Bayesian bivariate survival analysis using the power variance function copula

A novel approach to the analysis of Overall Survival (OS) as response with Progression-Free Interval (PFI) as condition based on the RNA-seq expression data in The Cancer Genome Atlas (TCGA)

BACKGROUND

Overall Survival (OS) and Progression-Free Interval (PFI) as survival times have been collected in The Cancer Genome Atlas (TCGA). It is of biomedical interest to consider their dependence in pathway detection and survival prediction. We intend to develop novel methods for integrating PFI as condition based on parametric survival models for identifying pathways associated with OS and predicting OS.

RESULTS

Based on the framework of conditional probability, we developed a family of frailty-based parametric-models for this purpose, with exponential or Weibull distribution as baseline. We also considered two classes of existing methods with PFI as a covariate. We evaluated the performance of three approaches by analyzing RNA-seq expression data from TCGA for lung squamous cell carcinoma and lung adenocarcinoma (LUNG), brain lower grade glioma and glioblastoma multiforme (GBMLGG), as well as skin cutaneous melanoma (SKCM). Our focus was on fourteen general cancer-related pathways. The 10-fold cross-validation was employed for the evaluation of predictive accuracy. For LUNG, p53 signaling and cell cycle pathways were detected by all approaches. Furthermore, three approaches with the consideration of PFI demonstrated significantly better predictive performance compared to the approaches without the consideration of PFI. For GBMLGG, ten pathways (e.g., Wnt signaling, JAK-STAT signaling, ECM-receptor interaction, etc.) were detected by all approaches. Furthermore, three approaches with the consideration of PFI demonstrated better predictive performance compared to the approaches without the consideration of PFI. For SKCM, p53 signaling pathway was detected only by our Weibull-baseline-based model. And three approaches with the consideration of PFI demonstrated significantly better predictive performance compared to the approaches without the consideration of PFI.

CONCLUSIONS

Based on our study, it is necessary to incorporate PFI into the survival analysis of OS. Furthermore, PFI is a survival-type time, and improved results can be achieved by our conditional-probability-based approach.

Dementia death rates prediction

BACKGROUND

Prevalence of dementia illness, causing certain morbidity and mortality globally, places burden on global public health. This study primary goal was to assess future risks of dying from severe dementia, given specific return period, within selected group of regions or nations.

METHODS

Traditional statistical approaches do not have benefits of effectively handling large regional dimensionality, along with nonlinear cross-correlations between various regional observations. In order to produce reliable long-term projections of excessive dementia death rate risks, this study advocates novel bio-system reliability technique, that being particularly suited for multi-regional environmental, biological, and health systems.

DATA

Raw clinical data has been used as an input to the suggested population-based, bio-statistical technique using data from medical surveys and several centers.

RESULTS

Novel spatiotemporal health system reliability methodology has been developed and applied to dementia death rates raw clinical data. Suggested methodology shown to be capable of dealing efficiently with spatiotemporal clinical observations of multi-regional nature. Accurate disease risks multi-regional spatiotemporal prediction being done, relevant confidence intervals have been presented as well.

CONCLUSIONS

Based on available clinical survey dataset, the proposed approach may be applied in a variety of clinical public health applications. Confidence bands, given for predicted dementia-associated death rate levels with return periods of interest, have been reasonably narrow, indicating practical values of advocated prognostics.

Global Cardiovascular Diseases Death Rate Prediction

Cardiovascular diseases (CVD) are heart and blood vessels diseases with considerable morbidity and mortality and presenting worldwide public health burden, moreover CVDs are the leading cause of death globally. This paper describes a novel bio-system reliability approach, particularly suitable for multi-regional environmental and health systems, observed over a sufficient period of time, resulting in a reliable long-term forecast of cardiovascular diseases mortality probability. Objective has been to determine extreme cardiovascular diseases death rate probability at any time in any region of interest. Traditional statistical methods dealing with temporal observations of multi-regional processes do not have the advantage of dealing efficiently with extensive regional dimensionality and cross-correlation between different regional observations. Design of this analysis was based on applying novel statistical methods directly to a raw clinical data, with subsequent data analysis using multicenter, population-based, medical survey data based bio-statistical approach. For this study, cardiovascular diseases annual numbers of recorded deaths in all 195 world countries were chosen. The suggested methodology can be used in various public health applications, based on their clinical survey data.

