Author: Joseph Larmarange

# Introduction to prevR

#### Joseph Larmarange

This package performs a methodological approach for spatial estimation of regional trends of a prevalence using data from surveys using a stratified two-stage sample design (as Demographic and Health Surveys). In these kind of surveys, positive and control cases are spatially positioned at the centre of their corresponding surveyed cluster.

This package provides functions to estimate a prevalence surface using a kernel estimator with adaptative bandwidths of equal number of persons surveyed (a variant of the nearest neighbor technique) or with fixed bandwidths. The prevalence surface could also be calculated using a spatial interpolation (kriging or inverse distance weighting) after a moving average smoothing based on circles of equal number of observed persons or circles of equal radius.

With the kernel estimator approach, it’s also possible to estimate a surface of relative risks.

The methodological approach has been described in:

- Larmarange Joseph, Vallo Roselyne, Yaro Seydou, Msellati Philippe and Meda Nicolas (2011) “Methods for mapping regional trends of HIV prevalence from Demographic and Health Surveys (DHS)”, Cybergeo: European Journal of Geography, no 558, https://journals.openedition.org/cybergeo/24606, DOI: 10.4000/cybergeo.24606

Application to generate HIV prevalence surfaces can be found at:

- Larmarange Joseph and Bendaud Victoria (2014) “HIV estimates at second subnational level from national population-based survey”, AIDS, n° 28, p. S469-S476, DOI: 10.1097/QAD.0000000000000480

Other papers using prevR could be found on Google Scholar.

## Importing data

To create a prevR object, you need three elements:

- a data.frame with one row per survey cluster and containing the number of observations, the number of positive cases and coordinates of the cluster (you could optionally use weighted numbers)
- a vector identifying the columns of the data.frame containing the corresponding variables
- an optional `SpatialPolygons` defining the studied area

    library(prevR, quietly = TRUE)

    ##
    ##
    ## Welcome to 'prevR': estimate regional trends of a prevalence.

    ##  - type help('prevR') for details
    ##  - type demo(prevR) for a demonstration
    ##  - type citation('prevR') to cite prevR in a publication.
    ##
    ##

    col <- c(
      id = "cluster",
      x = "x",
      y = "y",
      n = "n",
      pos = "pos",
      c.type = "residence",
      wn = "weighted.n",
      wpos = "weighted.pos"
    )
    dhs <- as.prevR(fdhs.clusters, col, fdhs.boundary)
    str(dhs)

    ## Formal class 'prevR' [package "prevR"] with 4 slots
    ##   ..@ clusters:'data.frame': 401 obs. of  10 variables:
    ##   .. ..$ id    : int [1:401] 1 10 100 101 102 103 104 105 106 107 ...
    ##   .. ..$ x     : num [1:401] -1.21 -1.79 -2.29 -2.71 -1.96 ...
    ##   .. ..$ y     : num [1:401] 7.29 6.13 5.96 6.04 5.12 ...
    ##   .. ..$ n     : num [1:401] 23 22 22 28 21 21 11 24 23 15 ...
    ##   .. ..$ pos   : num [1:401] 0 0 0 0 3 4 0 1 0 0 ...
    ##   .. ..$ c.type: Factor w/ 2 levels "Rural","Urban": 1 1 1 1 1 1 1 1 1 1 ...
    ##   .. ..$ wn    : num [1:401] 19.8 19.8 20.2 20.2 20.2 ...
    ##   .. ..$ wpos  : num [1:401] 0 0 0 0 2.88 ...
    ##   .. ..$ prev  : num [1:401] 0 0 0 0 14.3 ...
    ##   .. ..$ wprev : num [1:401] 0 0 0 0 14.3 ...
    ##   ..@ boundary:Classes 'sf' and 'data.frame':    1 obs. of  1 variable:
    ##   .. ..$ geometry:sfc_POLYGON of length 1; first list element: List of 1
    ##   .. .. ..$ : num [1:4056, 1:2] 1.28 1.25 1.23 1.22 1.22 ...
    ##   .. .. ..- attr(*, "class")= chr [1:3] "XY" "POLYGON" "sfg"
    ##   .. ..- attr(*, "sf_column")= chr "geometry"
    ##   .. ..- attr(*, "agr")= Factor w/ 3 levels "constant","aggregate",..:
    ##   .. .. ..- attr(*, "names")= chr(0)
    ##   .. ..- attr(*, "valid")= logi TRUE
    ##   ..@ proj    :List of 2
    ##   .. ..$ input: chr "+proj=longlat +datum=WGS84"
    ##   .. ..$ wkt  : chr "GEOGCRS[\"unknown\",\n    DATUM[\"World Geodetic System 1984\",\n        ELLIPSOID[\"WGS 84\",6378137,298.25722"| __truncated__
    ##   .. ..- attr(*, "class")= chr "crs"
    ##   ..@ rings   : list()

    print(dhs)

