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3-State Model

A lot of mortality statistics can be generated to analyse survival of a certain individual. The following functions return the expected value and variance associated with the lifetime statistic.

The functions can use either of the different inputs below to produce the required statistic:

  • list of transition probability matrices from get_trans_probs

  • simulated path matrix from simulate_health_state_paths

If the first option is used, the functions use simulation to find expected value and variance. Hence, there is a stochastic component to these results. If both inputs are provided, then the simulated path wil be used, and no simulation will occur within the function.

Set 'model_type' to be 'F' for frailty model. The function for frailty model simulates 'n' unique latent paths, which adds another level of randomness in the statistic. It also requires more parameters to produce a new set of transition probability matrices (see below examples). By default, frailty functions simulate 1000 unique latent factors.

For all code examples below, we will use a male individual aged 65 in year 2022.

Average Future Lifetime: health3_afl

The function calculates the average future lifetime for a given individual, and its variance.

health3_afl(model_type, init_age, init_state, trans_probs, simulated_path, female, year, param_file, n = 1000)

   Parameters:

     model_type : character

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

     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

     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:

     Mean and variance of average future lifetime

   Usage:

# trend model
trans_probs <- get_trans_probs(n_states=3, model_type='T', param_file=US_HRS, init_age=65, female=0, year = 2022)

# calculate average future lifetime
health3_afl(model_type = 'T', init_age = 65, init_state = 0, trans_probs)

# frailty model
health3_afl(model_type = 'F', init_age = 65, init_state = 0, female = 0, year = 2022, param_file = US_HRS)

Healthy Future Lifetime health3_hfl

This function calculates the average future lifetime spent in the healthy state, and its variance.

health3_hfl(init_age, init_state, trans_probs = NULL, simulated_path = NULL)

   Parameters:

     model_type : character

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

     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

     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:

     Mean and variance of healthy future lifetime

   Usage:

# trend model
trans_probs <- get_trans_probs(n_states=3, model_type='T', param_file=US_HRS, init_age=65, female=0, year = 2022)

# calculate healthy future lifetime
health3_hfl(model_type = 'T', init_age = 65, init_state = 0, trans_probs)

# frailty model
health3_hfl(model_type = 'F', init_age = 65, init_state = 0, female=0, year = 2022, param_file=US_HRS)

Average Disabled Future Lifetime: health3_dfl

This function calculates the average future lifetime spent in the disabled state, and its variance.

Not that under the same simulated lifetime, average future lifetime is equal to the sum of healthy lifetime and disabled lifetime.

health3_dfl(init_age, init_state, trans_probs = NULL, simulated_path = NULL)

   Parameters:

     model_type : character

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

     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

     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:

     Mean and variance of average lifetime spent in disabled state

   Usage:

# trend model
trans_probs <- get_trans_probs(n_states=3, model_type='T', param_file=US_HRS, init_age=65, female=0, year = 2022)

# calculate average future lifetime
health3_dfl(model_type = 'T', init_age = 65, init_state = 0, trans_probs)

# frailty model
health3_dfl(model_type = 'F', init_age = 65, init_state = 0, female=0, year = 2022, param_file=US_HRS)

Time until onset of Disability: health3_time_to_disabled

This function calculates average time for onset of disability, given that the individual becomes disabled.

Note that an initial state is not required for this function, as disabled initial state is trivial.

health3_time_to_disabled(init_age, trans_probs = NULL, simulated_path = NULL)

   Parameters:

     model_type : character

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

     init_age : numeric

       numeric denoting initial age of indiviudal

     init_state : numeric

       *initial state of individual, needs to be 0 for this function

     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

     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:

     Mean and variance of onset of first diability

   Usage:

# trend model
trans_probs <- get_trans_probs(n_states=3, model_type='T', param_file=US_HRS, init_age=65, female=0, year = 2022)

# calculate average future lifetime
health3_time_to_disabled(model_type = 'T', init_age = 65, init_state = 0, trans_probs)

# frailty model
health3_time_to_disabled(model_type = 'F', init_age = 65, init_state = 0, female=0, year = 2022, param_file=US_HRS)