Data preparation and lifetime risk estimation using R

Estimate lifetime risk using R package ltRISK

Qiong Chen Ph.D

Henan Cancer Center/Henan Cancer Hospital

Monday Nov 4, 2024(Beijing)

Introduction of lifetime risk

Contents

1. Introduction of lifetime risk

2. Introduction of R package ltRISK

3. Practice of lifetime risk estimation using GCO data

4. Results of Global and regional lifetime risk

Lifetime risk

A measure of the risk that a certain event will happen during a person’s lifetime. In cancer research, it is usually given as the likelihood that a person who is free of a certain type of cancer will develop or die from that type of cancer during his or her lifetime. ¹

Estimates of lifetime risk usually expressed as a percentage or as odds

• Percentage, eg.the risk that a man will develop cancer of the pancreas during his lifetime is 1.7%.
• Odds, 1 out of every 58 (100/1.7) men will develop pancreatic cancer during his lifetime.

1. source:https://www.cancer.gov/publications/dictionaries/cancer-terms/def/lifetime-risk.

Lifetime cancer risk

The lifetime risk of developing or dying from cancer refers to the chance a person has, over the course of their lifetime (from birth to death), of being diagnosed with or dying from cancer (Table 1).

Table 1: Lifetime risk of developing from certain cancers for men and women in the United States

	Male		Female
Cancer Sites	%	1 in	%	1 in
Any cancer	41.6	2	39.6	3
Prostate	12.9	8
Lung and bronchus	6.3	16	5.9	17
Colon and rectum	4.3	23	3.9	25
Bladder (includes in situ)	3.6	28	1.1	89
Melanoma of the skin*	3.6	28	2.5	41
Breast	0.1	726	13.0	8
Non-Hodgkin lymphoma	2.4	42	1.9	52
Kidney and renal pelvis	2.3	43	1.4	73
Leukemia	1.9	53	1.3	75
Pancreas	1.7	58	1.7	60
Liver and bile duct	1.5	65	0.7	143

Measures estimate lifetime cancer risk

• Cumulative rate (an approximation of the risk of developing a disease before age b (or between two ages a and b) in the absence of mortality)
• Cumulative risk
• Current Probability (IARC scientific publication)
• Devcan (SEER)
• AMP method

Cumulative rate

\[ \text{Cumrate} = \sum_{i=1}^{A} w_i p_i \]

• A is upper age-band limit for summation.
• \(w_i\) is the width of the \(i\)th age band in years.
• \(p_i\) is the age-specific annual incidence rate in the ith age-band.

1. first as a form of directly standardised incidence rate, comparisons between populations are immediately possible;
2. second it can be interpreted intuitively as an approximation to the cumulative risk an individual has of developing cancer up to a defined age, provided there are no other competing risks.

Cumulative risk

The cumulative rate can be converted into true cumulative risk using the following formula:

\[ \text{Cumrisk} = 1 - e^{\text{-cumrate}} \]

Although the cumulative risk does not give an estimate of the risk of developing cancer over a lifetime, it has been used as an approximation of this when the truncated upper age band is chosen as an age close to the average life expectancy of the population.

Current probability

A realistic estimate of the lifetime risk of getting cancer can be obtained by estimating the number of cancers that would arise during the lifetime of a hypothetical birth cohort. This approach was termed ‘current probability’ by Esteve et al (1994).

\[ p = \frac{1}{\ell_0} \sum_{x=1}^{g} L_x t_x \]

• \(p\) is the probability of developing a given cancer
• \(t_x\) is the incidence rate in the age group x
• \(L_x\) is the number of years lived by the survivors of age x during the age interval starting at x if they are subject only to the force of mortality of the general population.
• \(\ell_0\) is the size of this population at the beginning of the first age interval under consideration

Current probability

Two assumptions are made when using routine incidence data

• the incidence rates are based on a denominator of individuals who have never had cancer before
• the other is that the numerator only counts first cancers

DevCan method

The SEER analytical program adjusting the denominator in the current probability method

• Softwar could be download at https://surveillance.cancer.gov/devcan/download
• Uses a method that differs from the current probability method only in the way it deals with data in 5-year age bands
• DevCan assumes that data with only the first primary tumour per individual are available.

