Estimation of vaccine efficacy in a repeated measures study under heterogeneity of exposure or susceptibility to infection (original) (raw)
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BMC Medical Research Methodology, 2019
Background: In the context of environmentally influenced communicable diseases, proximity to environmental sources results in spatial heterogeneity of risk, which is sometimes difficult to measure in the field. Most prevention trials use randomization to achieve comparability between groups, thus failing to account for heterogeneity. This study aimed to determine under what conditions spatial heterogeneity biases the results of randomized prevention trials, and to compare different approaches to modeling this heterogeneity. Methods: Using the example of a malaria prevention trial, simulations were performed to quantify the impact of spatial heterogeneity and to compare different models. Simulated scenarios combined variation in baseline risk, a continuous protective factor (age), a non-related factor (sex), and a binary protective factor (preventive treatment). Simulated spatial heterogeneity scenarios combined variation in breeding site density and effect, location, and population density. The performances of the following five statistical models were assessed: a non-spatial Cox Proportional Hazard (Cox-PH) model and four models accounting for spatial heterogeneity-i.e., a Data-Generating Model, a Generalized Additive Model (GAM), and two Stochastic Partial Differential Equation (SPDE) models, one modeling survival time and the other the number of events. Using a Bayesian approach, we estimated the SPDE models with an Integrated Nested Laplace Approximation algorithm. For each factor (age, sex, treatment), model performances were assessed by quantifying parameter estimation biases, mean square errors, confidence interval coverage rates (CRs), and significance rates. The four models were applied to data from a malaria transmission blocking vaccine candidate. Results: The level of baseline risk did not affect our estimates. However, with a high breeding site density and a strong breeding site effect, the Cox-PH and GAM models underestimated the age and treatment effects (but not the sex effect) with a low CR. When population density was low, the Cox-SPDE model slightly overestimated the effect of related factors (age, treatment). The two SPDE models corrected the impact of spatial heterogeneity, thus providing the best estimates.
Bias reduction for risk ratio and vaccine effect estimators
Statistics in Medicine, 2001
We examine the structural bias for established estimators of vaccine e ects on susceptibility and for newer estimates of vaccine e ects on infectiousness. We then propose and analyse new bias corrections for vaccine e ect estimators of both susceptibility and infectiousness, as well as their combined e ect on infection transmission. Each estimator is evaluated empirically with computer simulations. Of the estimators examined in this paper, those with the least bias and root mean squared error are computed by adding one to the positive count in the placebo population. We also identify a source of bias for a standard Bayesian estimator of risk ratios.
Malaria journal, 2014
Recurrent events data analysis is common in biomedicine. Literature review indicates that most statistical models used for such data are often based on time to the first event or consider events within a subject as independent. Even when taking into account the non-independence of recurrent events within subjects, data analyses are mostly done with continuous risk interval models, which may not be appropriate for treatments with sustained effects (e.g., drug treatments of malaria patients). Furthermore, results can be biased in cases of a confounding factor implying different risk exposure, e.g. in malaria transmission: if subjects are located at zones showing different environmental factors implying different risk exposures. This work aimed to compare four different approaches by analysing recurrent malaria episodes from a clinical trial assessing the effectiveness of three malaria treatments [artesunate + amodiaquine (AS + AQ), artesunate + sulphadoxine-pyrimethamine (AS + SP) or ...
