Impact Calculation Tool code description

This page provides the detailed description of the calculation code in the key parameters of the Impact calculation tool (ICT) -model.

Mortality rate scenarios

Parameter identifier: Mort_rate_scenarios

Total mortality rate for different causes of death in different exposure scenarios is calculated based on the defined exposure levels, exposure-response functions (relative risk (RR) or absolute risk (AR)) and background mortality risk in the population. For those causes of death for which RR functions have been defined, change in the mortality rate is calculated based on the population attributable fraction (PAF) -method. In BAU scenario, the mortality rate is determined by the population and mortality input data. However, if the exposure in the BAU scenario is defined to change during the assessment follow-up period, the mortality and population input data only determine the mortality rate in the first year of the assessment, and any changes in the BAU exposure level in the following years will result in changes in the BAU mortality rate.

var a:= if Exp_age_class = 'Yes' then Si_pi1(Exposures, 5, Age_cat, age1, Age_help)*5 else Exposures;
var b:= Mortality_erf;
var c:= Mort_erf_unit;
c:= if c = 0 then 1 else c;
var d:=Pop_frac;
var e:= exp(ln(b[Erf_type='Relative Risk'])/c*a[@Fu_period=1]);
var f:=((e*d)+(1-d))[Exposure='Reference'];
var g:=((e*d)+(f*(1-d)))[Exposure='BAU'];
g:=(g-1)/g;
g:= Base_mort_rate-Base_mort_rate*g;
f:=Table(Exposure)(f, f, 1);
e:= exp(ln(b[Erf_type='Relative Risk'])/c*a);
f:=(e*d)+(f*(1-d));
g:=f*g;
Var h:= a-a[Exposure='BAU', @Fu_period=1];
h:= b[Erf_type='Absolute Risk']/c*h*d;
var i:= sum(Table(Erf_type)(g,h),Erf_type);
if Assessment_type='Health outcome scenarios' then 
var j:= Oc_scen_mort;
Si_pi1(j, 5, Age_cat, age1, Age_help)/Population
else i

Code description line-by-line:

1: Exposure level in different scenarios. If exposure has been defined age-specifically, then the age interval is changed from 5-year to 1-year.

2: Exposure-response functions for different mortality endpoints.

3-4: Exposure unit to which the exposure-response function relates to.

5: Fraction of exposed population in different scenarios.

6: Relative risk (RR) exposure-response function is adjusted to the exposure level on the first year of the assessment.

7: Calculation of the population average adjusted RR in reference scenario.

8: Calculation of the population average adjusted RR in BAU scenario.

9: Calculation of the population attributable fraction (PAF) in BAU scenario.

10: Calculation of the baseline mortality rate in the theoretical absence of the exposure.

11: Calculation of the adjusted RR for that fraction of population which is exposed only to the reference scenario level (usually no exposure or natural background exposure level).

12: Calculation of the adjusted RR for that fraction of population which is expose to the exposure level defined in for the scenario.

13: Calculation of the population average adjusted RR in different exposure scenarios.

14: Mortality rate in different scenarios is calculated for those causes of death for which RR exposure-response functions have been defined for by multiplying the baseline mortality rate in the theoretical absence of the exposure by the population average adjusted RR.

15: Difference in the exposure level in Reference and Alternative scenarios compared to BAU scenario.

16: Difference in mortality risk in Reference and Alternative scenarios compared to BAU scenario is calculated for those causes of death for which absolute risk (AR) exposure-response functions have been defined for.

17: Risk of mortality due to different causes of death and any changes in these risks compared to the BAU scenario are combined in one table.

Population in time, child

Parameter identifier: Pop_in_time_child

Population of 0-4 year-olds is projected in 1-year age and time steps for 100 years from the assessment start year onwards, after which the population in the beginning of each 5-year follow-up period is determined. Population of 0-4 year-olds is projected separately in 1-year age and time intervals because mortality risk can vary drastically within the 0-4 age group.

