<scp>B</scp>ayesian Survival Analysis

Ibrahim, Joseph G.; Chen, Ming‐Hui; Sinha, Debajyoti

doi:10.1002/0470011815.b2a11006

Cited by 120 publications

(88 citation statements)

References 81 publications

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“…In the model for the survival records, we model the intensity increment over a small time period, I i (s)ds, as the product of the integrated baseline hazard function, dΛ o (s), and whether record i is in the risk set, Y i (s), during that time period, [s, s + ds): I i (s)ds = Y i (s) 9 dΛ 0 (s). We assume constant integrated baseline hazards within each [s, s + ds) to have a proportional hazards form (Ibrahim et al 2005). To compare alternative models for density dependence in the survival process, we give I i (s)ds some functional form for the relationship between the intensity increment and the standardized log (l tÀ1 ).…”

Section: Process Modelsmentioning

confidence: 99%

Are the numbers adding up? Exploiting discrepancies among complementary population models

Stenglein

Zhu

Clayton

et al. 2014

Ecology and Evolution

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Large carnivores are difficult to monitor because they tend to be sparsely distributed, sensitive to human activity, and associated with complex life histories. Consequently, understanding population trend and viability requires conservationists to cope with uncertainty and bias in population data. Joint analysis of combined data sets using multiple models (i.e., integrated population model) can improve inference about mechanisms (e.g., habitat heterogeneity and food distribution) affecting population dynamics. However, unobserved or unobservable processes can also introduce bias and can be difficult to quantify. We developed a Bayesian hierarchical modeling approach for inference on an integrated population model that reconciles annual population counts with recruitment and survival data (i.e., demographic processes). Our modeling framework is flexible and enables a realistic form of population dynamics by fitting separate density-dependent responses for each demographic process. Discrepancies estimated from shared parameters among different model components represent unobserved additions (i.e., recruitment or immigration) or removals (i.e., death or emigration) when annual population counts are reliable. In a case study of gray wolves in Wisconsin (1980–2011), concordant with policy changes, we estimated that a discrepancy of 0% (1980–1995), −2% (1996–2002), and 4% (2003–2011) in the annual mortality rate was needed to explain annual growth rate. Additional mortality in 2003–2011 may reflect density-dependent mechanisms, changes in illegal killing with shifts in wolf management, and nonindependent censoring in survival data. Integrated population models provide insights into unobserved or unobservable processes by quantifying discrepancies among data sets. Our modeling approach is generalizable to many population analysis needs and allows for identifying dynamic differences due to external drivers, such as management or policy changes.

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Section: Process Modelsmentioning

confidence: 99%

Are the numbers adding up? Exploiting discrepancies among complementary population models

Stenglein

Zhu

Clayton

et al. 2014

Ecology and Evolution

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“…A frequently used term "survival analysis" (derived from applications in medical science) is used in the text instead of "duration analysis", "transition analysis" or "event history analysis" more common in economics and social science, respectively. Nonparametric and semiparametric statistical methods of survival analysis (Turnbull's estimate and an AFT regression model, respectively) are employed here, Bayesian models (Ibrahim, 2005) being, however, also well applicable in this case.…”

Section: Introductionmentioning

confidence: 99%

Modelling of Unemployment Duration in the Czech Republic

Čabla¹,

Malá²

2017

Prague Economic Papers

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The paper examines the duration of unemployment in the Czech Republic in the three selected years (2008, 2010 and 2014). It is based on the Czech Statistical Office data collected from the Labour Force Sample Survey. Lognormal probability distribution (unimodal positively skewed heavy-tailed distribution) is used in the Accelerated Failure Time regression model including the following factor explanatory variables: years (three levels, 2008, 2010, 2014), gender (two levels), education (four levels), five-year age groups (nine levels) and municipality size (five levels). Apart from this parametric model, Turnbull's nonparametric estimator of the survival function is evaluated for subsamples defined by the year, gender and education. The effects of education and gender -a strong positive one of the former and less significant one of the latter, respectively -are quantified and assessed.

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“…We fit 5, 7, and 9 basis functions. For each Monte Carlo iteration we selected the fit that had the best (highest) log pseudo marginal likelihood (Ibrahim, Chen, and Sinh, ) across number of basis functions.…”

Section: Simulation Studymentioning

confidence: 99%

Multilevel Quantile Function Modeling with Application to Birth Outcomes

et al. 2015

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Summary: Infants born preterm or small for gestational age have elevated rates of morbidity and mortality. Using birth certificate records in Texas from [2002][2003][2004] and Environmental Protection Agency air pollution estimates, we relate the quantile functions of birth weight and gestational age to ozone exposure and multiple predictors, including parental age, race, and education level. We introduce a semi-parametric Bayesian quantile approach that models the full quantile function rather than just a few quantile levels. Our multilevel quantile function model establishes relationships between birth weight and the predictors separately for each week of gestational age and between gestational age and the predictors separately across Texas Public Health Regions. We permit these relationships to vary nonlinearly across gestational age, spatial domain and quantile level and we unite them in a hierarchical model via a basis expansion on the regression coefficients that preserves interpretability. Very low birth weight is a primary concern, so we leverage extreme value theory to supplement our model in the tail of the distribution. Gestational ages are rounded into weekly values, so we present methodology for modeling quantile functions of discrete response data. In a simulation study we show that pooling information across gestational age and quantile level substantially reduces MSE of predictor effects relative to standard frequentist quantile regression. We find that ozone is negatively associated with the lower tail of gestational age in south Texas and across the distribution of birth weight for high gestational ages. Our methods are available in the R package BSquare.

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Bayesian Survival Analysis

Cited by 120 publications

References 81 publications

Are the numbers adding up? Exploiting discrepancies among complementary population models

Are the numbers adding up? Exploiting discrepancies among complementary population models

Modelling of Unemployment Duration in the Czech Republic

Multilevel Quantile Function Modeling with Application to Birth Outcomes

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