Use of Fixed Effects Models to Analyze Self-Controlled Case Series Data in Vaccine Safety Studies
Journal of Biometrics & Biostatistics, 2012
Conditional Poisson models have been used to analyze vaccine safety data from self-controlled case series (SCCS) design. In this paper, we derived the likelihood function of fixed effects models in analyzing SCCS data and showed that the likelihoods from fixed effects models and conditional Poisson models were proportional. Thus, the maximum likelihood estimates (MLEs) of time-varying variables including vaccination effect from fixed effects model and conditional Poisson model were equal. We performed a simulation study to compare empirical type I errors, means and standard errors of vaccination effect coefficient, and empirical powers among conditional Poisson models, fixed effects models, and generalized estimating equations (GEE), which has been commonly used for analyzing longitudinal data. Simulation study showed that both fixed effect models and conditional Poisson models generated the same estimates and standard errors for time-varying variables while GEE approach produced different results for some data sets. We also analyzed SCCS data from a vaccine safety study examining the association between measles mumps-rubella (MMR) vaccination and idiopathic thrombocytopenic purpura (ITP). In analyzing MMR-ITP data, likelihood-based statistical tests were employed to test the impact of time-invariant variable on vaccination effect. In addition a complex semi-parametric model was fitted by simply treating unique event days as indicator variables in the fixed effects model. We conclude that theoretically fixed effects models provide identical MLEs as conditional Poisson models. Because fixed effect models are likelihood based, they have potentials to address methodological issues in vaccine safety studies such as how to identify optimal risk window and how to analyze SCCS data with misclassification of adverse events
Ensemble Modeling of the Likely Public Health Impact of a Pre-Erythrocytic Malaria Vaccine
PLoS Medicine, 2012
Background: The RTS,S malaria vaccine may soon be licensed. Models of impact of such vaccines have mainly considered deployment via the World Health Organization's Expanded Programme on Immunization (EPI) in areas of stable endemic transmission of Plasmodium falciparum, and have been calibrated for such settings. Their applicability to low transmission settings is unclear. Evaluations of the efficiency of different deployment strategies in diverse settings should consider uncertainties in model structure. Methods and Findings: An ensemble of 14 individual-based stochastic simulation models of P. falciparum dynamics, with differing assumptions about immune decay, transmission heterogeneity, and treatment access, was constructed. After fitting to an extensive library of field data, each model was used to predict the likely health benefits of RTS,S deployment, via EPI (with or without catch-up vaccinations), supplementary vaccination of school-age children, or mass vaccination every 5 y. Settings with seasonally varying transmission, with overall pre-intervention entomological inoculation rates (EIRs) of two, 11, and 20 infectious bites per person per annum, were considered. Predicted benefits of EPI vaccination programs over the simulated 14-y time horizon were dependent on duration of protection. Nevertheless, EPI strategies (with an initial catch-up phase) averted the most deaths per dose at the higher EIRs, although model uncertainty increased with EIR. At two infectious bites per person per annum, mass vaccination strategies substantially reduced transmission, leading to much greater health effects per dose, even at modest coverage. Conclusions: In higher transmission settings, EPI strategies will be most efficient, but vaccination additional to the EPI in targeted low transmission settings, even at modest coverage, might be more efficient than national-level vaccination of infants. The feasibility and economics of mass vaccination, and the circumstances under which vaccination will avert epidemics, remain unclear. The approach of using an ensemble of models provides more secure conclusions than a single-model approach, and suggests greater confidence in predictions of health effects for lower transmission settings than for higher ones.
Assessing surrogate endpoints in vaccine trials with case-cohort sampling and the Cox model
The Annals of Applied Statistics, 2008
Assessing immune responses to study vaccines as surrogates of protection plays a central role in vaccine clinical trials. Motivated by three ongoing or pending HIV vaccine efficacy trials, we consider such surrogate endpoint assessment in a randomized placebo-controlled trial with case-cohort sampling of immune responses and a time to event endpoint. Based on the principal surrogate definition under the principal stratification framework proposed by Frangakis and Rubin [Biometrics 58 (2002) 21-29] and adapted by , we introduce estimands that measure the value of an immune response as a surrogate of protection in the context of the Cox proportional hazards model. The estimands are not identified because the immune response to vaccine is not measured in placebo recipients. We formulate the problem as a Cox model with missing covariates, and employ novel trial designs for predicting the missing immune responses and thereby identifying the estimands. The first design utilizes information from baseline predictors of the immune response, and bridges their relationship in the vaccine recipients to the placebo recipients. The second design provides a validation set for the unmeasured immune responses of uninfected placebo recipients by immunizing them with the study vaccine after trial closeout. A maximum estimated likelihood approach is proposed for estimation of the parameters. Simulated data examples are given to evaluate the proposed designs and study their properties.
