Inference About The Generalized Exponential Quantiles Based On Progressively Type-Ii Censored Data

In this study, we are interested in investigating the performance of likelihood inference procedures for the ℎ quantile of the Generalized Exponential distribution based on progressively censored data. The maximum likelihood estimator and three types of classical confidence intervals have been considered, namely asymptotic, percentile, and bootstrap-t confidence intervals. We considered Bayesian inference too. The Bayes estimator based on the squared error loss function and two types of Bayesian intervals were considered, namely the equal tailed interval and the highest posterior density interval. We conducted simulation studies to investigate and compare the point estimators in terms of their biases and mean squared errors. We compared the various types of intervals using their coverage probability and expected lengths. The simulations and comparisons were made under various types of censoring schemes and sample sizes. We presented two examples for data analysis, one of them is based on simulated data set and the other one based on a real lifetime data. Finally, we compared the classical inference and the Bayesian inference procedures. We concluded that Bias and MSE for classical statistics estimators show bitter results than the Bayesian estimators. Also, Bayesian intervals which attain the nominal error rate have the best average widths. We presented our conclusions and discussed ideas for possible future research

Semi-parametric methods for personalized treatment selection and multi-state models.

This dissertation contains three research projects on personalized medicine and a project on multi-state modelling. The idea behind personalized medicine is selecting the best treatment that maximizes interested clinical outcomes of an individual based on his or her genetic and genomic information. We propose a method for treatment assignment based on individual covariate information for a patient. Our method covers more than two treatments and it can be applied with a broad set of models and it has very desirable large sample properties. An empirical study using simulations and a real data analysis show the applicability of the proposed procedure. We then extend this idea for treatment section for survival outcomes under right-censoring by introducing re-weighted estimation to adjust the bias caused by censoring. Series of empirical studies using simulations show the desirable performance of re-weighted estimation concept in treatment selection in finite sample cases. We provide a real data application of the proposed procedure to illustrate the applicability for right-censored data. Next we propose a novel method for individualized treatment selection when the treatment response is multivariate. The proposed method uses a rank aggregation technique to estimate an ordering of treatments based on ranked lists of treatment performance measures such as smooth conditional means and conditional probability of a response for one treatment dominating others. An empirical study demonstrates very desirable performances of the proposed method in finite sample cases. We also present a data analysis using a HIV clinical trial data to show the applicability of the proposed procedure for real data. Multi-state models are extensions of simple survival models that incorporate the progression of a subject in an interconnected system such as a disease network. An important measure arising from a mutistate model is the subjects’ state occupational probabilities given baseline covariates. In the final portion of this dissertation we introduce an inverse censoring probability re-weighted semi-parametric single index model based approach to estimate conditional state occupation probabilities of a given individual in an acyclic multistate model under right-censoring. Besides obtaining a temporal regression function, we also test the potentially time varying effect of a baseline covariate on future state occupations. We show that the proposed technique has desirable finite sample performances. Its performance is competitive when compared with two other existing approaches. We illustrate the proposed methodology using two different data sets. First we re-examine a well known data set on various event times tracking the progression of a sample of leukemia patients undergoing bone marrow transplant. Our second illustration is based on the functional status of a set of spinal cord injured patients undergoing a rehabilitation program

Order-statistics-based inferences for censored lifetime data and financial risk analysis

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.This thesis focuses on applying order-statistics-based inferences on lifetime analysis and financial risk measurement. The first problem is raised from fitting the Weibull distribution to progressively censored and accelerated life-test data. A new orderstatistics- based inference is proposed for both parameter and con dence interval estimation. The second problem can be summarised as adopting the inference used in the first problem for fitting the generalised Pareto distribution, especially when sample size is small. With some modifications, the proposed inference is compared with classical methods and several relatively new methods emerged from recent literature. The third problem studies a distribution free approach for forecasting financial volatility, which is essentially the standard deviation of financial returns. Classical models of this approach use the interval between two symmetric extreme quantiles of the return distribution as a proxy of volatility. Two new models are proposed, which use intervals of expected shortfalls and expectiles, instead of interval of quantiles. Different models are compared with empirical stock indices data. Finally, attentions are drawn towards the heteroskedasticity quantile regression. The proposed joint modelling approach, which makes use of the parametric link between the quantile regression and the asymmetric Laplace distribution, can provide estimations of the regression quantile and of the log linear heteroskedastic scale simultaneously. Furthermore, the use of the expectation of the check function as a measure of quantile deviation is discussed