    ## Object of class 'prevR'

    ## Number of clusters: 401

    ## Number of observations: 8000

    ## Number of positive cases: 810

    ## The dataset is weighted.

    ##
    ## National prevalence: 10.12%

    ## National weighted prevalence: 10.16%

    ##
    ## Projection used: +proj=longlat +datum=WGS84

    ##
    ## Coordinate range

    ##        min     max
    ## x -5.37750  3.6850
    ## y  4.80326 14.1225

    ##
    ## Boundary coordinate range

    ##      xmin      ymin      xmax      ymax
    ## -5.518916  4.736723  3.851701 15.082593

An interactive helper function `import.dhs()` could be used to compute statistics per cluster and to generate the prevR object for those who downloaded individual files (SPSS format) and location of clusters (dbf format) from DHS website (https://dhsprogram.com/).

    imported_data <- import.dhs("data.sav", "gps.dbf")

Boudaries of a specific country could be obtained with `create.boundary()`.

## Plotting a prevR object

    plot(dhs, main = "Clusters position")

    plot(dhs, type = "c.type", main = "Clusters by residence")

    plot(dhs, type = "count", main = "Observations by cluster")

    plot(dhs, type = "flower", main = "Positive cases by cluster")

## Changing coordinates projection

    plot(dhs, axes = TRUE)

    dhs <- changeproj(
      dhs,
      "+proj=utm +zone=30 +ellps=WGS84 +datum=WGS84 +units=m +no_defs"
    )
    print(dhs)

    ## Object of class 'prevR'

    ## Number of clusters: 401

    ## Number of observations: 8000

    ## Number of positive cases: 810

    ## The dataset is weighted.

    ##
    ## National prevalence: 10.12%

    ## National weighted prevalence: 10.16%

    ##
    ## Projection used: +proj=utm +zone=30 +ellps=WGS84 +datum=WGS84 +units=m +no_defs

    ##
    ## Coordinate range

    ##        min     max
    ## x 240094.2 1231995
    ## y 531003.3 1562155

    ##
    ## Boundary coordinate range

    ##      xmin      ymin      xmax      ymax
    ##  224228.1  523628.1 1251165.0 1669034.2

    plot(dhs, axes = TRUE)

## Quick analysis

Function `quick.prevR()` allows to perform a quick analysis:

- an optimal value of N will be computed with `Noptim()`
- adaptative bandwidths will be calculated with `rings()`
- a prevalence surface will be computed with `kde()`
- the surface of rings radii will be generated with `krige()`
- a ggplot2 of the prevalence surface will be generated and rings radii will be added as a contour plot

    quick.prevR(fdhs)

Several values of N could be specified, and several options allows you to return detailed results.

    res <- quick.prevR(
      fdhs,
      N = c(100, 200, 300),
      return.results = TRUE,
      return.plot = TRUE,
      plot.results = FALSE,
      progression = FALSE,
      nb.cells = 50
    )
    res$plot

## Step by step analysis

    # Calculating rings of the same number of observations for different values of N
    dhs <- rings(fdhs, N = c(100, 200, 300, 400, 500), progression = FALSE)
    print(dhs)

    ## Object of class 'prevR'

    ## Number of clusters: 401

    ## Number of observations: 8000

    ## Number of positive cases: 810

    ## The dataset is weighted.

    ##
    ## National prevalence: 10.12%

    ## National weighted prevalence: 10.16%

    ##
    ## Projection used: +proj=longlat +datum=WGS84

    ##
    ## Coordinate range

    ##        min     max
    ## x -5.37750  3.6850
    ## y  4.80326 14.1225

    ##
    ## Boundary coordinate range

    ##      xmin      ymin      xmax      ymax
    ## -5.518916  4.736723  3.851701 15.082593

    ##
    ## Available (N,R) couples in the slot 'rings':

    ##    N   R
    ##  100 Inf
    ##  200 Inf
    ##  300 Inf
    ##  400 Inf
    ##  500 Inf

    summary(dhs)

