The objective of this package is to compute rates adjusted by a reference population or other rate. This is a very common procedure in epidemiology, allowing the comparison of rates of a event (like mortality) among groups that have different age distributions.
Some packages like the epitools compute these adjusted
rates. This package functions wraps the epitools functions
in a tidy way, allowing the computation of age adjusted rates for
several groups using key variables, like year and regions for
example.
Direct adjusted rate
Events and population data
Let’s use the Fleiss dataset, quoted by the epitools
package (Fleiss, 1981, p. 249 ).
population <- c(230061, 329449, 114920, 39487, 14208, 3052,
72202, 326701, 208667, 83228, 28466, 5375, 15050, 175702,
207081, 117300, 45026, 8660, 2293, 68800, 132424, 98301,
46075, 9834, 327, 30666, 123419, 149919, 104088, 34392,
319933, 931318, 786511, 488235, 237863, 61313)
population <- matrix(population, 6, 6,
dimnames = list(c("Under 20", "20-24", "25-29", "30-34", "35-39",
"40 and over"), c("1", "2", "3", "4", "5+", "Total")))
count <- c(107, 141, 60, 40, 39, 25, 25, 150, 110, 84, 82, 39,
3, 71, 114, 103, 108, 75, 1, 26, 64, 89, 137, 96, 0, 8, 63, 112,
262, 295, 136, 396, 411, 428, 628, 530)
count <- matrix(count, 6, 6,
dimnames = list(c("Under 20", "20-24", "25-29", "30-34", "35-39",
"40 and over"), c("1", "2", "3", "4", "5+", "Total")))
population
#> 1 2 3 4 5+ Total
#> Under 20 230061 72202 15050 2293 327 319933
#> 20-24 329449 326701 175702 68800 30666 931318
#> 25-29 114920 208667 207081 132424 123419 786511
#> 30-34 39487 83228 117300 98301 149919 488235
#> 35-39 14208 28466 45026 46075 104088 237863
#> 40 and over 3052 5375 8660 9834 34392 61313
count
#> 1 2 3 4 5+ Total
#> Under 20 107 25 3 1 0 136
#> 20-24 141 150 71 26 8 396
#> 25-29 60 110 114 64 63 411
#> 30-34 40 84 103 89 112 428
#> 35-39 39 82 108 137 262 628
#> 40 and over 25 39 75 96 295 530The Fleiss data present events (count object) and
population (population object) for six age groups on five
different groups (from 1 to 5+).
The tidyrates package present the same Fleiss data in a
tidy way, with a tibble in long format.
fleiss_data
#> key age_group name value
#> 1 k1 Under 20 population 230061
#> 2 k1 Under 20 events 107
#> 3 k1 20-24 population 329449
#> 4 k1 20-24 events 141
#> 5 k1 25-29 population 114920
#> 6 k1 25-29 events 60
#> 7 k1 30-34 population 39487
#> 8 k1 30-34 events 40
#> 9 k1 35-39 population 14208
#> 10 k1 35-39 events 39
#> 11 k1 40 and over population 3052
#> 12 k1 40 and over events 25
#> 13 k2 Under 20 population 72202
#> 14 k2 Under 20 events 25
#> 15 k2 20-24 population 326701
#> 16 k2 20-24 events 150
#> 17 k2 25-29 population 208667
#> 18 k2 25-29 events 110
#> 19 k2 30-34 population 83228
#> 20 k2 30-34 events 84
#> 21 k2 35-39 population 28466
#> 22 k2 35-39 events 82
#> 23 k2 40 and over population 5375
#> 24 k2 40 and over events 39
#> 25 k3 Under 20 population 15050
#> 26 k3 Under 20 events 3
#> 27 k3 20-24 population 175702
#> 28 k3 20-24 events 71
#> 29 k3 25-29 population 207081
#> 30 k3 25-29 events 114
#> 31 k3 30-34 population 117300
#> 32 k3 30-34 events 103
#> 33 k3 35-39 population 45026
#> 34 k3 35-39 events 108
#> 35 k3 40 and over population 8660
#> 36 k3 40 and over events 75
#> 37 k4 Under 20 population 2293
#> 38 k4 Under 20 events 1
#> 39 k4 20-24 population 68800
#> 40 k4 20-24 events 26
#> 41 k4 25-29 population 132424
#> 42 k4 25-29 events 64
#> 43 k4 30-34 population 98301
#> 44 k4 30-34 events 89
#> 45 k4 35-39 population 46075
#> 46 k4 35-39 events 137
#> 47 k4 40 and over population 9834
#> 48 k4 40 and over events 96
#> 49 k5plus Under 20 population 327
#> 50 k5plus Under 20 events 0
#> 51 k5plus 20-24 population 30666
#> 52 k5plus 20-24 events 8
#> 53 k5plus 25-29 population 123419
#> 54 k5plus 25-29 events 63
#> 55 k5plus 30-34 population 149919
#> 56 k5plus 30-34 events 112
#> 57 k5plus 35-39 population 104088
#> 58 k5plus 35-39 events 262
#> 59 k5plus 40 and over population 34392
#> 60 k5plus 40 and over events 295The key variable refers to the groups,
age_group to the age groups, name separates
the values into events and population.
