Spatial structure in infectious disease epidemiology: What does it mean?

1. Spatial structure in infectious disease epidemiology: What does it mean? MICHAEL WARD | Faculty of Veterinary Science

2. A conundrum in spatial analysis • a spatial analytical framework: find show explain interesting disease patterns • assume landscape / environment determine spatial structure • inevitably confounded by the population we study Is it the environment, or is it the host population? What is the most parsimonious explanation?

3. Multivariable versus multivariate modelling

5. Bayesian graphical network modelling A Bayesian graphical network represents the probabilistic relationships among a set of variables Equivalent to a network of multivariable generalised linear models. The joint probability distribution is encoded as a DAG (directed acyclic graph). Ref: http://www.bayesnets.com/

6. Bayesian graphical network modelling Structure discovery For <20 variables can use exact structure discovery methods of Koivisto & Sood (2004) As we have >20 variables, must use a heuristic approach to identify a ‘best consensus model’ Bayesian hill-climbing algorithm (Heckerman et al., 1995) vague priors placed on all nodes (covariates) and potential links (associations) Tens of thousands of searches starting from random locations in the multi-dimensional modelling space Each identifies a high scoring network structure Model averaging  50% consensus network model

7. Bayesian graphical network modelling multivariable confounding one outcome multivariate • Firestone, S.M., Schemann, K.A., Lewis, F.I., Ward, M.P., Toribio, J-A.L.M.L., Dhand, N.K. Modelling the associations between on-farm biosecurity practice and equine influenza infection during the 2007 outbreak in Australia. Preventive Veterinary Medicine 2013;110: 28-36 multiple inter-dependent variables 7

8. BGN Modelling and Spatial Analysis Case study: Salmonella infection in feral pigs

9. The Study Area 18.2S, 125.6E The Kimberley Fitzroy Crossing study site ~10 000 km2 Kimberley region >400 000 km2 EU: 10M km2

13. 3,500 feral pigs in 275 ‘herds’

17. Sampling distribution

18. Salmonella distribution • 651 pigs sampled • 240 pigs Salmonella +ve(~37%) • 39 different Salmonellaserovars isolated • S. typhimurium not isolated • previous work in the EU: upper limit of prevalence

19. Salmonella spatial structure scan statistic (Bernoulli model) fecal–positive pigs only observed:expected 1.5

20. Salmonella spatial structure

21. The data • faecal infection status • lymph node infection status • enhanced vegetation index 16, 32, 64, 128, 192 days • pig density • distance to a major waterway • distance to a minor waterway • distance to a waterbody • number of waterbodies • number of streams • slope • 542 observations

22. Multivariable and multivariate analyses • standard logistic regression (fecal, LN status separately as the outcome variable) • exact search using bootstrapping (with no parent limit) • bootstrap the dataset • find the best DAG • repeat many times until a stable majority consensus DAG obtained • exact search on the data without bootstrapping (in case above search was too conservative)

23. Multivariable analyses • glm(formula = LN_salmonella_pos ~ ., family = "binomial", data = mydat)Estimate Std. Error z value Pr(>|z|)    (Intercept) ‒5.9819791 3.3719186 ‒1.774 0.076054 .  faecal_infected1 0.9686363 0.2908965 3.330 0.000869 ***EVI_16 ‒0.0010645 0.0030285 ‒0.352 0.725211EVI_32 0.0096010 0.0078382 1.225 0.220614EVI_64 ‒0.0111865 0.0071712 ‒1.560 0.118778EVI_128 0.0079115 0.0050636 1.562 0.118186EVI_192 ‒0.0036400 0.0035296 ‒1.031 0.302422Pig_density‒3.7663023 6.6319403 ‒0.568 0.570100Dist_major_water 0.0001075 0.0002664 0.403 0.686631Dist_minor_water‒0.0227323 0.3054398 ‒0.074 0.940672Dist_waterbody‒0.0312163 0.2476048 ‒0.126 0.899674No_waterbodies 0.0665093 0.1277485 0.521 0.602627No_streams‒0.0011000 0.0461551 ‒0.024 0.980986Flat_sum 0.0025893 0.0033440 0.774 0.438757

24. Multivariable analyses • glm(formula = faecal_infected ~ ., family = "binomial", data = mydat)Estimate Std. Error z-value Pr(>|z|)(Intercept) 2.4726860 2.1058388 1.174 0.240313LN_salmonella_pos1 0.9904840 0.2885825 3.432 0.000599 ***EVI_16 ‒0.0004481 0.0019600 ‒0.229 0.819147EVI_32 0.0028477 0.0051640 0.551 0.581329EVI_64 ‒0.0002995 0.0038822 ‒0.077 0.938497EVI_128 ‒0.0039968 0.0032640 ‒1.224 0.220770EVI_192 0.0004255 0.0022379 0.190 0.849194Pig_density‒1.5544500 4.2949025 ‒0.362 0.717405Dist_major_water 0.0001489 0.0001691 0.880 0.378773Dist_minor_water‒0.5664415 0.1922911 ‒2.946 0.003222 ** Dist_waterbody‒0.1113402 0.1524897 ‒0.730 0.465299No_waterbodies 0.0927183 0.0802288 1.156 0.247814No_streams‒0.0350714 0.0293388 ‒1.195 0.231934Flat_sum 0.0014939 0.0023693 0.630 0.528370

25. Multivariable analyses distance to minor waterways LN Samonella status fecal Samonella status

26. stable majority consensus DAG using an exact search and boot-strapping (no parent limit) Multivariate analyses

27. Multivariate analyses - exact search without bootstrapping

28. The environment and Salmonella transmission • a relationship between distance to minor waterways and Salmonella fecal status not identified in either DAG analyses • forcing an arc into the DAG substantially reduced goodness of fit • logistic regression residuals non-Normal • identification of variable (P=0.003) probably spurious • so what drives Salmonella transmission within this environment?

29. How about the host population characteristics? • DICE (genetic similarity) • Salmonella status: • carrier (both pigs LN positive) • transient (≥1faecal positive) • age • gender • pregnancy status • lactation status • weight • condition • herd • pig density • 2,583 observations

30. Spatial structure in infectious disease epidemiology • local environment in effect a disease independent factor • simply describes the ecosystem which allows the pigs to survive • main driver of Salmonella infection is host attributes • spatial correlation does not imply spatial causation • space can be just a proxy for underlying factors such as host attributes • consider non-spatial factors first, then look for spatial explanations

31. Acknowledgements • Fraser Lewis, University of Zurich • Swiss National Science Foundation • Brendan Cowled, AusVet Animal Health Services • Shawn Laffan, University of New South Wales • funding: Australian Research Council • no funding: EU

32. Spatial structure in infectious disease epidemiology: What does it mean? MICHAEL WARD | Faculty of Veterinary Science