    ## Object of class 'prevR'

    ## SLOT CLUSTERS

    ##        x                 y                n              pos         c.type
    ##  Min.   :-5.3775   Min.   : 4.803   Min.   : 8.00   Min.   :0.00   Rural:230
    ##  1st Qu.:-1.7925   1st Qu.: 6.375   1st Qu.:17.00   1st Qu.:0.00   Urban:171
    ##  Median :-0.7650   Median : 7.455   Median :20.00   Median :2.00
    ##  Mean   :-0.6605   Mean   : 8.647   Mean   :19.95   Mean   :2.02
    ##  3rd Qu.: 0.1590   3rd Qu.:11.205   3rd Qu.:23.00   3rd Qu.:3.00
    ##  Max.   : 3.6850   Max.   :14.123   Max.   :31.00   Max.   :9.00
    ##        wn             wpos            prev            wprev
    ##  Min.   :18.58   Min.   :0.000   Min.   : 0.000   Min.   : 0.000
    ##  1st Qu.:19.84   1st Qu.:0.000   1st Qu.: 0.000   1st Qu.: 0.000
    ##  Median :20.04   Median :1.544   Median : 7.692   Median : 7.692
    ##  Mean   :19.95   Mean   :2.027   Mean   :10.143   Mean   :10.143
    ##  3rd Qu.:20.12   3rd Qu.:3.166   3rd Qu.:15.789   3rd Qu.:15.789
    ##  Max.   :21.76   Max.   :8.806   Max.   :43.750   Max.   :43.750

    ##
    ## SLOT RINGS FOR N=100 AND R=Inf

    ##      r.pos            r.n            r.prev          r.radius
    ##  Min.   : 0.00   Min.   :100.0   Min.   : 0.000   Min.   :  4.155
    ##  1st Qu.: 4.00   1st Qu.:105.0   1st Qu.: 4.000   1st Qu.: 23.046
    ##  Median :11.00   Median :110.0   Median : 9.483   Median : 37.853
    ##  Mean   :11.63   Mean   :110.7   Mean   :10.550   Mean   : 42.219
    ##  3rd Qu.:18.00   3rd Qu.:115.0   3rd Qu.:15.789   3rd Qu.: 57.861
    ##  Max.   :32.00   Max.   :127.0   Max.   :27.586   Max.   :142.042
    ##    r.clusters        r.wpos            r.wn           r.wprev
    ##  Min.   :4.000   Min.   : 0.000   Min.   : 79.76   Min.   : 0.000
    ##  1st Qu.:5.000   1st Qu.: 4.515   1st Qu.:100.25   1st Qu.: 3.895
    ##  Median :6.000   Median :11.175   Median :118.70   Median : 9.551
    ##  Mean   :5.591   Mean   :11.792   Mean   :111.52   Mean   :10.684
    ##  3rd Qu.:6.000   3rd Qu.:17.256   3rd Qu.:120.13   3rd Qu.:15.735
    ##  Max.   :7.000   Max.   :33.937   Max.   :140.88   Max.   :28.210

    ##
    ## SLOT RINGS FOR N=200 AND R=Inf

    ##      r.pos            r.n            r.prev           r.radius
    ##  Min.   : 2.00   Min.   :200.0   Min.   : 0.8929   Min.   :  7.171
    ##  1st Qu.: 9.00   1st Qu.:206.0   1st Qu.: 4.3902   1st Qu.: 37.579
    ##  Median :22.00   Median :211.0   Median :10.2804   Median : 58.657
    ##  Mean   :22.55   Mean   :210.8   Mean   :10.7053   Mean   : 64.005
    ##  3rd Qu.:33.00   3rd Qu.:216.0   3rd Qu.:15.4229   3rd Qu.: 89.381
    ##  Max.   :56.00   Max.   :226.0   Max.   :26.2136   Max.   :231.980
    ##    r.clusters        r.wpos           r.wn          r.wprev
    ##  Min.   : 9.00   Min.   : 2.47   Min.   :175.0   Min.   : 1.030
    ##  1st Qu.:10.00   1st Qu.:10.50   1st Qu.:199.8   1st Qu.: 4.563
    ##  Median :11.00   Median :22.30   Median :217.3   Median :10.485
    ##  Mean   :10.53   Mean   :22.66   Mean   :210.0   Mean   :10.824
    ##  3rd Qu.:11.00   3rd Qu.:31.98   3rd Qu.:220.0   3rd Qu.:15.797
    ##  Max.   :12.00   Max.   :53.47   Max.   :241.0   Max.   :26.666

