This vignette documents the method for calculating DSRs and their
confidence limits using the
PHEindicatormethods::calculate_dsr() function. The function
calculates confidence limits using the Dobson method, with an option to
adjust confidence intervals for non-independent events.
The function can be used to calculate DSRs for multiple groups. For example, DSRs for multiple geographic areas, sexes, time periods and/or indicators can be calculated in a single execution. It takes the following arguments as inputs:
| Argument | Type | Definition | Default value |
|---|---|---|---|
| data | data frame | data.frame containing the data to be standardised | none |
| x | unquoted string | field name from data containing the observed number of events for each standardisation category (eg ageband) within each grouping set (eg area or indicator) | none |
| n | unquoted string | field name from data containing the populations for each standardisation category (eg ageband) within each grouping set (eg area or indicator) | none |
| stdpop | unquoted string | field name from data containing the standard populations for each age group | NULL |
| type | quoted string | defines the data and metadata columns to include in output. Can by ‘value’, ‘lower’, ‘upper’, ‘standard’ or ‘full’ | “full” |
| confidence | numeric value | the required level of confidence expressed as a number between 0.9 and 1 or 90 and 100 | 0.95 |
| multiplier | numeric value | the multiplier used to express the final values (eg 100,000 = rate per 100,000 | 100,000 |
| independent_events | boolean | whether events are independent | TRUE |
| eventfreq | unquoted string | field name from data containing the event frequencies | NULL |
| ageband | unquoted string | field name form data containing the age bands for standardisation | NULL |
Note that the European Standard Population 2013 divided into 19
five-year agebands (0-4, 5-9, 10-14, …..90+) is provided in vector
format within the package. You can join this to your dataset to create a
standard population column prior to calling
calculate_dsr.
If multiple DSRs are required from a single data frame then the data frame must be grouped prior to inputting to the function - this is demonstrated below.
In a real situation we’d most likely be sourcing our numerators and denominators from different places so let’s create them separately for now.
pops <- data.frame(
indicator = rep(c("Ind1", "Ind2", "Ind3", "Ind4"), each = 19 * 2 * 5),
period = rep(2012:2016, each = 19 * 2, times = 4),
region = rep(rep(c("Area1", "Area2"), each = 19), times = 20),
ageband = rep(c(0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50,
55, 60, 65, 70, 75, 80, 85, 90), times = 40),
pop = sample(10000:20000, 19 * 2 * 5 * 4, replace = TRUE),
esp2013 = rep(esp2013, times = 40))
head(pops)
#> indicator period region ageband pop esp2013
#> 1 Ind1 2012 Area1 0 17819 5000
#> 2 Ind1 2012 Area1 5 12292 5500
#> 3 Ind1 2012 Area1 10 10241 5500
#> 4 Ind1 2012 Area1 15 15136 5500
#> 5 Ind1 2012 Area1 20 11563 6000
#> 6 Ind1 2012 Area1 25 11517 6000
deaths <- data.frame(
indicator = rep(c("Ind1", "Ind2", "Ind3", "Ind4"), each = 19 * 2 * 5),
period = rep(2012:2016, each = 19 * 2),
region = rep(rep(c("Area1", "Area2"), each = 19), times = 5),
ageband = rep(c(0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50,
55, 60, 65, 70, 75, 80, 85, 90), times = 10),
dths = sample(200, 19 * 2 * 5 * 4, replace = TRUE))
head(deaths)
#> indicator period region ageband dths
#> 1 Ind1 2012 Area1 0 26
#> 2 Ind1 2012 Area1 5 83
#> 3 Ind1 2012 Area1 10 13
#> 4 Ind1 2012 Area1 15 103
#> 5 Ind1 2012 Area1 20 48
#> 6 Ind1 2012 Area1 25 96Our data contains records for 4 different indicators, 5 time periods and 2 geographies so let’s calculate a DSR for each combination - that’s 40 separate DSRs from a single execution of the calculate_dsr function……
First we’ll need to join our datasets to create the input data frame for the function. We also need to specify our grouping sets:
By default the function will apply 95% confidence intervals, a 100,000 multiplier and will output 3 data fields against each grouping set:
It will also output 3 metadata fields as an audit showing which argument parameters were passed:
calculate_dsr(
data = df,
x = dths, # name of field containing count of events
n = pop, # name of field containing population denominators
stdpop = esp2013 # name of field containing standard populations
)
#> # A tibble: 40 × 11
#> indicator period region total_count total_pop value lowercl uppercl
#> <chr> <int> <chr> <int> <int> <dbl> <dbl> <dbl>
#> 1 Ind1 2012 Area1 1229 270951 494. 465. 523.
