# LARisk: An R package for Lifetime Attributable Risk Calculation

## Introduction

The R package, LARisk, to compute lifetime attributable risk (LAR) of radiation-induced cancer can be helpful with enhancement of the flexibility in research of projected risks of radiation-associated cancers. LARisk produces LAR estimates considering various options or arguments. In addition, it is possible to handle large-size data easily and compute LAR values by the group such as occupation, sex, age, group, etc., which can provide research topics for radiation-associated cancer risk.

This document provides a detailed description of the LARisk package with some examples. If the package is installed, then we can load it into an R session by

library(LARisk)

## Arguments of the LAR function

The LARisk package has 3 main functions for estimating lifetime attributable risk such as LAR, LAR_batch and LAR_group. LAR is a basic function to compute individual LAR values. And the others are extended functions to handle large batch data and calculate LAR estimates by group. The description of each function is in Functions for estimating LAR.

LAR(data, basedata, sim=300, seed=99, current=as.numeric(substr(Sys.Date(),1,4)),
ci=0.9, weight=NULL, DDREF=TRUE, basepy=1e+05)

The following table shows the arguments of the LAR function.

Arguments Description
data A data frame containing demographic and exposure information
basedata A list of data of lifetime and incidence rate tables
sim A scalar for the number of iteration
seed A scalar for a random seed number
current A scalar for a current year
ci A scalar for confidence level to compute confidence intervals for LAR estimates
weight A list containing values on [0,1] to compute LAR values based on ERR and EAR models for each cancer site
DDREF Logical. Whether apply the dose and dose-rate effectiveness factor for chronic exposure
basepy A scalar for the number of base person-years

### data

The data should have some prerequisite information such as sex and birth year(s) (birth), exposure year (exposure), exposed dose distributions (dosedist), fixed exposed radiation dose or parameters of dose distributions (dose1, dose2, dose3), sites where exposed (site), and exposure rate (exposure_rate). The name of variables in data should be written as expressed.

The following table expresses the essential variables of the argument, data.

Variables Format
sex one of the character strings ‘male’ or ‘female
birth numeric
expposure numeric
site one of the chracter strings ‘stomach’, ‘colon’, ‘liver’, ‘lung’, ‘breast’, ‘ovary’, ‘uterus’, ‘prostate’, ‘bladder’, ‘brain/cns’, ‘thyroid’, ‘remainder’, ‘oral’, ‘oesophagus’, ‘rectum’, ‘gallbladder’, ‘pancreas’, ‘kidney’, ‘leukemia’.
exposure_rate one of the character strings ‘chronic’ or ‘acute
dosedist one of the character strings ‘fixedvalue’, ‘lognormal’, ‘normal’, ‘triangular’, ‘logtriangular’, ‘uniform’, ‘loguniform
dose1 numeric
dose2 numeric
dose3 numeric

Because LAR is the function for each object, it is logically trivial that all sex and birth are same. Also, since the event dates of exposure must occur after the birth date, exposure should be larger than birth.

ex_data <- data.frame(sex = 'male', birth = 1900, exposure = 1980,
site = 'stomach', exposure_rate = "chronic",
dosedist = 'fixedvalue', dose1 = 10, dose2=NA, dose3=NA)

LAR(ex_data, basedata=list(life2010, incid2010)) ## error
#> Error in check_data(data, current): Age is not allowed to be greater than 100 years.

The maximum age in the function is set as 100 years old. If the data contains a birth year which makes attained age over 100, it occurs error.

For site, we put the irradiated organ site or cancer-site. LAR estimates excess cases with the site as ‘stomach’, ‘colon’, ‘liver’, ‘lung’, ‘breast’, ‘ovary’, ‘uterus’, ‘prostate’, ‘bladder’, ‘brain/cns’, ‘thyroid’, ‘remainder’, ‘oral’, ‘oesophagus’, ‘rectum’, ‘gallbladder’, ‘pancreas’, ‘kidney’, ‘leukemia’. In particular, site that are applicable in LAR differ by gender(sex). For male, ‘breast’, ‘ovary’ and ‘uterus’ are not allowed. Similarly, for female, ‘prostate’ is not allowed.

In dosedist, we insert the distribution of the exposed dose. It can have ‘fixedvalue’, ‘lognormal’, ‘normal’, ‘triangular’, ‘logtriangular’, ‘uniform’ or ‘loguniform’. Each distribution demands essential parameters. For instance, if the exposed dose has a normal distribution with the mean of 2.3 and the standard deviation of 0.8, we input dose1=2.3, dose2=0.8 and dose3=NA. If the dose has the fixed value of 3.2, we add values asdose1=3.2, dose2=NA and dose3=NA.

dose distribution dose1 dose2 dose3
fixedvalue value NA NA
lognormal median geometric standard deviation NA
normal mean standard deviation NA
triangular minimum mode maximum
logtriangular minimum mode maximum
uniform minimum maximum NA
loguniform minimum maximum NA

### basedata

The LAR and the other extended functions need lifetime and cancer incidence rate tables. We put these tables to the argument ‘basedata’ in which the first element is lifetime table and the second element is cancer incidence rate table.

LAR(data,
basedata = list("the first is lifetime table", "the second is cancer incidence rate table"))

LARisk includes these tables which were made in 2010 and 2018 in Korea: life2010, incid2010, life2018 and incid2018. Thus we can estimate the risk for the Korean population in 2010 or 2018 using these tables.

If we want to estimate the risks of the other population, we’ll need the lifetime and cancer incidence rate tables of the population. Similar to data, lifetime and cancer incidence rate tables must follow the specified format.

head(life2010)      ## lifetime table of the Korean in 2010.
#>   Age Prob_d_m Prob_d_f
#> 1   0  0.00369  0.00275
#> 2   1  0.00032  0.00030
#> 3   2  0.00025  0.00022
#> 4   3  0.00018  0.00015
#> 5   4  0.00015  0.00011
#> 6   5  0.00013  0.00009

The columns of a lifetime table are consist of ‘Age’, ‘Prob_d_m’, and ‘Prob_d_f’. Prob_d_m and Prob_d_f are the probabilities of death of male and female, respectively.

head(incid2010)     ## cancer incidence rate table of the Korean in 2010.
#>   Site Age Rate_m Rate_f
#> 1 oral   0    0.2    0.1
#> 2 oral   1    0.2    0.1
#> 3 oral   2    0.2    0.1
#> 4 oral   3    0.2    0.1
#> 5 oral   4    0.2    0.1
#> 6 oral   5    0.2    0.2

Also, the columns of a cancer incidence rate table consist of ‘Site’, ‘Age’, ‘Rate_m’, and ‘Rate_f’. Rate_m and Rate_f are incidence rates of each cancer site of male and female, respectively. The tables should have the range of age from 0 to 100 one by one.