var k: Birth_rate[Fu_year=Year_lt];
k:= if k = null then k[@Year_lt=Followup_time] else k;
var a:= if @Year_lt = 1 then population else (if @age1=1 then k else 0);
a:= a[age1=age_child];
var j:= sum(Mort_rate_scenarios,Mort_endpoint)[age1=age_child];
j:=if Mort_effect = 'Acute' then j[Exposure='BAU'] else j;
j:= if Exp_year_class = 'Yes' then 
(j:=j[Fu_period=period_lt];
j:= if j = null then j[Period_lt=max(Fu_period)] else j;
j:= Si_pi1(j, 5, Period_lt, Year_lt, Year_help)*5)
else j;
j:= if j < 0 then 0 else j;
j:= if j > 2 then 2 else j;
j:= (2-j)/(2+j);
var x:= 1;
while x<= min([size(age_child),size(Year_lt)]) do (
var b:= a*j;
b:= b[@age_child=@age_child-1, @Year_lt=@Year_lt-1];
a:= if b=null then a else b;
x:= x+1);
sum(if Year_lt = period_vs_year then a else 0,Year_lt)

Code description line by line:

1-2: Annual birth rate for 100 year time period starting from the assessment start year and based on the birth rate input data. If the assessment follow-up time < 100 years, the birth rate in the last follow-up year applies for the rest of the 100 year time period.

3-4: The population table for 0-4 year olds for which the projection is based on (age*follow-up year array). Population for all 0-4 year olds in the first year is based on the population input data and the population for 0 year olds in the rest of the follow-up years on the birth rate data.

5: Calculation of the annual total mortality rate (1-year age interval).

6: If mortality effects are defined to be of acute nature (i.e. ERF represents impact on daily instead of annual mortality), the population is projected only based on the total mortality risk in the BAU scenario.

7-11: If exposure is defined to change in the course of the assessment follow-up period, the exposure in one year time intervals based on the exposure input data given in 5-year time intervals. If the assessment follow-up period is < 100 years, the exposure level defined for the last follow-up 5-year period applies for the rest of the 100 years.

12-13: Total mortality rate is limited to be between 0 and 2.

14: Calculation of the annual survival rate.

15-20: The child population is projected through the 100 year time period. Population at a given 1-year age group and year is multiplied with the annual survival rate for that age. The result is the population of the next 1-year age group in the following year.

21: Population in the beginning of each 5-year follow-up period is derived from the annual projection.

Population in time, beginning of time step

Parameter identifier: Pop_in_time_beg

Population is projected in 5-year age and calendar year intervals for 100 years from the assessment start year onwards. The resulting table gives the population in the beginning of each 5-year time step.

var a:= sum(if floor(age1/5)+1 = @age_cat then population else 0, age1);
a:= if @age_cat=1 then sum(pop_in_time_child, age_child) else (if @period_lt = 1 then a else 0);
var j:= sum(Mort_rate_scenarios,Mort_endpoint);
j:=if Mort_effect = 'Acute' then j[Exposure='BAU'] else j;
j:= if Exp_year_class = 'Yes' then
(j:=j[Fu_period=period_lt];
j:= if j = null then j[Period_lt=max(Fu_period)] else j)
else j;
j:= if j < 0 then 0 else j;
j:= if j > 2 then 2 else j;
j:= (2-j)/(2+j);
j:= sum(if floor(age1/5)+1 = @age_cat then j else 0 , age1)/5;
var m:=j[@age_cat=@age_cat+1];
m:= if m=null then 0 else m;
var n:=((j^5)+(j^4*m)+(j^3*m^2)+(j^2*m^3)+(j*m^4))/5;
var x:= 1;
while x<= min([size(age_cat),size(period_lt)]) do (
var b:= a*n;
b:= b[@age_cat=@age_cat-1, @period_lt=@period_lt-1];
a:= if b=null then a else b;
x:= x+1);
a

Code description line by line:

1-2: The population table for which the projection is based on (age*follow-up year array). Population in the beginning of first 5-year time step is based on the population input data, which is summed up to derive population in 5-year age intervals. Population in age group 0-4 for the 100 year period is based on the child (0-4 years old) population projection.

3: Calculation of the annual total mortality rate (1-year age interval).

4: If mortality effects are defined to be of acute nature (i.e. ERF represents impact on daily instead of annual mortality), the population is projected only based on the total mortality risk in the BAU scenario.

5-8: If exposure is defined to change in the course of the assessment follow-up period, the exposure in 1-year time intervals based on the exposure input data given in 5-year time intervals. If the assessment follow-up period is < 100 years, the exposure level defined for the last follow-up 5-year period applies for the rest of the 100 years.