Optimal Experimental Planning of Reliability Experiments Based on Coherent Systems

In industrial engineering and manufacturing, assessing the reliability of a product or system is an important topic. Life-testing and reliability experiments are commonly used reliability assessment methods to gain sound knowledge about product or system lifetime distributions. Usually, a sample of items of interest is subjected to stresses and environmental conditions that characterize the normal operating conditions. During the life-test, successive times to failure are recorded and lifetime data are collected. Life-testing is useful in many industrial environments, including the automobile, materials, telecommunications, and electronics industries. There are different kinds of life-testing experiments that can be applied for different purposes. For instance, accelerated life tests (ALTs) and censored life tests are commonly used to acquire information in reliability and life-testing experiments with the presence of time and resource limitations. Statistical inference based on the data obtained from a life test and effectively planning a life-testing experiment subject to some constraints are two important problems statisticians are interested in. The experimental design problem for a life test has long been studied; however, the experimental planning considering putting the experimental units into systems for a life-test has not been studied. In this thesis, we study the optimal experimental planning problem in multiple stress levels life-testing experiments and progressively Type-II censored life-testing experiments when the test units can be put into coherent systems for the experiment. Based on the notion of system signature, a tool in structure reliability to represent the structure of a coherent system, under different experimental settings, models and assumptions, we derive the maximum likelihood estimators of the model parameters and the expected Fisher information matrix. Then, we use the expected Fisher information matrix to obtain the asymptotic variance-covariance matrix of the maximum likelihood estimators when $n$-component coherent systems are used in the life-testing experiment. Based on different optimality criteria, such as $D$-optimality, $A$-optimality and $V$-optimality, we obtain the optimal experimental plans under different settings. Numerical and Monte Carlo simulation studies are used to demonstrate the advantages and disadvantages of using systems in life-testing experiments

Contrubutions to the Analysis of Multistate and Degradation Data

Traditional methods in survival, reliability, actuarial science, risk, and other event-history applications are based on the analysis of time-to-occurrence of some event of interest, generically called ``failure''. In the presence of high-degrees of censoring, however, it is difficult to make inference about the underlying failure distribution using failure time data. Moreover, such data are not very useful in predicting failures of specific systems, a problem of interest when dealing with expensive or critical systems. As an alternative, there is an increasing trend towards collecting and analyzing richer types of data related to the states and performance of systems or subjects under study. These include data on multistate and degradation processes. This dissertation makes several contributions to the analysis of multistate and degradation data. The first part of the dissertation deals with parametric inference for multistate processes with panel data. These include interval, right, and left censoring, which arise naturally as the processes are not observed continuously. Most of the literature in this area deal with Markov models, for which inference with censored data can be handled without too much difficulty. The dissertation considers progressive semi-Markov models and develops methods and algorithms for general parametric inference. A combination of Markov Chain Monte Carlo techniques and stochastic approximation methods are used. A second topic deals with the comparison of the traditional method and the process method for inference about the time-to-failure distribution in the presence of multistate data. Here, time-to-failure is the time when the process enters an absorbing state. There is limited literature in this area. The gains in both estimation and prediction efficiency are quantified for various parametric models of interest. The second part of the dissertation deals with the analysis of data on continuous measures of performance and degradation with missing data. In this case, time-to-failure is the time at which the degradation measure exceeds a certain threshold or performance level goes below some threshold. Inference problems about the mean and variance of the degradation and the imputation of the missing are studied under different settings.Ph.D.StatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/86286/1/yangcn_1.pd

Inference for a General Class of Models for Recurrent Events with application to cancer data

