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
Introduction of lifetime risk
Introduction of R package ltRISK
Practice of lifetime risk estimation using GCO data
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.
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).
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
Cumrate=A∑i=1wipi
- A is upper age-band limit for summation.
- wi is the width of the ith age band in years.
- pi is the age-specific annual incidence rate in the ith age-band.
- first as a form of directly standardised incidence rate, comparisons between populations are immediately possible;
- 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:
Cumrisk=1−e-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=1ℓ0g∑x=1Lxtx
- p is the probability of developing a given cancer
- tx is the incidence rate in the age group x
- Lx 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.
- ℓ0 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.
- Multiple primaries cancer can’t precisely identified
- Individual cancer cases not available
- Smaller than estimate value using ‘current probability’
The AMP method
S=f∑i=1RiRi+Mi−DiˆS∗0(ai)×{1−exp(−wiNi(Ri+Mi−Di))}
- 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.
- ˆS∗0(ai) 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
Introduction of lifetime risk
Introduction of R package ltRISK
Practice of lifetime risk estimation using GCO data
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
or install it from local source file 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)
r1Cumulative Rate(1/1)
0.49771 Cumulative Rate(1/1)
0.29511 Cumulative Risk (1/100)
39.21 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")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
Point Estimate and Confidence Interval
You can aslo use post_ci function to wrap the lifetime risk and 95% CI.
[1] "26.85(26.70-27.00)"[1] "25.68(25.61-25.75)"[1] "23.80(23.74-23.86)"[1] "19.85(19.81-19.90)"[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
Introduction of lifetime risk
Introduction of R package ltRISK
Practice of lifetime risk estimation using GCO data
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.
[1] "region" "cancers" "sex" "age" "inci" "mort" "death"
[8] "pop" # 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 1169165Introduction 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.
Suggested citation from Global Cancer Observatory, Cancer Today 1
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
Introduction of lifetime risk
Introduction of R package ltRISK
Practice of lifetime risk estimation using GCO data
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.
Lifetime risk of developing cancer
Table 4 showed the lifetime risk of estimated initiated from different age stratified by region.
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.
Lifetime risk of dying from cancer
Table 6 showed the lifetime risk of estimated initiated from different age stratified by region.
Estimation of lifetime risk using R package ltRISK
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)