9-10: Total mortality rate is limited to be between 0 and 2

11: Calculation of the annual survival rate.

12: Calculation of the annual average survival rate for 5-year age groups.

13-15: Calculation of the average survival rate from one age group and 5-year follow-up period to the next age group and 5-year follow-up period.

16-22: The population is projected through the 100 year time period. Population at a beginning of a given age group and 5-year follow-up period is multiplied with the average 5-year-period survival rate for the age group. The result is the population of the next age group in the beginning of the following 5-year follow-up period.

Population in time, average for time step

Parameter identifier: Pop_in_time_ave

Based on the population projection which determines the population structure in the beginning of 5-year time steps, the average number of population during each 5-year time step for the assessment follow-up period is calculated. However, if the follow-up period is only 1 year, the population structure during this year is defined based on the population input data.

var a:=Pop_in_time_beg[Period_lt=Fu_period];
var b:=(Pop_in_time_beg[@Period_lt=@Period_lt+1])[Period_lt=Fu_period];
b:= if b = null then a[Fu_period=max(Fu_period)] else b;
b:=(a+b)/2;
if followup_time=1 then a else b

Code description line by line:

1: Population in the beginning of each 5-year time step during the assessment follow-up period.

2-3: Population in the beginning of the next 5-year time step.

4: Based on these, the model calculates the average number of population within all age groups for each 5-year time step.

5: If the assessment follow-up period is 1 year, population structure is the same as in the beginning of the population projection (i.e. calculated directly from the population input data)

Life years in time

Parameter identifier: Life_years

Calculates the number of life years lived by a given 5-year age group in a given 5-year time step 100 years onwards from the beginning of the assessment.

var a:= Pop_in_time_beg;
var b:=sum(Mort_rate_scenarios,Mort_endpoint);
b:= if Mort_effect = 'Acute' then b[Exposure='BAU'] else b; 
b:= if Exp_year_class = 'Yes' then
(b:=b[Fu_period=period_lt];
b:= if b = null then b[Period_lt=max(Fu_period)] else b)
else b;
b:= if b < 0 then 0 else b;
b:= if b>1 then 1 else b;
b:= ((2-b)/(2+b));
b:= sum(if floor(age1/5)+1 = @age_cat then b else 0 , age1)/5;
var c:=b[@age_cat=@age_cat+1];
c:= if c=null then c[age_cat='90-94'] else c;
var d:=((b^5)+(b^4*c)+(b^3*c^2)+(b^2*c^3)+(b*c^4))/5;
var e:= a-(a*d);
((a*d*5)+e*2.5)*Age_weight*Npv_life_year

Code description line-by-line:

1: Population projection for 100 years in the different exposure scenarios (population in the beginning of each 5-year time)

2: Calculation of the annual total mortality rate in different scenarios (one year age interval).

3: If mortality effects are defined to be of acute nature (i.e. ERF represents impact on daily instead of annual mortality), the age-adjusted life expectancy is calculated only based on the total mortality rate in the BAU scenario.

4-7: If exposure, and, hence, mortality rate, changes in the course of the assessment follow-up period, and the assessment follow-up period is < 100 years, the exposure level defined for the last 5-year period applies for the rest of the 100 years.

8-9: Total mortality rate is limited to be between 0 and 1

10: Calculation of the annual survival rate in different scenarios (1-year age interval).

11: Calculation of the annual average survival rate for 5-year age groups.

12-15: Calculation of the average survival rate from one 5-year age group and 5-year follow-up period to the next 5-year age group and 5-year follow-up period.

13: Number of deaths in a given 5-year age group and 5-year follow-up period is calculated based on the population projection and survival rate.

14: Number of life years lived in a given 5-year age group and 5-year follow-up period is calculated based on the population projection, survival rate and number of deaths. Those who survive to the next 5-year follow-up period gain 5 life years. Those who die during the 5-year follow-up period are assumed to gain in average 2.5 life years. The total number of life years lived in a given 5-year age group and 5-year follow-up period are multiplied by age weight and net present value of life years.