La necesidad del análisis de supervivencia aparece cuando necesitamos estudiar las propiedades estadísticas de una variable que describe el tiempo hasta que ocurre un evento único. En algunas ocasiones, podemos observar que el evento de interés ocurre repetidamente en un mismo individuo, como puede ser el caso de un paciente diagnosticado de cáncer que recae a lo largo del tiempo o cuando una persona es reingresada repetidas veces en un hospital. En este caso hablamos de análisis de supervivencia con eventos recurrentes. La naturaleza recurrente de los eventos hace necesario el uso de otras técnicas distintas a aquellas que utilizamos cuando analizamos tiempos de supervivencia para un evento único. En esta tesis, tratamos este tipo de análisis principalmente motivados por dos estudios en investigación en cáncer que fueron creados especialmente para este trabajo. Uno de ellos hace referencia a un estudio sobre readmisiones hospitalarias en pacientes diagnosticados con cáncer colorectal, mientras que el otro hace referencia a pacientes diagnosticados con linfomas no Hodgkinianos. Este último estudio es especialmente relevante ya que incluimos información sobre el efecto del tratamiento después de las recaídas y algunos autores han mostrado la necesidad de desarrollar un modelo específico para pacientes que presentan este tipo de enfermedades. Nuestra contribución al análisis univariante es proponer un método para construir intervalos de confianza para la mediana de supervivencia en el caso de eventos recurrentes. Para ello, hemos utilizado dos aproximaciones. Una de ellas se basa en las varianzas asintóticas derivadas de dos estimadores existentes de la función de supervivencia, mientras que el otro utiliza técnicas de remuestreo. Esta última aproximación es útil ya que uno de los estimadores utilizados todavía no tiene una forma cerrada para su varianza. La nueva contribución de este trabajo es el estudio de cómo hacer remuestreo en la presencia de datos con eventos recurrentes que aparecen de un esquema conocido como --sum-quota accrual" y la informatividad del mecanismo de censura por la derecha que presentan este tipo de datos. Demostramos la convergencia d bil y los intervalos de confianza asintóticos se construyen utilizando dicho resultado. Por otro lado, el análisis multivariante trata el problema de cómo incorporar más de una covariable en el análisis. En problemas con eventos recurrentes, también necesitamos tener en cuenta que además de las covariables, la hetereogeneidad, el número de ocurrencias, o especialmente, el efecto de las intervenciones después de las reocurrencias puede modificar la probabilidad de observar un nuevo evento en un paciente. Este último punto es muy importante ya que todavía no se ha tenido en cuenta en estudios biomédicos. Para tratar este problema, hemos basado nuestro trabajo en un nuevo modelo para eventos recurrentes propuesto por Peña y Hollander, 2004. Nuestra contribución a este punto es la adaptación de las recaídas en cáncer utilizando este modelo en el que el efecto de las intervenciones se representa mediante un proceso llamado --edad efectiva' que actúa sobre la función de riesgo basal. Hemos llamado a este modelo modelo dinámico de cáncer (--dynamic cancer model'). También tratamos el problema de la estimación de parámetros de la clase general de modelos para eventos recurrentes propuesta por Peña y Hollander donde el modelo dinámico de cáncer se puede ver como un caso especial de este modelo general. Hemos desarrollado dos aproximaciones. La primera se basa en inferencia semiparamétrica, donde la función de riesgo basal se especifica de forma no paramétrica y usamos el algoritmo EM. La segunda es una aproximación basada en verosimilitud penalizada donde adoptamos dos estrategias diferentes. Una de ellas se basa en penalizar la verosimilitud parcial donde la penalización recae en los coeficientes de regresión. La segunda penaliza la verosimilitud completa y da una estimación no paramétrica de la función de riesgo basal utilizando un estimador continuo. La solución se aproxima utilizando splines. La principal ventaja de este método es que podemos obtener fácilmente una estimación suave de la función de riesgo así como una estimación de la varianza de la varianza de la fragilidad, mientras que con las otras aproximaciones esto no es posible. Además este último método presenta un coste computacional bastante más bajo que los otros. Los resultados obtenidos con datos reales, indican que la flexibilidad de este modelo es una garantía para analizar datos de pacientes que recaen a lo largo del tiempo y que son intervenidos después de las recaídas tumorales.El aspecto computacional es otra de las contribuciones importantes de esta tesis al campo de los eventos recurrentes. Hemos desarrollado tres paquete de R llamados survrec, gcmrec y frailtypack que están accesibles en CRAN, http://www.r-project.org/. Estos paquetes permiten al usuario calcular la mediana de supervivencia y sus intervalos de confianza, estimar los par metros del modelo de Peña y Hollander (en particular el modelo dinámico de cáncer) utilizando el algoritmo EM y la verosimilitud penalizada, respectivamente.Survival analysis arises when we are interested in studying statistical properties of a variable which describes the time to a single event. In some situations, we may observe that the event of interest occurs repeatedly in the same individual, such as when a patient diagnosed with cancer tends to relapse over time or when a person is repeatedly readmitted in a hospital. In this case we speak about survival analysis with recurrent events. Recurrent nature of events makes necessary to use other techniques from those used when we analyze survival times from one single event. In this dissertation we deal with this type of analysis mainly motivatedby two studies on cancer research that were created specially for this research. One of them belongs to a study on hospital readmissions in patients diagnosed with colorectal cancer, while the other one deals with patients diagnosed with non-Hodgkin's lymphoma. This last study is mainly relevant since we include information about the effect of treatment after relapses and some authors have stated the needed of developing a specific model for relapsing patients in cancer settings.Our first contribution to univariate analysis is to propose a method to construct confidence intervals for the median survival time in the case of recurrent event settings. Two different approaches are developed. One of them is based on asymptotic variances derived from two existing estimators of survival function, while the other one uses bootstrap techniques. This last approach is useful since one of the estimators used, does not have any closed form for its variance yet. The new contribution to this work is the examination of the question of how to do bootstrapping in the presence of recurrent event data arising from a sum-quota accrual scheme and informativeness of right censoring mechanism. Weak convergence is proved and asymptotic confidence intervals are built to according this result. On the other hand, multivariate analysis addresses the problem of how incorporate more than one covariate in the analysis. In recurrent event settings, we also need to take into account that apart from covariates, the heterogeneity, the number of occurrences or specially, the effect of interventions after re occurrences may modify the probability of observing a new event in a patient. This last point is a very important one since it has not been taken into consideration in biomedical studies yet. To address this problem, we base our work on a new model for recurrent events proposed by Peña and Hollander. Our contribution to this topic is to accommodate the situation of cancer relapses to this model model in which the effect of interventions is represented by an effective age process acting on the baseline hazard function. We call this model dynamic cancer model.We also address the problem of estimating parameters of the general class of models for recurrent events proposed by Peña and Hollander, 2004, where the dynamic cancer model may be seen as a special case of this general model. Two general approaches are developed. First approach is based on semiparametric inference, where a baseline hazard function is nonparametrically specified and uses the EM algorithm. The second one is a penalized likelihood approach where two different strategies are adopted. One of them is based on penalizing the partial likelihood where the penalization bears on a regression coefficient. The second penalized approach penalized full likelihood, and it gives a non parametric estimation of the baseline hazard function using a continuous estimator. The solution is then approximated using splines. The main advantage of this method is that we caneasily obtain smooth estimates of the hazard function and an estimation of the variance of frailty variance, while in the other approaches this is not possible. In addition, this last approach has a quite less computational cost than the other ones. The results obtained using dynamic cancer model in real data sets, indicate that the flexibility of this method provides a safeguard for analyzing data where patients relapse over time and interventions are performed after tumoral reoccurrences.Computational issue is another important contribution of this work to recurrent event settings. We have developed three R packages called survrec, gcmrec, and frailtypack that are available at CRAN, http://www.r-project.org/. These packages allow users to compute median survival time and their confidence intervals, to estimate the parameters involved in the Peña and Hollander's model (in particular in the dynamic cancer model) using EM algorithm, and to estimate this parameters using penalized approach, respectively.Postprint (published version

