Relative risk calculations

Transcription

1 Relative risk calculations Introduction The assessment of the burden and impacts of air pollution on health is operated through a methodology that will be implemented in AirQ+ and it is briefly described in the following text. Before introducing the methodology and its formulas, it is important to introduce some definitions that provide the basis for the formulas that will be used in AirQ+. One section summarizes data needs and gives an example of calculations. Air pollution is usually investigated in two separate fields: ambient (outdoor) air pollution and household (indoor) air pollution. Furthermore, effects on health are usually considered for long-term (for example, yearly) and short-term exposure (for example, daily concentrations). The impacts considered include mortality, total and cause-specific and other relevant health outcomes, such as hospital admissions for cardiovascular diseases, hospital admissions for respiratory diseases. Agespecific impacts on mortality are calculated through the use of Life Tables using estimators such as years-of-life-lost). Three scenarios for resulting health effects are typically investigated by users: 1. partial reduction of exposure levels, e.g. 10% reduction of annual mean PM 10 ; 2. reduction of exposure to a specific target level, e.g. reduction of annual mean of PM 2.5 to 10μg/m 3 as suggested by WHO air quality guidelines; 3. absolute reduction of exposure, e.g. 5 ppb decrease in the annual mean for ozone. Ambient air pollution is discussed first, then household air pollution. The life table calculations for AirQ+ are described in a separate document, AirQ_plus_lifeTableModule_V01.docx. Definitions For defined air pollutants (risk factors 1 ) AirQ+ provides the associated relative risks (RR) of exposure. For a population exposed to a risk factor the RR is defined as Equation 1 RR = I e I cf I e : incidence rate 2 in the population exposed (e.g. number of new cases per population per year). 1 Such as particulate matter, particle sizes less or equal to 10 or 2.5 µm (PM 10, PM 2.5 ), nitrogen dioxide (NO 2 ), ozone (O 3 ) and black carbon (BC). 1

2 I cf : incidence rate in the counterfactual population The counterfactual population is a population that is comparable in composition to the exposed population, but is not exposed itself to the risk factor. In the scope of AirQ+ mortality rates (death rates) and morbidity rates are nothing but special incidence rates. Example of RR: RR for active smoking (AS) mortality due to lung cancer (LC), number of deaths per year per population (d): Equation 2 RR LC AS = LC d AS LC d non smokers With a, b, c, and d are the number of cases (deaths) defined in the following population risk table Lung cancer Risk Present Absent Smoker a b a+b Non-smoker c d c+d the smoking related relative risk for lung cancer is calculated as: RR LC a/(a + b) AS = c/(c + d) RR AS is the excess risk for smokers to die of lung cancer as compared to non-smokers. If there were no excess risk, RR AS would be equal to 1 (but there would still be cases of LC) 3 LC. Where d AS is the LC probability of death for lung cancer for active smokers and d non smokers is the probability of death for lung cancer for non smokers. If for example a = 10, b = 90, c = 1, and d = 99, then the relative risk of cancer associated with smoking would be equal to 10. Smokers would develop lung cancer ten times as likely as non-smokers. 2 Incidence rates are defined for the (sub-) group of population in question, in particular, if age groups are used, I age goup = n_cases age group no_of_peopleage This means that I all ages all age I age group group groups since the denominators are all different. 3 Theoretically it is also possible for a RR to be less than one, this means that exposure leads to a reduction in risk. The reason for this potential confusion is the epidemiological use of the phrase exposure, which differs from its everyday use, where exposure comes with a negative connotation. The epidemiological use is purely technical and therefore a population can be exposed to beneficial factors as well. Examples are exposure to medical treatment or physical activity. In the case for air pollution, since there is no beneficial health effects known, RRs are always greater than one. 2