### weight

weight is used to estimate LAR through the weighted average of LAR estimates based on ERR and EAR models. It has the form of list whose name of elements is site to decide organ and values of them is for a specific value of the weight. For example, if a weight of stomach cancer is 0.5, run the below code.

LAR(data, basedata, weight=list(stomach = 0.5))

LAR sets the default weight to 0.7 in most cancers. However, in lung cancer, the weight is 0.3, and cancers of breast and thyroid only have weights of 1 for LAR functions based on EAR or ERR models, respectively (see below table).

Cancer site LAR_ERR LAR_EAR weight
Most cancer 70% 30% 0.7
Lung 30% 70% 0.3
Breast 0% 100% 0.0
Thyroid 100% 0% 1.0
Brain/CNS 100% 0% 1.0

### DDREF

DDREF (dose and dose-rate effectiveness factor) is the logical option to select whether or not to consider DDREF in the LAR calculation. DDREF is to modify the effect of exposure, especially, for low-dose exposure. In addition, DDREF is considered differently according to exposure rate. However, if the site is leukemia, DDREF dose not apply even if DDREF = TRUE.

ex_data <- data.frame(sex = 'male', birth = 1990, exposure = 2015,
site = 'leukemia', exposure_rate = "chronic",
dosedist = 'fixedvalue', dose1 = 10, dose2=NA, dose3=NA)

LAR(ex_data, basedata=list(life2010, incid2010), DDREF=TRUE)
#> LAR:
#>   Lower    Mean   Upper
#>  2.6587  5.9803 13.4514
#>
#> Future LAR:
#>          Lower     Mean    Upper
#> F.LAR   2.5882   5.8191  13.0830
#> BFR   538.7711 538.7711 538.7711
#> TFR   541.3593 544.5902 551.8542
#> ---
LAR(ex_data, basedata=list(life2010, incid2010), DDREF=FALSE) ## the result are same
#> LAR:
#>   Lower    Mean   Upper
#>  2.6587  5.9803 13.4514
#>
#> Future LAR:
#>          Lower     Mean    Upper
#> F.LAR   2.5882   5.8191  13.0830
#> BFR   538.7711 538.7711 538.7711
#> TFR   541.3593 544.5902 551.8542
#> ---

### other arguments

seed is the random seed number. As long as the same seed number is provided, we obtain the same result in anytime. sim is the number of simulation runs. Note that as sim goes larger, the computation time takes longer although the simulation variation is getting smaller. i.e., even though seed is different, the large sim yields a similar outcome. In LARisk, sim=300 is default. basepy is the baseline person year such as 10,000 person year or 100,000 person year.

LAR(data, basedata, seed=1111)    ## changing seed number, the result is also changed
LAR(data, basedata, sim=1000)     ## the large 'sim' offers a stable simulation result
LAR(data, basedata, basepy=1e+03) ## setting the baseline person-year is 1000

current is the year to set as the moment of estimation. The default value is set as the system time of the computer. Since it is considered as the current year, we can change the option if we want to set the current time into other years. It recommends that the value should be in form of a year in 4 digits.

LAR(data, basedata, current=2019) ## setting the current year is 2019

Changing the current time affects the estimation of future lifetime attributable risk and future baseline risk.

ci is the level of significance to provide the confidence interval of LAR estimates, expressed in number between 0 and 1. The default value is 0.9, in other words, the LAR function provides the confidence interval at 90% level of significance in default setting.

LAR(data, basedata, ci=0.8) ## setting the confidence level is 0.8

## Functions for estimating LAR

As mentioned above, the package LARisk includes 3 main functions LAR, LAR_batch, and LAR_group that estimate the LAR values for various cases. These functions can be used for a variety of purposes by users. The functions give the three kinds of estimates such as lifetime risk, future risk and lifetime baseline risk. LAR and F_LAR are represented as LAR and future LAR estimates with confidence limits (lower and upper) for each cancer site, solid cancer and total.

We will use the toy example data ‘nuclear’ in this section, which is simulated with the assumption that all people are exposed to radiation at the same time (Details on this data are in “APPENDIX: Datasets in LARisk”).

### LAR: the function of estimating LAR for one person

LAR is the function to estimate LAR for one person. It returns an object of class LAR. LAR class contains the risks of the person, information of the person (gender and birth-year), and some options for calculating risks. The following is the table of components in the LAR object.

