# Estimate Measures of Injury Epidemiology

#### 2024-06-12

Source:`vignettes/estimate-epi-measures.Rmd`

`estimate-epi-measures.Rmd`

Whenever one collects and prepares the data, the next natural step is to summarize and explore these data. In this case, from a sports-applied point of view, one wants to know e.g.: how many and what type of injuries have occurred, how often they have occurred or what the load has been.

This document shows convenient functions from
`injurytools`

to describe sports injury data, in terms of
measures used in sports injury epidemiology (see Bahr and Holme (2003) and Waldén
et al. (2023)). Below, these
measures are explained and then, `calc_summary()`

and
`calc_prevalence()`

functions are illustrated.

## Measures of occurrence

### Rates

As Hodgson Phillips (2000) state,

*“Sports injuries occur when athletes are exposed to their given
sport and they occur under specific conditions, at a known time and
place.”*

Thus, when attempting to describe the distribution of injuries it is
necessary to relate this to the population at risk over a specified time
period. This is why the fundamental unit of measurement is
**rate**.

A rate is a measure that consists of a denominator and a numerator over a period of time. Denominator data can be a number of different things (e.g. number of minutes trained/played, number of matches played). As such, it reflects the speed at which new “injury-related” events occur.

### Prevalence

**Prevalence**, period prevalence, is a proportion that
refers to the number of players that have reported the injury of
interest (\(X\)) divided by the total
player-population at risk at any time during the specified period of
time (\(\Delta T\) time window). This
includes players who already had the injury at the start of the time
period as well as those who suffer it during that period.

\[P = \frac{X}{N}\] where \(X\) is the number of injury cases and \(N\) is the total number of players in the study at any point in the time window \(\Delta T\).

## In practice

Again, as in the prepare-data
vignette, we use the data sets available from the
`injurytools`

package: data from Liverpool Football Club
male’s first team players over two consecutive seasons, 2017-2018 and
2018-2019, scrapped from https://www.transfermarkt.com/ website^{1}.

### - `calc_summary()`

## Prepare data

```
df_exposures <- prepare_exp(raw_df_exposures, person_id = "player_name",
date = "year", time_expo = "minutes_played")
df_injuries <- prepare_inj(raw_df_injuries, person_id = "player_name",
date_injured = "from", date_recovered = "until")
injd <- prepare_all(data_exposures = df_exposures,
data_injuries = df_injuries,
exp_unit = "matches_minutes")
```

Now, the preprocessed data are passed to `calc_summary()`

to calculate injury summary statistics overall or playerwise:

```
df_summary <- calc_summary(injd)
#> Warning in summary_unit(unit, out, quiet):
#> Exposure time unit is matches_minutes
#> Case incidence and case burden are calculated per 100 athlete-matches of exposure (i.e. 90 minutes times 100)
#> Warning in summary_unit(unit, out, quiet):
#> Exposure time unit is matches_minutes
#> Case incidence and case burden are calculated per 100 athlete-matches of exposure (i.e. 90 minutes times 100)
```

```
df_summary_p <- calc_summary(injd, overall = FALSE)
#> Warning in summary_unit(unit, out, quiet):
#> Exposure time unit is matches_minutes
#> Case incidence and case burden are calculated per 100 athlete-matches of exposure (i.e. 90 minutes times 100)
#> Warning in summary_unit(unit, out, quiet):
#> Exposure time unit is matches_minutes
#> Case incidence and case burden are calculated per 100 athlete-matches of exposure (i.e. 90 minutes times 100)
```

We notice that some warning messages pop up (unless
`quiet = TRUE`

). They are displayed to make it clear what the
exposure time unit is^{2}.

To present the results in a more tidier and comprehensible way
(instead of **R** code styled output) the following can be
done:

```
# the 'playerwise' data frame
df_summary_p
```

## Code to format the table

```
# format the 'playerwise' data frame for output as a table
df_summary_p |>
arrange(desc(incidence)) |> # sort by decreasing order of incidence
mutate(iqr_dayslost = paste0(qt25_dayslost, " - ", qt75_dayslost)) |>
select("person_id", "ncases", "ndayslost", "mean_dayslost",
"median_dayslost", "iqr_dayslost", "totalexpo",
"incidence", "burden") |>
head(10) |>
kable(digits = 2, col.names = c("Player", "N injuries", "N days lost",
"Mean days lost", "Median days lost",
"IQR days lost",
"Total exposure", "Incidence", "Burden"))
```

