Mortality/Lapse Rate Calculations • expstudies

Start with the exposures_mod frame from the “Creating Exposure Intervals” article.

head(exposures_mod)

key	duration	start_int	end_int	exposure	issue_age	gender	attained_age
B10251C8	1	2010-04-10	2011-04-09	0.9993	35	M	35
B10251C8	2	2011-04-10	2012-04-09	1.002	35	M	36
B10251C8	3	2012-04-10	2013-04-09	0.9993	35	M	37
B10251C8	4	2013-04-10	2014-04-09	0.9993	35	M	38
B10251C8	5	2014-04-10	2015-04-09	0.9993	35	M	39
B10251C8	6	2015-04-10	2016-04-09	1.002	35	M	40

Add a death indicator and use a full exposure in the year of death when performing a mortality study.

exposures_mort <- exposures_mod %>% 
  group_by(key) %>% 
  mutate(exposure_mod = if_else(duration == max(duration), 1, exposure), 
         death_cnt = if_else(duration == max(duration), 1, 0)) 

tail(exposures_mort, 4)

key	duration	start_int	end_int	gender	attained_age	exposure_mod	death_cnt
D68554D5	12	2016-01-01	2016-12-31	F	41	1.002	0
D68554D5	13	2017-01-01	2017-12-31	F	42	0.9993	0
D68554D5	14	2018-01-01	2018-12-31	F	43	0.9993	0
D68554D5	15	2019-01-01	2019-04-04	F	44	1	1

We then aggregate by duration to calculate mortality rates.

duration_rate <- exposures_mort %>% 
  group_by(duration) %>% 
  summarise(q = sum(death_cnt)/sum(exposure_mod))

duration_rate

duration	q
1	0
2	0
3	0
4	0
5	0
6	0
7	0
8	0
9	0.5002
10	0
11	0
12	0
13	0
14	0
15	1

Or by attained age and gender.

attained_age_gender_rates <- exposures_mort %>% 
  group_by(attained_age, gender) %>% 
  summarise(q = sum(death_cnt)/sum(exposure_mod))

tail(attained_age_gender_rates)

attained_age	gender	q
41	M	0
42	F	0
42	M	0
43	F	0
43	M	1
44	F	1

##Expected mortality

Some mortality tables have been loaded in an easy to join format so that users can conduct A/E analysis.

summary(expstudies::mortality_tables)

##                                         Length Class  Mode
## AM92                                    3      -none- list
## GAM1983                                 3      -none- list
## UP1984                                  3      tbl_df list
## VBT2015_SmokerDistinct_ALB              2      -none- list
## CSO2017_Unloaded_PreferredStructure_ALB 2      -none- list
## CSO2017_Loaded_PreferredStructure_ALB   2      -none- list

The “table” column includes the table identifier from the SOA website’s collection of mortality tables.

head(mortality_tables$AM92$AM92_Ultimate)

table	attained_age	q_ult
t2360	19	0.000587
t2360	20	0.000582
t2360	21	0.000577
t2360	22	0.000572
t2360	23	0.000569
t2360	24	0.000567

We join the mortality table to the data frame using the attained age.

head(left_join(exposures_mort, mortality_tables$AM92$AM92_Ultimate, by = "attained_age"))

key	duration	start_int	end_int	gender	attained_age	exposure_mod	q_ult
B10251C8	1	2010-04-10	2011-04-09	M	35	0.9993	0.000689
B10251C8	2	2011-04-10	2012-04-09	M	36	1.002	0.000724
B10251C8	3	2012-04-10	2013-04-09	M	37	0.9993	0.000765
B10251C8	4	2013-04-10	2014-04-09	M	38	0.9993	0.000813
B10251C8	5	2014-04-10	2015-04-09	M	39	0.9993	0.00087
B10251C8	6	2015-04-10	2016-04-09	M	40	1.002	0.000937