The AMP method

AMP (Adjusted for Multiple Primaries) method can address the issue of multiple primary tumors in the same perions for registries can’t precisely identify them or for the situtation that individual data was not available.

Figure 1: Estimates of risk of developing cancer excluding NMSC using different method

• Multiple primaries cancer can’t precisely identified
• Individual cancer cases not available
• Smaller than estimate value using ‘current probability’

The AMP method

\[ S = \sum_{i=1}^{f} \frac{R_i}{R_i + M_i - D_i} \hat{S}^*_0(a_i) \times \left\{ 1 - \exp \left( \frac{-w_i}{N_i} (R_i + M_i - D_i) \right) \right\} \]

• S denotes the probability of being diagnosed with cancer;
• M_i denote the annual number of deaths (all-cause mortality);
• D_i denote the annual number of cancer deaths (cancer mortality);
• R_i denote the annual number of (registered) cancer cases;
• N_i denote the size of the mid-year population;
• w_i denote the width of age band i.
• \(\hat{S}^*_0(a_i)\) denotes the probability of being alive and cancer free at age ai;

The AMP method

Assumptions for AMP method

• The non-cancer mortality rates are the same in individuals without cancer as they are in the general population

• the risk of (a new) cancer is the same in individuals who have never previously had cancer as they are in the general population

• one cannot die of cancer if one has never had cancer;

• people with cancer have the same risk of developing cancer again as those who have never had cancer before;

• the probability of dying from other causes (not cancer) is the same between cancer patients and those who have never had cancer.

Introduction of R package ltRISK

Contents

1. Introduction of lifetime risk

2. Introduction of R package ltRISK

3. Practice of lifetime risk estimation using GCO data

4. Results of Global and regional lifetime risk

Software requirements

• Downlaod and install latest R (Rhttps://cloud.r-project.org)
• Download and install latest Rstudio(https://posit.co/download/rstudio-desktop/)

How to install ltRISK

We include the method AMP in R package ltRISK

We can install it from github repository

install.packages("remotes")
remotes::install_github("gigu003/ltRISK")

or install it from local source file ltRISK_0.1.0.tar.gz

install.packages("remotes")
remotes::install_local("ltRISK_0.1.0.tar.gz")

Calculate the cumulate rate and cumulate risk

library(ltRISK)
pop <- c(20005, 86920, 102502, 151494, 182932, 203107, 240289, 247076, 199665,
        163820, 145382, 86789, 69368, 51207, 39112, 20509, 12301, 6586, 1909)
inci <- c(156, 58, 47, 49, 48, 68, 120, 162, 160, 294, 417, 522, 546, 628,
         891, 831, 926, 731, 269)
mx <- inci / pop
r1 <- cumrate(mx, eage = 70)
r1

Cumulative Rate(1/1) 
             0.49771 

r2 <- cumrate(mx, eage = 65)
r2

Cumulative Rate(1/1) 
             0.29511 

cumrisk(r1, mp = 100, decimal = 2)

Cumulative Risk (1/100) 
                  39.21 

cumrisk(r2, mp = 100, decimal = 2)

Cumulative Risk (1/100) 
                  25.56 

Estimate lifetime risk using AMP method

Aggregated data in 5-year age groups was required, number of cancer cases, cancer deaths, all cause mortality, and population.

library(ltRISK)
ni <- c(
   73872987, 82029530, 72267070, 78303514, 99425613, 119915673, 98068725,
   96644427, 121225951, 121250720, 96012917, 79863455, 75972753, 52929797,
   37551107, 29047207, 19584254, 13854299)
mi <- c(
   60594, 17718, 18883, 28127, 37493, 75223, 83574, 100655, 211467, 278913,
   419663, 445223, 770865, 929008, 1058922, 1346942, 1576852, 2305312)
di <- c(
   3511, 2801, 2553, 3183, 4960, 9456, 13509, 23935, 62386, 111640, 147866,
   203955, 301892, 304985, 302785, 323804, 275557, 197614)
ri <- c(
   9303, 6887, 6248, 8509, 16961, 39439, 56670, 86535, 189251, 289320, 344395,
   411232, 552071, 491213, 433786, 395544, 292672, 173503)

Estimate lifetime risk using AMP method

The ltr function can estimate lifetime risk using the AMP method and return an object strore the result which is a list of 3 elements including age groups, age conditional propability, and variance in each agegroup.

