diff --git a/quarto-doc/pkg_doc.html b/quarto-doc/pkg_doc.html index 24205273..e692e9e1 100644 --- a/quarto-doc/pkg_doc.html +++ b/quarto-doc/pkg_doc.html @@ -206,9 +206,9 @@

2 Method: ITHIMTo assess uncertainty, we sample from the ITHIM output by sampling uncertain parameters multiple times and calculating the ITHIM. We specify parametric distributions or sampling strategies for all the uncertain parameters. Evaluating the ITHIM with uncertain parameters allows assessment of their impact on the outcome (AKA sensitivity analysis). We use EVPPI to calculate the expected reduction in uncertainty in the outcome were we to learn a parameter perfectly. This means we can implement models that are basic in their parametrisation, and learn at the end for which parameters it would be worthwhile spending dedicated time learning better.

--++ @@ -221,8 +221,7 @@

2 Method: ITHIM

- + @@ -379,7 +378,7 @@

2 Method: ITHIM

-+ @@ -702,7 +701,7 @@

2 Method: ITHIMModel

- @@ -811,6 +810,7 @@

2.2.3 AP–disease dose–response relative risk

We use each person’s exposure to PM2.5 (\(\check{W}_{i,s}\)) to calculate their relative risk of five diseases (IHD, lung cancer, COPD, stroke, LRI), using curves parametrised by four disease-specific variables [@Burnett2014]. Of the five diseases, two (IHD and stroke) have parameters specific to age groups starting at age 25.2 The other three (lung cancer, LRI and COPD) have one set of parameters for all ages.

  • 2 For any person of age lower than 25, we set the relative risk to 1.

    • +

    The curves are in the form of samples of the set of four parameters. We model the densities of these samples (using a quantile for parameter 3, kernel density estimation for parameter 2, and GAMs for parameters 1 and 4)3 in order to draw either the median or random samples via their quantiles (\(\xi_{h,w}\)) as follows:

  • 3 The four parameters refer, in numerical order, to \(\alpha, \beta, \gamma\) and tmrel in @Burnett2014.

    • \[\begin{aligned} \tilde{H}_{a,h,w=3}=&\text{CDF}_{H_{a,h,w=3}}^{-1}(\xi_{h,w=3})\\ @@ -960,11 +960,11 @@

    6 Dose–response

    a Age group15–69
    -(five years age group)    		15–69 (five years age group)
    g
    \(\lambda_{m\not\in\text{wal +\(\lambda_{m\not\in\text{wal k,cyc.}}\) In-vehicle MET surplus 0
    -+ - + @@ -977,9 +977,9 @@

