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A Bayesian CART algorithm 总被引：3，自引：0，他引：3
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An‐Min Tang Xingqiu Zhao Nian‐Sheng Tang 《Biometrical journal. Biometrische Zeitschrift》2017,59(1):57-78
This paper presents a novel semiparametric joint model for multivariate longitudinal and survival data (SJMLS) by relaxing the normality assumption of the longitudinal outcomes, leaving the baseline hazard functions unspecified and allowing the history of the longitudinal response having an effect on the risk of dropout. Using Bayesian penalized splines to approximate the unspecified baseline hazard function and combining the Gibbs sampler and the Metropolis–Hastings algorithm, we propose a Bayesian Lasso (BLasso) method to simultaneously estimate unknown parameters and select important covariates in SJMLS. Simulation studies are conducted to investigate the finite sample performance of the proposed techniques. An example from the International Breast Cancer Study Group (IBCSG) is used to illustrate the proposed methodologies. 相似文献
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In this article, we incorporate an autoregressive time-series framework into models for animal survival using capture-recapture data. Researchers modeling animal survival probabilities as the realization of a random process have typically considered survival to be independent from one time period to the next. This may not be realistic for some populations. Using a Gibbs sampling approach, we can estimate covariate coefficients and autoregressive parameters for survival models. The procedure is illustrated with a waterfowl band recovery dataset for northern pintails (Anas acuta). The analysis shows that the second lag autoregressive coefficient is significantly less than 0, suggesting that there is a triennial relationship between survival probabilities and emphasizing that modeling survival rates as independent random variables may be unrealistic in some cases. Software to implement the methodology is available at no charge on the Internet. 相似文献
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Fred M. Hoppe 《Journal of mathematical biology》1984,20(1):91-94
A Markov process of partitions of the natural numbers is constructed by defining a Pólya-like urn model. The marginal distributions of this process are the Ewens' sampling distributions of population genetics.Research supported in part by NSF Grant MCS-8108689 相似文献
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If the population is large and the sampling mechanism is random, the coalescent is commonly used to model the haplotypes in the sample. Ordered genotypes can then be formed by random matching of the derived haplotypes. However, this approach is not realistic when (1) there is departure from random mating (e.g., dominant individuals in breeding populations or monogamy in humans), or (2) the population is small and/or the individuals in the sample are ascertained by applying some particular non-random sampling scheme, as is usually the case when considering the statistical modeling and analysis of pedigree data. For such situations, we present here a data generation method where an ancestral graph with non-overlapping generations is first generated backwards in time, using ideas from coalescent theory. Alleles are randomly assigned to the founders, and subsequently the gene flow over the entire genome is simulated forwards in time by dropping alleles down the graph according to recombination model without interference. The parameters controlling the mating behavior of generated individuals in the graph (degree of monogamy) can be tuned in order to match a particular demographic situation, without restriction to simple random mating.The performance of the approach is illustrated with a simulation example. The software (written in C-language) is freely available for research purposes at http://www.rni.helsinki.fi/∼dag/. 相似文献
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This paper demonstrates the advantages of sharing information about unknown features of covariates across multiple model components in various nonparametric regression problems including multivariate, heteroscedastic, and semicontinuous responses. In this paper, we present a methodology which allows for information to be shared nonparametrically across various model components using Bayesian sum-of-tree models. Our simulation results demonstrate that sharing of information across related model components is often very beneficial, particularly in sparse high-dimensional problems in which variable selection must be conducted. We illustrate our methodology by analyzing medical expenditure data from the Medical Expenditure Panel Survey (MEPS). To facilitate the Bayesian nonparametric regression analysis, we develop two novel models for analyzing the MEPS data using Bayesian additive regression trees—a heteroskedastic log-normal hurdle model with a “shrink-toward-homoskedasticity” prior and a gamma hurdle model. 相似文献
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Summary. We propose a method for analyzing data which consist of curves on multiple individuals, i.e., longitudinal or functional data. We use a Bayesian model where curves are expressed as linear combinations of B-splines with random coefficients. The curves are estimated as posterior means obtained via Markov chain Monte Carlo (MCMC) methods, which automatically select the local level of smoothing. The method is applicable to situations where curves are sampled sparsely and/or at irregular time points. We construct posterior credible intervals for the mean curve and for the individual curves. This methodology provides unified, efficient, and flexible means for smoothing functional data. 相似文献
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Cheung YK 《Biometrics》2002,58(1):237-240
Gasparini and Eisele (2000, Biometrics 56, 609-615) propose a design for phase I clinical trials during which dose allocation is governed by a Bayesian nonparametric estimate of the dose-response curve. The authors also suggest an elicitation algorithm to establish vague priors. However, in situations where a low percentile is targeted, priors thus obtained can lead to undesirable rigidity given certain trial outcomes that can occur with a nonnegligible probability. Interestingly, improvement can be achieved by prescribing slightly more informative priors. Some guidelines for prior elicitation are established using a connection between this curve-free method and the continual reassessment method. 相似文献
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Mário de Castro Vicente G. Cancho Josemar Rodrigues 《Biometrical journal. Biometrische Zeitschrift》2009,51(3):443-455