    ##
    ## SLOT RINGS FOR N=300 AND R=Inf

    ##      r.pos            r.n            r.prev          r.radius
    ##  Min.   : 5.00   Min.   :300.0   Min.   : 1.587   Min.   :  9.971
    ##  1st Qu.:15.00   1st Qu.:304.0   1st Qu.: 4.983   1st Qu.: 45.750
    ##  Median :32.00   Median :310.0   Median :10.559   Median : 73.931
    ##  Mean   :33.37   Mean   :309.8   Mean   :10.764   Mean   : 79.767
    ##  3rd Qu.:47.00   3rd Qu.:315.0   3rd Qu.:15.142   3rd Qu.:108.783
    ##  Max.   :78.00   Max.   :327.0   Max.   :24.759   Max.   :268.172
    ##    r.clusters        r.wpos            r.wn          r.wprev
    ##  Min.   :13.00   Min.   : 4.284   Min.   :260.6   Min.   : 1.532
    ##  1st Qu.:15.00   1st Qu.:15.937   1st Qu.:299.2   1st Qu.: 5.080
    ##  Median :15.00   Median :33.525   Median :301.8   Median :10.319
    ##  Mean   :15.44   Mean   :33.297   Mean   :307.9   Mean   :10.853
    ##  3rd Qu.:16.00   3rd Qu.:46.856   3rd Qu.:320.0   3rd Qu.:15.429
    ##  Max.   :17.00   Max.   :76.990   Max.   :341.4   Max.   :25.273

    ##
    ## SLOT RINGS FOR N=400 AND R=Inf

    ##      r.pos            r.n            r.prev          r.radius
    ##  Min.   : 8.00   Min.   :400.0   Min.   : 2.000   Min.   : 12.70
    ##  1st Qu.:22.00   1st Qu.:405.0   1st Qu.: 5.327   1st Qu.: 54.42
    ##  Median :44.00   Median :410.0   Median :10.602   Median : 85.41
    ##  Mean   :44.18   Mean   :410.3   Mean   :10.764   Mean   : 94.79
    ##  3rd Qu.:58.00   3rd Qu.:415.0   3rd Qu.:14.217   3rd Qu.:127.73
    ##  Max.   :98.00   Max.   :427.0   Max.   :23.278   Max.   :293.64
    ##    r.clusters        r.wpos            r.wn          r.wprev
    ##  Min.   :18.00   Min.   : 8.229   Min.   :360.1   Min.   : 2.045
    ##  1st Qu.:20.00   1st Qu.:22.358   1st Qu.:399.9   1st Qu.: 5.345
    ##  Median :21.00   Median :43.851   Median :415.4   Median :10.315
    ##  Mean   :20.54   Mean   :44.298   Mean   :409.6   Mean   :10.851
    ##  3rd Qu.:21.00   3rd Qu.:58.963   3rd Qu.:421.0   3rd Qu.:14.341
    ##  Max.   :22.00   Max.   :95.591   Max.   :443.4   Max.   :23.452

    ##
    ## SLOT RINGS FOR N=500 AND R=Inf

    ##      r.pos             r.n            r.prev          r.radius
    ##  Min.   : 14.00   Min.   :500.0   Min.   : 2.783   Min.   : 16.38
    ##  1st Qu.: 31.00   1st Qu.:505.0   1st Qu.: 6.163   1st Qu.: 67.01
    ##  Median : 54.00   Median :510.0   Median :10.700   Median : 98.47
    ##  Mean   : 55.24   Mean   :510.3   Mean   :10.811   Mean   :107.68
    ##  3rd Qu.: 70.00   3rd Qu.:515.0   3rd Qu.:13.699   3rd Qu.:140.71
    ##  Max.   :116.00   Max.   :528.0   Max.   :22.612   Max.   :347.09
    ##    r.clusters        r.wpos            r.wn          r.wprev
    ##  Min.   :23.00   Min.   : 12.93   Min.   :455.7   Min.   : 2.499
    ##  1st Qu.:25.00   1st Qu.: 31.71   1st Qu.:499.5   1st Qu.: 6.138
    ##  Median :26.00   Median : 51.91   Median :510.9   Median :10.222
    ##  Mean   :25.53   Mean   : 55.12   Mean   :509.3   Mean   :10.869
    ##  3rd Qu.:26.00   3rd Qu.: 70.17   3rd Qu.:520.8   3rd Qu.:13.929
    ##  Max.   :28.00   Max.   :110.78   Max.   :555.8   Max.   :22.822