#> 2 Ind1 2012 Area2 2613 281371 941. 902. 981.
#> 3 Ind1 2013 Area1 1443 303770 454. 429. 480.
#> 4 Ind1 2013 Area2 1853 286019 723. 688. 760.
#> 5 Ind1 2014 Area1 1435 266717 524. 496. 553.
#> 6 Ind1 2014 Area2 1838 287502 643. 612. 675.
#> 7 Ind1 2015 Area1 2025 304898 656. 625. 687.
#> 8 Ind1 2015 Area2 1787 300808 635. 604. 667.
#> 9 Ind1 2016 Area1 1929 282076 675. 644. 707.
#> 10 Ind1 2016 Area2 1980 291663 747. 712. 782.
#> # ℹ 30 more rows
#> # ℹ 3 more variables: confidence <chr>, statistic <chr>, method <chr>
Alternatively, we can drop metadata fields by specifying the ‘type’ argument value as ‘standard’, and adjust the multiplier applied to the DSR:
calculate_dsr(
data = df,
x = dths,
n = pop,
stdpop = esp2013,
type = "standard",
confidence = 99.8,
multiplier = 10000
)
#> # A tibble: 40 × 8
#> indicator period region total_count total_pop value lowercl uppercl
#> <chr> <int> <chr> <int> <int> <dbl> <dbl> <dbl>
#> 1 Ind1 2012 Area1 1229 270951 49.4 44.9 54.1
#> 2 Ind1 2012 Area2 2613 281371 94.1 88.0 100.
#> 3 Ind1 2013 Area1 1443 303770 45.4 41.4 49.6
#> 4 Ind1 2013 Area2 1853 286019 72.3 66.8 78.1
#> 5 Ind1 2014 Area1 1435 266717 52.4 48.0 57.0
#> 6 Ind1 2014 Area2 1838 287502 64.3 59.4 69.4
#> 7 Ind1 2015 Area1 2025 304898 65.6 60.8 70.6
#> 8 Ind1 2015 Area2 1787 300808 63.5 58.7 68.5
#> 9 Ind1 2016 Area1 1929 282076 67.5 62.6 72.6
#> 10 Ind1 2016 Area2 1980 291663 74.7 69.3 80.3
#> # ℹ 30 more rows
In some cases you may wish to standardise against a different population to the default esp2013 one provided - such as the 1976 European Standard Population or an age and sex standardised population. This can be done by appending the required standard populations to your data frame before executing the function.
In the example below the data we have used previously are duplicated for males and females and then different standard populations are applied to each gender. For the purposes of the example, dummy standard populations have been used which very crudely represent more women living to the oldest age groups than men - these are not from any official source and should not be used in real analysis. Notice that despite the data counts and populations being the same for males and females the different standard populations used result in different DSRs being produced.
# duplicate data for males and females and apply different standard populations
# to each sex
df_f <- df %>%
mutate(
sex = "F",
esp_dummy = c(5000, 5500, 5500, 5500, 6000, 6000, 6500, 7000, 7000, 7000,
7000, 6500, 5500, 5000, 4500, 4000, 3000, 2000, 1500)
)
df_m <- df %>%
mutate(
sex = "M",
esp_dummy = c(5000, 5500, 5500, 5500, 6000, 6000, 6500, 7000, 7000, 7000,
7000, 6500, 6500, 6000, 5500, 4000, 2000, 1000, 500)
)
df_mf <- df_f %>%
bind_rows(df_m) %>%
group_by(sex, .add = TRUE) %>%
select(!"esp2013")
# add sex to the grouping variables then calculate the DSRs
dsrs_mf <- calculate_dsr(
df_mf,
x = dths,
n = pop,
stdpop = esp_dummy
)
head(dsrs_mf)
#> # A tibble: 6 × 12
#> indicator period region sex total_count total_pop value lowercl uppercl
#> <chr> <int> <chr> <chr> <int> <int> <dbl> <dbl> <dbl>
#> 1 Ind1 2012 Area1 F 1229 270951 492. 464. 521.
#> 2 Ind1 2012 Area1 M 1229 270951 495. 466. 526.
#> 3 Ind1 2012 Area2 F 2613 281371 945. 906. 985.
#> 4 Ind1 2012 Area2 M 2613 281371 937. 898. 978.
#> 5 Ind1 2013 Area1 F 1443 303770 456. 431. 483.
#> 6 Ind1 2013 Area1 M 1443 303770 451. 426. 478.