Player | N injuries | N days lost | Mean days lost | Median days lost | IQR days lost | Total exposure | Incidence | Burden |
---|---|---|---|---|---|---|---|---|

adam-lallana | 6 | 302 | 50.33 | 44.0 | 29.5 - 56.25 | 700 | 77.14 | 3882.86 |

daniel-sturridge | 3 | 122 | 40.67 | 51.0 | 33.5 - 53 | 927 | 29.13 | 1184.47 |

divock-origi | 1 | 5 | 5.00 | 5.0 | 5 - 5 | 366 | 24.59 | 122.95 |

philippe-coutinho | 3 | 62 | 20.67 | 25.0 | 18.5 - 25 | 1117 | 24.17 | 499.55 |

naby-keita | 3 | 89 | 29.67 | 20.0 | 19 - 35.5 | 1393 | 19.38 | 575.02 |

dejan-lovren | 6 | 160 | 26.67 | 17.0 | 10 - 32.25 | 3109 | 17.37 | 463.17 |

jordan-henderson | 8 | 91 | 11.38 | 7.5 | 6.25 - 12.75 | 4154 | 17.33 | 197.16 |

xherdan-shaqiri | 2 | 67 | 33.50 | 33.5 | 23.25 - 43.75 | 1057 | 17.03 | 570.48 |

joel-matip | 3 | 144 | 48.00 | 28.0 | 26.5 - 59.5 | 1994 | 13.54 | 649.95 |

fabinho | 3 | 22 | 7.33 | 9.0 | 5.5 - 10 | 2013 | 13.41 | 98.36 |

We used RMarkdown, in
particular `knitr::kable()`

function, to report these tables
in this way.

```
# the 'overall' data frame
df_summary
```

## Code to format the table

```
# format the table of total incidence and burden (main columns)
df_summary |>
mutate(iqr_dayslost = paste0(qt25_dayslost, " - ", qt75_dayslost)) |>
select("ncases", "ndayslost", "mean_dayslost", "median_dayslost",
"iqr_dayslost", "totalexpo", "incidence", "burden") |>
data.frame(row.names = "TOTAL") |>
kable(digits = 2,
col.names = c("N injuries", "N days lost", "Mean days lost",
"Median days lost", "IQR days lost",
"Total exposure", "Incidence", "Burden"),
row.names = TRUE) |>
kable_styling(full_width = FALSE)
```

N injuries | N days lost | Mean days lost | Median days lost | IQR days lost | Total exposure | Incidence | Burden | |
---|---|---|---|---|---|---|---|---|

TOTAL | 82 | 2049 | 24.99 | 12 | 6 - 25 | 73158 | 10.09 | 252.07 |

Note that to provide numbers that are easy to interpret and to avoid
small decimals, injury incidence and injury burden are reported ‘per 100
player-match exposure’. As in this example exposure time is
**minutes played in matches**, we multiply the rates by
90*100 (i.e. 90 minutes lasts a football match). The reported incidence
rate is estimated by \(\hat{I}_r =
\frac{82}{74690}\times90\times100\).

## Code to format the table

```
# format the table of total incidence and burden (point + ci estimates)
dfs_cis <- df_summary |>
select(starts_with("incid"), starts_with("burd")) |>
data.frame(row.names = "TOTAL")
dfs_cis$ci_incidence <- paste0("[", round(dfs_cis$incidence_lower, 1),
", ", round(dfs_cis$incidence_upper, 1), "]")
dfs_cis$ci_burden <- paste0("[", round(dfs_cis$burden_lower, 1),
", ", round(dfs_cis$burden_upper, 1), "]")
conf_level <- 0.95 * 100
dfs_cis |>
select(1, 9, 5, 10) |>
kable(digits = 2,
col.names = c("Incidence", paste0(conf_level, "% CI for \\(I_r\\)"),
"Burden", paste0(conf_level, "% CI for \\(I_{br}\\)")))
```

Incidence | 95% CI for \(I_r\) | Burden | 95% CI for \(I_{br}\) | |
---|---|---|---|---|

TOTAL | 10.09 | [7.9, 12.3] | 252.07 | [241.2, 263] |

Players with the highest injury incidence rate (all type of injuries) were Adam Lallana and Daniel Sturridge with 77.1 and 29.1 injuries per 100 player-matches respectively. The teams overall injury incidence was of 9.9 injuries per 100 player-matches and the injury burden of 246.9 days lost per 100 player-matches.

