**Pooled Bayesian Analysis ** **Pooled Bayesian Analysis **

**of 28 Studies on Radon Induced ** **of 28 Studies on Radon Induced **

**Lung Cancers** **Lung Cancers**

### Krzysztof Wojciech Fornalski, M.

### Krzysztof Wojciech Fornalski, M.Sc Sc., ., Eng Eng. .

### The The Andrzej So Andrzej So łtan ł tan Institute

### Institute for Nuclear for Nuclear Studies Studies Ś Ś wierk, wierk, Poland Poland

### Krzysztof W. Fornalski, Ludwik Dobrzy _{ń} ski

_{ń}

### Krzysztof W. Fornalski

### Krzysztof W. Fornalski 2 2

### Overview Overview

### Bayesian Bayesian analysis analysis

### Curve Curve fitting fitting

### Model Model selection selection

### Radon Radon

### Doses Doses from from radon radon

### 28 28 papers papers

### Results Results

### Bayesian

### Bayesian analysis analysis

### methodology

### methodology

### Krzysztof W. Fornalski

### Krzysztof W. Fornalski 4 4

### Curve

### Curve fitting fitting

### Bayesian Bayesian analysis analysis can can be be used used for for fitting fitting any any function function to to experimental experimental points points

### A A probability probability of of getting getting given given point: point:

### The The algorithm algorithm is is insensitive insensitive to to outliers outliers

### ( ) ^{exp} [ ^{(} ^{)} ^{/(} ^{2} ^{)} ] ^{(} ^{)}

### 2

### 1 _{2} _{2}

### σ σ σ

### σ π ^{T} ^{E} ^{p}

^{T}

^{E}

^{p}

*E*

*P* = − − ( ) ^{0} _{2}

### σ

### σ = σ

*p*

### Krzysztof W. Fornalski

### Krzysztof W. Fornalski 6 6

### Model

### Model selection selection

### Let Let two two alternative alternative models models fit well fit well to to the the same set

### same set of of experimental experimental points points

### Which Which of of the the models models has has higher higher reliability reliability ? ?

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### = *k*

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### 1 ( )

### ) ( min )

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### 2 2

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### ) exp (

### ) 1 (

### 1

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### ) 1 (

### 1

### π σ

### π σ

### σ

### σ

### Krzysztof W. Fornalski

### Krzysztof W. Fornalski 8 8

### Ockham

### Ockham ’ ’ s s razor razor

### Model

### Model selection selection in in bayesian bayesian approach approach is is always

### always giving giving preference preference to to simpler simpler models

### models , i.e. , i.e. the the ones ones with with a a fewer fewer number number

### of of parameters parameters

### Radon Radon

### the the data data

### Doses Doses

### Radon Radon concentration concentration : : Bq Bq /m /m ^{3} ^{3}

### Efective Efective dose dose from from radon: radon:

### 1 1 Bq Bq /m /m ^{3 } ^{3 } = 0.179 = 0.179 mSv mSv / / year year

### source

### source: : (UNSCEAR 2006, Annex E, Table 25) (UNSCEAR 2006, Annex E, Table 25)

### Two Two analysed analysed low low dose dose ranges ranges : :

### Up Up to 70 to 70 mSv mSv / / year year (391 (391 Bq Bq /m /m ^{3} ^{3} ) )

### Up Up to 150 to 150 mSv/ mSv /year year (838 (838 Bq Bq /m /m ^{3} ^{3} ) )

### Krzysztof W. Fornalski

### Krzysztof W. Fornalski 12 12

### Points

### Points from from all all 28 28 studies studies

### Uncertainties not shown in order to keep the readability!

### However, the scatter of points shows their real values.

### Results

### Results

### Krzysztof W. Fornalski

### Krzysztof W. Fornalski 14 14

### Results Results

### 7 7 mathematical mathematical models models were were tested tested

### Groups Groups of of data: data:

### up up to 70 to 70 and and 150 150 mSv mSv / / year year

### with with and and without without Cohen Cohen ’ ’ s s and and miners miners ’ ’ data data

### Model Model selection selection algorith algorith was was used used to to compare

### compare each each of of the the models models and and select select

### the the best best one one

### Models

### Models used used

### * * Model 1 Model 1 – – RR = 1 RR = 1 , ,

### * * Model 2 Model 2 – – RR = a RR = a , where , where a a denotes a constant to be fitted, denotes a constant to be fitted,

