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Fertility progression in Germany: An analysis using flexible nonparametric cure survival models ; ; Lambert, Philippe E-print/Working paper (2016) - Objective - This paper uses data from the German Socio-Economic Panel (GSOEP) to study the transition to second and third births. In particular, we seek to distinguish the factors that determine the ... [more ▼] - Objective - This paper uses data from the German Socio-Economic Panel (GSOEP) to study the transition to second and third births. In particular, we seek to distinguish the factors that determine the timing of fertility from the factors that influence ultimate parity progression. - Methods - As a method, we employ cure survival models, a technique that is commonly used in epidemiological studies and in the statistical literature, but is only rarely applied to fertility research. - Results - We find that education has a different impact on the timing and the ultimate probability of having a second and a third birth. Furthermore, we show that the shape of the fertility schedule for the total population differs from that of “susceptible women” (i.e., those who have a second or a third child). - Conclusion - Standard event history models conflate timing and quantum effects. Our approach overcomes this shortcoming. It estimates separate parameters for the hazard rate of having a next child for the “susceptible population,” and the ultimate probability of having another child for the entire population at risk. - Contribution - We go beyond standard cure survival models (also known as split population models) used in fertility research by specifying a flexible non-parametric model (using Bayesian P-splines) for the latent distribution (related to the timing of an extra birth), instead of a parametric model. Our approach is (so far) limited to time-constant covariates, but can be extended to include time-varying covariates as well. [less ▲] Detailed reference viewed: 36 (3 ULg)Flexible estimation in cure survival models using Bayesian P-splines ; Lambert, Philippe in Computational Statistics & Data Analysis (2016), 93 In the analysis of survival data, it is usually assumed that any unit will experience the event of interest if it is observed for a sufficiently long time. However, it can be explicitly assumed that an ... [more ▼] In the analysis of survival data, it is usually assumed that any unit will experience the event of interest if it is observed for a sufficiently long time. However, it can be explicitly assumed that an unknown proportion of the population under study will never experience the monitored event. The promotion time model, which has a biological motivation, is one of the survival models taking this feature into account. The promotion time model assumes that the failure time of each subject is generated by the minimum of N independent latent event times with a common distribution independent of N. An extension which allows the covariates to influence simultane- ously the probability of being cured and the latent distribution is presented. The latent distribution is estimated using a flexible Cox proportional hazard model where the logarithm of the baseline hazard function is specified using Bayesian P-splines. Introducing covariates in the latent distribution implies that the population hazard function might not have a proportional hazard structure. However, the use of P- splines provides a smooth estimation of the population hazard ratio over time. The identification issues of the model are discussed and a restricted use of the model when the follow up of the study is not sufficiently long is proposed. The accuracy of our methodology is evaluated through a simulation study and the model is illustrated on data from a Melanoma clinical trial. [less ▲] Detailed reference viewed: 27 (4 ULg)Parameter estimation and inference in dynamic systems described by linear partial differential equations Frasso, Gianluca ; ; Lambert, Philippe in AStA Advances in Statistical Analysis (2015) Differential equations (DEs) are commonly used to describe dynamic sys- tems evolving in one (ordinary differential equations or ODEs) or in more than one dimensions (partial differential equations or ... [more ▼] Differential equations (DEs) are commonly used to describe dynamic sys- tems evolving in one (ordinary differential equations or ODEs) or in more than one dimensions (partial differential equations or PDEs). In real data applications, the para- meters involved in the DE models are usually unknown and need to be estimated from the available measurements together with the state function. In this paper, we present frequentist and Bayesian approaches for the joint estimation of the parameters and of the state functions involved in linear PDEs. We also propose two strategies to include state (initial and/or