Age-adjusted life expectancy

Parameter indentifier: Ad_le

Var a:=Life_years;
var b:= 0;
var x:= 1;
while x<= min([size(age_cat),size(Period_lt)]) do (
b:= b + a;
a:= a[@age_cat=@age_cat+1, @Period_lt=@Period_lt+1];
a:= if a=null then 0 else a;
x:= x+1);
b:=b[@Period_lt=1]/Pop_in_time_beg[@Period_lt=1];
if isnan(b)=1 then 0 else b

Code description line-by-line:

1: Life years lived (age group*calendar year array) in different scenarios

2-8: The model calculates the total number of expected life years during the following 100 years for the population in each age group in the beginning of the assessment. This is done by summing up the life years diagonally over age group and time dimensions.

9-10: The average age-adjusted life-expectancy in at a given age is calculated by dividing the total number of expected life years by the size of the population in the same age group in the beginning of the assessment.

Life expectancy in a birth cohort

Parameter identifier: Le_cohort

var a:= sum(Mort_rate_scenarios,Mort_endpoint);
a:= if Mort_effect = 'Acute' then a[Exposure='BAU'] else a;
a:= if Exp_year_class = 'Yes' then
(a:=a[Fu_period=period_lt];
a:= if a = null then a[Period_lt=max(Fu_period)] else a;
a:= Si_pi1(a, 5, Period_lt, Year_lt, Year_help)*5)
else a;
a:=if a < 0 then 0 else a;
a:=if a>1 then 1 else a;
a:= ((2-a)/(2+a));
var b:=1;
var c:=0;
var d:=0;
var x:= 0;
while x<=99 do (
c:=b*a[age1=x, @Year_lt=x+1];
d:=d+c+(b-c)/2;
b:=c;
x:= x+1); 
d

Code description line-by-line:

1: Calculation of the annual total mortality rate in different scenarios (1-year age interval).

2: If mortality effects are defined to be of acute nature (i.e. ERF represents impact on daily instead of annual mortality), the life expectancy in a birth cohort is calculated only based on the total mortality rate in the BAU scenario.

3-7: If exposure, and, hence, mortality rate, changes in the course of the assessment follow-up period, and the assessment follow-up period is < 100 years, the exposure level defined for the last 5-year period applies for the rest of the 100 years. The change in the mortality rate in time is defined on an annual basis instead of 5-year time steps.

8-9: Mortality rate is limited to be between 0 and 1.

10: Calculation of the annual survival rate (1-year age interval).

11-20: The model calculates the cumulative survival rate at all ages. Cumulative survival rates are then summed up to give the average life expectancy in a birth cohort. It is assumed, that those who die at a given age gain in average 0.5 years during the year when they die. If the exposure, and, hence, age-specific mortality rates change in the course of the assessment, the cumulative survival rates are summed up diagonally over age and calendar year dimensions.

Mortality, specified

Parameter identifier: Ab_mortality_spec

Calculation of the number of deaths attributable to the exposure or hazard in different scenarios. The attributable deaths are presented for different age groups and 5-year follow-up time steps.

if Assessment_type = 'Exposure scenarios' then
var a:= Mort_rate_scenarios;
a:= sum(if floor(age1/5)+1 = @age_cat then a else 0 , age1)/5;
a:=if a<0 then 0 else a;
a:=if a>1 then 1 else a;
a:=a-a[exposure='Reference'];
a:= a*Pop_in_time_ave;
var b:=Table(Time_unit)(a, a*5);
a:= if followup_time <2 then a else b;
if Outcome= 'Change in EBD' then a[Exposure='Alternative']-a[Exposure='BAU'] else a

Code description line-by-line:

1: If the starting point for the assessment is ”Exposure scenarios”, i.e. the health impacts of an exposure are calculated based on exposure scenarios, exposure-response functions (relative risk or absolute risk), and incidence/prevalence data on mortality/morbidity in the population, then the attributable deaths are calculated based on the code on lines 2-10.

2: Annual mortality risk for different causes of death in different exposure scenarios in 1-year age groups.

3: The model calculates the average annual mortality rate for 5-year age groups based on the 1-year age interval mortality rates. It is assumed that the population is distributed evenly within the 5-year age groups.

4-5: Mortality risk is limited to be between 0 and 1.

6: Mortality risk attributable to the exposure/risk factor of interest in BAU and alternative scenarios is calculated by subtracting the reference scenario mortality risk (i.e. the mortality risk at no exposure/natural background exposure level) from the mortality risk in BAU/Alternative scenario.

7: Attributable deaths are calculated by multiplying the attributable mortality risk with the average annual population during each 5-year time step in different scenarios.

