Notes for Decomposition of Differentials in Health Expectancies from Multistate Life Tables

Wanying Ling

This is a code note for the decomposition approach to healthy life expectancy based on multistate life tables (Shen et.al, 2023).

Functions

It contains seven functions:

Function 1: l0_func

l0_func : Function for obtaining baseline population health structure.

Function 2: lx_func

lx_func : Function for obtaining $l_x$

Function 3: P_func

P_func : Function for obtaining the matrix of transition probabilities.

Function 4: All_P_func

All_P_func : Function for obtaining $ \prod_{k=x}^{\beta-1} \mathbf{P}_k}$.

Function 5: SUM_func

SUM_func : Function for obtaining $\mathbb{e}_x$ (Status­Based­HLE­and­ULE).

Function 6: HLE_func

HLE_func : Function for obtaining $e_x$ (Popualtion­Based LE,­HLE­and­ULE).

Function 7: Decom_func

Decom_func : Function for obtaining component from the initial population $\dot{\mathbf{l}}\alpha \cdot{ }{\beta-\alpha} \mathbb{e}_\alpha$.

Function 8: DecomByTrans_func

DecomByTrans_func : Function for decomposition of differences in transition probabilities.

Dataset

The dataset BASELINE.csv includes the initial health structure of the population. It contains four variables:

• state: health state (with 1 and 2, healthy and unhealthy respectively)

• ragender: gender

• pro: proportion of the population in that health state (they are rescaled to 1 by sex and iteration to calculated the HLE for male and female separately)

• iter: bootstrap iteration number

The dataset PROB.csv includes the transition probabilities by age. It contains seven variables:

• pre_state: the initial state

• ragender: gender

• age: age

• iter: bootstrap iteration number

• A: probability to "Healthy" given the initial state

• L: probability to "Unhealthy" given the initial state

• H: probability to "Death" given the initial state

Table 1 - Panel A : Baseline population health structure­(Table 1 - Panel A)

Table 1 - Panel B : Status Based HLE and ULE­(Table 1 - Panel B)

Table 1 - Panel C : Population Based HLE and ULE

Table 2 - Panel A: Difference in Expectancies

Table 2 - Panel B: From Initial Population

Table 2 - Panel C: From Transitions

Table 2 - Panel D: From Each Transition Probability

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