relating to reliability analysis by proposing a function of increasing-decreasing hazard function in the proportional hazard model. Regarding the third chapter, it deals with the use of extreme order statistics in industry, particularly in the detection of defective parts, the reliability of the cutting tool and the modeling of the best roughness surfaces. The last chapter focuses on the prediction of potential victims in AGA from historical data using the Peaks-Over Threshold approach
Achilonu, Okechinyere Juliet. "Modelling graft survival after kidney transplantation using semi-parametric and parametric survival models." Thesis, 2017. https://hdl.handle.net/10539/24024.
Full textThis study presents survival modelling and evaluation of risk factors of graft survival in the context of kidney transplant data generated in South Africa. Beyond the Kaplan-Meier estimator, the Cox proportional hazard (PH) model is the standard method used in identifying risk factors of graft survival after kidney transplant. The Cox PH model depends on the proportional hazard assumption, which is rarely met. Assessing and accounting for this assumption is necessary before using this model. When the PH assumption is not valid, modi cation of the Cox PH model could o er more insight into parameter estimates and the e ect of time-varying predictors at di erent time points. This study aims to identify the survival model that will e ectively describe the study data by employing the Cox PH and parametric accelerated failure time (AFT) models. To identify the risk factors that mediate graft survival after kidney transplant, secondary data involving 751 adults that received a single kidney transplant in Charlotte Maxeke Johannesburg Academic Hospital between 1984 and 2004 was analysed. The graft survival of these patients was analysed in three phases (overall, short-term and long-term) based on the follow-up times. The Cox PH and AFT models were employed to determine the signi cant risk factors. The purposeful method of variable selection based on the Cox PH model was used for model building. The performance of each model was assessed using the Cox-Snell residuals and the Akaike Information Criterion. The t of the appropriate model was evaluated using deviance residuals and the delta-beta statistics. In order to further assess how appropriately the best model t the study data for each time period, we simulated a right-censored survival data based on the model parameter-estimates. Overall, the PH assumption was violated in this study. By extending the standard Cox PH model, the resulting models out-performed the standard Cox PH model. The evaluation methods suggest that the Weibull model is the most appropriate in describing the overall graft survival, while the log-normal model is more reasonable in describing short-and long-term graft survival. Generally, the AFT models out-performed the standard Cox regression model in all the analyses. The simulation study resulted in parameter estimates comparable with the estimates from the real data. Factors that signi cantly in uenced graft survival are recipient age, donor type, diabetes, delayed graft function, ethnicity, no surgical complications, and interaction between recipient age and diabetes. Statistical inferences made from the appropriate survival model could impact on clinical practices with regards to kidney transplant in South Africa. Finally, limitations of the study are discussed in the context of further studies.
MT 2018
Li, Weihong. "Informative Random Censoring in Parametric Survival Models." Master's thesis, 2009. http://hdl.handle.net/10048/651.
Full textBiostatistics
Bahakeem, Shaher. "Will Mortality Rate of HIV-Infected Patients Decrease After Starting Antiretroviral Therapy (ART)?" Thesis, 2020. http://hdl.handle.net/1805/23574.
Full textBackground: Many authors have indicated that HIV-infected patients mortality risk is higher immediately following the start of Antiretroviral Therapy. However, mortality rate of HIV-infected patients is expected to decrease after starting Antiretroviral Therapy (ART) potentially complicating accurate statistical estimation of patient survival and, more generally, effective monitoring of the evolution of the worldwide epidemic. Method: In this thesis, we determine if mortality of HIV-patients increases or decreases after the initiation of ART therapy using flexible survival modelling techniques. To achieve this objective, this study uses semi-parametric statistical models for fitting and estimating survival time using different covariates. A combination of the Weibull distribution with splines is compared to the usual Weibull, exponential, and gamma distribution parametric models, and the Cox semi-parametric model. The objective of this study is to compare these models to find the best fitting model so that it can then be used to improve modeling of the survival time and explore the pattern of change in mortality rates for a cohort of HIV-infected patients recruited in a care and treatment program in Uganda. Results: The analysis shows that flexible survival Weibull models are better than usualoff-parametric and semi-parametric model fitting according to the AIC criterion. Conclusion: The mortality of HIV-patients is high right after the initiation of ART therapy and decreases rapidly subsequently.
He, Zhisheng, and 何致晟. "Parametric likelihood inference with censored survival data under the COM-Poisson cure models." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/a248zt.