8: A table is created, which presents the attributable deaths per different time units(average annual, per 5-year period).

9: If the assessment follow-up time is one year, the results are given in a table without the time unit dimension.

10: If the outcome of interest is "Change in EBD" (i.e. change in the environmental burden of disease in the alternative scenario compared to the BAU scenario), then the attributable deaths in BAU scenario are deducted from the attributable deaths in alternative scenario.

YLL, specified

Parameter identifier: Yll_spec

Calculation of the years of life lost due to mortality (YLL) for the mortality endpoints of interest. YLL is presented for different age groups and 5-year follow-up time steps.

if Assessment_type = 'Total burden of disease' then
var a:=Exposures;
var b: Mort_erf_bod;
var c:= Mort_erf_unit;
c:= if c = 0 then 1 else c;
var d:=Pop_frac;
var e:= exp(ln(b)/c*a);
Var f:=((e*d)+(1-d))[Exposure='Reference'];
var g:=((e*d)+(f*(1-d)))[Exposure='BAU'];
g:=(g-1)/g;
g:= As_total_yll-As_total_yll*g;
f:=Table(Exposure)(f, f, 1);
f:=(e*d)+(f*(1-d));
f:=f*g;
f-f[Exposure='Reference']
else if Mort_effect = 'Acute' then 
Ab_mortality_spec*Life_lost*Npv_life_year[period_lt=Fu_period]*Age_weight
else if App_yll = 'Life tables' then
var a:=Life_years[period_lt=fu_period];
a:= (a[Exposure='Reference']-a);
a:=Table(Time_unit)(a/5, a);
if Outcome= 'Change in EBD' then a[Exposure='Alternative']-a[Exposure='BAU'] else a
else
Ab_mortality_spec*Ad_le[Exposure='Reference']

Code description line-by-line:

1: If the starting point for the assessment is ”Total burden of disease”, i.e. the health impacts of an exposure are calculated based on exposure scenarios, exposure-response functions, and total burden of disease data for the mortality/morbidity endpoints of interest, then YLL is calculated based on the code on lines 2-15.

2: Exposure level.

3: Exposure-response functions (relative risks) for different mortality endpoints.

4-5: Exposure unit to which the exposure-response function relates to.

6: Fraction of exposed population.

7: Exposure-response function (relative risk) is adjusted to the exposure level defined for the scenario.

8: Calculation of the population average adjusted RR in reference scenario.

9: Calculation of the population average adjusted RR in BAU scenario.

10: Calculation of the fraction of mortality risk attributable to the exposure in BAU scenario.

11: Calculation of YLL in the absence of exposure.

12: RR for that fraction of population which is exposed only to the reference scenario level (zero or natural background exposure level).

13: Calculation of the population average adjusted RR in different exposure scenarios.

14: Calculation of total YLL for different mortality endpoints in different scenarios.

15: Calculation of YLL attributable to the exposure interest in BAU and Alternative scenarios.

16: If the starting point for the assessment is ”Exposure scenarios” or "Health outcome scenarios" and the mortality effects are defined to be acute (i.e. ERF represents impact on daily instead of annual mortality), then YLL is calculated based on the code on line 13.

17: YLL is calculated by multiplying the age-specific attributable deaths with the loss of life defined for an attributable death at a given age. YLL is further multiplied with age weights and net present value of life years.

18: If the starting point for the assessment is ”Exposure scenarios” or "Health outcome scenarios" and the mortality effects are defined to be chronic (i.e. ERF represents impact on annual mortality), and the approach for YLL calculation is “Life tables” (i.e. YLL is calculated based on the differences in life year projections for different exposure scenarios) then YLL is calculated based on the code on lines 19-22.

19: The modeled life years lived during the assessment follow-up period in different exposure scenarios (5-year age groups and 5-year follow-up time steps).

20: The absolute difference in life years lived in BAU and Alternative scenarios compared to Reference scenario.

21: A table is created, which presents YLL per different time units (average annual, per 5-year period).

22: If the outcome of interest is "Change in EBD" (i.e. change in the environmental burden of disease in the alternative scenario compared to the BAU scenario), then YLL in BAU scenario is deducted from YLL in alternative scenario.

