Bayesian Analysis of Hazard Regression Models under Order Restrictions on Covariate Effects and Ageing

We propose Bayesian inference in hazard regression models where the baseline hazard is unknown, covariate effects are possibly age-varying (non-proportional), and there is multiplicative frailty with arbitrary distribution. Our framework incorporates a wide variety of order restrictions on covariate dependence and duration dependence (ageing). We propose estimation and evaluation of age-varying covariate effects when covariate dependence is monotone rather than proportional. In particular, we consider situations where the lifetime conditional on a higher value of the covariate ages faster or slower than that conditional on a lower value; this kind of situation is common in applications. In addition, there may be restrictions on the nature of ageing. For example, relevant theory may suggest that the baseline hazard function decreases with age. The proposed framework enables evaluation of order restrictions in the nature of both covariate and duration dependence as well as estimation of hazard regression models under such restrictions. The usefulness of the proposed Bayesian model and inference methods are illustrated with an application to corporate bankruptcies in the UK.Bayesian nonparametrics; Nonproportional hazards; Frailty; Age-varying covariate e¤ects; Ageing

Bayesian Analysis of Hazard Regression Models under Order Restrictions on Covariate Effects and Ageing

We propose Bayesian inference in hazard regression models where the baseline hazard is unknown, covariate effects are possibly age-varying (non-proportional), and there is multiplicative frailty with arbitrary distribution. Our framework incorporates a wide variety of order restrictions on covariate dependence and duration dependence (ageing). We propose estimation and evaluation of age-varying covariate effects when covariate dependence is monotone rather than proportional. In particular, we consider situations where the lifetime conditional on a higher value of the covariate ages faster or slower than that conditional on a lower value; this kind of situation is common in applications. In addition, there may be restrictions on the nature of ageing. For example, relevant theory may suggest that the baseline hazard function decreases with age. The proposed framework enables evaluation of order restrictions in the nature of both covariate and duration dependence as well as estimation of hazard regression models under such restrictions. The usefulness of the proposed Bayesian model and inference methods are illustrated with an application to corporate bankruptcies in the UK

Measuring spatial association and testing spatial independence based on short time course data

Spatial association measures for univariate static spatial data are widely used. When the data is in the form of a collection of spatial vectors with the same temporal domain of interest, we construct a measure of similarity between the regions' series, using Bergsma's correlation coefficient $\rho$. Due to the special properties of $\rho$, unlike other spatial association measures which test for spatial randomness, our statistic can account for spatial pairwise independence. We have derived the asymptotic behavior of our statistic under null (independence of the regions) and alternate cases (the regions are dependent). We explore the alternate scenario of spatial dependence further, using simulations for the SAR and SMA dependence models. Finally, we provide application to modelling and testing for the presence of spatial association in COVID-19 incidence data, by using our statistic on the residuals obtained after model fitting.Comment: Keywords: Bergsma's correlation, spatial association measure, U-statistic, spatial autoregressive model, spatial moving average mode

Assessing bivariate independence: Revisiting Bergsma's covariance

Bergsma (2006) proposed a covariance $\kappa$(X,Y) between random variables X and Y. He derived their asymptotic distributions under the null hypothesis of independence between X and Y. The non-null (dependent) case does not seem to have been studied in the literature. We derive several alternate expressions for $\kappa$. One of them leads us to a very intuitive estimator of $\kappa$(X,Y) that is a nice function of four naturally arising U-statistics. We derive the exact finite sample relation between all three estimates. The asymptotic distribution of our estimator, and hence also of the other two estimators, in the non-null (dependence) case, is then obtained by using the U-statistics central limit theorem. For specific parametric bivariate distributions, the value of $\kappa$ can be derived in terms of the natural dependence parameters of these distributions. In particular, we derive the formula for $\kappa$ when (X,Y) are distributed as Gumbel's bivariate exponential. We bring out various aspects of these estimators through extensive simulations from several prominent bivariate distributions. In particular, we investigate the empirical relationship between $\kappa$ and the dependence parameters, the distributional properties of the estimators, and the accuracy of these estimators. We also investigate the powers of these measures for testing independence, compare these among themselves, and with other well known such measures. Based on these exercises, the proposed estimator seems as good or better than its competitors both in terms of power and computing efficiency.Comment: 36 pages, 6 figure

A Bayesian Mixed Regression Based Prediction of Quantitative Traits from Molecular Marker and Gene Expression Data

Peer reviewe

Meta Analytic Data Integration for Phenotype Prediction: Application to Chronic Fatigue Syndrome

Predictive modeling plays key role in providing accurate prognosis and enables us to take a step closer to personalized treatment. We identified two potential sources of human induced biases that can lead to disparate conclusions. We illustrate through a complex phenotype that robust results can still be drawn after accounting for such biases. Often predictive models build based in high dimensional data suffers from the drawback of lack of interpretability. To achieve interpretability in the form of description of the organism level phenomena in term of molecular or cellular level activities, functional and pathway information is often augmented. Functional information can greatly facilitate the interpretation of the results of the predictive model. However an important aspect of (vertical) data augmentation is routinely ignored, that is there could be several stages of analysis where such information could be meaningfully integrated. There is no know criteria to enable us to assess the effect of such augmentation. A novel aspect of the proposed work is in exploring possibilities of stages of analysis where functional information may be incorporated and in assessing the extent to which the ultimate conclusions would differ depending on level of amalgamation. To boost our confidence on the key findings a first level of meta-analysis is done by exploring different levels of data augmentation. This is followed by comparison of predictive models across different definitions of the same phenotype developed by different groups, which is also an extended form of meta-analysis. We have used real life data on a complex phenotype to illustrate the above. The data pertains to Chronic Fatigue Syndrome (CFS) and another novel aspect of the current work is in modeling the underlying continuous symptom measurements for CFS, which is the first for this disease to our knowledge.Comment: 2 Figures, 6 Tables, 1 Supplementary inf