Values Description
LAR Lifetime attributable risk (LAR) from the time of exposure to the end of the expected lifetime
F_LAR Future attributable risk from current to the expected lifetime
BFR Baseline future risk
TFR Total future risk
current Current year
ci Confidence level
pinfo Information of the person
nuclear1 <- nuclear[nuclear$ID=="ID01",] print(nuclear1) #> ID sex birth exposure site exposure_rate dosedist dose1 dose2 #> 1 ID01 female 1973 2011 ovary acute fixedvalue 50.06989 NA #> 2 ID01 female 1973 2011 oesophagus acute fixedvalue 50.37462 NA #> 3 ID01 female 1973 2011 bladder acute fixedvalue 52.46040 NA #> 4 ID01 female 1973 2011 lung acute fixedvalue 55.69177 NA #> 5 ID01 female 1973 2011 remainder acute fixedvalue 51.64678 NA #> 6 ID01 female 1973 2011 rectum acute fixedvalue 49.37011 NA #> 7 ID01 female 1973 2011 thyroid acute fixedvalue 54.14875 NA #> dose3 distance #> 1 NA 1 #> 2 NA 1 #> 3 NA 1 #> 4 NA 1 #> 5 NA 1 #> 6 NA 1 #> 7 NA 1 LAR(nuclear1, basedata = list(life2010, incid2010)) #> LAR: #> Lower Mean Upper #> 359.9479 671.3751 1203.8111 #> #> Future LAR: #> Lower Mean Upper #> F.LAR 337.3697 597.7655 1032.216 #> BFR 15992.9219 15992.9219 15992.922 #> TFR 16330.2917 16590.6874 17025.137 #> --- The LAR object prints the total LAR , total future LAR, total baseline future risk, and total future risk. If you want the more detailed results, you can use the summary function. summary(LAR(nuclear1, basedata = list(life2010, incid2010))) #> Information: #> sex birth #> female 1973 #> #> LAR: #> Lower Mean Upper LBR LFR #> lung 74.5065 156.5247 241.1717 3630.3464 0.0431 #> ovary 4.4880 13.3756 27.6491 697.6095 0.0192 #> bladder 13.0799 30.4405 58.7444 452.0590 0.0673 #> thyroid 83.9986 368.7603 877.5446 7318.8901 0.0504 #> remainder 33.5177 89.1794 169.3327 4237.3935 0.0210 #> oesophagus 0.2000 4.0450 10.4666 116.7920 0.0346 #> rectum 0.2670 9.0496 21.7567 2157.6294 0.0042 #> leukemia 0.0000 0.0000 0.0000 0.0000 NaN #> solid 359.9479 671.3751 1203.8111 18610.7199 0.0361 #> total 359.9479 671.3751 1203.8111 18610.7199 0.0361 #> #> Future LAR: #> Lower Mean Upper BFR TFR #> lung 73.4884 154.5469 238.6027 3574.2001 3728.7470 #> ovary 4.0861 12.0693 25.2806 597.5191 609.5885 #> bladder 13.0173 30.3006 58.5236 452.9404 483.2410 #> thyroid 68.7104 303.3691 745.8708 5117.1159 5420.4850 #> remainder 32.3341 84.9052 160.5547 4066.5835 4151.4887 #> oesophagus 0.1978 3.9420 10.2253 115.9270 119.8690 #> rectum 0.2558 8.6324 20.6083 2068.6359 2077.2682 #> leukemia 0.0000 0.0000 0.0000 0.0000 0.0000 #> solid 337.3697 597.7655 1032.2155 15992.9219 16590.6874 #> total 337.3697 597.7655 1032.2155 15992.9219 16590.6874 #> #> Confidence Level: 0.9 #> Current Year: 2022 #> --- The suumary function provides the person’s gender and year of birth, risks by cancer type, confidence levels, and current year. In summary results, the LAR tab includes site-specific LAR, lifetime baseline risk (LBR), and lifetime fractional risk (LFR). Also, the Future LAR tab contains site-specific future LAR, baseline future risk (BFR), and total future risk (TFR). ### LAR_batch: the function of estimating LAR for several people If you want to consider more than one person, you can use LAR'. But, for large observations, theLAR_batchfunction is useful. UnlikeLAR, it calculates each persons’ risks after reading multiple people’s data at once. Since data contains more than one person, the function requires an argument to distinguish each person. pid is the argument, which is a vector to distinguish each person in the dataset. For example, suppose that we want to calculate LAR estimates of several people in the nuclear dataset. Since the variable “ID” is the person ID for this data, we can estimate the LAR values as follows. ex_batch <- LAR_batch(nuclear, pid=nuclear$ID, basedata = list(life2010, incid2010))

class(ex_batch)
#> [1] "LAR_batch" "LAR"

class(ex_batch[[1]])
#> [1] "LAR"

The LAR_batch returns the LAR_batch class object. It is the form of the list of LAR class objects which names of elements are IDs for people, i.e., each element of LAR_batch class is LAR class object. Thus, printing the results of LAR_batch is similar to LAR.

print(ex_batch, max.id=3)
#> LAR result of ID01
#>
#> LAR:
#>     Lower      Mean     Upper
#>  359.9479  671.3751 1203.8111
#>
#> Future LAR:
#>            Lower       Mean     Upper
#> F.LAR   337.3697   597.7655  1032.216
#> BFR   15992.9219 15992.9219 15992.922
#> TFR   16330.2917 16590.6874 17025.137
#> ---
#>
#> LAR result of ID02
#>
#> LAR:
#>    Lower     Mean    Upper
#> 308.6326 532.0084 758.9928
#>
#> Future LAR:
#>           Lower       Mean      Upper
#> F.LAR   299.063   518.3091   732.8379
#> BFR   24653.092 24653.0924 24653.0924
#> TFR   24952.155 25171.4015 25385.9303
#> ---
#>
#> LAR result of ID03
#>
#> LAR:
#>     Lower      Mean     Upper
#>  791.5664 1241.2319 1734.6870
#>
#> Future LAR:
#>            Lower      Mean     Upper
#> F.LAR   772.5637  1217.909  1698.646
#> BFR   20338.3442 20338.344 20338.344
#> TFR   21110.9079 21556.253 22036.991
#> ---
#>
#> The results for 17 people are omitted.

If you want the minimum results, we can use the print. It also runs by default when simply calling the LAR_batch class object. Using the max.id option, you can control the maximum number of printing results (default is 50).

