Conference Agenda

Compartmental models based on ordinary differential equations (ODE’s) quantifying the interactions between susceptible, infectious, and recovered individuals within a population have played an important role in infectious disease modeling. The aim of the present talk is to explain the link between stochastic epidemic models based on the susceptible-infectious-recovered (SIR) model, and methods from survival analysis. We develop new approaches to infer time-constant or time-varying transmission rates by building on the available work in the field of survival analysis. We first illustrate the basic ideas and terminology and notation in a highly idealized setting, with idealized data where all events in a population are observed, and an idealized stochastic epidemic model where all individuals are similar, except for their infection history, and where the transmission rate is constant. In this setting we can derive an explicit MLE estimator that we will use as a benchmark. We will show how time-varying transmission rates can be inferred and tests for constancy can be performed, and we will relax assumptions with respect to the underlying epidemic model, allowing for differences between groups of individuals and allowing for differences between individuals, additive terms such as import of infection, and multiplicative terms such as control measures that affect transmission rate. We will also suggest approaches to relax the assumptions made about the idealized data and allow for unobserved events, incompletely observed events, and binned data.

Viral load (VL) in the respiratory tract is the leading proxy for assessing infectiousness potential. Understanding the dynamics of disease-related VL within the host is of great importance, as it helps to determine different policies and health recommendations. However, normally the VL is measured on individuals only once, in order to confirm infection, and furthermore, the infection date is rarely known. It is impossible to estimate the VL trajectory based on such observational data, and it is therefore necessary to design statistical approaches for this purpose. In order to be practical, the approach should be logistically simple so that reliable results can be obtained in a short time. We show here that, under plausible parametric assumptions, two measures of VL on infected individuals can be used to accurately estimate the VL mean function. Specifically, we consider a discrete time likelihood-based approach to modelling and estimating partial observed longitudinal samples. We study a multivariate normal model for the VL measures that accounts for correlation between measurements within individuals. We derive an expectation-maximization (EM) algorithm which treats the unknown time origins and the missing measurements as latent variables. Our main motivation is the reconstruction of the daily mean VL, given measurements on patients whose VLs were measured multiple times on different days. Such data should and can be collected at a beginning of a pandemic with the specific goal of estimating the VL dynamics. We further compare, by simulation, different study designs. For demonstration purposes, the method is applied to SARS-Cov-2 cycle-threshold-value data collected in Israel.

Background
HIV remains a major public health challenge in South Africa, particularly among young women and adolescents. Research indicates that sexual health behaviors—including contraceptive use, sexually transmitted infections (STIs), and condom use—do not operate independently but interact in complex ways that influence HIV risk. For example, inconsistent condom use, high STI prevalence, and certain contraceptive methods may increase susceptibility to HIV acquisition. However, traditional statistical approaches often fail to capture these interdependencies over time. Multivariate joint modeling provides an advanced analytical framework for examining these associations, offering a more comprehensive understanding of how sexual behaviors contribute to HIV transmission risk.

Methods
Inspired by the CAP004 clinical trial conducted by CAPRISA which enrolled sexually active, HIV-uninfected women aged 18 to 40 years in South Africa, this study employs multivariate joint modeling to analyze longitudinal data on sexual behaviors (contraceptive use, STIs, and condom use) alongside time-to-event outcomes (HIV infection and pregnancy, used as a proxy for HIV risk). By simultaneously accounting for correlated processes, this approach enables more accurate estimation of how these behaviors evolve and influence HIV acquisition over time. Data will be drawn from a cohort of individuals at high risk for HIV, with repeated measures of sexual health indicators and HIV outcomes. This modeling framework allows for the identification of trends and causal pathways that conventional regression techniques may overlook.

Results
We anticipate that inconsistent condom use, STI presence, and specific contraceptive methods—such as depot medroxyprogesterone acetate—will be associated with an increased risk of HIV acquisition. Multivariate joint modeling is expected to provide stronger evidence of how these factors interact over time, uncovering key risk patterns. The results will offer deeper insights into the longitudinal dynamics of sexual health behaviors and their contribution to HIV transmission, demonstrating the advantages of this modeling approach over traditional methods.

