During my PhD I developed dose-response models for C. burnetii [1][2] and then spatially correlated dose estimates to study spatial patterns of exposure during the large Q fever outbreaks in the Netherlands (Brooke et al. accepted, Brooke et al. accepted). To estimate the smooth dose field I used a Spatial Generalized Linear Mixed Models (SGLMM) as described by Diggle et al. in his piece in Applied Statistics in 1998 titled, ‘Model based geostatistics (with discussion)’ and applied in other works [3].

In his work he describes using a GLMM and including a spatial term to account for residual spatial correlation after including other covariates into the mixed model. Specifically, a SGLMM is structured as,

Y ~ f(μ)

μ = β_0 + β_1x_1 + β_2x_2 + … + β_nx_n + S + ε

where Y is the outcome, f(.) is the link function/error distribution, μ is the linear predictor, x are the covariates, β are the regression coefficients, S is the spatially correlated residuals term, and ε is the random intercept term (N(0, σ^2)).

The spatial term accounts for any residual spatial pattern in the model using a multivariate normal distribution with mean zero and a symmetrical covariance matrix defined by an exponential distance decay function. Specifically, the spatial term has the following structure,

S ~ MVN(0, Σ_s)

Σ_s = κ · exp(-λ · D_i,j)

where κ is the scale parameter, λ is the shape parameter, D_i,j is the euclidean distance between point i and point j.

Consulting Work

I have advised companies on how best to integrate satellite imagery, weather data, and spatially explicit insect infection rates to predict temporal trends of infection rates based on macro endemic and epidemic trends together with micro environmental trends.

Consulting work can focus on data limitations and artifacts associated with evidence synthesis of spatial data across multiple modalities. An example of the issues faced include leveraging different types of spatial data including point data with regional averages as well as macro level trends with micro level trends in hierarchical framework.