Formula - Days of Life Gained

Step 1 - Inputs and Assumptions

The average outdoor PM2.5 level reads 60 μg/m³ in Shanghai (ref [3]). It is assumed that a person spends around 6 hours a day, 250 days a year working in the office where filtration system is on and the average indoor PM2.5 level reads 10 μg/m³. To summarize, we have the following parameters:

Step 2 - Calculating the Average Daily PM2.5 Exposure

We first calculate the average of daily exposure to PM2.5 weighted by daily hour spent indoor and number of days indoor per year:

The result is then used to calculate the change in mortality based on the relationship shown in the following equation taken from ref [2]:

where y is the percent increase in daily mortality and x is the value of PM2.5.

Step 3 - Updating Hypothetical Death Count and YLL

A hypothetical death count value (reference death count = 80515 per 5 years) is introduced here to gauge the effect of the change in mortality shown above. It assumes the mortality rate of the reference case to be 1. The average PM2.5 from the reference is 105.1 μg/m³.

YLLs corresponding to daily average and from outdoor average of PM2.5 are calculated from a linear regression model based on data from ref [1]:

Step 4 - Combining the results for DLG

From the hypothetical death count and the YLLs we just calculated, the value of YLL per death (YLpD) can be obtained with the following equation:

Note that the afore-calculated hypothetical death count is a value over the course of 5 years due to the reference data being the case. The change in YLLs per death (ΔYLpD) calculated from daily average and outdoor average then quantifies the improvement of human health due to good indoor air.

• YLL per death from daily average: 606.44 / (73991 / (5 * 365)) = 14.96
• YLL per death from outdoor average: 626.29 / (75031 / (5 * 365)) = 15.23
• ΔYLpD: 14.96 - 15.23 = -0.27

The value of ΔYLpD means that per death, the year of life lost is decreased by 0.27 years. Given that we calculated every value based on a reference study that surveyed data for 5 years, it should be implied that a scenario created for this algorithm surveys for the same length. The final result in DLG per year, nevertheless, should be communitive. Hence, the final conversion of change in ΔYLpD to DLG per year follows:

-0.27 years lost per 5 years = 20.4 days gained per year
Days of Life Gained (DLG) = 20.4 days

We hereby consolidate our formulations with information from a recent study by Qi and Ruan et al. [4] in 2020. They have estimated that an improvement of indoor air PM2.5 levels to the WHO guideline level of 25 μg/m³ led to 0.14 years of gains in life expectancy for each death. With a period of investigation just shy of 4 years, their yearly average approximates to 0.035 years life gained per year. A quick re-calculation with our formulas with an improvement of indoor air quality to the same PM2.5 level yields 0.038 years life gained per year. So far, we have based our calculations on conservative assumptions and simple models. Yet the result we arrived at aligns beautifully with the result from ref [4] that implements more recent data and a more complex mathematic model. Therefore, we conclude that our formulation of days of life gain is a sound estimate.