boundary) conditions in the estimation procedure. We evaluate the performances of the proposed strategy through simulated examples and a real data analysis involving (known and necessary) state conditions. [less ▲] Detailed reference viewed: 48 (17 ULg)A Bayesian model for the Ebola epidemic in Sierra Leone Frasso, Gianluca ; Lambert, Philippe ; Bonou, Wilfried in Friedl, Herwig; Wagner, Helga (Eds.) 30th International Workshop on Statistical Modelling, Linz, Austria, 2015, Proceedings (2015, July) We propose a Bayesian model for the analysis of the 2014 ebola out- break in Sierra Leone. It is based on an extension of the popular compartmental SEIR model speci ed using a system of di erential ... [more ▼] We propose a Bayesian model for the analysis of the 2014 ebola out- break in Sierra Leone. It is based on an extension of the popular compartmental SEIR model speci ed using a system of di erential equations. [less ▲] Detailed reference viewed: 5 (3 ULg)Bayesian inference in an extended SEIR model with nonparametric disease transmission rate: an application to the Ebola epidemic in Sierra Leone Frasso, Gianluca ; Lambert, Philippe E-print/Working paper (2015) The 2014 Ebola outbreak in Sierra Leone is analyzed using an extension of the SEIR compartmental model. The unknown parameters of the system of differential equations are estimated by combining data on ... [more ▼] The 2014 Ebola outbreak in Sierra Leone is analyzed using an extension of the SEIR compartmental model. The unknown parameters of the system of differential equations are estimated by combining data on the number of new (laboratory confirmed) Ebola cases reported by the Ministry of Health and prior distributions for the transition rates elicited using information collected by the WHO Response Team (2014) during the follow-up of specific Ebola cases. The evolution over time of the disease transmission rate is modeled nonparametrically using penalized B-splines. Our framework represents a valuable and robust stochastic tool for the study of an epidemic dynamic from irregular and possibly aggregated case data. Simulations and the analysis of the 2014 Sierra Leone Ebola data highlight the merits of the proposed methodology. [less ▲] Detailed reference viewed: 102 (34 ULg)Inference in dynamic systems using B-splines and quasilinearized ODE penalties Frasso, Gianluca ; ; Lambert, Philippe in Biometrical Journal (2015) Nonlinear (systems of) ordinary differential equations (ODEs) are common tools in the analysis of complex one-dimensional dynamic systems.We propose a smoothing approach regularized by a quasilinearized ... [more ▼] Nonlinear (systems of) ordinary differential equations (ODEs) are common tools in the analysis of complex one-dimensional dynamic systems.We propose a smoothing approach regularized by a quasilinearized ODE-based penalty. Within the quasilinearized spline-based framework, the estimation reduces to a conditionally linear problem for the optimization of the spline coefficients. Furthermore, standard ODE compliance parameter(s) selection criteria are applicable.We evaluate the performances of the proposed strategy through simulated and real data examples. Simulation studies suggest that the proposed procedure ensures more accurate estimates than standard nonlinear least squares approaches when the state (initial and/or boundary) conditions are not known. [less ▲] Detailed reference viewed: 4 (2 ULg)Modelling the potential of focal screening and treatment as elimination strategy for Plasmodium falciparum malaria in the Peruvian Amazon Region ; ; et al in Parasites & Vectors (2015), 8(1), 261 BACKGROUND:Focal screening and treatment (FSAT) of malaria infections has recently been introduced in Peru to overcome the inherent limitations of passive case detection (PCD) and further decrease the ... [more ▼] BACKGROUND:Focal screening and treatment (FSAT) of malaria infections has recently been introduced in Peru to overcome the inherent limitations of passive case detection (PCD) and further decrease the malaria burden. Here, we used a relatively straightforward mathematical model to assess the potential of FSAT as elimination strategy for Plasmodium falciparum malaria in the Peruvian Amazon Region.METHODS:A baseline model was developed to simulate a scenario with seasonal malaria transmission and the effect of PCD and treatment of symptomatic infections on the P. falciparum malaria transmission in a low endemic area of the Peruvian Amazon. The model was then adjusted to simulate intervention scenarios for predicting the long term additional impact of FSAT on P. falciparum malaria prevalence and incidence. Model parameterization was done using data from a cohort study in a rural Amazonian community as well as published transmission parameters from previous studies in similar areas. The effect of FSAT timing and frequency, using either microscopy