This method computes the proportional change of absolute (rate differences) and relative (rate ratios) inequalities of prevalence rates for two different status groups, as proposed by Mackenbach et al. (2015).

inequ_trend(data, prev.low, prev.hi)

## Arguments

data

A data frame that contains the variables with prevalence rates for both low and high status groups (see 'Examples').

prev.low

The name of the variable with the prevalence rates for the low status groups.

prev.hi

The name of the variable with the prevalence rates for the hi status groups.

## Value

A data frame with the prevalence rates as well as the values for the proportional change in absolute (rd) and relative (rr) ineqqualities.

## Details

Given the time trend of prevalence rates of an outcome for two status groups (e.g. the mortality rates for people with lower and higher socioeconomic status over 40 years), this function computes the proportional change of absolute and relative inequalities, expressed in changes in rate differences and rate ratios. The function implements the algorithm proposed by Mackenbach et al. 2015.

## References

Mackenbach JP, Martikainen P, Menvielle G, de Gelder R. 2015. The Arithmetic of Reducing Relative and Absolute Inequalities in Health: A Theoretical Analysis Illustrated with European Mortality Data. Journal of Epidemiology and Community Health 70(7): 730-36. doi:10.1136/jech-2015-207018

## Examples

# This example reproduces Fig. 1 of Mackenbach et al. 2015, p.5

# 40 simulated time points, with an initial rate ratio of 2 and
# a rate difference of 100 (i.e. low status group starts with a
# prevalence rate of 200, the high status group with 100)

# annual decline of prevalence is 1% for the low, and 3% for the
# high status group

n <- 40
time <- seq(1, n, by = 1)
lo <- rep(200, times = n)
for (i in 2:n) lo[i] <- lo[i - 1] * .99

hi <- rep(100, times = n)
for (i in 2:n) hi[i] <- hi[i - 1] * .97

prev.data <- data.frame(lo, hi)

# print values
inequ_trend(prev.data, "lo", "hi")
#> \$data
#>          lo        hi       rr       rd
#> 1  200.0000 100.00000 2.000000 100.0000
#> 2  198.0000  97.00000 2.041237 101.0000
#> 3  196.0200  94.09000 2.083324 101.9300
#> 4  194.0598  91.26730 2.126280 102.7925
#> 5  192.1192  88.52928 2.170120 103.5899
#> 6  190.1980  85.87340 2.214865 104.3246
#> 7  188.2960  83.29720 2.260533 104.9988
#> 8  186.4131  80.79828 2.307141 105.6148
#> 9  184.5489  78.37434 2.354711 106.1746
#> 10 182.7034  76.02311 2.403262 106.6803
#> 11 180.8764  73.74241 2.452814 107.1340
#> 12 179.0677  71.53014 2.503387 107.5375
#> 13 177.2770  69.38424 2.555004 107.8927
#> 14 175.5042  67.30271 2.607684 108.2015
#> 15 173.7492  65.28363 2.661451 108.4655
#> 16 172.0117  63.32512 2.716326 108.6866
#> 17 170.2916  61.42537 2.772333 108.8662
#> 18 168.5886  59.58260 2.829494 109.0060
#> 19 166.9028  57.79513 2.887834 109.1076
#> 20 165.2337  56.06127 2.947377 109.1725
#> 21 163.5814  54.37943 3.008148 109.2020
#> 22 161.9456  52.74805 3.070172 109.1975
#> 23 160.3261  51.16561 3.133474 109.1605
#> 24 158.7229  49.63064 3.198082 109.0922
#> 25 157.1356  48.14172 3.264022 108.9939
#> 26 155.5643  46.69747 3.331321 108.8668
#> 27 154.0086  45.29655 3.400008 108.7121
#> 28 152.4685  43.93765 3.470111 108.5309
#> 29 150.9439  42.61952 3.541660 108.3243
#> 30 149.4344  41.34093 3.614684 108.0935
#> 31 147.9401  40.10071 3.689214 107.8394
#> 32 146.4607  38.89769 3.765280 107.5630
#> 33 144.9961  37.73076 3.842915 107.2653
#> 34 143.5461  36.59883 3.922150 106.9473
#> 35 142.1106  35.50087 4.003019 106.6098
#> 36 140.6895  34.43584 4.085555 106.2537
#> 37 139.2826  33.40277 4.169794 105.8799
#> 38 137.8898  32.40068 4.255769 105.4891
#> 39 136.5109  31.42866 4.343517 105.0823
#> 40 135.1458  30.48580 4.433074 104.6600
#>
#> attr(,"class")
#> [1] "sj_inequ_trend"

# plot trends - here we see that the relative inequalities
# are increasing over time, while the absolute inequalities
# are first increasing as well, but later are decreasing
# (while rel. inequ. are still increasing)
plot(inequ_trend(prev.data, "lo", "hi"))