Future world cancer death rate prediction

Cancer is a worldwide illness that causes significant morbidity and death and imposes an immense cost on global public health. Modelling such a phenomenon is complex because of the non-stationarity and complexity of cancer waves. Apply modern novel statistical methods directly to raw clinical data. To estimate extreme cancer death rate likelihood at any period in any location of interest. Traditional statistical methodologies that deal with temporal observations of multi-regional processes cannot adequately deal with substantial regional dimensionality and cross-correlation of various regional variables. Setting: multicenter, population-based, medical survey data-based biostatistical approach. Due to the non-stationarity and complicated nature of cancer, it is challenging to model such a phenomenon. This paper offers a unique bio-system dependability technique suited for multi-regional environmental and health systems. When monitored over a significant period, it yields a reliable long-term projection of the chance of an exceptional cancer mortality rate. Traditional statistical approaches dealing with temporal observations of multi-regional processes cannot effectively deal with large regional dimensionality and cross-correlation between multiple regional data. The provided approach may be employed in numerous public health applications, depending on their clinical survey data.

Quantile association regression on bivariate survival data

The association between two event times is of scientific importance in various fields. Due to population heterogeneity, it is desirable to examine the degree to which local association depends on different characteristics of the population. Here we adopt a novel quantile-based local association measure and propose a conditional quantile association regression model to allow covariate effects on local association of two survival times. Estimating equations for the quantile association coefficients are constructed based on the relationship between this quantile association measure and the conditional copula. Asymptotic properties for the resulting estimators are rigorously derived, and induced smoothing is used to obtain the covariance matrix. Through simulations we demonstrate the good practical performance of the proposed inference procedures. An application to age-related macular degeneration (AMD) data reals interesting varying effects of the baseline AMD severity score on the local association between two AMD progression times.

Flexible parametric copula modeling approaches for clustered survival data

Copula-based survival regression models, which consist of a copula function and marginal distribution (i.e., marginal survival function), have been widely used for analyzing clustered multivariate survival data. Archimedean copula functions are useful for modeling such dependence. For the likelihood inference, one-stage and two-stage estimation methods have been usually used. The two-stage procedure can give inefficient estimation results because of separate estimation of the marginal and copula's dependence parameters. The more efficient one-stage procedure has been mainly developed under a restrictive parametric assumption of marginal distribution due to complexity of the full likelihood with unknown marginal baseline hazard functions. In this paper, we propose a flexible parametric Archimedean copula modeling approach using a one-stage likelihood procedure. In order to reduce the complexity of the full likelihood, the unknown marginal baseline hazards are modeled based on a cubic M-spline basis function that does not require a specific parametric form. Simulation results demonstrate that the proposed one-stage estimation method gives a consistent estimator and also provides more efficient results over existing one- and two-stage methods. The new method is illustrated with three clinical data sets. The Appendix provides an R function so that the proposed method becomes directly accessible to interested readers.

Factor copula models for right-censored clustered survival data

In this article we extend the factor copula model to deal with right-censored event time data grouped in clusters. The new methodology allows for clusters to have variable sizes ranging from small to large and intracluster dependence to be flexibly modeled by any parametric family of bivariate copulas, thus encompassing a wide range of dependence structures. Incorporation of covariates (possibly time dependent) in the margins is also supported. Three estimation procedures are proposed: both one- and two-stage parametric and a two-stage semiparametric method where marginal survival functions are estimated by using a Cox proportional hazards model. We prove that the estimators are consistent and asymptotically normally distributed, and assess their finite sample behavior with simulation studies. Furthermore, we illustrate the proposed methods on a data set containing the time to first insemination after calving in dairy cattle clustered in herds of different sizes.

