22-infectious-disease: 1
Flexible parametric additive hazards regression for modeling excess mortality in pandemics
Liesbeth C de Wreede1, Marina T Dietrich2, Ilaria Prosepe1, Hein Putter1, Mar Rodriguez-Girondo1
1LUMC (the Netherlands); 2University of Augsburg (Germany)
Effective decision-making during a pandemic requires balancing hospital capacity, protecting vulnerable groups, and minimizing societal burden. To make optimal policy decisions, it is crucial to quantify the impact of the pandemic on (excess) mortality and to assess the effects of public health interventions across various groups, accounting for infection and vaccination dynamics. However, a major challenge in the analysis of pandemic data is the absence of reliable cause-of-death information, which complicates the assessment of the pandemic’s specific impact.
Relative survival techniques are often used to assess excess mortality in a specific patient population by splitting observed mortality into background and excess mortality. These methods have been widely used to estimate cancer-specific mortality without the need for precise cause-of-death data. However, applying these techniques to estimate excess mortality in pandemic settings presents special challenges: standard relative survival methods assume (1) excess hazards are always positive, (2) background mortality is specified externally rather than derived from the data and based solely on demographic factors, and (3) a single time scale suffices. Pandemics, however, can involve negative excess hazards due to the protective effects of public health measures, large variations in background mortality across groups, and multiple time scales, such as time since vaccination and infection, that impact mortality risk beyond the main calendar time scale. Moreover, unlike in settings where the study population is a small subset of the reference population, in pandemic settings the background and study populations refer to the same group observed at different time points (pre-pandemic vs. pandemic).
To address these challenges, we propose a novel flexible parametric additive hazards model for pre-pandemic and pandemic data, using B-splines to estimate baseline hazards and time-dependent covariate effects. This new perspective on excess mortality estimation through a single additive hazards model accommodates negative excess hazards and integrates relevant risk factors into background mortality, equal to pre-pandemic mortality and estimated from the data. Moreover, this approach can handle multiple time scales and is less prone to overfitting than the classical non-parametric Aalen’s method. We investigated two estimation procedures: one based on the least-squares approach used for Aalen’s method, and the other exploiting the equivalence between additive hazards models with piecewise constant hazards and Poisson models with an identity link. The performance of the approach is demonstrated through a simulation study based on the COVID-19 pandemic and scenarios mimicking plausible pandemic conditions.
22-infectious-disease: 2
Parameter Estimation in Compartmental Epidemic Models with Heterogeneity in Susceptibility
Yuwen Ding1, Jacco Wallinga1,2, Hein Putter1
1Leiden University Medical Center, Leiden, The Netherlands; 2National Institute for Public Health and the Environment, Bilthoven, The Netherlands
Introduction
During the COVID-19 pandemic, compartmental epidemic models were crucial for forecasting epidemic dynamics and informing infection control policies. The susceptible-infectious-recovered (SIR) model provides a foundational framework for studying disease transmission but assumes a homogeneous population. To account for heterogeneity in susceptibility, we incorporate a frailty model by scaling the transmission parameter with individual random effects.
Methods
This study focuses on estimating the transmission parameter and frailty variance. We consider three distributions from the power variance function (PVF) family — gamma, inverse Gaussian, and compound Poisson with probability mass at zero — in a completely observed epidemic scenario. Epidemic outbreaks are simulated in R, and the data are transformed into an individual-level representation. Using the Laplace transform of the PVF distribution, we derive the observed data likelihood function and obtain maximum likelihood estimates via the optim function. A profile Expectation-Maximization (EM) algorithm is also developed as an alternative approach.
Results
For each frailty distribution, estimates for the transmission parameter and frailty variance are consistently close to the true values across various combinations of parameters and sample sizes, each evaluated over 1000 replications. The mean squared error remains small (<0.1), and the coverage of 95% confidence intervals closely aligns with the target level. The EM algorithm produces similarly accurate estimates but is computationally inefficient.
Conclusion
Incorporating frailty distributions into the SIR model captures individual-level heterogeneity in susceptibility, providing a more nuanced representation of epidemic dynamics. The proposed estimation approach demonstrates both accuracy and efficiency. Future work will extend this method to handle more realistic data mechanisms, based on daily counts of new infections, and apply it to real-world epidemic scenarios.