# mi    The annual number of all-cause mortality deaths in each age group.
# di    The annual number of cancer-related deaths in each age group.
# ri    The annual number of diagnosed cancer cases in each age group.
# ni    The number of population in each age group.
# age_width The age width of each age group.
# type  Characters "developing" or "dying" indicate estimate the probability of developing cancer or dying from it.
ltr(mi, di, ri, ni, age_width = 5, type = "developing")

ll <- ltr(mi, di, ri, ni)
class(ll)

[1] "ltr"

names(ll)

[1] "age"  "si"   "vari"

Point Estimate and Confidence Interval

The estimate function can get the estimate value of lifetime risk and its 95%CI. When a starting age is specified, it is assumed that the individuals are cancer-free and alive at that age, so the lifetime cancer risk is the risk from that age until death.

• x Object of class ‘ltr’ generated by ltr function, or list of ’ltr’s.
• sage Initial age of lifetime risk.
• mp Multiplier, this parameter scales the estimated result.
• decimal Number of decimals of the result

estimate(x, sage = 0, mp = 100, decimal = 2)

Point Estimate and Confidence Interval

You can aslo use post_ci function to wrap the lifetime risk and 95% CI.

s <- estimate(ll)
post_ci(s)

[1] "26.85(26.70-27.00)"

s1 <- estimate(ll, sage = 40)
post_ci(s1)

[1] "25.68(25.61-25.75)"

s2 <- estimate(ll, sage = 50)
post_ci(s2)

[1] "23.80(23.74-23.86)"

s3 <- estimate(ll, sage = 60)
post_ci(s3)

[1] "19.85(19.81-19.90)"

s4 <- estimate(ll, sage = 70)
post_ci(s4)

[1] "13.20(13.17-13.23)"

Test difference between groups

You can use ztest function to test the difference between two groups.

Practice of lifetime risk estimation using GCO data

Contents

1. Introduction of lifetime risk

2. Introduction of R package ltRISK

3. Practice of lifetime risk estimation using GCO data

4. Results of Global and regional lifetime risk

Introduction of example data from GCO

We prepare an example dataset including the number of cancer cases, deaths, number of all-cause deaths, and size of mid-year population in 2022, which are from Global Cancer Observatory Today, and the World Population Prospects 2022.

data(GCO_Today)
names(GCO_Today)

[1] "region"  "cancers" "sex"     "age"     "inci"    "mort"    "death"  
[8] "pop"    

head(GCO_Today)

# A tibble: 6 × 8
  region                cancers   sex   age  inci  mort death     pop
  <chr>                   <int> <dbl> <dbl> <dbl> <dbl> <dbl>   <int>
1 Australia/New Zealand       1     1     0     0     0   632  930933
2 Australia/New Zealand       1     1     1     0     0    73  993835
3 Australia/New Zealand       1     1     2     0     0    99 1001248
4 Australia/New Zealand       1     1     3     1     0   364  949610
5 Australia/New Zealand       1     1     4     4     0   589 1019806
6 Australia/New Zealand       1     1     5    12     0   752 1169165

# Use ?GCO_Today to see the detailed description of GCO_Today dataset.
?GCO_Today

Introduction of example data from GCO

GCO_Today is a data frame with 40,824 rows and 8 variables, the description of variables was listed in Table 2.

Table 2: Introduction of variables from the GCO_Today example dataset

Variable name	Type	Description
region	Character	The regions are classified into 20 geographic areas as defined by the United Nations Population Division.
cancers	Integer	Cancers include the code of cancer sites which is the same as cancer dictionary in the GLOBOCAN database.
sex	Integer	Sex code, 1 for male, 2 for female, 3 for total.
age	Integer	The ages are grouped into 5-year intervals, where 0, 1, 2, 3, …, 17 represent the 0-4, 5-9, 10-14, 15-19, …, and 85+ age groups, respectively.
inci	Integer	Number of (registered) cancer cases.
mort	Integer	Number of cancer deaths (cancer mortality).
death	Integer	Number of deaths (all-cause mortality).
pop	Integer	The size of the mid-year population.