Bivariate lifetime models in presence of cure fraction: a comparative study with many different copula functions

In time-to-event studies it is common the presence of a fraction of individuals not expecting to experience the event of interest; these individuals who are immune to the event or cured for the disease during the study are known as long-term survivors. In addition, in many studies it is observed two lifetimes associated to the same individual, and in some cases there exists a dependence structure between them. In these situations, the usual existing lifetime distributions are not appropriate to model data sets with long-term survivors and dependent bivariate lifetimes. In this study, it is proposed a bivariate model based on a Weibull standard distribution with a dependence structure based on fifteen different copula functions. We assumed the Weibull distribution due to its wide use in survival data analysis and its greater flexibility and simplicity, but the presented methods can be adapted to other continuous survival distributions. Three examples, considering real data sets are introduced to illustrate the proposed methodology. A Bayesian approach is assumed to get the inferences for the parameters of the model where the posterior summaries of interest are obtained using Markov Chain Monte Carlo simulation methods and the Openbugs software. For the data analysis considering different real data sets it was assumed fifteen different copula models from which is was possible to find models with satisfactory fit for the bivariate lifetimes in presence of long-term survivors.

A general frailty model to accommodate individual heterogeneity in the acquisition of multiple infections: An application to bivariate current status data

The analysis of multivariate time-to-event (TTE) data can become complicated due to the presence of clustering, leading to dependence between multiple event times. For a long time, (conditional) frailty models and (marginal) copula models have been used to analyze clustered TTE data. In this article, we propose a general frailty model employing a copula function between the frailty terms to construct flexible (bivariate) frailty distributions with the application to current status data. The model has the advantage to impose a less restrictive correlation structure among latent frailty variables as compared to traditional frailty models. Specifically, our model uses a copula function to join the marginal distributions of the frailty vector. In this article, we considered different copula functions, and we relied on marginal gamma distributions due to their mathematical convenience. Based on a simulation study, our novel model outperformed the commonly used additive correlated gamma frailty model, especially in the case of a negative association between the frailties. At the end of the article, the new methodology is illustrated on real-life data applications entailing bivariate serological survey data.

A bivariate power generalized Weibull distribution: A flexible parametric model for survival analysis

We are concerned with the flexible parametric analysis of bivariate survival data. Elsewhere, we argued in favour of an adapted form of the 'power generalized Weibull' distribution as an attractive vehicle for univariate parametric survival analysis. Here, we additionally observe a frailty relationship between a power generalized Weibull distribution with one value of the parameter which controls distributional choice within the family and a power generalized Weibull distribution with a smaller value of that parameter. We exploit this relationship to propose a bivariate shared frailty model with power generalized Weibull marginal distributions linked by the BB9 or 'power variance function' copula, then change it to have adapted power generalized Weibull marginals in the obvious way. The particular choice of copula is, therefore, natural in the current context, and the corresponding bivariate adapted power generalized Weibull model a novel combination of pre-existing components. We provide a number of theoretical properties of the models. We also show the potential of the bivariate adapted power generalized Weibull model for practical work via an illustrative example involving a well-known retinopathy dataset, for which the analysis proves to be straightforward to implement and informative in its outcomes.

Bayesian Computational Methods for Sampling from the Posterior Distribution of a Bivariate Survival Model, Based on AMH Copula in the Presence of Right-Censored Data

In this paper, we study the performance of Bayesian computational methods to estimate the parameters of a bivariate survival model based on the Ali-Mikhail-Haq copula with marginal distributions given by Weibull distributions. The estimation procedure was based on Monte Carlo Markov Chain (MCMC) algorithms. We present three version of the Metropolis-Hastings algorithm: Independent Metropolis-Hastings (IMH), Random Walk Metropolis (RWM) and Metropolis-Hastings with a natural-candidate generating density (MH). Since the creation of a good candidate generating density in IMH and RWM may be difficult, we also describe how to update a parameter of interest using the slice sampling (SS) method. A simulation study was carried out to compare the performances of the IMH, RWM and SS. A comparison was made using the sample root mean square error as an indicator of performance. Results obtained from the simulations show that the SS algorithm is an effective alternative to the IMH and RWM methods when simulating values from the posterior distribution, especially for small sample sizes. We also applied these methods to a real data set.