### * * Model 3 Model 3 – – RR = a + bD RR = a + bD , where , where a a and and b b are fitting are fitting parameters, and

### parameters, and D D denotes the annual dose, denotes the annual dose ,

### * * Model 4 Model 4 – – RR = 1 + bD RR = 1 + bD , differs from , differs from Model 3 Model 3 by setting the by setting the parameter

### parameter a a to 1, to 1,

### * * Model 5 Model 5 – – same as same as Model 4 Model 4 but with the parameter but with the parameter b b

### constrained to the positive values (

### constrained to the positive values ( LNT model LNT model ), ),

### * * Model 6 Model 6 – – RR = a +bD + cD RR = a +bD + cD ^{2} ^{2} with a, b and c being fitting with a, b and c being fitting parameters,

### parameters,

### * * Model 7 Model 7 - - RR = 1 +bD + cD RR = 1 +bD + cD ^{2} ^{2} , , i.e. same as i.e. same as Model 6 Model 6 but with but with the parameter

### the parameter a a set to set to 1. 1 .

### Krzysztof W. Fornalski

### Krzysztof W. Fornalski 16 16

### Results

### Results #1 #1

### Linear Linear models models in in the the dose dose range range up up to 150 to 150 mSv/y mSv /y result

### result in in RR RR decreasing decreasing with with increasing increasing dose dose ( ( also also when when Cohen Cohen ’ ’ s s and and miners miners ’ ’ data data are are excluded excluded ) )

### In In the the narrower narrower range range , , up up to 70 to 70 mSv mSv / / year year , , when when Cohen

### Cohen ’ ’ s s and and miners miners ’ ’ data data are are excluded excluded , , the the linear linear models

### models exhibit exhibit statistically statistically insignificant insignificant increase increase

### Quadratic Quadratic models models result result in in hormetic hormetic effect effect

### However However , , when when Cohen Cohen ’s ’ s and and miners miners ’ ’ data are data are excluded

### excluded one arrives one arrives at at inverted inverted parabola. parabola. This This shows

### shows the the sensitivity sensitivity of of the the parabolic parabolic dependence dependence

### on on the the chosen chosen data set. data set.

### Results

### Results #2 #2

### The The most most likely likely is is Model 1, Model 1, where where RR = 1

### RR = 1 in in the the whole whole studied studied range range of of doses

### doses

### The The second second are are LNT LNT and and other other linear linear models

### models . . They They are are , , however however about about two two order

### order s s of of magnitude magnitude less less likely likely than than the the Model 1

### Model 1

### Quadratic Quadratic models models are are least least likely likely

### Krzysztof W. Fornalski

### Krzysztof W. Fornalski 18 18

### Conclusions Conclusions

### 7 7 models models were were tested tested in in the the analysis analysis of of the the radon data

### radon data coming coming from from 28 28 studies studies

### The The bayesian bayesian methods methods of of statistical statistical analysis analysis were were used used

### The The most most likely likely model model is is dose dose - - independent one independent one ( ( below below 150 mSv 150 mSv/ / year year ) )