    6 Dose–response

    - - - + + +
    [100 samples from AP dose–response curves] (cvd_strokeDR-sim.pdf){width=“40%”}
    diff --git a/quarto-doc/pkg_doc.qmd b/quarto-doc/pkg_doc.qmd index 314c8f67..41dae1d4 100644 --- a/quarto-doc/pkg_doc.qmd +++ b/quarto-doc/pkg_doc.qmd @@ -42,42 +42,39 @@ We calculate the ITHIM by combining the modules' outputs in terms of the health To assess uncertainty, we sample from the ITHIM output by sampling uncertain parameters multiple times and calculating the ITHIM. We specify parametric distributions or sampling strategies for all the uncertain parameters. Evaluating the ITHIM with uncertain parameters allows assessment of their impact on the outcome (AKA sensitivity analysis). We use EVPPI to calculate the expected reduction in uncertainty in the outcome were we to learn a parameter perfectly. This means we can implement models that are basic in their parametrisation, and learn at the end for which parameters it would be worthwhile spending dedicated time learning better. -+-------+----------------------+----------------------+ -| Label | Name | Levels | -+=======+======================+======================+ -| *a* | Age group | 15--69\ | -| | | (five years age | -| | group) | -| | | -+-------+----------------------+----------------------+ -| *g* | | Male\ | -| | | Female | -+-------+----------------------+----------------------+ -| *h* | Disease | | -+-------+----------------------+----------------------+ -| *i* | Individual index | | -+-------+----------------------+----------------------+ -| *j* | Trip index | | -+-------+----------------------+----------------------+ -| *m* | Transport mode | walk\ | -| | | cycling (cyc.)\ | -| | | bus\ | -| | | car\ | -| | | motorbike (mot.)\ | -| | | goods vehicles (GV)\ | -| | | subway (sub.) | -+-------+----------------------+----------------------+ -| *o* | Outcome | Death\ | -| | | YLL | -+-------+----------------------+----------------------+ -| *s* | Scenario | 3 | -+-------+----------------------+----------------------+ -| *w* | AP RR hyperparameter | 1, 2, 3, 4 | -+-------+----------------------+----------------------+ -| *x* | PA RR hyperparameter | 1, 2, 3 | -+-------+----------------------+----------------------+ -| *z* | PA dose | | -+-------+----------------------+----------------------+ ++-------------+----------------------+-------------------------------+ +| Label | Name | Levels | ++=============+======================+===============================+ +| *a* | Age group | 15--69 (five years age group) | ++-------------+----------------------+-------------------------------+ +| *g* | | Male\ | +| | | Female | ++-------------+----------------------+-------------------------------+ +| *h* | Disease | | ++-------------+----------------------+-------------------------------+ +| *i* | Individual index | | ++-------------+----------------------+-------------------------------+ +| *j* | Trip index | | ++-------------+----------------------+-------------------------------+ +| *m* | Transport mode | walk\ | +| | | cycling (cyc.)\ | +| | | bus\ | +| | | car\ | +| | | motorbike (mot.)\ | +| | | goods vehicles (GV)\ | +| | | subway (sub.) | ++-------------+----------------------+-------------------------------+ +| *o* | Outcome | Death\ | +| | | YLL | ++-------------+----------------------+-------------------------------+ +| *s* | Scenario | 3 | ++-------------+----------------------+-------------------------------+ +| *w* | AP RR hyperparameter | 1, 2, 3, 4 | ++-------------+----------------------+-------------------------------+ +| *x* | PA RR hyperparameter | 1, 2, 3 | ++-------------+----------------------+-------------------------------+ +| *z* | PA dose | | ++-------------+----------------------+-------------------------------+ | Abbreviation | Meaning | |:-------------|:----------------------------------------------| @@ -109,57 +106,106 @@ To assess uncertainty, we sample from the ITHIM output by sampling uncertain par {#inputs} -| \[\[inputs\]\]{label= "inputs"} | | *ITHIM-R reference* | | | -|:-----------------------------------------------|-----------------------------------------------------------------|:-----------------------------------|-------------------------------|--------------------| -| **Name** | **Description** | **Value in Accra model** | **Label** | **Model/ Setting** | -| *Global values* | | | | | -| $U_ { a,g,h,o}$ | Background burden of disease | Constant | GBD_DATA | Setting | -| $N_{a,g}$ | Population by age and gender in GBD_DATA | Constant | GBD_DATA | Setting | -| $\bar { N}_{a,g}$ | Population by age and gender | Constant | DEMOGRAPHIC | Setting | -| $\rho_h$ | Chronic disease scalar | 1 or Lnorm(0,0.18) | CHRONIC_DISEASE_SCALAR | Setting | -| *Travel values* | | | | | -| $Z _ {m=walk}$ | Walk speed | 4.8 | MODE_SPEEDS | Setting | -| $Z _ {m=cyc.}$ | Cycle speed | 14.5 | MODE_SPEEDS | Setting | -| $Z _ {m=bus}$ | Bus speed | 15 | MODE_SPEEDS | Setting | -| $Z _ {m=car}$ | Car speed | 21 | MODE_SPEEDS | Setting | -| $Z _ {m=mot.