# Details of the incidence class

#### Thibaut Jombart, Zhian N. Kamvar

#### 2020-11-03

This vignette details the structure of incidence objects, as produced by the `incidence` function.

# Structure of an incidence object.

We generate a toy dataset of dates to examine the content of incidence objects.

    library(incidence)
    set.seed(1)
    dat <- sample(1:50, 200, replace = TRUE, prob = 1 + exp(1:50 * 0.1))
    sex <- sample(c("female", "male"), 200, replace = TRUE)

The incidence by 48h period is computed as:

    i <- incidence(dat, interval = 2)
    i
    #> <incidence object>
    #> [200 cases from days 5 to 49]
    #>
    #> $counts: matrix with 23 rows and 1 columns
    #> $n: 200 cases in total
    #> $dates: 23 dates marking the left-side of bins
    #> $interval: 2 days
    #> $timespan: 45 days
    #> $cumulative: FALSE
    plot(i)

We also compute incidence by gender:

    i.sex <- incidence(dat, interval = 2, group = sex)
    i.sex
    #> <incidence object>
    #> [200 cases from days 5 to 49]
    #> [2 groups: female, male]
    #>
    #> $counts: matrix with 23 rows and 2 columns
    #> $n: 200 cases in total
    #> $dates: 23 dates marking the left-side of bins
    #> $interval: 2 days
    #> $timespan: 45 days
    #> $cumulative: FALSE
    plot(i.sex)

The object `i` is a `list` with the class incidence:

    class(i)
    #> [1] "incidence"
    is.list(i)
    #> [1] TRUE
    names(i)
    #> [1] "dates"      "counts"     "timespan"   "interval"   "n"
    #> [6] "cumulative"

Items in `i` can be accessed using the same indexing as any lists, but it’s safer to use the accessors for each item:

    ## use name
    head(i$dates)
    #> [1]  5  7  9 11 13 15

    head(get_dates(i))
    #> [1]  5  7  9 11 13 15

In the following sections, we examine each of the components of the object.

## `$dates`

The `$dates` component contains a vector for all the dates for which incidence have been computed, in the format of the input dataset (e.g. `Date`, `numeric`, `integer`).

    date_bins <- get_dates(i)
    class(date_bins)
    #> [1] "integer"
    class(dat)
    #> [1] "integer"

    date_bins
    #>  [1]  5  7  9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49

The dates correspond to the lower bounds of the time intervals used as bins for the incidence. Bins always include the lower bound and exclude the upper bound. In the example provided above, this means that the first bin counts events that happened at day 5-6, the second bin counts events from 7-8, etc.

Note that if we had actual `Date`-class dates, they would be returned as dates

    dat_Date <- as.Date("2018-10-31") + dat
    head(dat_Date)
    #> [1] "2018-12-17" "2018-12-16" "2018-12-12" "2018-11-26" "2018-12-18"
    #> [6] "2018-11-27"
    i.date <- incidence(dat_Date, interval = 2, group = sex)
    i.date
    #> <incidence object>
    #> [200 cases from days 2018-11-05 to 2018-12-19]
    #> [2 groups: female, male]
    #>
    #> $counts: matrix with 23 rows and 2 columns
    #> $n: 200 cases in total
    #> $dates: 23 dates marking the left-side of bins
    #> $interval: 2 days
    #> $timespan: 45 days
    #> $cumulative: FALSE
    get_dates(i.date)
    #>  [1] "2018-11-05" "2018-11-07" "2018-11-09" "2018-11-11" "2018-11-13"
    #>  [6] "2018-11-15" "2018-11-17" "2018-11-19" "2018-11-21" "2018-11-23"
    #> [11] "2018-11-25" "2018-11-27" "2018-11-29" "2018-12-01" "2018-12-03"
    #> [16] "2018-12-05" "2018-12-07" "2018-12-09" "2018-12-11" "2018-12-13"
    #> [21] "2018-12-15" "2018-12-17" "2018-12-19"
    class(get_dates(i.date))
    #> [1] "Date"

These can be converted to integers, counting the number of days from the first date.

    get_dates(i.date, count_days = TRUE)
    #>  [1]  0  2  4  6  8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44
    get_dates(i, count_days = TRUE)
    #>  [1]  0  2  4  6  8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44

To facilitate modelling, it’s also possible to get the center of the interval by using the `position = "center"` argument:

    get_dates(i.date, position = "center")
    #>  [1] "2018-11-06" "2018-11-08" "2018-11-10" "2018-11-12" "2018-11-14"
    #>  [6] "2018-11-16" "2018-11-18" "2018-11-20" "2018-11-22" "2018-11-24"
    #> [11] "2018-11-26" "2018-11-28" "2018-11-30" "2018-12-02" "2018-12-04"
    #> [16] "2018-12-06" "2018-12-08" "2018-12-10" "2018-12-12" "2018-12-14"
    #> [21] "2018-12-16" "2018-12-18" "2018-12-20"
    get_dates(i.date, position = "center", count_days = TRUE)
    #>  [1]  1  3  5  7  9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45