or a supposed field PCR, was assessed on both predicted incidence and prevalence rates.RESULTS:The intervention model indicated that the addition of FSAT to PCD significantly reduced the predicted P. falciparum incidence and prevalence. The strongest reduction was observed when three consecutive FSAT were implemented at the beginning of the low transmission season, and if malaria diagnosis was done with PCR. Repeated interventions for consecutive years (10 years with microscopy or 5 years with PCR), would allow reaching near to zero incidence and prevalence rates.CONCLUSIONS:The addition of FSAT interventions to PCD may enable to reach P. falciparum elimination levels in low endemic areas of the Amazon Region, yet the progression rates to those levels may vary substantially according to the operational criteria used for the intervention. [less ▲] Detailed reference viewed: 3 (1 ULg)Testing the proportional odds assumption in multiply imputed ordinal longitudinal data Donneau, Anne-Françoise ; ; Lambert, Philippe et al in Journal of Applied Statistics (2015), 42(10), 2257-2279 Detailed reference viewed: 42 (11 ULg)Simulation-based study comparing multiple imputation methods for non-monotone missing ordinal data in longitudinal settings Donneau, Anne-Françoise ; ; Lambert, Philippe et al in Journal of Biopharmaceutical Statistics (2015), 25(03), 570-601 The application of multiple imputation (MI) techniques as a preliminary step to handle missing values in data analysis is well established. The MI method can be classified into two broad classes, the ... [more ▼] The application of multiple imputation (MI) techniques as a preliminary step to handle missing values in data analysis is well established. The MI method can be classified into two broad classes, the joint modeling and the fully conditional specification approaches. Their relative performance for the longitudinal ordinal data setting under the missing at random (MAR) assumption is not well documented. This paper intends to fill this gap by conducting a large simulation study on the estimation of the parameters of a longitudinal proportional odds model. The two MI methods are also illustrated in quality of life data from a cancer clinical trial. [less ▲] Detailed reference viewed: 119 (31 ULg)Analysis of MRI stomach scans using differential equations Frasso, Gianluca ; Lambert, Philippe ; Poster (2014, September) Differential equations (DE) are commonly used to describe dynamic systems evolving in one (e.g. time) or more dimensions (e.g. space and time). In real applications the parameters defining the theoretical ... [more ▼] Differential equations (DE) are commonly used to describe dynamic systems evolving in one (e.g. time) or more dimensions (e.g. space and time). In real applications the parameters defining the theoretical model describing the phenomenon under consideration are often unknown and need to be estimated from the available measurements. This estimation task has been extensively discussed in the statistical literature and probably the most popular procedures are those relying on nonlinear least squares (Bielger et al, 1986). These approaches are computationally intensive and often poorly suited for statistical inference. An attractive alternative is represented by the penalized smoothing procedure introduced by Ramsay et al. (2007). This approach can be viewed as a generalization of the L-spline framework (see Welham et al., 2006 among others) where the flexibility of a high dimensional B-spline expansion of the state function is counterbalanced by a penalty term defining the (set of) differential equation(s) synthesizing the dynamics under investigation. The fidelity of the extracted signal to the hypothesized model is then tuned by a “DE-compliance” parameter to be extracted form the data too. This approach works reasonably well both with linear and nonlinear differential models but, in the latter case, due to the implicit link between the vector of unknown DE parameters and the spline coefficients, the computational burden tends to increase and the optimization of the compliance parameter can be demanding. To overcome these drawbacks we adopt the quasilinearized (QL) ODE-P-spline approach proposed by Frasso et al. (2014). The quasilinearization (Bellman and Kalaba, 1965) step greatly reduces the computational cost of the estimation procedure making the penalty term a second order polynomial function of the DE parameters. As motivating example we present the results of a QL-ODE-P-spline analysis of a set of MRI scans describing stomach contractions during digestion. For illustrative purposes we analyze the measurements related to a single slice of the stomach. Finally, we conclude with a discussion of the possible further extensions of the presented methodology. [less ▲] Detailed reference viewed: 12 (2 ULg)ASSESSMENT OF THE