Suggested citation from Global Cancer Observatory, Cancer Today ¹

1. Ferlay J, Ervik M, Lam F, Laversanne M, Colombet M, Mery L, Piñeros M, Znaor A, Soerjomataram I, Bray F (2024). Global Cancer Observatory: Cancer Today (version 1.1). Lyon, France: International Agency for Research on Cancer. Available from: https://gco.iarc.who.int/today, accessed [DD Month YYYY].

Estimate age conditional probability

library(ltRISK)
library(dplyr)
data(GCO_Today)
data <- GCO_Today |> 
  filter(region == "World", cancers == 39) |>
  mutate(sex = factor(sex, levels= c(1, 2, 3), labels = c("Male", "Female", "Total"))) |> 
  group_by(sex)
model <- data |> 
  reframe(model_develop = list(ltr(death, mort, inci, pop, type = "developing")),
          model_dying = list(ltr(death, mort, inci, pop, type = "dying")))
model$model_develop[[1]]

$age
 [1]  0  5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85

$si
 [1] 0.0006451535 0.0004885180 0.0004816078 0.0005774606 0.0007812455
 [6] 0.0012558958 0.0018863017 0.0026858277 0.0042788911 0.0072884901
[11] 0.0130064996 0.0196248331 0.0295701570 0.0376395945 0.0407228256
[16] 0.0383286564 0.0290418626 0.0278566411

$vari
 [1] 4.162422e-07 5.216538e-11 1.249082e-10 5.752388e-11 5.298314e-11
 [6] 1.345461e-10 2.526803e-10 3.535544e-10 5.925897e-10 1.049516e-09
[11] 1.698918e-09 1.958084e-09 2.333881e-09 2.225952e-09 1.846702e-09
[16] 1.520990e-09 9.331459e-10 3.543868e-10

attr(,"class")
[1] "ltr"

Estimate lifetime risk overall

The overall lifetime cancer risk refers to the risk of developing cancer for an individual throughout their entire life time, from birth to death.

res <- model |>   
  mutate(lr_developing = post_ci(estimate(model_develop)),
         lr_dying = post_ci(estimate(model_dying)))
res

# A tibble: 3 × 5
  sex    model_develop model_dying lr_developing      lr_dying          
  <fct>  <list>        <list>      <chr>              <chr>             
1 Male   <ltr>         <ltr>       25.62(25.49-25.74) 15.85(15.80-15.90)
2 Female <ltr>         <ltr>       23.91(23.80-24.02) 13.10(13.06-13.14)
3 Total  <ltr>         <ltr>       24.81(24.69-24.92) 14.50(14.45-14.54)

Estimate lifetime risk from age x to death

When a starting age is specified, it is assumed that the individuals are cancer-free and alive at that age, so the lifetime cancer risk is the risk from that age until death.

res <- model |>   
  mutate(lr_deve_40 = post_ci(estimate(model_develop, sage = 40)),
         lr_deve_50 = post_ci(estimate(model_develop, sage = 50)),
         lr_deve_60 = post_ci(estimate(model_develop, sage = 60)),
         lr_deve_70 = post_ci(estimate(model_develop, sage = 70)),
         lr_deve_80 = post_ci(estimate(model_develop, sage = 80))
         ) |> 
  select(-model_develop, -model_dying)
res

# A tibble: 3 × 6
  sex    lr_deve_40         lr_deve_50         lr_deve_60  lr_deve_70 lr_deve_80
  <fct>  <chr>              <chr>              <chr>       <chr>      <chr>     
1 Male   24.74(24.71-24.76) 23.58(23.56-23.60) 20.32(20.3… 13.59(13.… 5.69(5.68…
2 Female 22.39(22.35-22.42) 20.19(20.16-20.22) 16.42(16.4… 11.29(11.… 5.57(5.56…
3 Total  23.61(23.59-23.63) 21.95(21.93-21.96) 18.43(18.4… 12.50(12.… 5.65(5.64…