}$ | Motorbike speed | 25 | MODE_SPEEDS | Setting | -| \$\\epsilon \$ | Walk time to bus | 5 or Lnorm(log (5),0.18) | BUS_WALK_TIME | Setting | -| $\mu_{m=HGV}$ | Truck distance relative to car | 0.21 or Beta(3,10) | TRUCK_TO\_ CAR_RATIO | Setting | -| $\mu_{m=bus}$ | Bus driver distance relative to bus passenger distance | 1/45 or Bet a(20,600) \| | BUS_TO_PASSENGER_RATIO | Setting | -| $\mu_ {m=mot.}$ | Motorcycle fleet distance relative to total motorcycle distance | 37/68 or Beta(37/3+ 1,31/3+1) \| | FLEET_TO_MOTORCYCLE_RATIO | Setting | -| $T_j$ | Trip-level data | Constant | SYNTHETIC_TRIPS | Setting | -| *Injury model values* | | | | | -| $I _ {a,g,m_{\ text{vi c} },m_{\text{str}}}$ | Fatalities table | Constant | INJURY_TABLE | Setting | -| $\sigma$ | Injury reporting rate | 1 or Beta(8,3) | INJURY_REPORTING_RATE | Setting | -| $\omega$ | Sum of distance exponents | 1.9 or Lnorm(l og(1.9),l og(1.03)) | SIN_EXPONENT_SUM | Model | -| $\psi$ | Casualty fraction of $\omega$ | 0.5 or Beta(20,20) \| | CASUALTY_EXPONENT_FRACTION | Model | -| *Pollution model values* | | | | | -| $\eta$ | Background PM2.5 concentration | 50 or Lnorm(log( 50),0.18) \| | PM_CONC_BASE | Setting | -| $\zeta$ | Fraction of measured PM2.5 concentration due to road transport | 0.225 or Beta(5,20) \| | PM_TRANS_SHARE | Setting | -| $\ g amma_{m}$ | Vehicle emission inventory | Constant or Dirichlet | EMISSION_INVENTORY | Setting | -| $P$ | Vehicle emission confidence | 1 | EMISSION_INVENTORY_CONFIDENCE | Setting | -| *Pollution & health model values* | | | | | -| $C_1$ | Base-level inhalation rate | 1 | BASE_LEVEL_INHALATION_RATE | Model | -| $C_2$ | Exposure ratio window closed | 0.5 | CLOSED_WINDOW_PM\_ RATIO | Model | -| $C_3$ | Proportion of travel with closed windows | 0.5 | C LOSED_WIN DOW_RATIO | Setting | -| $C_4$ | Parameter for on-road PM2.5 level | 3.216 | ROAD\_ RATIO_MAX | Model | -| $C_5$ | Parameter for on-road PM2.5 level | 0.379 | ROAD_RA TIO_SLOPE | Model | -| $C_6$ | Exposure ratio for underground | 0.8 | SUBWAY \_PM_RATIO | Setting | -| \$ H \_{a,h,w}\$ | AP dose- -res ponse--curve parameters | Constant | DR_AP | Model | -| $\ xi_{h,w}$ | Quantiles for AP RR functions | 0.5 or Unif(0,1) | AP_DOSE_R ESPONSE\_ QUANTILE | Model | -| *Physical activity model values* | | | | | -| $\chi$ | Day-to-week travel scalar | 7 or 7 $\times$Beta(20,3) | DAY_TO_WEEK_TRAVEL_SCALAR | Model | -| $Y_i$ | Individual n on-transport MMETs | Constant | PA_SET\$ work_ltpa \_marg_met | Setting | -| $\theta$ | Background PA scalar | 1 or Lnorm(0,0.18) | BACKGROUND\_ PA_SCALAR | Setting | -| $\ tilde{Y}$ | Confidence in PA survey | 1 | BACKGROUND_PA_C ONFIDENCE | Setting | -| $\tilde {\theta}$ | Background PA zeros quantile | 0.5 or Unif(0,1) | BACKGROUND \_PA_ZEROS | Setting | -| $\lambda_{m=\text{cyc.}}$ | Cycling MET surplus | 4.63 or Lnorm(log (4.63),1) | MMET_CYCLING | Model | -| $\lambda_{m=\text{walk}}$ | Walking MET surplus | 2.53 or Lnorm(log (2.53),1) | MMET_WALKING | Model | -| $\lambda_{m\not\in\text{wal - k,cyc.}}$ | In-vehicle MET surplus | 0 | | Model | -| *Physical activity & health model values* | | | | | -| \$\\G\_{h,x,z}\$ | Look-up table for relative risk truncated normal distribution | Constant | | Model | -| \$\phi\_{h}\$ | Quantiles for PA RR functions | 0.5 or Unif(0,1) | PA_DOSE_RESPONSE_QUANTILE | Model | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| \[\[inputs\]\]{label= "inputs"} | | *ITHIM-R reference* | | | ++:================================================+=================================================================+:===================================+===============================+====================+ +| **Name** | **Description** | **Value in Accra model** | **Label** | **Model/ Setting** | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| *Global values* | | | | | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| $U_ { a,g,h,o}$ | Background burden of disease | Constant | GBD_DATA | Setting | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| $N_{a,g}$ | Population by age and gender in GBD_DATA | Constant | GBD_DATA | Setting | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| $\bar { N}_{a,g}$ | Population by age and gender | Constant | DEMOGRAPHIC | Setting | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| $\rho_h$ | Chronic disease scalar | 1 or Lnorm(0,0.18) | CHRONIC_DISEASE_SCALAR | Setting | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| *Travel values* | | | | | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| $Z _ {m=walk}$ | Walk speed | 4.8 | MODE_SPEEDS | Setting | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| $Z _ {m=cyc.}$ | Cycle speed | 14.5 | MODE_SPEEDS | Setting | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| $Z _ {m=bus}$ | Bus speed | 15 | MODE_SPEEDS | Setting | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| $Z _ {m=car}$ | Car speed | 21 | MODE_SPEEDS | Setting | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| $Z _ {m=mot.