Robust Methods for Interval-Censored Life History Data

Interval censoring arises frequently in life history data, as individuals are often only observed at a sequence of assessment times. This leads to a situation where we do not know when an event of interest occurs, only that it occurred somewhere between two assessment times. Here, the focus will be on methods of estimation for recurrent event data, current status data, and multistate data, subject to interval censoring. With recurrent event data, the focus is often on estimating the rate and mean functions. Nonparametric estimates are readily available, but are not smooth. Methods based on local likelihood and the assumption of a Poisson process are developed to obtain smooth estimates of the rate and mean functions without specifying a parametric form. Covariates and extra-Poisson variation are accommodated by using a pseudo-profile local likelihood. The methods are assessed by simulations and applied to a number of datasets, including data from a psoriatic arthritis clinic. Current status data is an extreme form of interval censoring that occurs when each individual is observed at only one assessment time. If current status data arise in clusters, this must be taken into account in order to obtain valid conclusions. Copulas offer a convenient framework for modelling the association separately from the margins. Estimating equations are developed for estimating marginal parameters as well as association parameters. Efficiency and robustness to the choice of copula are examined for first and second order estimating equations. The methods are applied to data from an orthopedic surgery study as well as data on joint damage in psoriatic arthritis. Multistate models can be used to characterize the progression of a disease as individuals move through different states. Considerable attention is given to a three-state model to characterize the development of a back condition known as spondylitis in psoriatic arthritis, along with the associated risk of mortality. Robust estimates of the state occupancy probabilities are derived based on a difference in distribution functions of the entry times. A five-state model which differentiates between left-side and right-side spondylitis is also considered, which allows us to characterize what effect spondylitis on one side of the body has on the development of spondylitis on the other side. Covariate effects are considered through multiplicative time homogeneous Markov models. The robust state occupancy probabilities are also applied to data on CMV infection in patients with HIV

