class: center, middle, inverse, title-slide # Spread-rate of lumpy skin disease in the Balkans and Turkey (2014-2019) ###
Facundo Muñoz
, A. Mercier, R. Lancelot, J. Cauchard
facundo.munoz@cirad.fr
famuvie
### GT2 DNC. Paris, Nov 2019 --- background-image: url(img/LSD_progress_cases.gif) background-size: contain --- class: large # Objectives 1. Epidemiological description 1. Spread-rate __estimates__ 1. __Methodology__ 1. __Uncertainty__ assessment --- class: inverse, center, middle # Estimates --- # Spatial distribution of cases ![](slides_FMunoz_files/figure-html/plot-spatial-cases-1.png)<!-- --> --- # Spatial distribution of cases ![](slides_FMunoz_files/figure-html/plot-density-cases-1.png)<!-- --> --- # Balkan peninsula and Turkey ![](slides_FMunoz_files/figure-html/plot-balkey-region-1.png)<!-- --> --- # Evolution of cases per country ![](slides_FMunoz_files/figure-html/unnamed-chunk-2-1.png)<!-- --> --- # Average spread-rate estimate .pull-left[ ![Estimate of global average spread rate: mean and 89% MC interval.](slides_FMunoz_files/figure-html/average-spread-rate-plot-1.png) ] .pull-right[ Median: __46.3 km/mo__ 89% MCI: __(42.9, 49.7)__ ] --- # Local variation in spread-rate - Range from __9.7__ to __259.4 km/mo__ - __67.4 %__ of the estimates below the average ![Monte Carlo marginal density estimates of spread rate. The average density is highlighted in black while the average global mean SR is highlighted in red.](slides_FMunoz_files/figure-html/fig:mc-marginal-density-1.png) --- # Temporal trends of spread-rate ![Local spread rates by day and Monte Carlo estimates of trend.](slides_FMunoz_files/figure-html/temporal-trend-1.png) --- # Spatial local estimates ![Estimated spread-rate and standard error.](slides_FMunoz_files/figure-html/sr-point-avg-sd-1.png) <!-- --- --> <!-- # Large estimates, large uncertainties --> <!-- - <font color="#F8766D">Highest</font> local estimate: __7.7 (2.4, 17.6) km/mo__ --> <!-- - <font color="#00BA38">Average</font> local estimate: __2.9 (1.8, 4.3) km/mo__ --> <!-- ![:scale 70%](asf_spread_BEL_files/figure-latex/mc-density-locations-1.png) --> --- class: inverse, center, middle # Methodology --- # Outline 1. Filter __earliest observations__ 2. Interpolate surface of __first-invasion date__ 3. Derive surface of __spread rate__ --- # 1: Earliest observations .pull-left[ ![](asf_spread_BEL_files/figure-latex/min-neigh-1.png) ] .pull-right[ - Only the first observed cases in a __neighbourhood__ are relevant - __Neighbouring-tolerance parameter__: how far apart two cases can be to still be considered at the _same place_? ] - Assign the __earliest observed date__ in the neighbourhood to each _representative_ location --- # 2: Date of first-invasion surface - Fit __Thin-plate regression splines__ model to _earliest observations_ + Interpolate observations ![](img/fa_surf.png) --- # 3: Derive surface of spread-rate - __Inverse slope__ of first-invasion date surface ![](slides_FMunoz_files/figure-html/unnamed-chunk-5-1.png)<!-- --> --- class: inverse, center, middle # Uncertainty assessment --- # Sources of variation - __Data__ - Missed observations - Precision of (spatio-temporal) location - Heterogeneous protocols and definitions of case - ... - Tuning __parameters__ of the method - Neighbouring-tolerance parameter --- # Monte Carlo approach ## Introduce __perturbations__ into data and parameters and reproduce... __many times__ (999) ![](slides_FMunoz_files/figure-html/MC-circle-1.png)<!-- --> Spatial coordinates: uniformly shifted within a radius of __1 km__ ![](slides_FMunoz_files/figure-html/MC-time-1.png)<!-- --> Observation dates: __± 1 day__ with prob. 1/4 ![](slides_FMunoz_files/figure-html/MC-neigh-1.png)<!-- --> Neighbouring-tolerance distance: Normally distributed __between 400 and 1200 m__ at 99.9 % --- # Monte Carlo results - 999 potential estimates of spread rate ![](slides_FMunoz_files/figure-html/unnamed-chunk-6-1.png)<!-- --> --- # Interpretation and processing - A sample from a __distribution of spread-rate surfaces__, accounting for input uncertainty - Compute __summaries__ such as mean, sd, quantiles of __any function__ of the estimates --- class: inverse, center, middle # Limitations and lines of work --- ## The __interpolation__ with Thin-plate splines regression is __not optimal__ - particularly around extremes (which do not need smoothing) - the level of smoothing is optimised for the observed values (not for their slopes) --- ## The current method does not account for __explanatory covariates__ - Can't leverage potentially informative __risk factors__ - Need to interpret variations in spread rate at a later stage - Not really a statistical model <!-- --- --> <!-- # Work in progress --> <!-- - __Augment__ the base of splines with a few __cones__ (sharp --> <!-- vertices) --> <!-- - Their number and location are estimated in a __statistical model__, --> <!-- with supplementary __covariates__ --> <!-- ![](img/wip_breakpoints.png) --> <!-- --- --> <!-- # Work in progress --> <!-- - Develop a Markov Chain Monte Carlo algorithm to sample from the model --> <!-- $$ --> <!-- \begin{aligned} --> <!-- y_i & \sim \mathcal N(\delta_{x[i]}, \sigma) \\ --> <!-- \nu_x & = 1/|\nabla\delta_x| --> <!-- \end{aligned} --> <!-- $$ --> <!-- where `\(\delta_x\)` is the date of first-invasion surface and the spread --> <!-- rate surface `\(\nu_x\)` is modelled in terms of the splines base and --> <!-- other available covariates --> --- class: left, middle, inverse ![:scale 20%](img/CirBlanc_L230px.png) <!-- <img src=\"../img/CirBlanc_L230px.png\" style=\"width: 25%\" align=\"top\" /> --> # Thanks! .small[ <!-- <a href="http://twitter.com/famuvie"> --> <i class="fab fa-twitter"></i> famuvie<br> <!-- </a><br> --> <!-- <a href="http://github.com/famuvie"> --> <i class="fab fa-github"></i> famuvie<br> <!-- </a><br> --> <a href="mailto:facundo.munoz@cirad.fr"> <i class="fa fa-paper-plane fa-fw"></i> facundo.munoz@cirad.fr </a> ]