3 Ideally, the counterfactual population is not exposed to the risk factor. Like in the example: only smokers are exposed to AS. Non-smokers are also exposed, but to second hand smoke (SHS), which is studied using distinct SHS relative risks. The concept of a counterfactual is needed in studying air pollution since usually the whole population is exposed. Therefore, no studies are available for comparable populations with and without exposure. For air pollution, analysis is carried out asking: how does the actual situation relate to one with a lower exposure level? Any specific counterfactual (exposure) depends on specific assumptions, like the lowest value for which data is available, or the natural level of exposure, or an exposure level under which no adverse health effects are expected to occur. From epidemiological studies we have several RRs available both for long-term and short term effects and various health outcomes. In general, AirQ+ supplies stratified relative risks: Equation 3 RR pollutant = RR pollutant (level of exposure, health outcome, age, sex) This means that RRs are built as specific functions of the level of exposure, the health outcome, age and sex of the population. A health outcome can be mortality or a specific type of disease, like lung cancer (LC). Intervals for age groups are typically five years. RRs stratified by sex (male, female) is only available for indoor air pollution (IAP). In any case, AirQ+ should be capable of calculating integrated effects for all ages and all sexes. Ambient air pollution: Formulas For outdoor air pollution, the whole population is assumed to be exposed. Population attributable fraction (PAF) estimates the proportion of cases that are prevented if the exposure were zero. In case the whole population is exposed Equation 4 PAF = RR 1 RR Example: dispersed particulate matter (PM) is an air pollutant that has a RR LC greater than one for lung cancer. If the level of exposure were reduced in a population to a (counterfactual) level where RR is equal to one, PAF would be zero. Please note that there is still a risk to die of lung cancer due to causes other than exposure to PM in that population. If only a fraction p of a population is exposed, as in the case of AS, the formula is generalized to: Equation 5 PAF = p(rr 1) p(rr 1) + 1, 0 < p 1 3

4 Household air pollution: Formulas Equation 5 is also applied in the case of studying the effect of indoor air pollution, since under certain conditions frequency and levels of exposure of females to indoor air pollution are higher than for men. The percentage of the population exposed to household air pollution can be calculated by country (or by city if local data are available). Relative risks are calculated separately for men, women and children, based on the integrated exposure-response functions (IER) for all diseases but COPD. The suggested counterfactual concentration is between 5.8 and 8.8 μg/m3 (the concentration under which no adverse health effects are expected). The country population attributable fractions for ALRI, COPD, LC, stroke and IHD are calculated using Equation 4; p is the percentage of the population exposed to that level of air pollution, i.e. the percentage of the population using solid fuels for cooking. Table 1 Household air pollution RRs Disease RR (95% CI) women RR (95% CI) men ALRI 2.9 ( ) for children COPD 2.3 ( ) 1.9 ( ) Lung Cancer 2.3 ( ) 1.9 ( ) IHD ( ) ( ) Stroke ( ) ( ) Source: WHO ( If the whole population is exposed, then p = 1 and Equation 5 becomes Equation 4. General formulas In a specific population the number of cases or the fraction of all cases attributable to a specific pollutant and health outcome is of interest to calculate the attributable burden (AB): Equation 6 AB = BoD PAF The burden of disease (BoD) is the total burden of a specific health outcome. The same formula holds for the attributable deaths (AD). For example, let s consider a population with 100 deaths in a given year due to stroke in the age group How many are attributable to PM 2.5? The yearly average level of exposure is 28 µg/m 3. The relative risk (Equation 3) RR PM2.5 (28 µg/m 3, stroke, years) 4 RR PM2.5 (28 µg, stroke, 40 to 45 years) = m3 4 The red numbers are the example values taken from Table 3 to Table 5 in the next section. 4