Full text國立中央大學
統計研究所
105
Rodrigues et al. (2009) proposed the Conway-Maxwell-Poisson (COM-Poisson) distribution as a model for a cure rate in censored survival data. We consider computational algorithms for maximum likelihood estimation under the Bernoulli cure rate model, a special case of the COM-Poisson cure rate model. The Weibull distribution (Balakrishnan and Pal 2016) and the generalized gamma distribution (Balakrishnan and Pal 2015) are considered as lifetime distributions. We obtain all the expressions of the score function and Hessian matrix to perform the Newton-Raphson and EM algorithms. Simulations are conducted to compare the performance between the EM algorithm and Newton-Raphson algorithms. Finally, a real data is analyzed to illustrate the methods.
Cheng, Yu-Chieh, and 鄭宇傑. "A Semi-Parametric Survival Extrapolation Method: Model Validation Using RERF Cohort." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/74322071472277291903.
Full text國立臺灣大學
流行病學與預防醫學研究所
99
Background How long can a human immunodeficiency virus (HIV)-infected patient live is a crucial question, especially for the evaluation of the cost-effectiveness of medical interventions. A semi-parametric survival extrapolation method has been developed based on a logit survival ratio W between a patient cohort and a reference population. If the excess hazard of a specific disease/exposure remains constant, then the logit survival ratio curve will converge to a straight line over time, which allows linear extrapolation to estimate survival beyond the follow-up time. The accuracy of short-term projection has been validated, while the validity and accuracy of life-long projection remains unclear. Method and Principal Findings We used a subset of the Life Span Study (LSS) cohort, which comprised atomic bomb survivors from Hiroshima and Nagasaki and is one of the longest follow-up data cohorts in the world. With this dataset, we tested the validity and accuracy of life-long semi-parametric extrapolation as well as developed mathematical criteria for applying this method to data of limited sample size. We first proved the biological premise that disease/exposure is associated with premature mortality when compared with age- and gender-matched general populations, which is mathematically equivalent to a negative slope in the logit W plot at all times. In addition, we developed a slope-time diagnostic plot. Using those cohort members with >1000 mGy radiation exposure as the index group, we found that (1) the logit W curve continued to converge toward zero at the end of a 48-year follow-up, which indicated that extrapolation based on the right end of the curve should provide a more accurate estimate than that based on the central part of the curve; (2) the slope of the logit W curve can have large random variation if the length of time used for regression is short, such as 6 months, and the diagnostic plot allows users to select the shortest time length that provides a stable slope estimation; (3) a 38-year extrapolation from the end of the 10 year (1950–1960) follow-up data, using the above-stated criteria to select the length of time and the time period for regression, yielded an accurate projection in comparison with the actual 38-year follow-up (1960–1998) data if the cohort members without radiation exposure were used as the source of reference. If the 1960 life table is used as the source of reference, then the projection will underestimate the true long-term survival due to the discrepancy between the time period and the cohort life expectancy. Conclusion Long-term semi-parametric survival extrapolation can be valid and accurate. The recommended steps in applying this methodology are as follows: 1.Create a logit W(t) plot from the follow-up data. 2.Create Slope-Time diagnostic plots using different lengths of time (for example: 6, 12, 24, 36, and 48 months) for regression. Select the shortest length of time that provides stable slope estimation without significant random variations. 3.For the selected diagnostic plot, exclude the time periods with positive slopes and find the time period as close to the end of the follow-up time as possible to obtain the best slope estimate for extrapolation.
Martínez, Vargas Danae Mirel. "Régression de Cox avec partitions latentes issues du modèle de Potts." Thèse, 2019. http://hdl.handle.net/1866/22552.
Full textHsu, Ren-hua, and 徐人華. "Semi-parametric Joint Model with Generalized Gamma Frailty for Recurrent Event Survival Analysis." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/08757712158244797331.
Full text國立中央大學
統計研究所
103
In this study, we establish a more general semi-parametric joint model, which can deal with not only the single event but also the multiple events. We use the unspecified baseline hazard with Cox proportional hazards model or accelerated failure time model to fit the multiple event times with correlation between the events described by shared frailty model. We assume that frailty factor is from the generalized gamma distribution. When estimating the parameters, we treat the random effects from linear mixed effect model and shared frailty model as missing values, thus expectation-maximization algorithm can be implemented to find the maximum likelihood estimates. In E-step, Monte Carlo integration method is used to approximate complex integrals. In M-step, we adopt Nelder-Mead simplex method to find the maximum likelihood estimates. AIDS data is used to demonstrate the usefulness of the proposed method.