}$ | Motorbike speed | 25 | MODE_SPEEDS | Setting | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| \$\\epsilon \$ | Walk time to bus | 5 or Lnorm(log (5),0.18) | BUS_WALK_TIME | Setting | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| $\mu_{m=HGV}$ | Truck distance relative to car | 0.21 or Beta(3,10) | TRUCK_TO\_ CAR_RATIO | Setting | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| $\mu_{m=bus}$ | Bus driver distance relative to bus passenger distance | 1/45 or Bet a(20,600) \| | BUS_TO_PASSENGER_RATIO | Setting | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| $\mu_ {m=mot.}$ | Motorcycle fleet distance relative to total motorcycle distance | 37/68 or Beta(37/3+ 1,31/3+1) \| | FLEET_TO_MOTORCYCLE_RATIO | Setting | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| $T_j$ | Trip-level data | Constant | SYNTHETIC_TRIPS | Setting | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| *Injury model values* | | | | | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| $I _ {a,g,m_{\ text{vi c} },m_{\text{str}}}$ | Fatalities table | Constant | INJURY_TABLE | Setting | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| $\sigma$ | Injury reporting rate | 1 or Beta(8,3) | INJURY_REPORTING_RATE | Setting | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| $\omega$ | Sum of distance exponents | 1.9 or Lnorm(l og(1.9),l og(1.03)) | SIN_EXPONENT_SUM | Model | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| $\psi$ | Casualty fraction of $\omega$ | 0.5 or Beta(20,20) \| | CASUALTY_EXPONENT_FRACTION | Model | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| *Pollution model values* | | | | | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| $\eta$ | Background PM2.5 concentration | 50 or Lnorm(log( 50),0.18) \| | PM_CONC_BASE | Setting | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| $\zeta$ | Fraction of measured PM2.5 concentration due to road transport | 0.225 or Beta(5,20) \| | PM_TRANS_SHARE | Setting | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| $\ g amma_{m}$ | Vehicle emission inventory | Constant or Dirichlet | EMISSION_INVENTORY | Setting | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| $P$ | Vehicle emission confidence | 1 | EMISSION_INVENTORY_CONFIDENCE | Setting | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| *Pollution & health model values* | | | | | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| $C_1$ | Base-level inhalation rate | 1 | BASE_LEVEL_INHALATION_RATE | Model | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| $C_2$ | Exposure ratio window closed | 0.5 | CLOSED_WINDOW_PM\_ RATIO | Model | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| $C_3$ | Proportion of travel with closed windows | 0.5 | C LOSED_WIN DOW_RATIO | Setting | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| $C_4$ | Parameter for on-road PM2.5 level | 3.216 | ROAD\_ RATIO_MAX | Model | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| $C_5$ | Parameter for on-road PM2.5 level | 0.379 | ROAD_RA TIO_SLOPE | Model | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| $C_6$ | Exposure ratio for underground | 0.8 | SUBWAY \_PM_RATIO | Setting | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| \$ H \_{a,h,w}\$ | AP dose- -res ponse--curve parameters | Constant | DR_AP | Model | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| $\ xi_{h,w}$ | Quantiles for AP RR functions | 0.5 or Unif(0,1) | AP_DOSE_R ESPONSE\_ QUANTILE | Model | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| *Physical activity model values* | | | | | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| $\chi$ | Day-to-week travel scalar | 7 or 7 $\times$Beta(20,3) | DAY_TO_WEEK_TRAVEL_SCALAR | Model | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| $Y_i$ | Individual n on-transport MMETs | Constant | PA_SET\$ work_ltpa \_marg_met | Setting | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| $\theta$ | Background PA scalar | 1 or Lnorm(0,0.18) | BACKGROUND\_ PA_SCALAR | Setting | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| $\ tilde{Y}$ | Confidence in PA survey | 1 | BACKGROUND_PA_C ONFIDENCE | Setting | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| $\tilde {\theta}$ | Background PA zeros quantile | 0.5 or Unif(0,1) | BACKGROUND \_PA_ZEROS | Setting | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| $\lambda_{m=\text{cyc.}}$ | Cycling MET surplus | 4.63 or Lnorm(log (4.63),1) | MMET_CYCLING | Model | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| $\lambda_{m=\text{walk}}$ | Walking MET surplus | 2.53 or Lnorm(log (2.53),1) | MMET_WALKING | Model | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| $\lambda_{m\not\in\text{wal | In-vehicle MET surplus | 0 | | Model | +| k,cyc.