### The The data data give give no no base base to to claim claim that that radon radon bears bears

### a a risk risk to to health health , , at at least least in in this this range range of of doses doses

## Thank

## Thank you you ! !

### krzysztof krzysztof .fornalski@ .fornalski@ gmail gmail . . com com

### Krzysztof W. Fornalski

### Krzysztof W. Fornalski 20 20

### Data

### Data from from 28 28 studies studies (#1) (#1)

**Country/region/group** **Source** **Comment**

### Austria Oberaigner et al, 2002 b

### Canada, Winnipeg Letourneau et al., 1994 a

### China, Gansu Wang et al., 2002 c

### China, Shenyang Blot et al., 1990 a, c

### Czech Rep. Tomášek et al., 2001 b

### England, south-west Darby et al., 1998 b

### Finland I Auvinen et al., 1996 a, b

### Finland II Ruosteenoja, 1991 a

### Finland III Ruosteenoja et al., 1996 b

### a – paper is a part of 8 pooled studies, which were analyzed by (Lubin et al., 1997b; UNSCEAR, 2000)

### b – paper is a part of 13 pooled European studies, which were analyzed by (Darby et al., 2004; UNSCEAR, 2006) c – paper is a part of pooled Chinese studies, which were analyzed by (Lubin et al., 2004)

### d – paper contains only cancer mortalities, not all incidences

### Data

### Data from from 28 28 studies studies (#2) (#2)

### a – paper is a part of 8 pooled studies, which were analyzed by (Lubin et al., 1997b; UNSCEAR, 2000)

**Country/region/group** **Source** **Comment**

### France Baysson et al., 2004 b

### Germany Wichmann et al., 2005 b

### Germany, Saxony Conrady & Martin, 1996 cited in Becker, 2003

### Germany, Schneeberg Conrady et al., 2002

### Germany, western Kreienbrock et al., 2001 b

### Italy, Mediterranean Bochicchio et al., 2005 b

### Italy, Alps Pisa et al., 2001

### Japan, Misasa Sobue et al., 2000

### Uranium miners Lubin et al., 1997a cited in UNSCEAR, 2000 d

### Spain Barros-Dios et al., 2002 b

### Krzysztof W. Fornalski

### Krzysztof W. Fornalski 22 22

### Data

### Data from from 28 28 studies studies (#3) (#3)

### a – paper is a part of 8 pooled studies, which were analyzed by (Lubin et al., 1997b; UNSCEAR, 2000)

### b – paper is a part of 13 pooled European studies, which were analyzed by (Darby et al., 2004; UNSCEAR, 2006) c – paper is a part of pooled Chinese studies, which were analyzed by (Lubin et al., 2004)