Results of Global and regional lifetime risk

Contents

1. Introduction of lifetime risk

2. Introduction of R package ltRISK

3. Practice of lifetime risk estimation using GCO data

4. Results of Global and regional lifetime risk

Lifetime risk of developing cancer

code

data(GCO_Today)
data <- GCO_Today |> 
  filter(cancers == 39) |>
  mutate(sex = factor(sex, levels= c(1, 2, 3), labels = c("Male", "Female", "Total"))) |> 
  group_by(region, sex)
model <- data |> 
  reframe(model_develop = list(ltr(death, mort, inci, pop, type = "developing")),
          model_dying = list(ltr(death, mort, inci, pop, type = "dying")))
res1 <- model |>  
  mutate(ltr1 = post_ci(estimate(model_develop)),
         ltr2 = post_ci(estimate(model_develop, sage = 40)),
         ltr3 = post_ci(estimate(model_develop, sage = 50)),
         ltr4 = post_ci(estimate(model_develop, sage = 60)),
         ltr5 = post_ci(estimate(model_develop, sage = 70)),
         ltr6 = post_ci(estimate(model_develop, sage = 80))) |> 
  select(-model_develop, -model_dying)

Lifetime risk of developing cancer worldwide

Table 3 showed the lifetime risk of estimated initiated from different age stratified by sex.

Table 3: Lifetime risk of developing cancer Worldwide

Sex	Birth-death	40-death	50-death	60-death	70-death	80-death
Male	25.62(25.49-25.74)	24.74(24.71-24.76)	23.58(23.56-23.60)	20.32(20.30-20.33)	13.59(13.58-13.61)	5.69( 5.68- 5.70)
Female	23.91(23.80-24.02)	22.39(22.35-22.42)	20.19(20.16-20.22)	16.42(16.40-16.44)	11.29(11.27-11.30)	5.57( 5.56- 5.57)
Total	24.81(24.69-24.92)	23.61(23.59-23.63)	21.95(21.93-21.96)	18.43(18.42-18.45)	12.50(12.49-12.51)	5.65( 5.64- 5.65)

Lifetime risk of developing cancer

Table 4 showed the lifetime risk of estimated initiated from different age stratified by region.

Table 4: Lifetime risk of developing cancer Worldwide

Sex	Birth-death	40-death	50-death	60-death	70-death	80-death
Australia/New Zealand	58.52(57.74-59.29)	55.48(54.99-55.98)	50.78(50.37-51.18)	41.47(41.15-41.79)	27.56(27.33-27.79)	13.08(12.97-13.20)
Caribbean	26.34(26.01-26.66)	25.10(24.83-25.36)	23.64(23.40-23.88)	20.21(20.02-20.40)	14.20(14.07-14.33)	7.12( 7.04- 7.19)
Central America	18.46(18.23-18.69)	17.15(17.04-17.26)	15.86(15.76-15.97)	13.34(13.26-13.42)	9.10( 9.04- 9.16)	4.26( 4.23- 4.30)
Eastern Africa	11.34(11.24-11.44)	10.21(10.16-10.26)	8.95( 8.90- 9.00)	6.84( 6.80- 6.88)	3.85( 3.82- 3.88)	1.23( 1.22- 1.25)
Eastern Asia	32.31(32.17-32.45)	30.71(30.65-30.78)	28.56(28.50-28.61)	24.30(24.25-24.34)	17.10(17.07-17.12)	8.28( 8.26- 8.29)
Eastern Europe	26.00(25.77-26.23)	24.42(24.34-24.50)	22.24(22.17-22.31)	17.34(17.29-17.39)	9.45( 9.42- 9.48)	2.74( 2.73- 2.75)
Melanesia	17.74(17.26-18.22)	16.63(16.19-17.07)	14.84(14.45-15.22)	11.51(11.20-11.83)	6.61( 6.38- 6.84)	2.19( 2.06- 2.32)
Micronesia/Polynesia	31.07(27.07-35.06)	30.16(26.46-33.86)	28.30(25.08-31.52)	23.89(21.31-26.46)	16.48(14.75-18.21)	7.67( 6.82- 8.52)
Middle Africa	8.65( 8.55- 8.76)	7.84( 7.78- 7.90)	6.85( 6.79- 6.90)	5.24( 5.19- 5.29)	2.89( 2.85- 2.92)	0.82( 0.80- 0.84)
Northern Africa	16.99(16.80-17.17)	15.87(15.76-15.98)	14.30(14.21-14.38)	11.36(11.29-11.42)	7.06( 7.02- 7.11)	2.75( 2.73- 2.78)
Northern America	47.68(47.39-47.97)	45.60(45.47-45.73)	42.75(42.64-42.86)	36.29(36.21-36.37)	25.05(24.99-25.11)	12.07(12.05-12.10)
Northern Europe	48.43(47.97-48.89)	46.58(46.29-46.86)	44.08(43.84-44.32)	38.23(38.04-38.41)	27.15(27.02-27.27)	13.17(13.11-13.22)
South America	26.53(26.33-26.73)	25.13(25.04-25.21)	23.48(23.41-23.56)	19.87(19.80-19.93)	13.65(13.61-13.70)	6.48( 6.46- 6.50)
South Central Asia	10.32(10.24-10.41)	9.55( 9.53- 9.57)	8.38( 8.36- 8.40)	6.25( 6.23- 6.26)	3.44( 3.43- 3.45)	1.12( 1.11- 1.12)
South-Eastern Asia	16.76(16.59-16.93)	15.57(15.51-15.62)	13.96(13.91-14.00)	10.95(10.92-10.99)	6.72( 6.70- 6.75)	2.66( 2.65- 2.68)
Southern Africa	14.66(14.52-14.80)	13.47(13.37-13.57)	11.56(11.48-11.65)	8.91( 8.84- 8.99)	4.66( 4.61- 4.70)	1.37( 1.34- 1.39)
Southern Europe	43.02(42.60-43.45)	41.09(40.86-41.32)	38.64(38.45-38.83)	33.18(33.03-33.33)	23.27(23.17-23.37)	11.05(11.01-11.09)
Western Africa	8.22( 8.14- 8.29)	7.51( 7.47- 7.55)	6.61( 6.57- 6.65)	4.95( 4.92- 4.98)	2.65( 2.63- 2.67)	0.66( 0.65- 0.67)
Western Asia	23.77(23.55-23.99)	22.58(22.44-22.72)	21.13(21.01-21.26)	17.91(17.81-18.01)	11.89(11.83-11.96)	5.30( 5.26- 5.34)
Western Europe	47.70(47.35-48.06)	45.85(45.64-46.06)	43.38(43.21-43.55)	37.69(37.56-37.83)	26.84(26.75-26.93)	12.90(12.87-12.94)