Similarly, using the summary, you can get more detailed results. The result of the function is the same as listing the summary of each person.

summary(ex_batch, max.id=3)
#> summaries of LAR result :  ID01
#>
#> Information:
#>     sex birth
#>  female  1973
#>
#> LAR:
#>               Lower     Mean     Upper        LBR    LFR
#> lung        74.5065 156.5247  241.1717  3630.3464 0.0431
#> ovary        4.4880  13.3756   27.6491   697.6095 0.0192
#> bladder     13.0799  30.4405   58.7444   452.0590 0.0673
#> thyroid     83.9986 368.7603  877.5446  7318.8901 0.0504
#> remainder   33.5177  89.1794  169.3327  4237.3935 0.0210
#> oesophagus   0.2000   4.0450   10.4666   116.7920 0.0346
#> rectum       0.2670   9.0496   21.7567  2157.6294 0.0042
#> leukemia     0.0000   0.0000    0.0000     0.0000    NaN
#> solid      359.9479 671.3751 1203.8111 18610.7199 0.0361
#> total      359.9479 671.3751 1203.8111 18610.7199 0.0361
#>
#> Future LAR:
#>               Lower     Mean     Upper        BFR        TFR
#> lung        73.4884 154.5469  238.6027  3574.2001  3728.7470
#> ovary        4.0861  12.0693   25.2806   597.5191   609.5885
#> bladder     13.0173  30.3006   58.5236   452.9404   483.2410
#> thyroid     68.7104 303.3691  745.8708  5117.1159  5420.4850
#> remainder   32.3341  84.9052  160.5547  4066.5835  4151.4887
#> oesophagus   0.1978   3.9420   10.2253   115.9270   119.8690
#> rectum       0.2558   8.6324   20.6083  2068.6359  2077.2682
#> leukemia     0.0000   0.0000    0.0000     0.0000     0.0000
#> solid      337.3697 597.7655 1032.2155 15992.9219 16590.6874
#> total      337.3697 597.7655 1032.2155 15992.9219 16590.6874
#>
#> Confidence Level: 0.9
#> Current Year: 2022
#> ---
#>
#> summaries of LAR result :  ID02
#>
#> Information:
#>   sex birth
#>  male  1981
#>
#> LAR:
#>                Lower     Mean    Upper        LBR     LFR
#> colon        91.2117 191.6816 305.6734  4478.9565  0.0428
#> lung         74.4763 168.8631 279.8595  9283.1503  0.0182
#> prostate    -86.4482  25.0355 145.8765  5267.9372  0.0048
#> thyroid      22.3790  96.6625 222.4750  1752.7121  0.0552
#> oral          3.5526  17.3279  37.6939   910.2072  0.0190
#> gallbladder -47.0215  -3.5972  35.1159  1660.5321 -0.0022
#> pancreas      7.0824  36.0351  75.1721  1444.6747  0.0249
#> leukemia      0.0000   0.0000   0.0000     0.0000     NaN
#> solid       308.6326 532.0084 758.9928 24798.1701  0.0215
#> total       308.6326 532.0084 758.9928 24798.1701  0.0215
#>
#> Future LAR:
#>                Lower     Mean    Upper        BFR        TFR
#> colon        90.4213 189.4351 302.3448  4487.5107  4676.9459
#> lung         74.5179 169.0736 280.2397  9376.4058  9545.4794
#> prostate    -87.1754  25.1826 146.7595  5338.8263  5364.0089
#> thyroid      19.4114  85.7532 192.9084  1419.3347  1505.0879
#> oral          3.4014  16.6222  36.3778   899.9821   916.6043
#> gallbladder -47.0382  -3.5969  35.1253  1675.7064  1672.1095
#> pancreas      6.9750  35.8394  74.8672  1455.3263  1491.1657
#> leukemia      0.0000   0.0000   0.0000     0.0000     0.0000
#> solid       299.0630 518.3091 732.8379 24653.0924 25171.4015
#> total       299.0630 518.3091 732.8379 24653.0924 25171.4015
#>
#> Confidence Level: 0.9
#> Current Year: 2022
#> ---
#>
#> summaries of LAR result :  ID03
#>
#> Information:
#>   sex birth
#>  male  1988
#>
#> LAR:
#>               Lower      Mean     Upper       LBR    LFR
#> stomach    282.2981  484.3981  719.4266 10050.485 0.0482
#> prostate  -209.3797   60.6094  306.9072  5240.937 0.0116
#> remainder  408.0930  696.2245 1095.6493  5028.838 0.1384
#> leukemia     0.0000    0.0000    0.0000     0.000    NaN
#> solid      791.5664 1241.2319 1734.6870 20320.261 0.0611
#> total      791.5664 1241.2319 1734.6870 20320.261 0.0611
#>
#> Future LAR:
#>               Lower      Mean     Upper       BFR       TFR
#> stomach    279.9070  481.0488  714.4396 10100.598 10581.647
#> prostate  -210.9228   60.7878  308.2314  5286.830  5347.618
#> remainder  394.4592  676.0721 1062.5141  4950.916  5626.988
#> leukemia     0.0000    0.0000    0.0000     0.000     0.000
#> solid      772.5637 1217.9087 1698.6464 20338.344 21556.253
#> total      772.5637 1217.9087 1698.6464 20338.344 21556.253
#>
#> Confidence Level: 0.9
#> Current Year: 2022
#> ---
#>
#> The results for 17 people are omitted.

### LAR_group: the function of averaging estimated LAR by group The function LAR_group is averaging the calculated risks according to groups. It offers grouped LAR, grouped future LAR, and grouped baseline risk values based on values of simulation for each person. It provides each LAR value for each group, which makes new LAR values, and then these new LAR values are taken to present summarized LAR values for each group.

This function requires not only the value distinguishing the person but also the value for the group. group is the vector or list that groups the data. The function returns the LAR_group class object which is the form of a list of LAR class objects.