#> # ℹ 3 more variables: confidence <chr>, statistic <chr>, method <chr>
Methodological advice on calculating directly standardised rates when observed events are not independent can be found in the DSR chapter of the Fingertips Public Health Technical Guidance.
This method adjusts the confidence intervals around the DSR by considering the frequency of events per individual. In the example below, event frequency data is added to the input data frame and the calculate_dsr function is then applied with the independent_events argument set to FALSE. The event frequency and age band column names are additionally passed into the function. Note that the DSRs output are identical to those produced for the df data frame at the beginning of this vignette, but the 95% confidence intervals are wider.
# Generate some dummy data
# breakdown original dataset to show event frequencies and to count unique individuals
df_freq <- df %>%
mutate(
f3 = floor((dths * 0.1) / 3), # 10% of events in individuals with 3 events
f2 = floor((dths * 0.2) / 2), # 20% of events in individuals with 2 events
f1 = (dths - (3 * f3) - (2 * f2))) %>% # 70% of events in individuals with 1 event
select(!"dths") %>%
pivot_longer(
cols = c("f1", "f2", "f3"),
names_to = "eventfrequency",
values_to = "uniqueindividuals",
names_prefix = "f") %>%
mutate(eventfrequency = as.integer(eventfrequency)
)
# calculate the dsrs - notice that output DSRs values match those calculated
# earlier for the same data frame but confidence intervals are wider
df_freq %>%
group_by(eventfrequency, .add = TRUE) %>%
calculate_dsr(
x = uniqueindividuals, # count of unique individuals experiencing the frequency of events in eventfreq
n = pop,
stdpop = esp2013,
independent_events = FALSE, # calculate CIs assuming events are not independent
eventfreq = eventfrequency, # name of column containing the event frequencies (e.g. 1, 2, ...)
ageband = ageband # name of column containing age bands
)
#> # A tibble: 40 × 11
#> indicator period region total_count total_pop value lowercl uppercl
#> <chr> <int> <chr> <dbl> <int> <dbl> <dbl> <dbl>
#> 1 Ind1 2012 Area1 1229 270951 494. 461. 528.
#> 2 Ind1 2012 Area2 2613 281371 941. 895. 988.
#> 3 Ind1 2013 Area1 1443 303770 454. 425. 485.
#> 4 Ind1 2013 Area2 1853 286019 723. 682. 766.
#> 5 Ind1 2014 Area1 1435 266717 524. 492. 558.
#> 6 Ind1 2014 Area2 1838 287502 643. 607. 681.
#> 7 Ind1 2015 Area1 2025 304898 656. 620. 692.
#> 8 Ind1 2015 Area2 1787 300808 635. 599. 672.
#> 9 Ind1 2016 Area1 1929 282076 675. 638. 713.
#> 10 Ind1 2016 Area2 1980 291663 747. 706. 788.
#> # ℹ 30 more rows
#> # ℹ 3 more variables: confidence <chr>, statistic <chr>, method <chr>
This is a fairly common scenario, especially when working with small populations where there may be no deaths in some of the younger age groups. The calculate_dsr function can handle this scenario and will assume a zero death count where it is missing or recorded as NA.
Let’s create a couple of data frames to demonstrate this. In this example, there are no deaths in the 10-14, 15-20 and 20-14 age bands. If we join these data frames to produce the input data frame required for the calculate_dsr function then we get NA values in the Deaths column.
pops2 <- data.frame(
ageband = c( 0, 5, 10, 15, 20, 25, 30, 35, 40, 45,
50, 55, 60, 65, 70, 75, 80, 85, 90),
pop = c(30, 35, 35, 35, 40, 40, 45, 50, 50, 50,
60, 60, 70, 75, 70, 60, 20, 20, 15),
esp2013 = esp2013
)
deaths2 <- data.frame(
ageband = c(0, 5, 25, 30, 35, 40, 45, 50, 55,
60, 65, 70, 75, 80, 85, 90),
dths = c(1, 1, 1, 1, 3, 3, 3, 3, 10,
10, 10, 10, 8, 8, 8, 8)
)
df2 <- left_join(pops2, deaths2, by = "ageband")
head(df2)
#> ageband pop esp2013 dths
#> 1 0 30 5000 1
#> 2 5 35 5500 1
#> 3 10 35 5500 NA
#> 4 15 35 5500 NA
#> 5 20 40 6000 NA
#> 6 25 40 6000 1
calculate_dsr(
df2,
x = dths,
n = pop,
stdpop = esp2013
)
#> total_count total_pop value lowercl uppercl confidence statistic
#> 1 88 860 8283.016 6570.819 10289.65 95% dsr per 100000
#> method
#> 1 Dobson