grantbrown
commented
8 years ago Those are good questions, and touch on an area where the documentation could be better.
As for your first question, understanding the distance matrix structure is important for fitting interesting models in ABSEIR. Each matrix has a separate spatial auto-correlation parameter, so the amount of flexibility you want to include in the spatial model will determine how many matrices you will include. The specification included in the West Africa example uses three distance matrices because it allows a different contact parameter for each national border.
For example, the first distance matrix only captures contact between Guinea and Liberia. If you look at DM1, it should look like:
0,1,0,
1,0,0,
0,0,0This gets multiplied by a spatial autocorrelation parameter; let's call it p1:
0,p1,0,
p1,0,0,
0,0,0The rows correspond to spatial locations: Guinea, Liberia, and Sierra Leone. The columns are the same locations, capturing epidemic contact from each location to the corresponding row. With that in mind, this first distance matrix only describes contact (in a symmetric way) between the first two locations: Guinea and Liberia. Adding in the other two distance matrices and their spatial auto-correlation parameters, the final specification is:
0,p1,p2,
p1,0,p3,
p2,p3,0If you want to assume that all of the national borders have the same contact rates, you could do something like the traditional CAR model:
DM1 = matrix(c(0,1,1,1,0,1,1,1,0), nrow = 3, byrow = TRUE)This would produce a matrix with 1's on the off-diagonal:
0,1,1,
1,0,1,
1,1,0The corresponding parameterized version would be:
0,p1,p1,
p1,0,p1,
p1,p1,0In my opinion, if we know the relationship between city 1 and city 2, then we also get the relationship between city 2 and city 1.
That's often the case, but not necessarily true. Consider an example where one population center is downstream from another, and you're interested in water-borne illnesses. In this case, the contact process would be asymmetric. The distance matrix structure is designed to be flexible enough to handle cases like this.
Moreover, if the number of city is large, it will be not wisely to build the DistanceModel on each DM. As far as i know, there are some packages (such as spdep and surveillance package) which is so convenient to build the spatial weight matrix only if we have the shp file.
I'd be interested in seeing an example of this for areal data; it sounds like something which would be useful to incorporate into a vignette. In general, I've just used R to programmatically generate complex distance structures. If you have a data set of locations with, for example, administrative unit centroid latitude and longitude, it is relatively straightforward to automatically generate a distance matrix just using basic R code. Another way I've often addressed this problem is to obtain or build a list of administrative borders. This can be used to generate a CAR style distance matrix, with 1's in the positions where a border is present.
If you have a specific example I may be able to help you build such a matrix, and add the process to the documentation.
Another question is that whether the method is suitable for the vaccine-preventable disease? As the vaccine immunization level in each city is different, is there any way to change the format of the model and then take the vaccine level into consideration (eg. build the SEIRV model)
This is a very good question. Currently, this kind of data must be incorporated directly into the exposure process design matrix; ABSEIR only fits spatial SEIR models. I am currently working on more general compartmental modeling software, but in the meantime this kind of data needs to be encoded into the transitions, rather than introducing additional compartments (i.e., V).
The design matrix for the S to E transition is a currently a little peculiar, but I've had trouble coming up with a better design. Basically, for every spatial location, you have a design matrix with T rows (number of time points) and p columns (number of covariate). Clearly, these covariates can either be time varying, or just vary between spatial units.
Consider the following example:
- 5 spatial locations
- 100 time points
- Each spatial location gets a different intercept
- all spatial locations share a linear function of time
In this case, we could specify the design matrix as follows:
intercepts <- diag(5)[rep(1:5, each = 100),]
temporalTerm <- rep(1:100/100, 5)
designMatrix <- cbind(intercepts, temporalTerm)Note: The order in which the spatial location information is included must be the same as the ordering of the rows/columns of the distance matrices.
Information on public health interventions, including vaccination campaigns or rates, can be incorporated as temporally or spatially varying covariates. You can also choose appropriate prior means and precisions for the corresponding parameters.
Let me know if that doesn't clear things up. If you have an example data set I'd be happy to help you work through the ABSEIR specification
Spatial-R
Thanks for your ABSEIR package. To run theSPatialSEIRModel, we firstly need set the DistanceModel object. Fox example, the distance was created by the followed codes: DM1 = matrix(c(0,1,0,1,0,0,0,0,0), nrow = 3, byrow = TRUE) DM2 = matrix(c(0,0,1,0,0,0,1,0,0), nrow = 3, byrow = TRUE) DM3 = matrix(c(0,0,0,0,0,1,0,1,0), nrow = 3, byrow = TRUE) distance_model = DistanceModel(list(DM1, DM2, DM3), priorAlpha = 1, priorBeta = 25)
If the DM1 represents the adjacent relationship between the city A and other two cities（B and C）, why should we also need the DM2 and DM3? In my opinion, if we know the relationship between city A and city B, then we also get the relationship between city B and city A. Moreover, if the number of city is large, it will be not wisely to build the DistanceModel on each DM. As far as i know, there are some packages (such as spdep and surveillance package) which is so convenient to build the spatial weight matrix only if we have the shp file.
Another question is that whether the method is suitable for the vaccine-preventable disease? As the vaccine immunization level in each city is different, is there any way to change the format of the model and then take the vaccine level into consideration (eg. build the SEIRV model)