Age Adjusted Rates in Epidemiology

Age-specific rate

Weather to understand a broder prespecitve or to compare across population, these rates are often analyzed stratified by sex and age. This also helps to remove the confounding effection of these factors. The incidence/mortality rate per age-group is usually referred to as Age-specific rates where rates are computed for each age-groups. This is often desirable since factor age has a strong effect on mortality and incidence of most disease especially the cronic one.

Age-adjusted rate

Many research articles, however presents the age-adjusted rates. Age-adjusted rates are standardized (weighted) using some standard population age-structure. For example, many european studies on melanoma uses european standard age distribution. While any reasonal studies have also used world standard population. Cancer registry in their reports sometimes uses age-structure of that country in some given year. For instance, Norway² and Finland³ have used the their population in 2014 as standard population in their recent cancer report while Australia have used 2001 Australian population⁴.

Standardized (adjusted) rates makes comparison between the population possible. Figure 1 shows the difference in the age distribution between world population and European population. Following table are some of the standard population often used in the study. Further on standard popuation see seer.cancer.gov⁵.

Example

The following example have used the Austrailian cancer data with 5-year age-group⁶ after filtering melanoma cases from 1982 to 2018. The dataset has yearly count and age-specific incidence rate of melanoma for men and women.

Let us use the above European standard population to find the yearly age-standardized incidence by sex.

data <- fread("melanoma.csv")
std_pop <- popEpi::stdpop18

data[AgeGroup %in% c("85-89", "90+"), AgeGroup := "85+"]
setnames(std_pop, c("AgeGroup", "World", "Europe", "Nordic"))
std_pop[AgeGroup == "85", AgeGroup := "85+"]
std_pop[, c(2:4) := lapply(.SD, prop.table), .SDcols = 2:4]
asp_data <- merge.data.table(data, std_pop[, .(AgeGroup, World)], by = "AgeGroup")
asp <- asp_data[, .(AgeAdjRate = sum(ASR * World)), by = .(Year, Sex)]

asp[, tail(.SD, 8), by = Sex] %>%
    dcast.data.table(
        formula = Sex ~ Year,
        value.var = "AgeAdjRate") %>% 
        kableExtra::kbl(caption = paste(
            "Age-standardized incidence rate of melanoma",
            "Australia from 2011 to 2018"
    )) %>% 
    kableExtra::kable_styling(full_width = FALSE)

Now, let us compare the age-specific rates (crude rates) and age-standardized rates with a plot,

Compare the age-specific rates and age-adjusted rates

Plot

Figure 2: Age-standardized melanoma rate in Australia

Code

ggplot() +
    geom_line(
        data = data, 
        aes(
            x = Year, 
            y = ASR, 
            group = AgeGroup,
            color = "Crude"
        )
    ) +
    geom_line(
        data = asp,
        aes(
            x = Year, 
            y = AgeAdjRate, 
            group = 1,
            color = "Age-adjusted"
        )
    ) +
    geom_text(
        data = data[Year == max(Year)],
        check_overlap = TRUE,
        size = rel(2),
        color = "#0f0f0f",
        aes(
            x = Year + 2,
            y = ASR,
            label = AgeGroup
        )
    ) +
    scale_x_continuous(breaks = scales::breaks_extended(8)) +
    scale_y_continuous(breaks = scales::breaks_extended(8)) +
    scale_color_manual(NULL, values = c("firebrick", "grey")) +
    facet_grid(cols = vars(Sex)) +
    theme_minimal() +
    theme(
        panel.border = element_rect(fill = NA, color = "darkgrey"),
        legend.position = c(0, 1),
        legend.justification = c(0, 1)
    ) +
    labs(
        x = "Diagnosis year",
        y = paste(
            "Age-adjusted incidence rate",
            "per 100,000 person year",
            sep = "\n"
        )
    )

Compare the age-adjusted rates by sex

Plot

Figure 3: Age-standardized melanoma rate in Australia

Code

ggplot() +
    geom_line(
        data = data, 
        aes(
            x = Year, 
            y = ASR, 
            group = AgeGroup,
            color = "Crude"
        )
    ) +
    geom_line(
        data = asp,
        aes(
            x = Year, 
            y = AgeAdjRate, 
            group = 1,
            color = "Age-adjusted"
        )
    ) +
    geom_text(
        data = data[Year == max(Year)],
        check_overlap = TRUE,
        size = rel(2),
        color = "#0f0f0f",
        aes(
            x = Year + 2,
            y = ASR,
            label = AgeGroup
        )
    ) +
    scale_x_continuous(breaks = scales::breaks_extended(8)) +
    scale_y_continuous(breaks = scales::breaks_extended(8)) +
    scale_color_manual(NULL, values = c("firebrick", "grey")) +
    facet_grid(cols = vars(Sex)) +
    theme_minimal() +
    theme(
        panel.border = element_rect(fill = NA, color = "darkgrey"),
        legend.position = c(0, 1),
        legend.justification = c(0, 1)
    ) +
    labs(
        x = "Diagnosis year",
        y = paste(
            "Age-adjusted incidence rate",
            "per 100,000 person year",
            sep = "\n"
        )
    )

Discussion

Figure @fig(rate-plot) shows that the incidence of melanoma has larger difference in men between the age-groups than in women and men also have a sharp increase in older age group. In addition, the Figure @fig(adj-rate-plot) shows that males have higher age-adjusted incidence of melanoma than women in Australia and this trend is increasing over time with rapid increase before 1983 before a drop.

Age-adjusted rates are useful for comparing rates between population but it cannot give the interpretation required for comparing within a population or over a time period in that population. This is one of the reason, cancer registry uses the internal (population structure of their own population) to compute the age-adjusted rates.