23: If the starting point for the assessment is ”Exposure scenarios” or "Health outcome scenarios", the mortality effects are defined to be chronic (i.e. ERF represents impact on annual mortality), and the approach for YLL calculation is “Attributable deaths” (i.e. YLL is calculated based on the no. of age-specific attributable deaths in different exposure scenarios and age-adjusted life expectancy) then YLL is calculated based on the code on lines 25.

25: YLL is calculated by multiplying the no. of age-specific attributable deaths with the age-adjusted life expectancy in Reference scenario.

Morbidity rate scenarios

Parameter identifier: Morb_rate_scenarios

Total morbidity rate in different exposure scenarios is calculated for those morbidity endpoints for which relative risk (RR) exposure-response function and background morbidity incidence/prevalence data has been provided. Change in the morbidity rate is calculated based on the population attributable fraction (PAF) -method. Morbidity rate in BAU scenario is determined based on the population and morbidity incidence/prevalence input data. However, if the exposure in BAU scenario is defined to change during the assessment follow-up period, the population and morbidity input data only determine the morbidity rate in the first year of the assessment, and any changes in the BAU exposure level in the following years will result in changes in the BAU morbidity rate.

var a:= if Exp_age_class = 'Yes' then Si_pi1(Exposures, 5, Age_cat, age1, Age_help)*5 else Exposures;
var b:= Morbidity_erf;
var c:= Morb_erf_unit;
c:= if c = 0 then 1 else c;
var d:=Pop_frac;
var e:= exp(ln(b[Erf_type='Relative Risk'])/c*a[@Fu_period=1]);
var f:= e[@Fu_period=1];
var g:= ((f*d)+(1-d))[Exposure='Reference'];
var h:=((g*d)+(g*(1-d)))[Exposure='BAU'];
h:=((h-1)/h);
h:= Base_morb_rate-Base_morb_rate*h;
g:=Table(Exposure)(g, g, 1);
f:=(e*d)+(g*(1-d));
h:=f*h;

Code description line-by-line

1: Exposure level in different scenarios. If exposure has been defined age-specifically, then the age interval is changed from 5-year to 1-year.

2: Exposure-response functions for different morbidity endpoints.

3-4: Exposure unit to which the exposure-response function relates to.

5: Fraction of exposed population in different scenarios.

6: Relative risk (RR) exposure-response function is adjusted to the exposure level in the different scenarios.

7: Relative risk adjusted to the exposure level defined for the first year of the assessment.

8: Calculation of the population average adjusted RR in reference scenario.

9: Calculation of the population average adjusted RR in BAU scenario.

10: Calculation of the population attributable fraction (PAF) in BAU scenario.

11: Calculation of the baseline morbidity rate in the theoretical absence of the exposure.

12: Calculation of the adjusted RR for that fraction of population which is exposed only to the reference scenario level (usually no exposure or natural background exposure level).

13: Calculation of the adjusted RR for that fraction of population which is exposed to the exposure level defined for the scenario.

14: Morbidity rate in different scenarios is calculated by multiplying the baseline morbidity rate in the theoretical absence of the exposure by the population average adjusted RR.

Morbidity, specified

Parameter identifier: Ab_morbidity_spec

Calculation of the number of morbidity cases attributable to the exposure or hazard in different scenarios. The attributable morbidity cases are presented for different age groups and 5-year follow-up time steps.

if Assessment_type = 'Exposure scenarios' then
var a:= Exposures;
var b:= Morbidity_erf;
b:= sum(if floor(age1/5)+1 = @age_cat then b else 0, age1)/5;
var c:= Morb_erf_unit;
c:= if c = 0 then 1 else c;
var d:= Pop_frac;
var e:= Morb_rate_scenarios;
e:= sum(if floor(age1/5)+1 = @age_cat then e else 0 , age1)/5;
var f:= b[Erf_type='Absolute Risk']/c*a*d;
var g:=sum(Table(Erf_type)(e,f),erf_type);
g:=g-g[Exposure='Reference'];
g:=g*Pop_in_time_ave;
var h:=Table(Time_unit)(g, g*5);
h:= if followup_time <2 then g else h;
if Outcome= 'Change in EBD' then h[Exposure='Alternative']-h[Exposure='BAU'] else h

Code description line-by-line:

1: If the starting point for the assessment is ”Exposure scenarios”, i.e. the health impacts of an exposure are calculated based on exposure scenarios, exposure-response functions (relative risk or absolute risk), and incidence/prevalence data on mortality/morbidity in the population, then the attributable morbidity cases are calculated based on the code on lines 2-21.