Suppose that we want to estimate the average LAR of the people in the nuclear dataset by the distance. Then we can put group=nuclear$distnace in LAR_group. ex_group1 <- LAR_group(nuclear, pid = nuclear$ID, group = nuclear$distance, basedata = list(life2010, incid2010)) summary(ex_group1) #> summaries of LAR result : Group 1 #> #> Group Information: #> sex count birth #> female 35 1962.600 #> male 45 1962.222 #> #> LAR: #> Lower Mean Upper LBR LFR #> stomach 50.9850 66.2373 87.8936 2926.1714 0.0226 #> colon 43.4301 56.1274 72.3353 2160.0832 0.0260 #> liver 7.0657 10.4933 15.2987 808.9772 0.0130 #> lung 39.1538 53.4791 70.6998 3097.9930 0.0173 #> breast 2.8636 4.2821 6.0646 331.2576 0.0129 #> ovary 0.3206 0.9554 1.9749 49.8292 0.0192 #> uterus 0.0216 0.1491 0.3288 68.4665 0.0022 #> prostate -15.4917 6.2743 27.6037 960.8121 0.0065 #> bladder 10.5122 16.1598 23.8353 430.7553 0.0375 #> brain/cns 0.7414 1.3918 2.2998 46.3592 0.0300 #> thyroid 67.7618 185.2396 350.2187 1648.0018 0.1124 #> remainder 34.5468 56.8793 88.6948 912.3992 0.0623 #> oral 0.3038 1.3365 2.7663 105.2675 0.0127 #> oesophagus 2.7255 5.3313 8.1798 208.5186 0.0256 #> rectum 0.3667 1.3777 2.5946 618.5623 0.0022 #> gallbladder -6.2708 -0.9336 4.2742 420.9955 -0.0022 #> pancreas 3.4377 7.4064 11.9408 493.6795 0.0150 #> kidney 1.0530 3.2226 6.5984 203.1165 0.0159 #> leukemia 0.0713 0.2012 0.5677 19.9927 0.0101 #> solid 339.2210 475.4092 659.3305 15491.2456 0.0307 #> total 339.4012 475.6104 659.5318 15511.2384 0.0307 #> #> Future LAR: #> Lower Mean Upper BFR TFR #> stomach 48.2294 63.3542 84.7154 2490.0371 2553.3913 #> colon 40.9639 53.4541 69.9636 1902.1381 1955.5921 #> liver 6.0418 9.0587 13.2437 571.8794 580.9381 #> lung 38.4091 52.5642 69.9525 2877.2243 2929.7885 #> breast 2.3678 3.5644 5.0447 157.2215 160.7859 #> ovary 0.2919 0.8621 1.8058 42.6799 43.5420 #> uterus 0.0203 0.1258 0.2655 41.5060 41.6318 #> prostate -15.5887 6.2226 27.5255 881.1613 887.3839 #> bladder 10.3276 16.0169 23.7049 387.4721 403.4890 #> brain/cns 0.6220 1.1373 1.8552 35.4464 36.5837 #> thyroid 60.0224 170.7748 330.0385 1233.1081 1403.8830 #> remainder 33.7594 54.9135 84.8616 837.8480 892.7615 #> oral 0.2668 1.2582 2.6651 87.9061 89.1643 #> oesophagus 2.4342 4.4985 6.7130 162.4755 166.9740 #> rectum 0.3337 1.2961 2.4649 524.0167 525.3128 #> gallbladder -6.0139 -0.8791 4.1981 361.3716 360.4925 #> pancreas 3.2450 7.1431 11.5463 453.7292 460.8723 #> kidney 0.9721 3.1387 6.5336 183.9500 187.0887 #> leukemia 0.0827 0.1485 0.2667 13.7139 13.8624 #> solid 318.3267 448.5040 621.6234 13231.1713 13679.6753 #> total 318.4752 448.6524 621.7718 13244.8852 13693.5376 #> #> Confidence Level: 0.9 #> Current Year: 2022 #> --- #> #> summaries of LAR result : Group 2 #> #> Group Information: #> sex count birth #> female 12 1987.417 #> male 5 1956.000 #> #> LAR: #> Lower Mean Upper LBR LFR #> colon 372.7596 534.3113 750.7850 2319.0697 0.2304 #> liver 33.3218 57.2681 87.5048 1184.1939 0.0484 #> lung 846.3382 1072.5057 1355.1944 903.6865 1.1868 #> breast 222.3765 302.6915 391.8901 1117.4866 0.2709 #> ovary 9.4594 24.1729 47.0888 183.7846 0.1315 #> bladder 142.6668 242.1335 363.4800 559.0715 0.4331 #> brain/cns 21.8762 44.8910 77.9991 154.8744 0.2899 #> thyroid 6.3675 20.9331 49.7293 208.9864 0.1002 #> remainder 70.0662 148.2741 249.0938 996.9884 0.1487 #> oral 4.7167 12.1716 21.1804 85.6799 0.1421 #> rectum -0.0033 13.9800 30.7953 822.0275 0.0170 #> gallbladder -30.2879 -3.1930 21.6224 392.5105 -0.0081 #> kidney 13.8521 63.7456 115.0254 108.8816 0.5855 #> leukemia 0.0000 0.0000 0.0000 0.0000 NaN #> solid 2151.0610 2533.8854 2926.4130 9037.2418 0.2804 #> total 2151.0610 2533.8854 2926.4130 9037.2418 0.2804 #> #> Future LAR: #> Lower Mean Upper BFR TFR #> colon 364.4924 525.4833 742.8677 2213.9874 2739.4707 #> liver 29.5310 49.2922 73.7681 889.0078 938.3000 #> lung 846.3634 1072.4452 1355.3351 904.4108 1976.8560 #> breast 217.7182 295.4201 380.9547 1023.7419 1319.1619 #> ovary 9.0491 23.0481 45.7178 173.2399 196.2880 #> bladder 140.4023 238.6815 361.0392 532.7003 771.3818 #> brain/cns 19.1969 36.5269 63.6421 137.3470 173.8739 #> thyroid 4.3048 14.3870 34.6246 102.4385 116.8256 #> remainder 64.0335 134.6180 223.1729 889.7768 1024.3948 #> oral 4.4367 11.4174 19.7983 81.9720 93.3894 #> rectum 0.0109 11.7686 25.5870 644.5561 656.3247 #> gallbladder -28.4010 -2.9860 20.1886 368.7285 365.7425 #> kidney 13.8496 63.4438 114.7303 108.1452 171.5890 #> leukemia 0.0000 0.0000 0.0000 0.0000 0.0000 #> solid 2097.9502 2473.5461 2862.3532 8070.0522 10543.5984 #> total 2097.9502 2473.5461 2862.3532 8070.0522 10543.5984 #> #> Confidence Level: 0.9 #> Current Year: 2022 #> --- #> #> summaries of LAR result : Group 3 #> #> Group Information: #> sex count birth #> female 1 1933 #> male 2 2004 #> #> LAR: #> Lower Mean Upper LBR LFR #> colon 1209.822 1769.6169 2469.1052 2222.3599 0.7963 #> oral 6.602 17.1635 29.4681 62.4035 0.2750 #> rectum 13.638 298.1917 594.8688 1749.5705 0.1704 #> leukemia 0.000 0.0000 0.0000 0.0000 NaN #> solid 1372.524 2084.9721 2843.2003 4034.3339 0.5168 #> total 1372.524 2084.9721 2843.2003 4034.3339 0.5168 #> #> Future LAR: #> Lower Mean Upper BFR TFR #> colon 1209.3299 1768.8959 2468.3009 2227.0219 3995.9179 #> oral 4.7252 12.1299 20.4353 31.9436 44.0735 #> rectum 13.6274 298.2743 595.1193 1753.3920 2051.6663 #> leukemia 0.0000 0.0000 0.0000 0.0000 0.0000 #> solid 1369.2378 2079.3001 2838.2846 4012.3575 6091.6576 #> total 1369.2378 2079.3001 2838.2846 4012.3575 6091.6576 #> #> Confidence Level: 0.9 #> Current Year: 2022 #> --- The result of the LAR_group is similar to those of LAR_batch. The difference is the Group Information tab, which provides the gender frequency table within the group and the average birth-year within the group, instead of each individuals’ gender and birth-year. The risks are the estimates of the average LAR in groups. ## Write the result in a file LARisk includes the functions which write a result of LAR, LAR_batch, and LAR_group. write_LAR is the function that saves the LAR class family into a CSV file. write_LAR(x, filename) In this function, x is an object that wants to save into a CSV file. When you put the file name or connection to write into filename, the object is saved there. Note that if there exists the csv file which has the same title with filename, it would be overlapped. Therefore, before deciding a file name, be cautious to check whether or not the name is duplicated. In the same way as above, the result from the LAR batch function can be saved as a CSV file. If the object is a LAR class object, the format of the saved file is that: Lower Mean Upper F.Lower F.Mean F.Upper LBR BFR LFR TFR site-name solid total The function exports a table whose row is represented as site-names, solid, total, and whose column is the risks. Since the LAR_batch class object is a list of LAR objects, it is difficult to export files in the same form as above. Thus, if the object’s class is LAR_batch, the function saves a file whose values are represented in a horizontal way for each organ, solid, and total. Despite the case of the LAR function is somehow intuitive, the LAR_batch function is not simple. We make space for all organs, and values from the function are put in their own space. Therefore, there are 190 columns including the person ID column (PID), and the number of rows depends on the number of ids in the data. The columns are ordered in (LAR)-(Future LAR)-(Baseline Risk)-(Total Future Risk) in general. In LAR and Future LAR, each is made up of lower limit, upper limit, and mean values, and for the Baseline Risk, it is made up of baseline risk of exposed age, the baseline risk of attained age, and LFR. The last part is the total future risk for each site. Hence, for each component, there are values of all-organ, all-solid-cancer, and each organ, i.e. 21 elements. So that, the file has somehow wide shape with 210 columns. If the class of the object is LAR_group, the format of the saved file is the same. In this case, the first column is GROUP instead of PID. ## Examples Now, consider the toy example of organ data. This data has 20 people which are exposed to radiation several times. head(organ) #> ID sex birth exposure site exposure_rate dosedist dose1 #> 1 ID01 male 1985 2011 oesophagus chronic fixedvalue 0.001954895 #> 2 ID01 male 1985 2011 kidney chronic fixedvalue 0.003855487 #> 3 ID01 male 1985 2011 rectum chronic fixedvalue 0.003855487 #> 4 ID01 male 1985 2011 thyroid chronic fixedvalue 0.005104447 #> 5 ID01 male 1985 2013 oesophagus chronic fixedvalue 0.089358392 #> 6 ID01 male 1985 2013 kidney chronic fixedvalue 0.176234606 #> dose2 dose3 occup #> 1 NA NA 1 #> 2 NA NA 1 #> 3 NA NA 1 #> 4 NA NA 1 #> 5 NA NA 1 #> 6 NA NA 1 Assume that we want to calculate the risks with the current year is 2021. In this example, we calculate the risks for the population in Korea, in 2018. First, the estimated risks of ‘ID01’ is that: organ1 <- organ[organ$ID=='ID01',]
ex_organ1 <- LAR(organ1, baseda=list(life2018, incid2018), current=2021)