Conclusion
While the application of joint models in South African HIV research remains limited, studies in other contexts have shown their potential to uncover critical risk factor interactions. This study will contribute novel insights into the complex interplay of sexual health behaviors and HIV risk in South Africa, informing the development of more effective, evidence-based HIV prevention strategies tailored to high-risk populations.

The study of platelet aggregation kinetics often requires methods that can capture the full complexity of dynamic processes. Traditional approaches frequently rely on summary statistics, which can obscure critical information embedded within the temporal evolution of the data. This work presents a powerful alternative: a Functional Data Analysis (FDA) approach that models aggregation curves using penalized splines within a Linear Mixed Model (LMM) framework.

Our method leverages the flexibility of Truncated Polynomial Splines (TPS) to represent complex curve shapes. TPS combines polynomial terms and truncated power functions, enabling smooth curve estimation while penalizing roughness through the LMM structure. By treating polynomial coefficients as fixed effects and truncated terms as random effects, we can utilize Best Linear Unbiased Prediction (BLUP) for robust estimation and analytical derivation of derivatives.

A key innovation of this approach lies in the estimation and interpretation of derivatives, such as velocity and acceleration, which provide critical insights into the underlying kinetics of the system. Unlike traditional methods that focus on static endpoints, these derivatives allow us to model the dynamic system using differential equations, revealing phenomena such as bistability and phase transitions.

We demonstrate the utility of this method through an application to platelet aggregation kinetics, where we analyze the effects of ADP and gold nanoparticles on aggregation profiles. This application showcases how the method can capture the nuances of complex biological interactions, revealing the interplay between ADP concentration, purinergic receptor activation, and nanoparticle-induced effects. Specifically, the method allowed for discerning the underlying kinetics, as well as to study the effects of ADP dosage and perturbation with gold nanoparticles.

This FDA approach, implemented using R with the nlme package, offers significant advantages over traditional methods. By capturing full temporal profiles and identifying metastable states, it provides a more comprehensive understanding of platelet aggregation dynamics. However, it's crucial to address the computational challenges associated with high-dimensional random effects and the sensitivity of derivatives to noise.

This method's generality makes it applicable to other temporal biomedical datasets requiring kinetic analysis. By providing a flexible and statistically rigorous framework for modeling dynamic processes, this work contributes to a deeper understanding of complex biological systems.

Longitudinal studies offer critical insights into health conditions but face challenges in integrating survey and psychometric data into standardized frameworks like the Observational Medical Outcomes Partnership (OMOP) Common Data Model (CDM). With the cancellation of the survey_conduct table in CDM 6.0, this study proposes a novel methodology to map standardized instruments such as PHQ-9 and GAD-7 into the OMOP CDM, addressing critical gaps in the model.

The methodology leverages a structured process for data integration, starting with the creation of measurements using vocabularies like LOINC and SNOMED. Instrument scores and individual panel items are mapped as observations, with relationships like “Has Answer” ensuring consistency. Tying measurements to visit occurrences through observation_event_id maintains data integrity across longitudinal encounters. Conditions such as "anxiety disorder" are identified and mapped using SNOMED concepts, linked back to corresponding measurements. Insights from OHDSI forums informed iterative refinements, ensuring compatibility with existing vocabularies.

Results show that the methodology effectively integrates psychometric instruments into the OMOP CDM, enabling advanced analysis of mental health outcomes. By addressing the absence of survey_conduct capabilities, the framework facilitates machine learning applications, such as predictive modeling and clustering of longitudinal data, while preserving the semantic integrity of health data.

This work provides a scalable solution for mapping survey data into the OMOP CDM, bridging a key gap in longitudinal data management and advancing global health research. The framework enhances data standardization and usability, contributing to evidence-based policy-making and interventions. Future efforts will extend this methodology to emerging instruments and vocabularies, supporting the evolution of data science frameworks in health research.