5 AirQ+ implements alternative methods for RR values, which can be chosen by the user. RR values are either calculated by AirQ+ based on defined formulas or ranges of values (see Annex 1) or picked from a table that contains about RR-values in steps of 1 µg/m 3 for all health outcomes and age groups. Table 3 is based on such a RR value table 5. The BoD in this case is the total number of deaths by stroke in that age group is (males plus females) d(stroke, 40 to 45 years) = 100 Thus, according to Equation 4 and Equation 6 (see Table 3 and Table 4 for the values): AB PM2.5 (stroke, 40 to 45 years) = = 45.4 This means that approximately 45 out of 100 deaths for stroke in the age group are attributable to the exposure to air pollution measured as an average yearly value of 28 µg/m 3 PM 2.5. The total attributable burden for stroke is the sum over all age groups AB PM2.5 (stroke) = AB PM2.5 (stroke, age group) = 4775 all age groups This means repeating the same calculation for all the age groups, considering the respective values of mortality and RRs and sum them up. Finally, to assess the total burden for PM 2.5 the total number of deaths for all causes in that year needs to be known. In this example d total = The total AB for PM 2.5 (see table 3) is the sum overall health outcomes 6 : AB PM2.5 = AB PM2.5 (health outcome, age group) all health all age outcomes groups = Thus, the total attributable burden of disease fraction (ABF) due to PM 2.5 exposure in that specific population is ABF PM2.5 = = 15.2% The following Equations 7-9 summarize the previous calculations. The last two sums in general notation: 5 In practice there are two ways to consider effects on health due to change of concentrations of an air pollutant. One can consider the change to linear and the available analyses suggest that it is reasonable to use linear CRFs to assess risks within Europe, given the expected levels of PM 2.5 in This is especially the case for all-cause mortality. For more specific causes of death, a supra-linear function, steeper in lower concentrations, may fit the data slightly better (WHO, 2013: 14). So, a second possibility is to consider changing RRs values according to concentration values. 6 Health outcomes for PM 2.5 would be acute lower respiratory infections (ALRI), ischemic heart disease (IHD), chronic obstructive pulmonary disease (COPD), stroke and lung cancer (LC). 5

6 Equation 7 and AB pollutant (health outcome) = AB pollutant (health outcome, age group) Equation 8 all age groups AB pollutant = AB pollutant (health outcome, age group) all health all age outcomes groups For calculation of the attributable fraction (ABF) the total burden by all causes (in the example above: total number of deaths from non-external 7 all causes) needs to be available: Equation 9 ABF pollutant = AB pollutant Total BoD Relation between RR for all ages and RR by age groups Sometimes relative risks are not available by age groups, but as a single number for all ages. For the whole population and a certain health outcome Equation 6 is applied with BoD being the number of all cases in the population. If a specific age group is being investigated, RR all ages is used for that age group, too. Note: in case age group specific RRs are available, RR all ages needs to be supplied separately since, due to the definition of RR involving incidences (Equation 1), there is no simple relationship between RR all ages and age group specific relative risks, like: RR all ages 1 n all age groups RR age group 7 External causes are all kinds of accidents, such as traffic mortality or drownings. 6

7 Structure of BoD data for RR calculations There are two basic methods for the determination of the RRs 8 : 1. RRs implemented as analytical functions; 2. RR values pre-calculated in simulations and tabulated in units by one per health outcome (Integrated exposure risk functions (IER), worksheet 4.) IER RRs in Excel file, provided by WHO). The two analytical functions are defined in Bart Ostro: Outdoor Air Pollution. Table 2 Analytical RR functions (excerpt), X is pollutant concentration, X o the value of the counterfactual Source: B. Ostro Equation 10 Equation 11 RR = exp [β ln(x X 0 )] RR = [(X + 1)/(X 0 + 1)] β RR = exp[β(ln(x+1) - ln(x 0 +1))] 8 Excel file: 2B_RR_forumlas_and_tables.xslm 7

8 The two parameters, β and X 0, depend on the type of pollutant, the health outcome and (sometimes) age; they are provided by WHO. Note on slang: Ostro refers to the first equation as linear and the second one as log-linear. Instead, AirQ 2.2 used a really linear function for BoD calculation, i.e. RR = 1 + β(x-x 0 ), and Equation 10 for life tables. In order to clearly distinguish between the three cases, we use the terms exponential linear and exponential log-linear in the Excel file. The really linear function is provided in the Excel file, too, but it is not intended to implement it in AirQ+ since for small values of the exponent results are comparable to those from Equation 10 due to the Taylor series expansion of the exp-function. In order to calculate the burden of disease due to a certain pollutant according to Equation 7 to Equation 8 the following data needs to be available: the level of exposure; the relative risk function for the pollutant (Equation 3); the BoD distribution by age groups and causes (e.g. number of deaths by cause); the total BoD (e.g. number of deaths by all causes). The following example is based on a real sample population. It illustrates how calculations are performed and potential constraints due to a lack of information, for example, for many age groups there is no health outcome specific data. The sample population is exposed to PM 2.5 at a level of 28µg/m 3 (Table 3 to Table 5). In this example, there s no additional risk due to exposure to PM 2.5 for concentrations equal or below 5 µg/m 3, which is the counterfactual in this case. The actual RR values would be provided by WHO as a table. ALRI is of special relevance for young children, that s why only the age group 0-4 years is of relevance. The other four outcomes, COPD, IHD, Stroke and LC are only considered for adults (ages of 25 years or older). Two of those, COPD and LC, have RR values for all ages only, which are applied to the respective age groups for calculating the number of attributable deaths. Table 3 Relative risks for PM 2.5 exposure of 28 µg/m 3, type of health outcome and age group. Note that age groups start at age 25 years; for some age groups, RR values are not available. Age group ALRI 9 COPD IHD Stroke LC Age ALRI is for 0-4 years of age only. 8