PROPORTIONAL ODDS ASSUMPTION IN LONGITUDINAL STUDIES WITH MISSING ORDINAL OUTCOME DATA Donneau, Anne-Françoise ; ; Lambert, Philippe et al Poster (2014, July) Detailed reference viewed: 15 (5 ULg)SIMULATION-BASED COMPARATIVE PERFORMANCE OF MULTIPLE IMPUTATION METHODS FOR INCOMPLETE LONGITUDINAL ORDINAL DATA Donneau, Anne-Françoise ; ; Lambert, Philippe et al Conference (2014, July) Detailed reference viewed: 12 (0 ULg)Bayesian penalized smoothing approaches in models specified using affine differential equations with unknown error distributions Jaeger, Jonathan ; Lambert, Philippe in Journal of Applied Statistics (2014), 41(12), 2709-2726 A full Bayesian approach based on ODE-penalized B-splines and penalized Gaussian mixture is proposed to jointly estimate ODE-parameters, state function and error distribution from the observation of some ... [more ▼] A full Bayesian approach based on ODE-penalized B-splines and penalized Gaussian mixture is proposed to jointly estimate ODE-parameters, state function and error distribution from the observation of some state functions involved in systems of affine differential equations. Simulations inspired by pharmacokinetic studies show that the proposed method provides comparable results to the method based on the standard ODE-penalized B-spline approach (i.e. with the Gaussian error distribution assumption) and outperforms the standard ODE-penalized B-splines when the distribution is not Gaussian. This methodology is illustrated on the Theophylline dataset. [less ▲] Detailed reference viewed: 48 (20 ULg)Estimation and approximation in nonlinear dynamic systems using quasilinearization Frasso, Gianluca ; Jaeger, Jonathan ; Lambert, Philippe E-print/Working paper (2014) Nonlinear (systems of) ordinary differential equations (ODEs) are common tools in the analysis of complex one-dimensional dynamic systems. In this paper we propose a smoothing approach regularized by a ... [more ▼] Nonlinear (systems of) ordinary differential equations (ODEs) are common tools in the analysis of complex one-dimensional dynamic systems. In this paper we propose a smoothing approach regularized by a quasilinearized ODE-based penalty in order to approximate the state functions and estimate the parameters defining nonlinear differential systems from noisy data. Within the quasilinearized spline based framework, the estimation process reduces to a conditionally linear problem for the optimization of the spline coefficients. Furthermore, standard ODE compliance parameter(s) selection criteria are easily applicable and conditions on the state function(s) can be eventually imposed using soft or hard constraints. The approach is illustrated on real and simulated data. [less ▲] Detailed reference viewed: 22 (6 ULg)Spline approximation to conditional Archimedean copula Lambert, Philippe in Stat (2014), 3(1), 200-217 We propose a flexible copula model to describe changes with a covariate in the dependence structure of (conditionally exchangeable) random variables. The starting point is a spline approximation to the ... [more ▼] We propose a flexible copula model to describe changes with a covariate in the dependence structure of (conditionally exchangeable) random variables. The starting point is a spline approximation to the generator of an Archimedean copula. Changes in the dependence structure with a covariate x are modelled by flexible regression of the spline coefficients on x. The performances and properties of the spline estimate of the reference generator and the abilities of these conditional models to approximate conditional copulas are studied through extensive simulations. Inference is made using Bayesian arguments with posterior distributions explored using importance sampling or adaptive MCMC algorithms. The modelling strategy is illustrated with the analysis of bivariate growth curve data. [less ▲] Detailed reference viewed: 51 (8 ULg)Semiparametric Bayesian frailty model for clustered interval-censored data Cetinyürek, Aysun ; Lambert, Philippe Report (2014) The shared frailty model is one of the popular tool to analyze correlated right-censored time-to-event data. In the shared frailty model, the latent frailty is assumed to be shared by the members of a ... [more ▼] The shared frailty model is one of the popular tool to analyze correlated right-censored time-to-event data. In the shared frailty model, the latent frailty is assumed to be shared by the members of a cluster and is assigned a parametric distribution, typically, a gamma distribution due to its conjugacy. However, in case of interval-censored time-to-event data, the inclusion of gamma frailties results in complicated intractable likelihoods, where the conjugacy property does not hold anymore. Here, we propose a semiparametric Bayesian frailty model for analyzing such data. We discuss three parametric specifications for frailty