These summaries can be done by type of injury:

`dfs_pertype <- calc_summary(injd, by = "injury_type", quiet = T)`

These are the results of the team regarding injury incidence and injury burden by type of injury:

`dfs_pertype`

## Code to format the table

```
dfs_pertype |>
select(1:5, 9:15) |>
mutate(ncases2 = paste0(ncases, " (", percent_ncases, ")"),
ndayslost2 = paste0(ndayslost, " (", percent_ndayslost, ")"),
iqr_dayslost = paste0(qt25_dayslost, " - ", qt75_dayslost),
median_dayslost2 = paste0(median_dayslost, " (", iqr_dayslost, ")")) |>
select(1, 13:14, 16, 4:5, 12) |>
arrange(desc(burden)) |>
kable(digits = 2,
col.names = c("Type of injury", "N injuries (%)", "N days lost (%)",
"Median days lost (IQR)",
"Total exposure", "Incidence", "Burden"),
row.names = TRUE) |>
kable_styling(full_width = FALSE)
```

Type of injury | N injuries (%) | N days lost (%) | Median days lost (IQR) | Total exposure | Incidence | Burden | |
---|---|---|---|---|---|---|---|

1 | Muscle | 25 (30.49) | 735 (35.87) | 21 (12 - 36) | 73158 | 3.08 | 90.42 |

2 | Ligament | 9 (10.98) | 596 (29.09) | 28 (7 - 54) | 73158 | 1.11 | 73.32 |

3 | Unknown | 21 (25.61) | 332 (16.2) | 7 (4 - 18) | 73158 | 2.58 | 40.84 |

4 | Concussion | 16 (19.51) | 213 (10.4) | 10.5 (5.75 - 14.5) | 73158 | 1.97 | 26.20 |

5 | Bone | 11 (13.41) | 173 (8.44) | 9 (4.5 - 16.5) | 73158 | 1.35 | 21.28 |

### - `calc_prevalence()`

## Prepare data

```
df_exposures <- prepare_exp(raw_df_exposures, person_id = "player_name",
date = "year", time_expo = "minutes_played")
df_injuries <- prepare_inj(raw_df_injuries, person_id = "player_name",
date_injured = "from", date_recovered = "until")
injd <- prepare_all(data_exposures = df_exposures,
data_injuries = df_injuries,
exp_unit = "matches_minutes")
```

We calculate the injury prevalence and the proportions of injury-free players on a season basis:

```
prev_table1 <- calc_prevalence(injd, time_period = "season")
prev_table1
#> # A tibble: 4 × 5
#> season status n n_athlete prop
#> <fct> <fct> <int> <int> <dbl>
#> 1 season 2017/2018 Available 7 23 30.4
#> 2 season 2017/2018 Injured 16 23 69.6
#> 3 season 2018/2019 Available 2 19 10.5
#> 4 season 2018/2019 Injured 17 19 89.5
```

Making use of `knitr::kable()`

:

Season | Status | N | Total | % |
---|---|---|---|---|

season 2017/2018 | Available | 7 | 23 | 30.4 |

season 2017/2018 | Injured | 16 | 23 | 69.6 |

season 2018/2019 | Available | 2 | 19 | 10.5 |

season 2018/2019 | Injured | 17 | 19 | 89.5 |

Overall, there were more injured players in the 18-19 season than in the previous season. Let’s calculate it monthly:

```
prev_table2 <- calc_prevalence(injd, time_period = "monthly")
## compare two seasons July and August
prev_table2 |>
group_by(season) |>
slice(1:4)
#> # A tibble: 8 × 6
#> # Groups: season [2]
#> season month status n n_athlete prop
#> <fct> <fct> <fct> <int> <int> <dbl>
#> 1 season 2017/2018 Jul Available 21 23 91.3
#> 2 season 2017/2018 Jul Injured 2 23 8.7
#> 3 season 2017/2018 Aug Available 18 23 78.3
#> 4 season 2017/2018 Aug Injured 5 23 21.7
#> 5 season 2018/2019 Jul Available 16 19 84.2
#> 6 season 2018/2019 Jul Injured 3 19 15.8
#> 7 season 2018/2019 Aug Available 15 19 78.9
#> 8 season 2018/2019 Aug Injured 4 19 21.1
```

```
## compare two seasons January and February
prev_table2 |>
group_by(season) |>
slice(13:16)
#> # A tibble: 8 × 6
#> # Groups: season [2]
#> season month status n n_athlete prop
#> <fct> <fct> <fct> <int> <int> <dbl>
#> 1 season 2017/2018 Jan Available 18 23 78.3
#> 2 season 2017/2018 Jan Injured 5 23 21.7
#> 3 season 2017/2018 Feb Available 21 23 91.3
#> 4 season 2017/2018 Feb Injured 2 23 8.7
#> 5 season 2018/2019 Jan Available 9 19 47.4
#> 6 season 2018/2019 Jan Injured 10 19 52.6
#> 7 season 2018/2019 Feb Available 12 19 63.2
#> 8 season 2018/2019 Feb Injured 7 19 36.8
```