Lifetime risk of dying from cancer

code

res2 <- model |>  
  mutate(ltr1 = post_ci(estimate(model_dying)),
         ltr2 = post_ci(estimate(model_dying, sage = 40)),
         ltr3 = post_ci(estimate(model_dying, sage = 50)),
         ltr4 = post_ci(estimate(model_dying, sage = 60)),
         ltr5 = post_ci(estimate(model_dying, sage = 70)),
         ltr6 = post_ci(estimate(model_dying, sage = 80))) |> 
  select(-model_develop, -model_dying)

Lifetime risk of dying from cancer worldwide

Table 5 showed the lifetime risk of estimated initiated from different age stratified by sex.

Table 5: Lifetime risk of dying from cancer Worldwide

Sex	Birth-death	40-death	50-death	60-death	70-death	80-death
Male	15.85(15.80-15.90)	15.52(15.51-15.54)	14.98(14.97-15.00)	13.34(13.33-13.36)	9.85( 9.84- 9.86)	5.04( 5.03- 5.04)
Female	13.10(13.06-13.14)	12.71(12.69-12.73)	12.04(12.03-12.06)	10.64(10.62-10.65)	8.20( 8.19- 8.21)	4.70( 4.70- 4.71)
Total	14.50(14.45-14.54)	14.14(14.13-14.15)	13.54(13.53-13.55)	12.01(12.00-12.02)	9.04( 9.03- 9.04)	4.87( 4.86- 4.87)

Lifetime risk of dying from cancer

Table 6 showed the lifetime risk of estimated initiated from different age stratified by region.