On Optimal Designs of Some Censoring Schemes

The main objective of this paper  is to explore suitability of some entropy-information measures for introducing a new optimality censoring criterion and to apply it to some censoring schemes from some underlying life-time models.  In addition, the  paper investigates four related issues namely; the  effect of the parameter of parent distribution on optimal scheme, equivalence of schemes based on Shannon and Awad sup-entropy measures, the conjecture that the optimal scheme is one stage scheme, and  a conjecture by Cramer and Bagh (2011) about Shannon minimum and maximum schemes when parent distribution is reflected power. Guidelines for designing an optimal censoring plane are reported together with theoretical and numerical results and illustrations

Inference for a General Class of Models for Recurrent Events with application to cancer data

La necesidad del análisis de supervivencia aparece cuando necesitamos estudiar las propiedades estadísticas de una variable que describe el tiempo hasta que ocurre un evento único. En algunas ocasiones, podemos observar que el evento de interés ocurre repetidamente en un mismo individuo, como puede ser el caso de un paciente diagnosticado de cáncer que recae a lo largo del tiempo o cuando una persona es reingresada repetidas veces en un hospital. En este caso hablamos de análisis de supervivencia con eventos recurrentes. La naturaleza recurrente de los eventos hace necesario el uso de otras técnicas distintas a aquellas que utilizamos cuando analizamos tiempos de supervivencia para un evento único. En esta tesis, tratamos este tipo de análisis principalmente motivados por dos estudios en investigación en cáncer que fueron creados especialmente para este trabajo. Uno de ellos hace referencia a un estudio sobre readmisiones hospitalarias en pacientes diagnosticados con cáncer colorectal, mientras que el otro hace referencia a pacientes diagnosticados con linfomas no Hodgkinianos. Este último estudio es especialmente relevante ya que incluimos información sobre el efecto del tratamiento después de las recaídas y algunos autores han mostrado la necesidad de desarrollar un modelo específico para pacientes que presentan este tipo de enfermedades. Nuestra contribución al análisis univariante es proponer un método para construir intervalos de confianza para la mediana de supervivencia en el caso de eventos recurrentes. Para ello, hemos utilizado dos aproximaciones. Una de ellas se basa en las varianzas asintóticas derivadas de dos estimadores existentes de la función de supervivencia, mientras que el otro utiliza técnicas de remuestreo. Esta última aproximación es útil ya que uno de los estimadores utilizados todavía no tiene una forma cerrada para su varianza. La nueva contribución de este trabajo es el estudio de cómo hacer remuestreo en la presencia de datos con eventos recurrentes que aparecen de un esquema conocido como --sum-quota accrual" y la informatividad del mecanismo de censura por la derecha que presentan este tipo de datos. Demostramos la convergencia d bil y los intervalos de confianza asintóticos se construyen utilizando dicho resultado. Por otro lado, el análisis multivariante trata el problema de cómo incorporar más de una covariable en el análisis. En problemas con eventos recurrentes, también necesitamos tener en cuenta que además de las covariables, la hetereogeneidad, el número de ocurrencias, o especialmente, el efecto de las intervenciones después de las reocurrencias puede modificar la probabilidad de observar un nuevo evento en un paciente. Este último punto es muy importante ya que todavía no se ha tenido en cuenta en estudios biomédicos. Para tratar este problema, hemos basado nuestro trabajo en un nuevo modelo para eventos recurrentes propuesto por Peña y Hollander, 2004. Nuestra contribución a este punto es la adaptación de las recaídas en cáncer utilizando este modelo en el que el efecto de las intervenciones se representa mediante un proceso llamado --edad efectiva' que actúa sobre la función de riesgo basal. Hemos llamado a este modelo modelo dinámico de cáncer (--dynamic cancer model'). También tratamos el problema de la estimación de parámetros de la clase general de modelos para eventos recurrentes propuesta por Peña y Hollander donde el modelo dinámico de cáncer se puede ver como un caso especial de este modelo general. Hemos desarrollado dos aproximaciones. La primera se basa en inferencia semiparamétrica, donde la función de riesgo basal se especifica de forma no paramétrica y usamos el algoritmo EM. La segunda es una aproximación basada en verosimilitud penalizada donde adoptamos dos estrategias diferentes. Una de ellas se basa en penalizar la verosimilitud parcial donde la penalización recae en los coeficientes de regresión. La segunda penaliza la verosimilitud completa y da una estimación no paramétrica de la función de riesgo basal utilizando un estimador continuo. La solución se aproxima utilizando splines. La principal ventaja de este método es que podemos obtener fácilmente una estimación suave de la función de riesgo así como una estimación de la varianza de la varianza de la fragilidad, mientras que con las otras aproximaciones esto no es posible. Además este último método presenta un coste computacional bastante más bajo que los otros. Los resultados obtenidos con datos reales, indican