5-State Model

With the use of simulated paths, a lot of mortality statistics can be generated to analyse or simply gain insight into the survival characteristics of certain individuals.

For the 5 state model, we use the simulated paths as inputs to calculate:

the average time of entering a certain state (such as the D state: Healthy and functionally disabled)
the total time spent in each state

As results are stochastic (statistics are derived from random simulated lifetimes), we can also study the variance of these statistics. This will be beneficial in quantifying the risk, allowing for more robust pricing methods.

Average First Time Entering State

health5_first_time_stats(model_type, state, init_age, init_state, trans_probs, simulated_path, female, year, wave_index, latent, param_file, n = 1000)

Parameters:

model_type : character

'S' for static model, 'T' for trend model, 'F' for frailty model

state : numeric

integer denoting which state we are entering or leaving

0 for first time leaving H state, only used when initial state is 0

1 for first time entering M state

2 for first time entering D state

3 for first time entering MD state

-1 for first time entering the dead state

init_age : numeric

numeric denoting initial age of indiviudal

init_state : numeric

initial state of individual: 0 for healthy, 1 for disabled

trans_probs : list

list of transition probability matrices, only needed for static and trend models.

simulated_path : matrix

matrix containing life path simulations, only needed for static and trend models.

female : numeric

0 for male, 1 for female, compulsory variable for frailty model

year : numeric

numeric denoting current year, compulsory variable for frailty model

wave_index : numeric

integer for the wave index = (interview year - 1998)/2 + 1, required in 5-state model and ignored in 3-state model

latent : numeric

initial value of latent factor, normally take the value 0

param_file : character OR dataframe/tibble

File path, or dataframe/tibble of parameters (generally, use US_HRS or china_CLHLS), compulsory variable for frailty model

n : numeric

numeric denoting number of unique latent factor simulations

Returns:

Column vector of first time entering the specified state

Usage:

# trend model
trans_probs <- get_trans_probs(n_states=5, model_type='T', param_file=US_HRS_5, init_age=65, female=0, year = 2022, wave_index = 13, latent = 0)
simulated_path <- simulate_health_state_paths(trans_probs, init_age=65, init_state = 0, cohort = 10000)

# time until entering M state, ill health but not functionally disabled
time_to_M <- health5_first_time_stats(model_type = 'T', state = 1, init_age = 65, init_state = 0, trans_probs)

# average initial time of entering state 1
print(mean(time_to_M, na.rm = TRUE))

# frailty model
time_to_M <- health5_first_time_stats(model_type = 'F', state = 1, init_age = 65, init_state = 0, female = 0, year = 2022, wave_index = 13, latent = 0, param_file = US_HRS_5)
print(mean(time_to_M, na.rm = TRUE))

Total Time Spent in State

health5_total_time_stats(simulated_path, state)