9 Table 4 Number of annual deaths in a sample population, type of health outcome and age groups. Highlighted cells indicate values relevant for the computations. Age group ALRI COPD IHD Stroke LC Up to Total Table 5 Attributable deaths for a sample population due to ambient air pollution at PM 2.5 = 28 µg/m 3 ALRI COPD IHD Stroke LC Up to

10 Total Number of attributable deaths, all health outcomes: Total number of deaths in the sample population by all causes in the relevant age groups: In this example, the total number of deaths ( ) corresponds to the total BoD of Equation 9. It is the sum of all annual deaths in the sample population for the age groups 0-4 years plus 25 years and older. Data input The data can be entered by the user, but some defaults will be available after installation, for example relative risk values and total BoD by country. The level of exposure needs to be calculated based on the air pollution data that the user has available: two main possibilities are possible: 1) the input is one average value for a given period of time (that is a common case when a user has no access to primary data from monitoring stations, satellite data, or dispersion modelling; 2) the user has a complete time series of daily averages for one year; then AirQ+ calculates the average yearly value. The original data can be a single table that covers data from one source (for example one monitoring station) or multiple sources (two or more monitoring stations). The user has to input one table of air pollution data. In the case of PM or NOx the data input are the daily average values in µg/m 3. The case of Ozone is different because the concentration data are calculated as SOMO35 10, Sum of Means over 35 PPB (parts per billion) that corresponds to 70 µg/m 3. Ozone Calculations for Ozone follow the same procedure used for PM, but the differences between the average concentrations that the population is exposed and a counterfactual have not to be considered in the formula because the levels of Ozone are calculated against a value, usually 35ppb. The user should be interested in measuring the burden of Ozone when it has a certain value, for example 45ppm. In this case the calculations of the exposure levels, measured by the level of pollution, should be done outside. 10 SOMO35 = AB pollutant max i (0, Ci 35ppm) where Ci is the maximum daily 8-hour average concentration and the summation is from day i=1 to 365 per year. 10

11 Annex 1 Recommended concentration response functions for particulate matter, long-term exposure (HRAPIE project: WHO Regional Office for Europe, 2013) Table: RRs for air pollutants (PM10, PM2.5, NO2, O3 and BC). Pollutant metric PM 2.5 Annual mean Health outcome Population RR (95% CI) per 10 μg/m 3 Mortality, all-cause (natural) age 30+ years ( ) Range of concentration PM 2.5 Annual mean Mortality, cerebrovascular disease (includes stroke), ischaemic heart disease, chronic obstructive pulmonary disease (COPD) and trachea, bronchus and lung cancer age 30+ years CRFs used in the GBD 2010 study (see IER section) PM 10 Annual mean Postneonatal infant mortality, allcause age 1 12 months) 1.04 ( ) PM 10 Prevalence of bronchitis in children age 6 12 (or 6 18) years 1.08 ( ) PM 10 Incidence of chronic bronchitis in adults age 18+ years ( ) Source: based on HRAPIE project: recommendations for concentration response functions of particulate matter, ozone and nitrogen dioxide (WHO Regional Office for Europe, 2013) Recommended concentration response functions for particulate matter, short-term exposure Pollutant metric Health outcome Population RR (95% CI) per 10 μg/m 3 Mortality, all-cause (natural) ages PM 2.5 Range of concentration daily mean ( ) PM 2.5 daily mean Hospital admissions, Cardiovascular diseases (CVDs) (includes stroke) ages ( ) PM 2.5 daily mean Hospital admissions, respiratory diseases ages ( ) 11