22-infectious-disease: 3
Unobserved intermediate events in multi-state models in a pandemic setting
Ilaria Prosepe, Hein Putter, Mar Rodriguez-Girondo, Liesbeth C. de Wreede
Department of Biomedical Data Sciences, Leiden University Medical Center, the Netherlands
Background/Introduction: Multi-state models are valuable for studying infectious diseases, as they allow to study mortality accounting for various relevant events, interventions and covariates. In a pandemic setting, the most relevant intermediate events are infections and vaccinations. However, under-reporting of infections and (to a lesser extent) vaccinations is common. While the topic of under-reporting has received a fair amount of attention in infectious disease modeling, limited guidance exists on handling missing state transitions and transition times in multi-state models. In our work we aim to explore methodology to address this issue.
Methods: We consider a semi-parametric (Cox-model based) illness-death model, with the intermediate state (illness) representing infection. The intermediate state is under-reported. In this model, our key estimands are the transition hazards, comprising baseline hazards and regression coefficients associated with relevant covariates, and the transition probabilities. Naïve estimation approaches that do not account for the under-reporting of infections underestimate the hazard of infection and overestimate the hazard of dying without illness. To overcome this, we explore how external knowledge can improve identifiability of each transition hazard by developing methods for incorporating it. Specifically, we investigate two approaches: recalibration of the naïve hazards by external data and multiple imputation of infection times with both data in the dataset and auxiliary external information on an aggregated level, such as hospitalization data.
Results: We will report results from an extensive simulation study to evaluate how external information can be employed for the estimation of the transition hazards and transition probabilities in different settings. We will report point estimates, variance, empirical standard error, absolute bias and root mean square error.
Conclusions: We present a framework of conditions under which the transition hazards of an illness-death model may be identified despite under-reporting of the intermediate state. We propose estimation methods and formulate an overview of pros and cons on how to proceed under different settings and under different types of external information. This helps to model the true burden of a pandemic.
22-infectious-disease: 4
Controlled vaccine efficacy using a joint model for sparse immunological data and time-to-disease.
Grigorios Papageorgiou1, Silvia Noirjean2, Toufik Zahaf3, Andrea Callegaro3
1GSK, Amsterdam, Netherlands, The; 2GSK, Siena, Italy; 3GSK, Wavre, Belgium
In vaccine development a key objective is to understand the immunological mechanisms that drive protection against the risk of disease. Typically, immune responses are collected at their expected peak level following the last vaccination dose planned. These peak measurements are subsequently used to establish correlates of protection (CoP) which means that the immunological biomarker can reliably predict vaccine efficacy (VE) and therefore act as a surrogate. There are several limitations and challenges that are typical in this setting. First, the immune response is expected to decay over time, and this might not be captured if only the peak measurements of the immunologic biomarker are used. Second, the sparsity in the collection of immune data over time poses an additional challenge in using approaches that exploit the whole immunological profile over time instead of the peak measurement.
To address these limitations and challenges we work under the joint modeling (JM) framework for longitudinal immunological data and time-to-disease data. This modeling approach enables us to use the whole immunological profile post vaccination and thus better understand the mechanisms that drive vaccine efficacy while improving its prediction. We view the sub-sampling of longitudinal responses as a missing data problem and show that under a missing at random (MAR) mechanism, inferences from the joint model are equivalent to analyzing the full cohort data if they were available. Furthermore, we leverage mediation analysis to define a causal effect called “controlled vaccine efficacy”, which captures the direct effect of the vaccine under different hypothetical immunological profiles. We show how this causal effect can be estimated using the joint model. Finally, we conduct a simulation study based on standard vaccine RCT settings to illustrate our approach, compare it with standard approaches and assess its performance under different scenarios and settings.
Our results suggest that the JM framework can overall improve the prediction of vaccine efficacy in terms of accuracy. The proposed JM controlled vaccine efficacy approach, enables the evaluation of longitudinal immune responses over time, rather than just peak levels, as a CoP.
22-infectious-disease: 5
Infectious Disease Estimands That Are Insensitive to Interference
Mats Stensrud
EPFL, Switzerland
The treatment of one individual often affects outcomes other individuals. A canonical example occurs in infectious disease settings, where vaccinating one individual can reduce disease transmission and thereby affect the health outcomes of others. This type of interference implies that individuals cannot plausibly be perceived as independent and identically distributed (iid). Extensive methodological research has recently been motivated by interference problems and the violation of conventional iid assumptions. However, despite growing interest in this topic, there remains controversy over whether and when existing methods capture causal effects of practical interest, such as in clinical medicine and public health.
In this talk, I will present causal methodology—motivated by infectious disease settings—for addressing interference. The central idea is to define estimands that are insensitive to the interference structure. This approach is not merely a workaround to avoid interference; rather, I will argue that the estimands have a clear interpretation and can guide decisions by doctors and patients. Specifically, these estimands can quantify vaccine waning and sieve effects, as illustrated by examples concerning COVID-19 and HIV.
|