    ##
    ## QUANTILES OF r.radius (in kilometers):

    ##              0%   10%   25%   50%    75%    80%    90%    95%    99%   100%
    ## N100.RInf  4.15  7.84 23.05 37.85  57.86  62.99  79.63  93.12 121.77 142.04
    ## N200.RInf  7.17 14.58 37.58 58.66  89.38  94.40 114.97 134.81 173.37 231.98
    ## N300.RInf  9.97 18.75 45.75 73.93 108.78 114.65 138.17 159.10 211.31 268.17
    ## N400.RInf 12.70 31.42 54.42 85.41 127.73 136.67 163.91 177.11 241.44 293.64
    ## N500.RInf 16.38 41.15 67.01 98.47 140.71 156.53 181.92 201.87 286.18 347.09

    # Prevalence surface for N=300
    prev.N300 <- kde(dhs, N = 300, nb.cells = 200, progression = FALSE)
    plot(
      prev.N300["k.wprev.N300.RInf"],
      pal = prevR.colors.red,
      lty = 0,
      main = "Regional trends of prevalence (N=300)"
    )

    # with ggplot2
    library(ggplot2)
    ggplot(prev.N300) +
      aes(fill = k.wprev.N300.RInf) +
      geom_sf(colour = "transparent") +
      scale_fill_gradientn(colours = prevR.colors.red()) +
      labs(fill = "Prevalence (%)") +
      theme_prevR_light()

    # Surface of rings' radius
    radius.N300 <- krige("r.radius", dhs, N = 300, nb.cells = 200)

    ## [using ordinary kriging]

    plot(
      radius.N300,
      pal = prevR.colors.blue,
      lty = 0,
      main = "Radius of circle (N=300)"
    )

## Functions and methods provided by prevR

The content of prevR can be broken up as follows:

### Datasets

- `fdhs` is a fictive dataset used for testing the package.
- `TMWorldBorders` provides national borders of every countries in the World and could be used to define the limits of the studied area.

### Creating objects

prevR functions takes as input objects of class prevR.

- `import.dhs()` allows to import easily, through a step by step procedure, data from a DHS (Demographic and Health Surveys) downloaded from http://www.measuredhs.com.
- `as.prevR()` is a generic function to create an object of class prevR.
- `create.boundary()` could be used to select borders of a country and transfer them to as.prevR in order to define the studied area.

### Data visualization

- Methods `show()`, `print()` and `summary()` display a summary of a object of class prevR.
- The method `plot()` could be used on a object of class prevR for visualizing the studied area, spatial position of clusters, number of observations or number of positive cases by cluster.

### Data manipulation

- The method `changeproj()` changes the projection of the spatial coordinates.
- The method `as.data.frame()` converts an object of class prevR into a data frame.
- The method `export()` export data and/or the studied area in a text file, a dbf file or a shapefile.

### Data analysis

- `rings()` calculates rings of equal number of observations and/or equal radius.
- `kde()` calculates a prevalence surface or a relative risks surface using gaussian kernel density estimators (kde) with adaptative bandwidths.
- `krige()` executes a spatial interpolation using an ordinary kriging.
- `idw()` executes a spatial interpolation using an inverse distance weighting (idw) technique.

### Results visualization and export

- Outputs of `kde()`, `krige()` and `idw()` are objects of class `SpatialPixelsDataFrame` (sp package).
- Results could be plotted using the function `spplot()` from sp.
- prevR provides several continuous color palettes (see `prevR.colors`) compatible with `spplot()`.
- Calculated surfaces could be export using the function `writeRaster()` from terra (see examples in the documentation of `kde()` and `krige()`.