Looking at monthly basis, there were more differences w.r.t. player availability in Liverpool FC 1st male team, during the winter January/February months. More injured players in the 18-19 season.

`prev_table3 <- calc_prevalence(injd, time_period = "monthly", by = "injury_type")`

## Tidy up

```
## season 1
prev_table3 |>
filter(season == "season 2017/2018", month == "Jan") |>
kable(col.names = c("Season", "Month", "Status", "N", "Total", "%"),
caption = "Season 2017/2018") |>
kable_styling(full_width = FALSE, position = "float_left")
## season 2
prev_table3 |>
filter(season == "season 2018/2019", month == "Jan") |>
kable(col.names = c("Season", "Month", "Status", "N", "Total", "%"),
caption = "Season 2018/2019") |>
kable_styling(full_width = FALSE, position = "left")
```

Season | Month | Status | N | Total | % |
---|---|---|---|---|---|

season 2017/2018 | Jan | Available | 18 | 23 | 78.3 |

season 2017/2018 | Jan | Ligament | 1 | 23 | 4.3 |

season 2017/2018 | Jan | Muscle | 3 | 23 | 13.0 |

season 2017/2018 | Jan | Unknown | 1 | 23 | 4.3 |

Season | Month | Status | N | Total | % |
---|---|---|---|---|---|

season 2018/2019 | Jan | Available | 9 | 19 | 47.4 |

season 2018/2019 | Jan | Bone | 1 | 19 | 5.3 |

season 2018/2019 | Jan | Concussion | 2 | 19 | 10.5 |

season 2018/2019 | Jan | Ligament | 1 | 19 | 5.3 |

season 2018/2019 | Jan | Muscle | 3 | 19 | 15.8 |

season 2018/2019 | Jan | Unknown | 4 | 19 | 21.1 |

## Further implementation

In the near future there will be available the negative binomial
(`method = "negbin"`

argument), zero-inflated poisson
(“`zinfpois`

”) and zero-inflated negative binomial
(`"zinfnb"`

) methods in `calc_incidence()`

and
`calc_burden()`

functions.

Finally, this document shows how to perform descriptive analyses for injury epidemiology, but naturally, following these analyses further statistical inferences or multivariate regression analyses may be chosen to infer about the player’s/athletes population properties (e.g. to test whether there are differences between the injury incidence rates of two cohorts) or to evaluate the influence of independent factors (e.g. previous injuries, workload) on the injuries occurred.

## Notes

**NOTE 1:** as Bahr, Clarsen, and
Ekstrand (2018) state, injury
incidence (likelihood) and injury burden (severity) should be reported
and assessed in conjunction rather than in isolation. In this regard,
see the risk matrix plot provided by `gg_injriskmatrix()`

function.

**NOTE 2:** neither injury incidence (\(I_r\)) nor injury burden (\(I_{br}\)) are ratios, and they are not
interpreted as a probability; they are rates and their unit
(person-time)\(^{-1}\) (e.g. per 1000h
of player-exposure, per player-season etc.).

**NOTE 3:** as Waldén et al. (2023) point out, incidence-based
measures that provide a standardized time window for the population at
risk (e.g., injuries per hour) are preferred over measures in which the
time at risk varies among individuals (e.g., injuries per athletic
exposure, injuries per number of matches). This preference for measures
with standardized time scales aids in the comparison of statistics
across different cohorts and sports.

## References

*British Journal of Sports Medicine*52 (16): 1018–21. https://doi.org/10.1136/bjsports-2017-098160.

*British Journal of Sports Medicine*37 (5): 384–92. https://doi.org/10.1136/bjsm.37.5.384.

*British Journal of Sports Medicine*34 (2): 133–36. https://doi.org/10.1136/bjsm.34.2.133.

*British Journal of Sports Medicine*. https://doi.org/10.1136/bjsports-2022-106405.