6.4 Calculations: specific health outcomes

6.4.1 Risk of health outcome

Risk of the health outcome (e.g., risk of dying) is the outcome of a multivariable predictive risk algorithm. An example of the mutlivariable risk algorithm is:

\[ \text{Risk} = \sum_t h_0(t) * e^{\beta_{pred.smoking}*x_{smoking}+\beta_{pred.cancer}*x_{cancer} + \beta_{pred.age}*x_{age} +...} \] Where:

  • \(t\) = survival time
  • \(h_0(t)\) = the baseline hazard
  • \(\beta_{pred}\) = predictive hazard ratios for the exposures
  • \(x\) = the exposure. The exposure can be continuous (e.g., age) or categorical (e.g., smoking status).

Categorical exposures are represented by dummy/factor variables. Each category has its own beta and the exposure is binary. For example smoking status is categorical variable with categories: current, former <= 5 years, former >5 years, or never smoked. For \(\beta_{pred.current.smoker}\) the exposure: \(x_{current.smoker}\) = 1 if the individual currently smokes or 0 if the individual is another type of smoker.

6.4.2 Number of health outcomes

The number of health outcomes (e.g., summary - deaths) is calculated through the following steps:

  1. Risk of the health outcome is calculated for each individual (row) in the data set using the mutlivariable predictive risk algorithm.

  2. Each individual’s (row) risk is weighted with their corresponding survey weight (CCHS PUMF = WTS_M and CCHS shared file = WTS_S).

  3. The weighted mean of the health outcome (e.g., mean risk of death) is calculated.

  4. The weighted mean is then multiplied with the total number of individuals in the population to generate the number of health outcomes (e.g., number of deaths in 5 years).

6.4.3 Life expectancy

Life expectancy is calculated using abridge life tables using a modified Chaing approach (Chiang 1984) (Hsieh 1991). (link to reference for Chiang and Hsieh and also one of our papers). Life expectancy is calculated by two methods: one for summary life expectancy, and a second for by row life expectancy.

6.4.3.1 Summary Life Expectancy

Life expectancy is calculated separately for males and females.

Males:

  1. The mortality risk for each male individual is calculated using the male mortality mutlivariable predictive risk algorithm for mortality (MPoRT). Details about the MPoRT can be found in Appendix A.

  2. Male individuals are grouped into the 5-year age groups that are used in the 5-year abridge life tables (e.g., 40-44 years old).

  3. The weighted average risk of death for each age group is calculated.

  4. A male 5-year abridge life table is created using the weighted average risks of death (q(x)) for each age group and the median age for the age group.

Females

Steps 1-4 used to calculate life expectancy for males, are repeated for females using the female MPoRT and a female 5-year abridge life table.

Summary life expectancy

  1. The summary life expectancy, or life expectancy of the entire population, is calculated by adding the male life expectancy with the female life expectancy, and taking its average.

Summary life expectancy by strata

Steps (1-4) are repeated for each strata. There will be strata specific weighted risk of death and strata specific life tables.

Step 5 is repeated with the average life expectancy calculated across all strata.

6.4.3.2 By row life expectancy

An individual’s life expectancy is calculated by creating a new life table specific to that individual.

These life tables are 1-year abridge life tables, and begin at the individual’s age (e.g., an individual that is 43 years old, will have the life table start at 43 years).

  1. The probability of death for a person’s current age is calculated using the respective MPoRT (male or female), and the individual’s health profile (e.g., never smoked, 15 drinks weekly, has hypertension, is a Canadian Citizen, etc) (e.g., \(q_x\), where \(x=43\)).

  2. The probability of death is recalculated for incremental older ages (additional rows of the life table) up to age 90 years ( \(q_\text{(x+1)}, q_\text{(x+2)}...q_{90}\)). For each life table row, age is the only variable that is changed for MPoRT risk calculation.

Note: The result for By Row Life Expectancy are the predicted years of life that the individual still has left to live based on thier age (e.g., 43). To calculate age of death, add the respondent’s age to their by row life expectancy estimate.
Note: By row life expectancy does not account for the individual’s weight, and therefore can not be used to estimate the summary life expectancy.

D Bibilography

Chiang, C. L. 1984. The Life Table and Its Applications. Book. Malabar, Florida: Robert E. Krieger Publ. Co.

Hsieh, J. J. 1991. “Construction of Expanded Continuous Life Tables–a Generalization of Abridged and Complete Life Tables.” Journal Article. Mathematical Biosciences 103 (2): 287–302.