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BMC Med Res Methodol. 2019 Jul 15;19(1):149. doi: 10.1186/s12874-019-0759-z.

"Spatial heterogeneity of environmental risk in randomized prevention trials: consequences and modeling".

Author information

1
Aix Marseille Univ, INSERM, IRD, SESSTIM, Sciences Economiques & Sociales de la Santé & Traitement de l'Information Médicale, Marseille, France. abdoulaye.guindo@etu.univ-amu.fr.
2
Malaria Research and Training Center - Ogobara K Doumbo, FMOS-FAPH, Mali-NIAID-ICER, Université des Sciences, des Techniques et des Technologies de Bamako, Bamako, Mali. abdoulaye.guindo@etu.univ-amu.fr.
3
Aix Marseille Univ, INSERM, IRD, SESSTIM, Sciences Economiques & Sociales de la Santé & Traitement de l'Information Médicale, Marseille, France.
4
Malaria Research and Training Center - Ogobara K Doumbo, FMOS-FAPH, Mali-NIAID-ICER, Université des Sciences, des Techniques et des Technologies de Bamako, Bamako, Mali.
5
Direction des systèmes d'information en santé, Ministère de la santé, Ouagadougou, Burkina Faso.
6
AP-HP, Hôpital Bichat, Unité de Recherche Clinique PNVS, Paris, France.
7
Laboratory of Malaria Immunology and Vaccinology, National Institute of Allergy and Infectious Diseases, National Institutes of Health, Rockville, Maryland, USA.
8
Aix Marseille Univ, APHM, INSERM, IRD, SESSTIM, Hop Timone, BioSTIC, Biostatistic & ICT, Marseille, France.

Abstract

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.

CONCLUSION:

Our results show that when spatial heterogeneity is important but not measured, randomization alone cannot achieve comparability between groups. In such cases, prevention trials should model spatial heterogeneity with an adapted method.

TRIAL REGISTRATION:

The dataset used for the application example was extracted from Vaccine Trial #NCT02334462 ( ClinicalTrials.gov registry).

KEYWORDS:

Environmental factors; Integrated Nested Laplace Approximation; Randomized prevention trials; Spatial heterogeneity; Stochastic Partial Differential Equation

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