distribution in the analysis of interval-censored data. Afterwards we call particular attention to nonparametric specification of the frailty distribution. The results of the simulation study suggest that the proposed approach is robust to misspecification of the frailty distribution. Moreover, the performance of the proposed methodology is quite good in practical situations where the frailty distribution is multimodal or skewed. The approach is applied to dental data arising from the Signal Tandmobiel Study. [less ▲] Detailed reference viewed: 80 (18 ULg)Inflated discrete Beta regression models for Likert and discrete rating scale outcomes ; Lambert, Philippe E-print/Working paper (2014) Discrete ordinal responses such as Likert scales are regularly proposed in questionnaires and used as dependent variable in modeling. The response distribution for such scales is always discrete, with ... [more ▼] Discrete ordinal responses such as Likert scales are regularly proposed in questionnaires and used as dependent variable in modeling. The response distribution for such scales is always discrete, with bounded support and often skewed. In addition, one particular level of the scale is frequently inflated as it cumulates respondents who invari- ably choose that particular level (typically the middle or one extreme of the scale) without hesitation with those who chose that alternative but might have selected a neighboring one. The inflated discrete beta regression (IDBR) model addresses those four critical characteristics that have never been taken into account simultaneously by existing models. The mean and the dispersion of rates are jointly regressed on covariates using an underlying beta distribution. The probability that choosers of the inflated level invariably make that choice is also regressed on covariates. Simulation studies used to evaluate the statistical properties of the IDBR model suggest that it produces more precise predictions than competing models. The ability to jointly model the location and dispersion of (the distribution of) an ordinal response, as well as to characterize the profile of subject selecting an ”inflated” alternative are the most relevant features of the IDBR model. It is illustrated with the analysis of the political positioning on a ”left-right” scale of the Belgian respondents in the 2012 European Social Survey. [less ▲] Detailed reference viewed: 22 (4 ULg)Estimation and approximation in multidimensional dynamics Frasso, Gianluca ; Jaeger, Jonathan ; Lambert, Philippe E-print/Working paper (2013) Differential equations (DEs) are commonly used to describe dynamic systems evolving in one (ordinary differential equations or ODEs) or in more than one dimensions (partial differential equations or PDEs ... [more ▼] Differential equations (DEs) are commonly used to describe dynamic systems evolving in one (ordinary differential equations or ODEs) or in more than one dimensions (partial differential equations or PDEs). In real data applications the parameters involved in the DE models are usually unknown and need to be estimated from the available measurements together with the state function. In this paper, we present frequentist and Bayesian approaches for the joint estimation of the parameters and of the state functions involved in PDEs. We also propose two strategies to include differential (initial and/or boundary) conditions in the estimation procedure. We evaluate the performances of the proposed strategy on simulated and real data applications. [less ▲] Detailed reference viewed: 56 (13 ULg)Spline approximation to conditional Archimedean copula Lambert, Philippe E-print/Working paper (2013) We propose a flexible copula model to describe changes with a covari- ate in the dependence structure of (conditionally exchangeable) random variables. The starting point is a spline approximation to the ... [more ▼] We propose a flexible copula model to describe changes with a covari- ate in the dependence structure of (conditionally exchangeable) random variables. The starting point is a spline approximation to the generator of an Archimedean copula. Changes in the dependence structure with a covariate x are modelled by flexible regression of the spline coefficients on x. The performances and properties of the spline estimate of the reference generator and the abilities of these conditional models to approximate conditional copulas are studied through simulations. Inference is made using Bayesian arguments with posterior distributions explored using im- portance sampling or adaptive MCMC algorithms. The modelling strategy is illustrated with two examples. [less ▲] Detailed reference viewed: 11 (1 ULg)Penalized smoothing approaches for PDEs Frasso, Gianluca ; ; Lambert, Philippe Conference (2013, October) Detailed reference viewed: 1 (0 ULg) |
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