2: Exposure level in different scenarios.

3-4: Exposure-response functions for different morbidity endpoints. If age-specific exposure-response functions are applied in the assessment, the model calculates the average exposure-response function for each 5-year age group based on the input functions defined in 1-year age intervals. It is assumed that the population is distributed evenly within the 5-year age groups.

5-6: Exposure unit to which the exposure-response function relates to.

7: Fraction of exposed population in different scenarios.

8-9. Annual total morbidity rate in different exposure scenarios for those morbidity endpoints for which relative risk (RR) exposure-response functions are applied. The model calculates the average annual morbidity rate for each 5-year age group based on the 1-year age interval mortality rates. It is assumed that the population is distributed evenly within the 5-year age groups.

10: Morbidity risk attributable to the exposure in different scenarios is calculated for those morbidity endpoints for which absolute risk (AR) exposure-response functions have been defined.

11: Morbidity risks for different endpoints is combined to one table.

12: Morbidity risk attributable to the exposure in BAU and Alternative scenarios is calculated by subtracting the total/attributable morbidity risk in the Reference scenario from those in the BAU/Alternative scenarios.

13: Attributable morbidity cases are calculated by multiplying the attributable morbidity risk with the average annual population during each 5-year time step in different scenarios.

14: A table is created, which presents the attributable morbidity cases per different time units(average annual, per 5-year period).

15: If the assessment follow-up time is one year, the results are given in a table without the time unit dimension.

16: If the outcome of interest is "Change in EBD" (i.e. change in the environmental burden of disease in the alternative scenario compared to the BAU scenario), the attributable morbidity cases in BAU scenario are deducted from the attributable morbidity cases in alternative scenario.

YLD, specified

Parameter identifier: Yld_spec

Calculation of the years of life lost due to disease (YLD) for the morbidity endpoints of interest. YLD is presented for different age groups and 5-year follow-up time steps.

if Assessment_type = 'Total burden of disease' then
var a:=Exposures;
var b: Morb_erf_bod;
var c:= Morb_erf_unit;
c:= if c = 0 then 1 else c;
var d:=Pop_frac;
var e:= exp(ln(b)/c*a);
Var f:=((e*d)+(1-d))[Exposure='Reference'];
var g:=((e*d)+(f*(1-d)))[Exposure='BAU'];
g:=(g-1)/g;
g:= As_total_yld-As_total_yld*g;
f:=Table(Exposure)(f, f, 1);
f:=(e*d)+(f*(1-d));
f:=f*g;
f-f[Exposure='Reference']
else
var a:= Ab_morbidity_spec*Duration*Daly_weight*Npv_life_year[period_lt=Fu_period];
if isnan(a)=1 then 0 else a;

Code description line-by-line:

1: If the starting point for the assessment is ”Total burden of disease”, i.e. the health impacts of an exposure are calculated based on exposure scenarios, exposure-response functions, and total burden of disease data for the mortality/morbidity endpoints of interest, then YLD is calculated based on the code on lines 2-11.

2: Exposure level.

3: Exposure-response functions (relative risks) for different morbidity endpoints.

4-5: Exposure unit to which the exposure-response function relates to.

6: Fraction of exposed population.

7: Exposure-response function (relative risk) is adjusted to the exposure level defined for the scenario.

8: Calculation of the population average adjusted RR in reference scenario.

9: Calculation of the population average adjusted RR in BAU scenario.

10: Calculation of the fraction or disability risk attributable to the exposure in BAU scenario.

11: Calculation of YLD in the absence of exposure.

12: RR for that fraction of population which is exposed only to the reference scenario level (zero or natural background exposure level).

13: Calculation of the population average adjusted RR in different exposure scenarios.

14: Calculation of total YLD for different disability endpoints in different scenarios.

15: Calculation of YLD attributable to the exposure of interest in BAU and Alternative scenarios.

16: If the starting point for the assessment is ”Exposure scenarios” or "Health outcome scenarios", then YLD is calculated based on the code on lines 17-18.

17: YLD is calculated by multiplying the no. of attributable morbidity cases with the severity weight and duration defined for the morbidity endpoint. If age-weighting or time discounting is applied, YLD is multiplied with age-specific age-weights and follow-up period -specific time discount factors.