ex_organ1
#> LAR:
#>  Lower   Mean  Upper
#> 1.1149 1.6981 2.5132
#>
#> Future LAR:
#>           Lower      Mean     Upper
#> F.LAR    1.1132    1.6759    2.4744
#> BFR   6694.6423 6694.6423 6694.6423
#> TFR   6695.7555 6696.3182 6697.1167
#> ---

The estimated LAR of the person ID01 is 1.6981 with the 90% confidence interval (1.1149, 2.5132). The future risk is 1.6759 with the 90% confidence interval (1.1132, 2.4744)

summary(ex_organ1)
#> Information:
#>   sex birth
#>  male  1985
#>
#> LAR:
#>             Lower   Mean  Upper      LBR   LFR
#> thyroid    0.4673 0.9709 1.8205 1771.543 5e-04
#> oesophagus 0.1025 0.1824 0.2729 1048.947 2e-04
#> rectum     0.0978 0.2385 0.4111 2893.126 1e-04
#> kidney     0.1416 0.3064 0.5160 1338.149 2e-04
#> leukemia   0.0000 0.0000 0.0000    0.000   NaN
#> solid      1.1149 1.6981 2.5132 7051.764 2e-04
#> total      1.1149 1.6981 2.5132 7051.764 2e-04
#>
#> Future LAR:
#>             Lower   Mean  Upper      BFR      TFR
#> thyroid    0.4507 0.9512 1.7587 1453.492 1454.443
#> oesophagus 0.1025 0.1823 0.2728 1055.583 1055.766
#> rectum     0.0977 0.2379 0.4108 2877.117 2877.355
#> kidney     0.1406 0.3045 0.5153 1308.450 1308.755
#> leukemia   0.0000 0.0000 0.0000    0.000    0.000
#> solid      1.1132 1.6759 2.4744 6694.642 6696.318
#> total      1.1132 1.6759 2.4744 6694.642 6696.318
#>
#> Confidence Level: 0.9
#> Current Year: 2021
#> ---

With summary, we can get a more detailed report of the result. By the result, the person ID01 is a man born in 1985. This person was exposed radiation to thyroid, oesophagus, ‘rectum’, and kidney. Since leukemia is not included in this data, the result for leukemia is zero.