You may use this same structure for your use case data.
Reference population data
The Fleiss example uses the average population as standard population reference.
standard<-apply(population[,-6], 1, mean)
standard
#> Under 20 20-24 25-29 30-34 35-39 40 and over
#> 63986.6 186263.6 157302.2 97647.0 47572.6 12262.6Using tidyrates, we must supply a tibble with two
variables: age group and population.
Rate computation
To use the direct adjustment procedure, tidyrate present
the rate_adj_direct function. The .data
argument must be a tibble with the events and population data, and the
.std argument must be standard population tibble. The
.keys argument must point to grouping variables on the
.data tibble, if available.
The rate_adj_direct will compute the crude rate,
adjusted rate and exact confidence intervals for each group.
rate_adj_direct(fleiss_data, .std = standard_pop, .keys = "key")
#> # A tibble: 5 × 5
#> key crude.rate adj.rate lci uci
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 k1 0.000563 0.000923 0.000804 0.00106
#> 2 k2 0.000676 0.000912 0.000824 0.00101
#> 3 k3 0.000833 0.000851 0.000772 0.000942
#> 4 k4 0.00115 0.000927 0.000800 0.00115
#> 5 k5plus 0.00167 0.000755 0.000677 0.00188Indirect adjusted rate
Events and population data
Let’s use the Selvin dataset, quoted by the epitools
package (Selvin, 2004).
dth40 <- c(45, 201, 320, 670, 1126, 3160, 9723, 17935,
22179, 13461, 2238)
pop40 <- c(906897, 3794573, 10003544, 10629526, 9465330,
8249558, 7294330, 5022499, 2920220, 1019504, 142532)The tidyrates present the same dataset in a tidy
way.
selvin_data_1940
#> # A tibble: 22 × 3
#> age_group name value
#> <chr> <chr> <dbl>
#> 1 <1 events 45
#> 2 1-4 events 201
#> 3 5-14 events 320
#> 4 15-24 events 670
#> 5 25-34 events 1126
#> 6 35-44 events 3160
#> 7 45-54 events 9723
#> 8 55-64 events 17935
#> 9 65-74 events 22179
#> 10 75-84 events 13461
#> # ℹ 12 more rowsEvents and population reference data
dth60 <- c(141, 926, 1253, 1080, 1869, 4891, 14956, 30888,
41725, 26501, 5928)
pop60 <- c(1784033, 7065148, 15658730, 10482916, 9939972,
10563872, 9114202, 6850263, 4702482, 1874619, 330915)The tidyrates present the same dataset in a tidy
way.
selvin_data_1960
#> # A tibble: 22 × 3
#> age_group name value
#> <chr> <chr> <dbl>
#> 1 <1 events 141
#> 2 1-4 events 926
#> 3 5-14 events 1253
#> 4 15-24 events 1080
#> 5 25-34 events 1869
#> 6 35-44 events 4891
#> 7 45-54 events 14956
#> 8 55-64 events 30888
#> 9 65-74 events 41725
#> 10 75-84 events 26501
#> # ℹ 12 more rowsRate computation
To use the indirect adjustment procedure, tidyrate
present the rate_adj_indirect function. The
.data argument must be a tibble with the events and
population data, and the .std argument must be also a
tibble with the events and population data. The .keys
argument must point to grouping variables on the .data
tibble, if available.
The rate_adj_indirect will compute the crude rate,
adjusted rate and exact confidence intervals for each group.
rate_adj_indirect(selvin_data_1940, selvin_data_1960)
#> # A tibble: 1 × 4
#> crude.rate adj.rate lci uci
#> <dbl> <dbl> <dbl> <dbl>
#> 1 0.00120 0.00120 0.00119 0.00120