Vaccine Efficacy at a Point in Time
2021
Vaccine trials are generally designed to assess efficacy on clinical disease. The vaccine effect on infection, while important both as a proxy for transmission and to describe a vaccine’s total effects, requires frequent longitudinal sampling to capture all infections. Such sampling may not always be feasible. A logistically easy approach is to collect a sample to test for infection at a regularly scheduled visit. Such point or cross-sectional sampling does not permit estimation of classic vaccine effiacy on infection, as long duration infections are sampled with higher probability. Building on work by Rinta-Kokko and others (2009) we evaluate proxies of the vaccine effect on transmission at a point in time; the vaccine efficacy on prevalent infection and on prevalent viral load, VEPI and VEPV L, respectively. Longer infections with higher viral loads should have more transmission potential and prevalent vaccine efficacy naturally captures this aspect. We apply a proportional hazard...
Biometrics, 2021
Estimating population‐level effects of a vaccine is challenging because there may be interference, that is, the outcome of one individual may depend on the vaccination status of another individual. Partial interference occurs when individuals can be partitioned into groups such that interference occurs only within groups. In the absence of interference, inverse probability weighted (IPW) estimators are commonly used to draw inference about causal effects of an exposure or treatment. Tchetgen Tchetgen and VanderWeele proposed a modified IPW estimator for causal effects in the presence of partial interference. Motivated by a cholera vaccine study in Bangladesh, this paper considers an extension of the Tchetgen Tchetgen and VanderWeele IPW estimator to the setting where the outcome is subject to right censoring using inverse probability of censoring weights (IPCW). Censoring weights are estimated using proportional hazards frailty models. The large sample properties of the IPCW estimat...
Joint modelling of time-to-clinical malaria and parasite count in a cohort in an endemic area
Journal of Medical Statistics and Informatics, 2019
Background: In malaria endemic areas such as sub-Saharan Africa, repeated exposure to malaria results in acquired immunity to clinical disease but not infection. In prospective studies, time-to-clinical malaria and longitudinal parasite count trajectory are often analysed separately which may result in inefficient estimates since these two processes can be associated. Including parasite count as a time-dependent covariate in a model of time-to-clinical malaria episode may also be inaccurate because while clinical malaria disease frequently leads to treatment which may instantly affect the level of parasite count, standard time-to-event models require that timedependent covariates be external to the event process. We investigated whether jointly modelling time-to-clinical malaria disease and longitudinal parasite count improves precision in risk factor estimates and assessed the strength of association between the hazard of clinical malaria and parasite count. Methods: Using a cohort data of participants enrolled with uncomplicated malaria in Malawi, a conventional Cox Proportional Hazards (PH) model of time-to-first clinical malaria episode with time-dependent parasite count was compared with three competing joint models. The joint models had different association structures linking a quasi-Poisson mixed-effects of parasite count and event-time Cox PH sub-models.
A stochastic model of vaccine trials for endemic infections using group randomization
Epidemiology and Infection, 2004
To clarify the determinants of vaccine trial power for non-typable Haemophilus influenzae, we constructed stochastic SIS models of infection transmission in small units (e.g. day-care centres) to calculate the equilibrium distribution of the number infected. We investigated how unit size, contact rate (modelled as a function of the unit size), external force of infection and infection duration affected the statistical power for detection of vaccine effects on susceptibility or infectiousness. Given a frequency-dependent contact rate, the prevalence, proportion of infections generated internally and the power to detect vaccine effects each increased slightly with unit size. Under a density-dependent model, unit size had much stronger effects. To maximize information allowing inference from vaccine trials, contact functions should be empirically evaluated by studying units of differing size and molecular methods should be used to help distinguish internal vs. external transmission.