que la flexibilidad de este modelo es una garantía para analizar datos de pacientes que recaen a lo largo del tiempo y que son intervenidos después de las recaídas tumorales.El aspecto computacional es otra de las contribuciones importantes de esta tesis al campo de los eventos recurrentes. Hemos desarrollado tres paquete de R llamados survrec, gcmrec y frailtypack que están accesibles en CRAN, http://www.r-project.org/. Estos paquetes permiten al usuario calcular la mediana de supervivencia y sus intervalos de confianza, estimar los par metros del modelo de Peña y Hollander (en particular el modelo dinámico de cáncer) utilizando el algoritmo EM y la verosimilitud penalizada, respectivamente.Survival analysis arises when we are interested in studying statistical properties of a variable which describes the time to a single event. In some situations, we may observe that the event of interest occurs repeatedly in the same individual, such as when a patient diagnosed with cancer tends to relapse over time or when a person is repeatedly readmitted in a hospital. In this case we speak about survival analysis with recurrent events. Recurrent nature of events makes necessary to use other techniques from those used when we analyze survival times from one single event. In this dissertation we deal with this type of analysis mainly motivatedby two studies on cancer research that were created specially for this research. One of them belongs to a study on hospital readmissions in patients diagnosed with colorectal cancer, while the other one deals with patients diagnosed with non-Hodgkin's lymphoma. This last study is mainly relevant since we include information about the effect of treatment after relapses and some authors have stated the needed of developing a specific model for relapsing patients in cancer settings.Our first contribution to univariate analysis is to propose a method to construct confidence intervals for the median survival time in the case of recurrent event settings. Two different approaches are developed. One of them is based on asymptotic variances derived from two existing estimators of survival function, while the other one uses bootstrap techniques. This last approach is useful since one of the estimators used, does not have any closed form for its variance yet. The new contribution to this work is the examination of the question of how to do bootstrapping in the presence of recurrent event data arising from a sum-quota accrual scheme and informativeness of right censoring mechanism. Weak convergence is proved and asymptotic confidence intervals are built to according this result. On the other hand, multivariate analysis addresses the problem of how incorporate more than one covariate in the analysis. In recurrent event settings, we also need to take into account that apart from covariates, the heterogeneity, the number of occurrences or specially, the effect of interventions after re occurrences may modify the probability of observing a new event in a patient. This last point is a very important one since it has not been taken into consideration in biomedical studies yet. To address this problem, we base our work on a new model for recurrent events proposed by Peña and Hollander. Our contribution to this topic is to accommodate the situation of cancer relapses to this model model in which the effect of interventions is represented by an effective age process acting on the baseline hazard function. We call this model dynamic cancer model.We also address the problem of estimating parameters of the general class of models for recurrent events proposed by Peña and Hollander, 2004, where the dynamic cancer model may be seen as a special case of this general model. Two general approaches are developed. First approach is based on semiparametric inference, where a baseline hazard function is nonparametrically specified and uses the EM algorithm. The second one is a penalized likelihood approach where two different strategies are adopted. One of them is based on penalizing the partial likelihood where the penalization bears on a regression coefficient. The second penalized approach penalized full likelihood, and it gives a non parametric estimation of the baseline hazard function using a continuous estimator. The solution is then approximated using splines. The main advantage of this method is that we caneasily obtain smooth estimates of the hazard function and an estimation of the variance of frailty variance, while in the other approaches this is not possible. In addition, this last approach has a quite less computational cost than the other ones. The results obtained using dynamic cancer model in real data sets, indicate that the flexibility of this method provides a safeguard for analyzing data where patients relapse over time and interventions are performed after tumoral reoccurrences.Computational issue is another important contribution of this work to recurrent event settings. We have developed three R packages called survrec, gcmrec, and frailtypack that are available at CRAN, http://www.r-project.org/. These packages allow users to compute median survival time and their confidence intervals, to estimate the parameters involved in the Peña and Hollander's model (in particular in the dynamic cancer model) using EM algorithm, and to estimate this parameters using penalized approach, respectively