Consider the risks of the female / male groups of the organ.

ex_organ2 <- LAR_group(organ, pid=organ$ID, group=organ$sex,
basedata=list(life2018, incid2018), current=2021)

summary(ex_organ2)
#> summaries of LAR result : Group female
#>
#> Group Information:
#>     sex count    birth
#>  female   166 1976.313
#>
#> LAR:
#>               Lower    Mean   Upper       LBR     LFR
#> colon        0.6832  1.1392  1.7064 1080.1190  0.0011
#> lung         2.3739  2.8990  3.5941 1353.2750  0.0021
#> uterus       0.1447  0.2874  0.4696  338.1363  0.0008
#> bladder      0.9560  1.3026  1.7539  155.9481  0.0084
#> remainder    2.9905  4.5565  6.7692 1875.6871  0.0024
#> oral         0.1509  0.2311  0.3413  130.7238  0.0018
#> oesophagus   0.0203  0.0768  0.1583   18.0691  0.0043
#> rectum       0.2375  0.4315  0.6480  873.1753  0.0005
#> gallbladder -0.1736 -0.0274  0.1067  290.7825 -0.0001
#> pancreas     0.0661  0.1089  0.1608  283.0072  0.0004
#> leukemia     0.0792  0.1800  0.4092   81.1517  0.0022
#> solid        9.3445 11.0056 13.3345 6398.9234  0.0017
#> total        9.5265 11.1856 13.5145 6480.0751  0.0017
#>
#> Future LAR:
#>               Lower    Mean   Upper       BFR       TFR
#> colon        0.6658  1.0964  1.6314 1051.6541 1052.7505
#> lung         2.3673  2.8906  3.5837 1352.5231 1355.4137
#> uterus       0.1423  0.2825  0.4686  296.3270  296.6095
#> bladder      0.9503  1.2916  1.7359  154.4180  155.7096
#> remainder    2.8942  4.4153  6.5409 1792.3971 1796.8124
#> oral         0.1444  0.2181  0.3177  119.1196  119.3377
#> oesophagus   0.0201  0.0762  0.1568   18.0923   18.1685
#> rectum       0.2346  0.4186  0.6327  835.6204  836.0390
#> gallbladder -0.1735 -0.0274  0.1066  292.4045  292.3771
#> pancreas     0.0653  0.1079  0.1591  281.1836  281.2915
#> leukemia     0.0944  0.1773  0.3603   77.5662   77.7435
#> solid        9.1382 10.7697 12.9982 6193.7399 6204.5095
#> total        9.3172 10.9470 13.1770 6271.3060 6282.2530
#>
#> Confidence Level: 0.9
#> Current Year: 2021
#> ---
#>
#> summaries of LAR result : Group male
#>
#> Group Information:
#>   sex count    birth
#>  male   805 1966.561
#>
#> LAR:
#>               Lower    Mean   Upper        LBR     LFR
#> stomach      3.3791  3.8814  4.5159  2861.1179  0.0014
#> colon        2.9728  3.5787  4.2951   891.9982  0.0040
#> liver        0.7400  0.9784  1.2916   328.3202  0.0030
#> lung         1.7903  2.1896  2.7012  1379.3554  0.0016
#> prostate    -0.1064  0.8221  1.7976  1553.0173  0.0005
#> bladder      0.9763  1.2158  1.5097   530.2854  0.0023
#> brain/cns    0.1014  0.1315  0.1718    75.0266  0.0018
#> thyroid      1.1497  1.6947  2.4809   508.2328  0.0033
#> remainder    7.3442  8.7682 10.4821  1396.0668  0.0063
#> oral         0.4086  0.5480  0.7018   355.2983  0.0015
#> oesophagus   0.4106  0.4973  0.5973   299.5552  0.0017
#> rectum       0.3106  0.4829  0.6906   619.8016  0.0008
#> gallbladder -0.2683 -0.0629  0.1323   281.3131 -0.0002
#> pancreas     0.4762  0.6373  0.8672   262.5764  0.0024
#> kidney       0.6250  0.8268  1.0208   477.9452  0.0017
#> leukemia     0.4202  0.9776  2.2777    98.4367  0.0099
#> solid       23.8700 26.1898 28.7939 11819.9106  0.0022
#> total       24.8542 27.1674 29.7754 11918.3472  0.0023
#>
#> Future LAR:
#>               Lower    Mean   Upper        BFR        TFR
#> stomach      2.9529  3.3947  3.9262  2755.3275  2758.7222
#> colon        2.7211  3.2932  3.9434   870.3818   873.6751
#> liver        0.6131  0.8033  1.0509   274.2192   275.0226
#> lung         1.7390  2.1254  2.6232  1389.8859  1392.0113
#> prostate    -0.1170  0.8140  1.7755  1582.8508  1583.6647
#> bladder      0.9560  1.1886  1.4847   533.9888   535.1774
#> brain/cns    0.0800  0.1066  0.1424    64.5289    64.6355
#> thyroid      0.6714  0.9920  1.3906   331.6146   332.6066
#> remainder    6.5417  7.7960  9.4301  1277.7412  1285.5372
#> oral         0.3365  0.4629  0.6085   326.9197   327.3826
#> oesophagus   0.3778  0.4561  0.5447   296.6060   297.0622
#> rectum       0.2574  0.4175  0.6129   582.9204   583.3379
#> gallbladder -0.2587 -0.0614  0.1289   285.0148   284.9534
#> pancreas     0.4322  0.5781  0.7887   256.1738   256.7519
#> kidney       0.4992  0.6462  0.7967   409.5781   410.2243
#> leukemia     0.3114  0.7470  1.7946    83.8317    84.5786
#> solid       20.8728 23.0132 25.3536 11237.7516 11260.7648
#> total       21.6190 23.7602 26.1058 11321.5832 11345.3434
#>
#> Confidence Level: 0.9
#> Current Year: 2021
#> ---

By the result, the estimated average lifetime risk of a female group is 11.1856 (9.5265, 13.5145). Similarly, the estimated average lifetime risk of a male group is 27.1674 (23.8700, 28.7939).