## `$counts`

The `$counts` component contains the actual incidence, i.e. counts of events for the defined bins. It is a `matrix` of `integers` where rows correspond to time intervals, with one column for each group for which incidence is computed (a single, unnamed column if no groups were provided). If groups were provided, columns are named after the groups. We illustrate the difference comparing the two objects `i` and `i.sex`:

    counts <- get_counts(i)
    class(counts)
    #> [1] "matrix" "array"
    storage.mode(counts)
    #> [1] "integer"

    counts
    #>       [,1]
    #>  [1,]    3
    #>  [2,]    0
    #>  [3,]    1
    #>  [4,]    0
    #>  [5,]    1
    #>  [6,]    0
    #>  [7,]    1
    #>  [8,]    0
    #>  [9,]    3
    #> [10,]    3
    #> [11,]    3
    #> [12,]    5
    #> [13,]    9
    #> [14,]    4
    #> [15,]    5
    #> [16,]   12
    #> [17,]   13
    #> [18,]   16
    #> [19,]   15
    #> [20,]   25
    #> [21,]   28
    #> [22,]   28
    #> [23,]   25
    get_counts(i.sex)
    #>       female male
    #>  [1,]      2    1
    #>  [2,]      0    0
    #>  [3,]      0    1
    #>  [4,]      0    0
    #>  [5,]      1    0
    #>  [6,]      0    0
    #>  [7,]      0    1
    #>  [8,]      0    0
    #>  [9,]      2    1
    #> [10,]      1    2
    #> [11,]      1    2
    #> [12,]      2    3
    #> [13,]      3    6
    #> [14,]      3    1
    #> [15,]      0    5
    #> [16,]      6    6
    #> [17,]      8    5
    #> [18,]      7    9
    #> [19,]      7    8
    #> [20,]     17    8
    #> [21,]     15   13
    #> [22,]     12   16
    #> [23,]     12   13

You can see the dimensions of the incidence object by using `dim()`, `ncol()`, and `nrow()`, which returns the dimensions of the counts matrix:

    dim(get_counts(i.sex))
    #> [1] 23  2
    dim(i.sex)
    #> [1] 23  2
    nrow(i.sex) # number of date bins
    #> [1] 23
    ncol(i.sex) # number of groups
    #> [1] 2

There are also accessors for handling groups:

    # Number of groups
    ncol(i.sex)
    #> [1] 2
    ncol(i)
    #> [1] 1

    # Names of groups
    group_names(i.sex)
    #> [1] "female" "male"
    group_names(i)
    #> NULL

    # You can also rename the groups
    group_names(i.sex) <- c("F", "M")
    group_names(i.sex)
    #> [1] "F" "M"

Note that a `data.frame` containing dates and counts can be obtained using `as.data.frame`:

    ## basic conversion
    as.data.frame(i)
    #>    dates counts
    #> 1      5      3
    #> 2      7      0
    #> 3      9      1
    #> 4     11      0
    #> 5     13      1
    #> 6     15      0
    #> 7     17      1
    #> 8     19      0
    #> 9     21      3
    #> 10    23      3
    #> 11    25      3
    #> 12    27      5
    #> 13    29      9
    #> 14    31      4
    #> 15    33      5
    #> 16    35     12
    #> 17    37     13
    #> 18    39     16
    #> 19    41     15
    #> 20    43     25
    #> 21    45     28
    #> 22    47     28
    #> 23    49     25
    as.data.frame(i.sex)
    #>    dates  F  M
    #> 1      5  2  1
    #> 2      7  0  0
    #> 3      9  0  1
    #> 4     11  0  0
    #> 5     13  1  0
    #> 6     15  0  0
    #> 7     17  0  1
    #> 8     19  0  0
    #> 9     21  2  1
    #> 10    23  1  2
    #> 11    25  1  2
    #> 12    27  2  3
    #> 13    29  3  6
    #> 14    31  3  1
    #> 15    33  0  5
    #> 16    35  6  6
    #> 17    37  8  5
    #> 18    39  7  9
    #> 19    41  7  8
    #> 20    43 17  8
    #> 21    45 15 13
    #> 22    47 12 16
    #> 23    49 12 13