The main goal of this paper is to investigate a cure rate model that comprehends some well‐known proposals found in the literature. In our work the number of competing causes of the event of interest follows the negative binomial distribution. The model is conveniently reparametrized through the cured fraction, which is then linked to covariates by means of the logistic link. We explore the use of Markov chain Monte Carlo methods to develop a Bayesian analysis in the proposed model. The procedure is illustrated with a numerical example. 相似文献
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Rainer Schlittgen 《Biometrical journal. Biometrische Zeitschrift》1999,41(8):943-954
Regression trees allow to search for meaningful explanatory variables that have a non linear impact on the dependent variable. Often they are used when there are many covariates and one does not want to restrict attention to only few of them. To grow a tree at each stage one has to select a cut point for splitting a group into two subgroups. The basis for this are the maxima of the test statistics related to the possible splits due to every covariate. They or the resulting P-values are compared as measure of importance. If covariates have different numbers of missing values, ties, or even different measurement scales the covariates lead to different numbers of tests. Those with a higher number of tests have a greater chance to achieve a smaller P-value if they are not adjusted. This can lead to erroneous splits even if the P-values are looked at informally. There is some theoretical work by Miller and Siegmund (1982) and Lausen and Schumacher (1992) to give an adjustment rule. But the asymptotic is based on a continuum of split points and may not lead to a fair splitting rule when applied to smaller data sets or to covariates with only few different values. Here we develop an approach that allows determination of P-values for any number of splits. The only approximation that is used is the normal approximation of the test statistics. The starting point for this investigation has been a prospective study on the development of AIDS. This is presented here as the main application. 相似文献
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Mixture modeling is a popular approach to accommodate overdispersion, skewness, and multimodality features that are very common for health care utilization data. However, mixture modeling tends to rely on subjective judgment regarding the appropriate number of mixture components or some hypothesis about how to cluster the data. In this work, we adopt a nonparametric, variational Bayesian approach to allow the model to select the number of components while estimating their parameters. Our model allows for a probabilistic classification of observations into clusters and simultaneous estimation of a Gaussian regression model within each cluster. When we apply this approach to data on patients with interstitial lung disease, we find distinct subgroups of patients with differences in means and variances of health care costs, health and treatment covariates, and relationships between covariates and costs. The subgroups identified are readily interpretable, suggesting that this nonparametric variational approach to inference can discover valid insights into the factors driving treatment costs. Moreover, the learning algorithm we employed is very fast and scalable, which should make the technique accessible for a broad range of applications. 相似文献
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Performing causal inference in observational studies requires we assume confounding variables are correctly adjusted for. In settings with few discrete-valued confounders, standard models can be employed. However, as the number of confounders increases these models become less feasible as there are fewer observations available for each unique combination of confounding variables. In this paper, we propose a new model for estimating treatment effects in observational studies that incorporates both parametric and nonparametric outcome models. By conceptually splitting the data, we can combine these models while maintaining a conjugate framework, allowing us to avoid the use of Markov chain Monte Carlo (MCMC) methods. Approximations using the central limit theorem and random sampling allow our method to be scaled to high-dimensional confounders. Through simulation studies we show our method can be competitive with benchmark models while maintaining efficient computation, and illustrate the method on a large epidemiological health survey. 相似文献
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A new estimation procedure for mixed regression models is introduced. It is a development of Henderson's best linear unbiased prediction procedure which uses the joint distribution of the observed dependent random variables and the unknown realisations of the random components of the model. It is proposed to replace the likelihood of the observations given the random components by the asymptotic likelihood of the maximum likelihood estimators and the prior distribution of the random components by a restricted prior distribution which is consistent with the usual restrictions placed on the random components when they are considered conditionally fixed. 相似文献
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R. A. Maller 《Biometrical journal. Biometrische Zeitschrift》1987,29(2):231-238
An approximate representation is given for the partial likelihood estimate of the regression coefficient in Cox's proportional hazard model which indicates how it measures the association between survival time and covariate. The case of a single covariate is concentrated on. The representation is closely related to the first step of a Newton-Raphson iteration, i.e. to the score test. A similar representation for the Feigl-Zelen exponential model shows that a similar type of association is being measured, if observed lifetimes are interpreted as expected lifetimes of ordered exponentials. Necessary and sufficient conditions for the existence of Cox's estimate in the simple case are also written down. 相似文献
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Farrington CP 《Biometrics》2000,56(2):473-482
We develop diagnostic tools for use with proportional hazards models for interval-censored survival data. We propose counterparts to the Cox-Snell, Lagakos (or martingale), deviance, and Schoenfeld residuals. Many of the properties of these residuals carry over to the interval-censored case. In particular, the interval-censored versions of the Lagakos and Schoenfeld residuals may be derived as components of suitable score statistics. The Lagakos residuals may be used to check regression relationships, while the Schoenfeld residuals can help to detect nonproportional hazards in semiparametric models. The methods apply to parametric models and to the semiparametric model with discrete observation times. 相似文献