12 PM 2.5 two-week average, converted to PM2.5, annual average Restricted activity days (RADs) ages ( ) PM 2.5 two-week average, converted to PM2.5, annual average Work days lost, working-age population age years ( ) PM 10 daily mean Incidence of asthma symptoms in asthmatic children 5-19 years ( ) Source: based on HRAPIE project: recommendations for concentration response functions of particulate matter, ozone and nitrogen dioxide (WHO Regional Office for Europe, 2013) Recommended concentration response functions for ozone: long-term Pollutant metric Health outcome Population O3, summer months (April September), average of daily maximum 8-hour mean over 35 parts per billion (ppb) Mortality, respiratory diseases RR (95% CI) per 10 μg/m 3 age 30+ years ( ) Range of concentration >35 ppb (>70 μg/m³) Source: based on HRAPIE project: recommendations for concentration response functions of particulate matter, ozone and nitrogen dioxide (WHO Regional Office for Europe, 2013) Recommended concentration response functions for ozone: short-term Pollutant metric Health outcome Population O3, daily maximum Range of concentration RR (95% CI) per 10 μg/m 3 Mortality, all (natural) causes ages ( ) >35 ppb (>70 μg/m³) O3, daily maximum Mortality, all (natural) causes ages ( ) >10 ppb (>20 μg/m³) O3, daily maximum Mortality, CVDs and respiratory diseases ages CVD: ( ); respiratory: ( ) >35 ppb (>70 μg/m³) O3, daily maximum Mortality, CVDs and respiratory diseases ages CVD: ( ); respiratory: ( ) >10 ppb (>20 μg/m³) O3, daily maximum Hospital admissions, CVDs (excluding stroke) and respiratory disease age 65+ years CVD: ( ); respiratory: ( ) >35 ppb (>70 μg/m³) 12

13 O3, daily maximum Hospital admissions, CVDs (excluding stroke) and respiratory disease age 65+ years CVD: ( ); respiratory: ( ) >10 ppb (>20 μg/m³) O3, daily maximum O3, daily maximum Minor restricted activity days (MRADs) Minor restricted activity days (MRADs) ages ( ) >35 ppb (>70 μg/m³) ages ( ) >10 ppb (>20 μg/m³) Source: based on HRAPIE project: recommendations for concentration response functions of particulate matter, ozone and nitrogen dioxide (WHO Regional Office for Europe, 2013) Recommended concentration response functions for nitrogen dioxide: long-term Pollutant metric Health outcome Population RR (95% CI) per 10 μg/m 3 NO2, annual mean Mortality, all (natural) causes age 30+ years Range of concentration >20 μg/m³ ( ) NO2, annual mean Prevalence of bronchitic symptoms in asthmatic children Age 5 14 years ( ) per 1μg/m³ change in annual mean NO2 Source: based on HRAPIE project: recommendations for concentration response functions of particulate matter, ozone and nitrogen dioxide (WHO Regional Office for Europe, 2013) and Faustini et al. (2014) Recommended concentration response functions for nitrogen dioxide: short-term Pollutant metric Health outcome Population RR (95% CI) per 10 μg/m 3 Range of concentration NO2, daily maximum 1-hour mean Mortality, all (natural) causes ages ( ) NO2, daily maximum 1-hour mean Hospital admissions, respiratory diseases ages ( ) NO2, daily maximum 24-hour mean Hospital admissions, respiratory diseases ages ( ) Source: based on HRAPIE project: recommendations for concentration response functions of particulate matter, ozone and nitrogen dioxide (WHO Regional Office for Europe, 2013) Recommended concentration response functions for black carbon: long-term 13

14 Pollutant metric Health outcome Population RR (95% CI) per 10 μg/m 3 BC, Annual mean Mortality, all (natural) causes age 30+ years 1.06 Range of concentration ( ) For Household air pollution, a table with data on the estimation of the yearly use of solid fuels is needed for calculations. See example below. Country Data source Population (%) using solid fuels Year: 2013 Afghanistan Multi-level 80 Albania Multi-level 37 Algeria Multi-level <5 Andorra High-income <5 Angola Multi-level 54 Antigua and Barbuda Multi-level <5 Venezuela (Bolivarian Republic of) Multi-level <5 Viet Nam Multi-level 47 Yemen Multi-level 32 Zambia Multi-level 82 Zimbabwe Multi-level 71 14