A Note on Random Intensities and Conditional Survival Functions

One of the interesting directions of research in IIASA's Population Program deals with the methodological aspects of population heterogeneity dynamics. The crucial notion in this analysis is the stochastic intensity which is widely used in the stochastic processes models of human morbidity and mortality or technical failure. This paper provides the probabilistic specification of this notion which gives an opportunity to use the results of modern general theory of processes in analyzing factors that influence demographic characteristics

Adaptive treatment allocation and selection in multi-arm clinical trials : a Bayesian perspective

Background: Adaptive designs offer added flexibility in the execution of clinical trials, including the possibilities of allocating more patients to the treatments that turned out more successful, and early stopping due to either declared success or futility. Commonly applied adaptive designs, such as group sequential methods, are based on the frequentist paradigm and on ideas from statistical significance testing. Interim checks during the trial will have the effect of inflating the Type 1 error rate, or, if this rate is controlled and kept fixed, lowering the power. Results: The purpose of the paper is to demonstrate the usefulness of the Bayesian approach in the design and in the actual running of randomized clinical trials during phase II and III. This approach is based on comparing the performance of the different treatment arms in terms of the respective joint posterior probabilities evaluated sequentially from the accruing outcome data, and then taking a control action if such posterior probabilities fall below a pre-specified critical threshold value. Two types of actions are considered: treatment allocation, putting on hold at least temporarily further accrual of patients to a treatment arm, and treatment selection, removing an arm from the trial permanently. The main development in the paper is in terms of binary outcomes, but extensions for handling time-to-event data, including data from vaccine trials, are also discussed. The performance of the proposed methodology is tested in extensive simulation experiments, with numerical results and graphical illustrations documented in a Supplement to the main text. As a companion to this paper, an implementation of the methods is provided in the form of a freely available R package 'barts'. Conclusion: The proposed methods for trial design provide an attractive alternative to their frequentist counterparts.Peer reviewe

Bayesian estimation of the number of individuals in a sample with a known weight

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Estimation of dynamic SNP-heritability with Bayesian Gaussian process models

Motivation: Improved DNA technology has made it practical to estimate single nucleotide polymorphism (SNP)-heritability among distantly related individuals with unknown relationships. For growth and development related traits, it is meaningful to base SNP-heritability estimation on longitudinal data due to the time-dependency of the process. However, only few statistical methods have been developed so far for estimating dynamic SNP-heritability and quantifying its full uncertainty. / Results: We introduce a completely tuning-free Bayesian Gaussian process (GP) based approach for estimating dynamic variance components and heritability as their function. For parameter estimation, we use a modern Markov Chain Monte Carlo (MCMC) method which allows full uncertainty quantification. Several data sets are analysed and our results clearly illustrate that the 95 % credible intervals of the proposed joint estimation method (which "borrows strength" from adjacent time points) are significantly narrower than of a two-stage baseline method that first estimates the variance components at each time point independently and then performs smoothing. We compare the method with a random regression model using MTG2 and BLUPF90 softwares and quantitative measures indicate superior performance of our method. Results are presented for simulated and real data with up to 1000 time points. Finally, we demonstrate scalability of the proposed method for simulated data with tens of thousands of individuals. / Availability: The C++ implementation dynBGP and simulated data are available in GitHub (https://github.com/aarjas/dynBGP). The programs can be run in R. Real datasets are available in QTL archive (https://phenome.jax.org/centers/QTLA). / Supplementary information: Supplementary data are available at Bioinformatics online

Bayesian non-parametric ordinal regression under a monotonicity constraint

Compared to the nominal scale, the ordinal scale for a categorical outcome variable has the property of making a monotonicity assumption for the covariate effects meaningful. This assumption is encoded in the commonly used proportional odds model, but there it is combined with other parametric assumptions such as linearity and additivity. Herein, the considered models are non-parametric and the only condition imposed is that the effects of the covariates on the outcome categories are stochastically monotone according to the ordinal scale. We are not aware of the existence of other comparable multivariable models that would be suitable for inference purposes. We generalize our previously proposed Bayesian monotonic multivariable regression model to ordinal outcomes, and propose an estimation procedure based on reversible jump Markov chain Monte Carlo. The model is based on a marked point process construction, which allows it to approximate arbitrary monotonic regression function shapes, and has a built-in covariate selection property. We study the performance of the proposed approach through extensive simulation studies, and demonstrate its practical application in two real data examples

Reversing conditional orderings

We analyze some specific aspects concerning conditional orderings and relations among them. To this purpose we define a suitable concept of reversed conditional ordering and prove some related results. In particular we aim to compare the univariate stochastic orderings ≤ st, ≤ hr, and ≤ lr in terms of differences among different notions of conditional orderings. Some applications of our result to the analysis of positive dependence will be detailed. We concentrate attention to the case of a pair of scalar random variables X, Y ​. Suitable extensions to multivariate cases are possible

Disability by occupation in Finland 1986-90

The present paper describes differences in the standardized disability ratio between occupations in Finland in 1986-1990. Furthermore, it gives an overview of the relationship between occupational disability and mortality. The data are based on the 1985 census records in Finland linked with all disability pensions during the period 1986-1990. The study includes the entire male and female labor force aged 25-54 years in 1985. An indirect standardization method was used to calculate the standardized disability ratio for each occupation. Results indicated clear differences in disability by occupations for both men and women. Among both sexes, the manual workers occupations had higher standardized disability ratios and white-collar occupations had lower ratios than the entire labor force. The disability of male occupations correlated strongly with occupational mortality, whereas among women the correlation between mortality and disability was weaker

Graphical models for marked point processes based on local independence

A new class of graphical models capturing the dependence structure of events that occur in time is proposed. The graphs represent so-called local independences, meaning that the intensities of certain types of events are independent of some (but not necessarily all) events in the past. This dynamic concept of independence is asymmetric, similar to Granger non-causality, so that the corresponding local independence graphs differ considerably from classical graphical models. Hence a new notion of graph separation, called delta-separation, is introduced and implications for the underlying model as well as for likelihood inference are explored. Benefits regarding facilitation of reasoning about and understanding of dynamic dependencies as well as computational simplifications are discussed.Comment: To appear in the Journal of the Royal Statistical Society Series