Table 6: Lifetime risk of dying from cancer stratified by region

Sex	Birth-death	40-death	50-death	60-death	70-death	80-death
Australia/New Zealand	25.89(25.43-26.34)	25.68(25.24-26.11)	25.27(24.86-25.69)	23.92(23.56-24.28)	20.61(20.35-20.87)	14.10(13.95-14.24)
Caribbean	17.94(17.76-18.12)	17.54(17.37-17.71)	16.94(16.78-17.10)	15.38(15.24-15.52)	12.26(12.15-12.38)	7.38( 7.30- 7.46)
Central America	10.73(10.64-10.82)	10.33(10.26-10.39)	9.86( 9.79- 9.92)	8.77( 8.71- 8.83)	6.63( 6.58- 6.68)	3.50( 3.47- 3.53)
Eastern Africa	8.55( 8.49- 8.62)	7.94( 7.89- 7.98)	7.16( 7.12- 7.20)	5.64( 5.61- 5.68)	3.36( 3.33- 3.38)	1.15( 1.14- 1.17)
Eastern Asia	21.27(21.22-21.33)	21.00(20.95-21.04)	20.44(20.40-20.48)	18.81(18.77-18.84)	14.98(14.96-15.01)	8.66( 8.64- 8.67)
Eastern Europe	14.69(14.62-14.75)	14.37(14.32-14.41)	13.64(13.59-13.68)	11.41(11.38-11.45)	7.16( 7.14- 7.19)	2.62( 2.61- 2.63)
Melanesia	12.13(11.79-12.46)	11.68(11.36-12.00)	10.84(10.54-11.15)	9.00( 8.72- 9.27)	5.82( 5.59- 6.04)	2.22( 2.08- 2.36)
Micronesia/Polynesia	21.77(18.85-24.68)	21.68(18.77-24.59)	21.03(18.29-23.77)	18.67(16.43-20.91)	13.97(12.43-15.52)	7.54( 6.65- 8.42)
Middle Africa	6.46( 6.39- 6.53)	6.01( 5.95- 6.06)	5.37( 5.33- 5.42)	4.24( 4.20- 4.29)	2.48( 2.44- 2.51)	0.78( 0.76- 0.80)
Northern Africa	12.45(12.35-12.55)	12.04(11.96-12.12)	11.32(11.25-11.39)	9.63( 9.57- 9.68)	6.76( 6.71- 6.81)	3.20( 3.17- 3.24)
Northern America	18.95(18.88-19.02)	18.71(18.65-18.77)	18.30(18.24-18.35)	16.90(16.85-16.96)	13.82(13.78-13.86)	8.87( 8.84- 8.89)
Northern Europe	25.93(25.71-26.16)	25.73(25.53-25.93)	25.30(25.11-25.49)	23.86(23.70-24.03)	20.04(19.92-20.16)	12.53(12.47-12.59)
South America	15.47(15.39-15.54)	15.07(15.02-15.12)	14.50(14.45-14.55)	13.02(12.97-13.06)	10.03(10.00-10.07)	5.63( 5.60- 5.65)
South Central Asia	7.23( 7.19- 7.28)	6.88( 6.87- 6.90)	6.24( 6.23- 6.26)	4.81( 4.80- 4.82)	2.80( 2.79- 2.80)	1.01( 1.00- 1.01)
South-Eastern Asia	11.97(11.90-12.05)	11.54(11.50-11.58)	10.75(10.72-10.78)	8.95( 8.92- 8.98)	6.01( 5.99- 6.03)	2.66( 2.65- 2.68)
Southern Africa	9.38( 9.30- 9.46)	8.89( 8.81- 8.96)	8.00( 7.94- 8.07)	6.55( 6.49- 6.61)	3.94( 3.90- 3.99)	1.61( 1.58- 1.63)
Southern Europe	24.78(24.56-25.00)	24.57(24.38-24.75)	24.05(23.88-24.21)	22.30(22.17-22.43)	18.29(18.20-18.38)	11.16(11.12-11.20)
Western Africa	5.88( 5.83- 5.92)	5.49( 5.46- 5.52)	4.93( 4.90- 4.96)	3.84( 3.81- 3.86)	2.20( 2.17- 2.22)	0.60( 0.58- 0.61)
Western Asia	16.52(16.41-16.63)	16.15(16.05-16.24)	15.62(15.53-15.71)	14.03(13.95-14.11)	10.34(10.28-10.40)	5.34( 5.30- 5.38)
Western Europe	25.06(24.88-25.24)	24.85(24.69-25.00)	24.34(24.20-24.48)	22.53(22.41-22.64)	18.46(18.37-18.54)	11.26(11.23-11.30)