    ## long format for ggplot2
    as.data.frame(i.sex, long = TRUE)
    #>    dates counts groups
    #> 1      5      2      F
    #> 2      7      0      F
    #> 3      9      0      F
    #> 4     11      0      F
    #> 5     13      1      F
    #> 6     15      0      F
    #> 7     17      0      F
    #> 8     19      0      F
    #> 9     21      2      F
    #> 10    23      1      F
    #> 11    25      1      F
    #> 12    27      2      F
    #> 13    29      3      F
    #> 14    31      3      F
    #> 15    33      0      F
    #> 16    35      6      F
    #> 17    37      8      F
    #> 18    39      7      F
    #> 19    41      7      F
    #> 20    43     17      F
    #> 21    45     15      F
    #> 22    47     12      F
    #> 23    49     12      F
    #> 24     5      1      M
    #> 25     7      0      M
    #> 26     9      1      M
    #> 27    11      0      M
    #> 28    13      0      M
    #> 29    15      0      M
    #> 30    17      1      M
    #> 31    19      0      M
    #> 32    21      1      M
    #> 33    23      2      M
    #> 34    25      2      M
    #> 35    27      3      M
    #> 36    29      6      M
    #> 37    31      1      M
    #> 38    33      5      M
    #> 39    35      6      M
    #> 40    37      5      M
    #> 41    39      9      M
    #> 42    41      8      M
    #> 43    43      8      M
    #> 44    45     13      M
    #> 45    47     16      M
    #> 46    49     13      M

Note that `incidence` has an argument called `na_as_group` which is `TRUE` by default, which will pool all missing groups into a separate group, in which case it will be a separate column in `$counts`.

## `$timespan`

The `$timespan` component stores the length of the time period covered by the object:

    get_timespan(i)
    #> [1] 45
    print(date_range <- range(get_dates(i)))
    #> [1]  5 49
    diff(date_range) + 1
    #> [1] 45

## `$interval`

The `$interval` component contains the length of the time interval for the bins:

    get_interval(i)
    #> [1] 2
    diff(get_dates(i))
    #>  [1] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

## `$n`

The `$n` component stores the total number of events in the data:

    get_n(i)
    #> [1] 200

Note that to obtain the number of cases by groups, one can use:

    colSums(get_counts(i.sex))
    #>   F   M
    #>  99 101

## `$weeks`

The `$weeks` component is optional, and used to store aweek objects whenever they have been used. Weeks are used by default when weekly incidence is computed from dates (see argument `standard` in `?incidence`).

    library(outbreaks)
    dat <- ebola_sim$linelist$date_of_onset
    i.7 <- incidence(dat, "1 epiweek", standard = TRUE)
    i.7
    #> <incidence object>
    #> [5888 cases from days 2014-04-06 to 2015-04-26]
    #> [5888 cases from MMWR weeks 2014-W15 to 2015-W17]
    #>
    #> $counts: matrix with 56 rows and 1 columns
    #> $n: 5888 cases in total
    #> $dates: 56 dates marking the left-side of bins
    #> $interval: 1 week
    #> $timespan: 386 days
    #> $cumulative: FALSE
    i.7$weeks
    #> <aweek start: Sunday>
    #>  [1] "2014-W15" "2014-W16" "2014-W17" "2014-W18" "2014-W19" "2014-W20"
    #>  [7] "2014-W21" "2014-W22" "2014-W23" "2014-W24" "2014-W25" "2014-W26"
    #> [13] "2014-W27" "2014-W28" "2014-W29" "2014-W30" "2014-W31" "2014-W32"
    #> [19] "2014-W33" "2014-W34" "2014-W35" "2014-W36" "2014-W37" "2014-W38"
    #> [25] "2014-W39" "2014-W40" "2014-W41" "2014-W42" "2014-W43" "2014-W44"
    #> [31] "2014-W45" "2014-W46" "2014-W47" "2014-W48" "2014-W49" "2014-W50"
    #> [37] "2014-W51" "2014-W52" "2014-W53" "2015-W01" "2015-W02" "2015-W03"
    #> [43] "2015-W04" "2015-W05" "2015-W06" "2015-W07" "2015-W08" "2015-W09"
    #> [49] "2015-W10" "2015-W11" "2015-W12" "2015-W13" "2015-W14" "2015-W15"
    #> [55] "2015-W16" "2015-W17"

Because `$weeks` is an optional element, it does not have a dedicated accessor. If the element is not present, attempting to access it will result in a `NULL`:

    i$weeks
    #> NULL

Both dates and weeks are returned when converting an `incidence` object to `data.frame`:

    head(as.data.frame(i.7))
    #>        dates    weeks counts
    #> 1 2014-04-06 2014-W15      1
    #> 2 2014-04-13 2014-W16      1
    #> 3 2014-04-20 2014-W17      4
    #> 4 2014-04-27 2014-W18      4
    #> 5 2014-05-04 2014-W19     12
    #> 6 2014-05-11 2014-W20     15