We can also set the variables for group. For example, we want the average risks of female and occup is 1

ex_organ3 <- LAR_group(organ, pid=organ$ID, group=list(organ$sex, organ$occup), basedata=list(life2018, incid2018), current=2021) print(ex_organ3, max.id=3) #> LAR result of female.1 #> #> LAR: #> Lower Mean Upper #> 4.7547 6.2051 8.0758 #> #> Future LAR: #> Lower Mean Upper #> F.LAR 4.7348 6.1773 8.0388 #> BFR 3746.8142 3746.8142 3746.8142 #> TFR 3751.5490 3752.9915 3754.8530 #> --- #> #> LAR result of male.1 #> #> LAR: #> Lower Mean Upper #> 37.9314 41.3941 45.0670 #> #> Future LAR: #> Lower Mean Upper #> F.LAR 32.3847 35.4936 38.7843 #> BFR 12300.1490 12300.1490 12300.1490 #> TFR 12332.5337 12335.6426 12338.9333 #> --- #> #> LAR result of female.4 #> #> LAR: #> Lower Mean Upper #> 0.1310 0.4694 0.8903 #> #> Future LAR: #> Lower Mean Upper #> F.LAR 0.1299 0.4655 0.8830 #> BFR 108.5540 108.5540 108.5540 #> TFR 108.6839 109.0195 109.4369 #> --- #> #> The results for 4 groups are omitted. ## APPENDIX: Datasets in LARisk The LARisk package include two toy example datasets, nuclear and organ. These datasets are simulated assuming two situation: One is that all people were exposed to radiation at the same time, and the other is that each person was exposed to radiation over a long period of time. Each data has 11 variables, including 9 essential variables for calculating the LAR. ### nuclear: a simulated dataset assuming radioactive explosion nuclear was simulated assuming the scenario in which everyone is exposed to radiation at the same time. This data includes 20 people, who were exposed to radiation at the same time in 2011. The age exposed to radiation is from 3 to 81 years old, and there are 10 males and 10 females. All values of exposure_rate are acute and all values of dosedist are fixedvalue. str(nuclear) #> 'data.frame': 100 obs. of 11 variables: #>$ ID           : chr  "ID01" "ID01" "ID01" "ID01" ...
#>  $sex : chr "female" "female" "female" "female" ... #>$ birth        : int  1973 1973 1973 1973 1973 1973 1973 1981 1981 1981 ...
#>  $exposure : num 2011 2011 2011 2011 2011 ... #>$ site         : chr  "ovary" "oesophagus" "bladder" "lung" ...
#>  $exposure_rate: chr "acute" "acute" "acute" "acute" ... #>$ dosedist     : chr  "fixedvalue" "fixedvalue" "fixedvalue" "fixedvalue" ...
#>  $dose1 : num 50.1 50.4 52.5 55.7 51.6 ... #>$ dose2        : logi  NA NA NA NA NA NA ...
#>  $dose3 : logi NA NA NA NA NA NA ... #>$ distance     : chr  "1" "1" "1" "1" ...

ID is the variable that is used to identify the individual. We generated the sex, birth, and site fully random. And the exposure dose (dose1) was generated from the log-normal distribution, and a variable called distance was created by dividing it into three groups.

### organ: a simulated dataset assuming the workers at interventional radiology departments

Unlike nuclear, organ assumes that people have been exposed to radiation over several times. There are 20 people in this data, 14 of whom are male and 6 are female. Also, this data includes job information of people (occup).

people in organ dataset
ID sex birth occup ID sex birth occup
ID01 male 1985 1 ID11 male 1965 6
ID02 male 1960 1 ID12 male 1976 1
ID03 male 1979 6 ID13 female 1986 5
ID04 male 1982 1 ID14 male 1983 1
ID05 male 1981 6 ID15 male 1980 1
ID06 male 1966 6 ID16 female 1980 6
ID07 female 1980 1 ID17 male 1982 6
ID08 female 1980 1 ID18 female 1968 5
ID09 male 1992 1 ID19 male 1965 1
ID10 female 1984 4 ID20 male 1983 5
str(organ)
#> 'data.frame':    971 obs. of  11 variables:
#>  $ID : chr "ID01" "ID01" "ID01" "ID01" ... #>$ sex          : chr  "male" "male" "male" "male" ...
#>  $birth : num 1985 1985 1985 1985 1985 ... #>$ exposure     : num  2011 2011 2011 2011 2013 ...
#>  $site : chr "oesophagus" "kidney" "rectum" "thyroid" ... #>$ exposure_rate: chr  "chronic" "chronic" "chronic" "chronic" ...
#>  $dosedist : chr "fixedvalue" "fixedvalue" "fixedvalue" "fixedvalue" ... #>$ dose1        : num  0.00195 0.00386 0.00386 0.0051 0.08936 ...
#>  $dose2 : num NA NA NA NA NA NA NA NA NA NA ... #>$ dose3        : num  NA NA NA NA NA NA NA NA NA NA ...
#>  \$ occup        : chr  "1" "1" "1" "1" ...

All values of exposure_rate are chronic and all values of dosedist are fixedvalue. The birth-year of people has a range from 1960 to 1992, and the exposed age is from 23 to 60 years old.

sex, birth, site, and occup were randomly selected, and exposure was generated before 2021 (This means that this data assumed that the current year is 2021). The exposure dose (dose1`) was generated from the Gaussian mixture distribution, which mimics data of workers at interventional radiology departments in Korea (Lee, et al., 2021).

## Reference

1. De Gonzalez, A. B., et al. (2012). RadRAT: a radiation risk assessment tool for lifetime cancer risk projection. Journal of Radiological Protection, 32(3), 205.

2. Lee, W. J., Bang, Y. J., Cha, E. S., Kim, Y. M., & Cho, S. B. (2021). Lifetime cancer risks from occupational radiation exposure among workers at interventional radiology departments. International Archives of Occupational and Environmental Health, 94(1), 139-145.