arXiv subjects

Sangita Kulathinal

Publications and source records attributed to Sangita Kulathinal.

6 recordsLinked to original sources

arXiv2026

Discrete-time, discrete-state multistate Markov models from the perspective of algebraic statistics

We study discrete-time, discrete-state multistate Markov models from the perspective of algebraic statistics. These models are widely studied in event history analysis, and are characterized by the state space, the initial distribution and the transition probabilities. A finite path under the multistate Markov model is a particular set of states occupied at finite time instances $\{1, \dots, n\}$. The main goal of this paper is to establish a bridge between event history analysis and algebraic statistics. The joint probabilities of finite paths in these models have a natural monomial parametrization in terms of the initial distribution and the transition probabilities. We study the polynomial relations among joint path probabilities. When the statistical constraints on the parameters are disregarded, nonhomogeneous multistate Markov models of arbitrary order can be viewed as slices of decomposable hierarchical models. This yields a complete description of their vanishing ideals as toric ideals generated by explicit families of binomials. Moreover, the variety of this vanishing ideal equals the nonhomogeneous multistate Markov model on the probability simplex. In contrast, homogeneous multistate Markov models exhibit different algebraic behavior, as time homogeneity imposes additional polynomial relations, leading to vanishing ideals that are strictly larger than in the nonhomogeneous case. We also derive families of binomial relations that vanish on homogeneous multistate Markov models. We investigate maximum likelihood estimation from statistical and algebraic perspectives. For nonhomogeneous models, classical and algebraic formulas agree; in the homogeneous case, the algebraic approach is more complex. Lastly, we provide data applications where we demonstrate the statistical theory to obtain the maximum likelihood estimates of the parameters under specific multistate Markov models.

math.ST↗

arXiv2025

Estimating Transition Rates in Two-State Non-Homogeneous Markov Jump Processes with Intermittent Observations: A Pseudo-Marginal McMC Approach via Honest Times

A possibly time-dependent transition intensity matrix or generator $(Q(t))$ characterizes the law of a Markov jump process (MP). For a time homogeneous MP, the transition probability matrix (TPM) can be expressed as a matrix exponential of $Q$. However, when dealing with a time non-homogeneous MP, there is often no simple analytical form of the TPM in terms of $Q(t)$, unless they all commute. This poses a challenge because when a continuous MP is observed intermittently, a TPM is required to build a likelihood. In this paper, we show that the estimation of the transition intensities of a two-state nonhomogeneous Markov model can be carried out by augmenting the intermittent observations with honest random times associated with two independent driving Poisson point processes, and that sampling the full path is not required. We propose a pseudo-marginal McMC algorithm to estimate the transition rates using the augmented data. Finally, we illustrate our approach by simulating a continuous MP and by using observed (intermittent) time grids extracted from real clinical visits data.

stat.ME↗

arXiv2024

Efficiency gain in association studies based on population surveys by augmenting outcome data from the target population

Routinely collected nation-wide registers contain socio-economic and health-related information from a large number of individuals. However, important information on lifestyle, biological and other risk factors is available at most for small samples of the population through surveys. A majority of health surveys lack detailed medical information necessary for assessing the disease burden. Hence, traditionally data from the registers and the surveys are combined to have necessary information for the survey sample. Our idea is to base analyses on a combined sample obtained by adding a (large) sample of individuals from the population to the survey sample. The main objective is to assess the bias and gain in efficiency of such combined analyses with a binary or time-to-event outcome. We employ (i) the complete-case analysis (CCA) using the respondents of the survey, (ii) analysis of the full survey sample with both unit- and item-nonresponse under the missing at random (MAR) assumption and (iii) analysis of the combined sample under mixed type of missing data mechanism. We handle the missing data using multiple imputation (MI)-based analysis in (ii) and (iii). We utilize simulated as well as empirical data on ischemic heart disease obtained from the Finnish population. Our results suggested that the MI methods improved the efficiency of the estimates when we used the combined data for a binary outcome, but in the case of a time-to-event outcome the CCA was at least as good as the MI using the larger datasets, in terms of the the mean absolute and squared errors. Increasing the participation in the surveys and having good statistical methods for handling missing covariate data when the outcome is time-to-event would be needed for implementation of the proposed ideas.

stat.ME↗

arXiv2023

SANSformers: Self-Supervised Forecasting in Electronic Health Records with Attention-Free Models

Despite the proven effectiveness of Transformer neural networks across multiple domains, their performance with Electronic Health Records (EHR) can be nuanced. The unique, multidimensional sequential nature of EHR data can sometimes make even simple linear models with carefully engineered features more competitive. Thus, the advantages of Transformers, such as efficient transfer learning and improved scalability are not always fully exploited in EHR applications. Addressing these challenges, we introduce SANSformer, an attention-free sequential model designed with specific inductive biases to cater for the unique characteristics of EHR data. In this work, we aim to forecast the demand for healthcare services, by predicting the number of patient visits to healthcare facilities. The challenge amplifies when dealing with divergent patient subgroups, like those with rare diseases, which are characterized by unique health trajectories and are typically smaller in size. To address this, we employ a self-supervised pretraining strategy, Generative Summary Pretraining (GSP), which predicts future summary statistics based on past health records of a patient. Our models are pretrained on a health registry of nearly one million patients, then fine-tuned for specific subgroup prediction tasks, showcasing the potential to handle the multifaceted nature of EHR data. In evaluation, SANSformer consistently surpasses robust EHR baselines, with our GSP pretraining method notably amplifying model performance, particularly within smaller patient subgroups. Our results illuminate the promising potential of tailored attention-free models and self-supervised pretraining in refining healthcare utilization predictions across various patient demographics.

cs.LG↗

arXiv2020

Estimation of marriage incidence rates by combining two cross-sectional retrospective designs: Event history analysis of two dependent processes

The aim of this work is to develop methods for studying the determinants of marriage incidence using marriage histories collected under two different types of retrospective cross-sectional study designs. These designs are: sampling of ever married women before the cross-section, a prevalent cohort, and sampling of women irrespective of marital status, a general cross-sectional cohort. While retrospective histories from a prevalent cohort do not identify incidence rates without parametric modelling assumptions, the rates can be identified when combined with data from a general cohort. Moreover, education, a strong endogenous covariate, and marriage processes are correlated. Hence, they need to be modelled jointly in order to estimate the marriage incidence. For this purpose, we specify a multi-state model and propose a likelihood-based estimation method. We outline the assumptions under which a likelihood expression involving only marriage incidence parameters can be derived. This is of particular interest when either retrospective education histories are not available or related parameters are not of interest. Our simulation results confirm the gain in efficiency by combining data from the two designs, while demonstrating how the parameter estimates are affected by violations of the assumptions used in deriving the simplified likelihood expressions. Two Indian National Family Health Surveys are used as motivation for the methodological development and to demonstrate the application of the methods.

stat.ME↗

arXiv2017

Optimal design of observational studies: overview and synthesis

We review typical design problems encountered in the planning of observational studies and propose a unifying framework that allows us to use the same concepts and notation for different problems. In the framework, the design is defined as a probability measure in the space of observational processes that determine whether the value of a variable is observed for a specific unit at the given time. The optimal design is then defined, according to Bayesian decision theory, to be the one that maximizes the expected utility related to the design. We present examples on the use of the framework and discuss methods for deriving optimal or approximately optimal designs.

math.ST↗