}}$ | | | | | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| *Physical activity & health model values* | | | | | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| \$\\G\_{h,x,z}\$ | Look-up table for relative risk truncated normal distribution | Constant | | Model | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ +| \$\phi\_{h}\$ | Quantiles for PA RR functions | 0.5 or Unif(0,1) | PA_DOSE_RESPONSE_QUANTILE | Model | ++-------------------------------------------------+-----------------------------------------------------------------+------------------------------------+-------------------------------+--------------------+ ## Data module {#data} @@ -173,7 +219,7 @@ We create a "synthetic population" by matching individuals surveyed for travel t we could create a synthetic population as described in Appendix [8.3](#synthpop){reference-type="ref" reference="synthpop"}, which allows uncertainty in the propensity to travel. This method operates with person-level, rather than trip-level, information. -### Scenarios +### Scenarios {#scenarios} From the synthetic population we create "scenarios" of different pictures of travel by changing certain trips (e.g. swapping the mode of travel for particular trips and/or particular people). For the purposes of illustration, we have created three scenarios mentioned in the table @tbl-scen-specs, where each mode such as `cycle` has propensities in three different distance categories: `0-2 km`, `2-6 km` and `6+ km`. What the scenario does that in each of those distance categories, it increases the current mode share by the propensities. So for instance, if in a city the baseline mode share of `cycle` is `10` percent for short trips (`0-2 km`), then in the `cycle` scenario, it increases upto 15.6 (10 + 5.6). @@ -219,11 +265,11 @@ Ventilation rates are calculated for each mode, assuming a base-level inhalation ### AP--disease dose--response relative risk -We use each person's exposure to PM2.5 ($\check{W}_{i,s}$) to calculate their relative risk of five diseases (IHD, lung cancer, COPD, stroke, LRI), using curves parametrised by four disease-specific variables [@Burnett2014]. Of the five diseases, two (IHD and stroke) have parameters specific to age groups starting at age 25.[^2] The other three (lung cancer, LRI and COPD) have one set of parameters for all ages. +We use each person's exposure to PM2.5 ($\check{W}_{i,s}$) to calculate their relative risk of seven causes/diseases (all-cause mortality, IHD, stroke, COPD, LRI, Lung cancer and Type 2 Diabetes (T2D)). These diseases operate in three levels. The Level 1 is for all-cause mortality. The Level 2 combines IHD and stroke to CHD, and COPD, LRI, Lung cancer and T2D as respiratory disease mortality, and then in level 3, we have all diseases separately. Of the five diseases, two (IHD and stroke) have parameters specific to age groups starting at age 25.[^2] The other three (lung cancer, LRI and COPD) have one set of parameters for all ages. [^2]: For any person of age lower than 25, we set the relative risk to 1. -The curves are in the form of samples of the set of four parameters. We model the densities of these samples (using a quantile for parameter 3, kernel density estimation for parameter 2, and GAMs for parameters 1 and 4)[^3] in order to draw either the median or random samples via their quantiles ($\xi_{h,w}$) as follows: +![AP disease levels](images/ap-levels-min.png)The curves are in the form of samples of the set of four parameters. We model the densities of these samples (using a quantile for parameter 3, kernel density estimation for parameter 2, and GAMs for parameters 1 and 4)[^3] in order to draw either the median or random samples via their quantiles ($\xi_{h,w}$) as follows: [^3]: The four parameters refer, in numerical order, to $\alpha, \beta, \gamma$ and tmrel in @Burnett2014. @@ -399,13 +445,13 @@ The objective of learning the value of information formulated in this way is to (){#PADR width="90%"} -| | | -|:----------------------------------------------------------------------------------:|:---------------------------------------------------------------------------------:| ++:----------------------------------------------------------------------------------:+:---------------------------------------------------------------------------------:+ | ![100 samples from AP dose--response curves](cvd_ihdDR-sim.pdf){#APDR width="40%"} | \[100 samples from AP dose--response curves\] (cvd_strokeDR-sim.pdf){width="40%"} | ++------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------+ -| | | | -|:-----------------------------------------------------------------:|:------------------------------------------------------------:|:------------------------------------------------------------------:| ++:-----------------------------------------------------------------:+:------------------------------------------------------------:+:------------------------------------------------------------------:+ | ![100 samples from AP dose--response curv es](neo_lungDR-sim.pdf) | ![100 samples from AP dose--response c urves](lriDR-sim.pdf) | ![100 samples from AP dose--response curve s](resp_copdDR-sim.pdf) | ++-------------------------------------------------------------------+--------------------------------------------------------------+--------------------------------------------------------------------+ ::: landscape \# Tabulated ITHIM equations {#tableequations}