### d – paper contains only cancer mortalities, not all incidences

**Country/region/group** **Source** **Comment**

### Sweden I Lagarde et al., 2001 b

### Sweden II Pershagen et al., 1992 a, b

### Sweden III Pershagen et al., 1994 a, b

### USA Cohen, 1995 d

### USA, Iowa Field et al., 2000

### USA, Missouri I Alavanja et al., 1994 a

### USA, Missouri II Alavanja et al., 1999

### USA, New Jersey Schoenberg et al., 1990 a

### USA, Worcester Thompson et al., 2008

### UNSCEAR 2000

### UNSCEAR 2000

### Krzysztof W. Fornalski

### Krzysztof W. Fornalski 24 24

### 8 8 studies studies

### Selected

### Selected W W _{m} _{m} values _{values}

### M1/M2 = 400 M1/M2 = 400

### M1/M5 = 100 M1/M5 = 100

### M1/M6 = 1200 M1/M6 = 1200

### Krzysztof W. Fornalski

### Krzysztof W. Fornalski 26 26

### Results of pooled Bayesian analysis of 28 radon studies up to 150 mSv (838 Bq m

^{-3}

### ) per year.

**Type of data** **Model 2**

**(Constant)**

**Model 3**
**(Linear 1)**

**Model 4**
**(Linear 2)**

**Model 6**
**(Quadratic 1)**

**Model 7**
**(Quadratic 2)**

**Original data – set 1**

major data* a = 0.976 ± 0.003

a = 0.988 ± 0.005
b = (-7.3 ± 3.0) · 10^{-}

4

a = 1 b = (-10.2 ± 1.6) ·

10^{-4}

a = 1.031 ± 0.002
b = (-4.4 ± 0.2) · 10^{-3}

c = (0.3 ± 0.1) · 10^{-4}

a = 1
b = (-2.4 ± 0.2) · 10^{-3}

c = (0.1 ± 0.1) · 10^{-4}

plus reference points^{x} a = 0.988 ± 0.003

a = 0.998 ± 0.005
b = (-8.5 ± 3.8) · 10^{-}

4

a = 1
b = (-9.1 ± 2.1) · 10^{-4}

a = 1.018 ± 0.003
b = (-3.1 ± 0.2) · 10^{-3}

c = (0.2 ± 0.1) · 10^{-4}

a = 1
b = (-1.8 ± 0.2) · 10^{-3}

c = (0.1 ± 0.1) · 10^{-4}

without Cohen’s and

miners’ data^{y} a = 1.060 ± 0.028

a = 1.069 ± 0.056
b = (-3.4 ± 5.1) · 10^{-}

4

a = 1
b = (10.6 ± 2.1) · 10^{-}

4

a = 0.932 ± 0.037
b = (8.5 ± 1.4) · 10^{-3}
c = (-0.6 ± 0.2) · 10^{-4}

a = 1
b = (5.5 ± 1.1) · 10^{-3}
c = (-0.4 ± 0.2) · 10^{-4}
**Partly pooled data**^{z}**– set 2**

major data^{z} a = 0.981 ± 0.003

a = 0.998 ± 0.005 b = (-10.5 ± 3.7) ·

10^{-4}

a = 1 b = (-11.0 ± 2.1) ·

10^{-4}

a = 1.053 ± 0.003
b = (-5.9 ± 0.2) · 10^{-3}

c = (0.4 ± 0.1) · 10^{-4}

a = 1
b = (-2.2 ± 0.2) · 10^{-3}

c = (0.1 ± 0.1) · 10^{-4}

plus reference

points^{x} a = 0.982 ± 0.003

a = 1.000 ± 0.005 b = (-12.0 ± 3.4) ·

10^{-4}

a = 1 b = (-12.1 ± 2.0) ·

10^{-4}

a = 1.050 ± 0.003
b = (-5.9 ± 0.2) · 10^{-3}

c = (0.4 ± 0.1) · 10^{-4}

a = 1
b = (-2.4 ± 0.2) · 10^{-3}

c = (0.1 ± 0.1) · 10^{-4}

without Cohen’s and

miners’ data^{y} a = 1.060 ± 0.023

a = 1.074 ± 0.033
b = (-5.6 ± 4.3) · 10^{-}

4

a = 1
b = (8.6 ± 2.1) · 10^{-4}

a = 0.975 ± 0.030
b = (6.8 ± 1.3) · 10^{-3}
c = (-0.5 ± 0.3) · 10^{-4}

a = 1
b = (5.6 ± 1.1) · 10^{-3}
c = (-0.4 ± 0.3) · 10^{-4}

### * - data as in Fig. 1

### x – reference points set as RR = 1 for the lowest doses

### y – Cohen’s data (Cohen, 1995) and miner’s data (Lubin et al., 1997a; UNSCEAR, 2000) contains only cancer mortalities

### z – papers labeled “13 European studies”, “8 studies” and “Chinese studies” are substituted with pooled studies of (Darby et al., 2004; Lubin et

### al., 1997b, 2004; UNSCEAR, 2000, 2006)

### Results of pooled Bayesian analysis of 28 radon studies up to 70 mSv per year (391 Bq m

^{-3}

### ).

**Type of data** **Model 2**

**(constant)**

**Model 3**
**(Linear 1)**

**Model 4**
**(Linear 2)**

**Model 6**
**(quadratic 1)**

**Model 7**
**(quadratic 2)**

**Original data – set 1**

major data* a = 0.976 ± 0.003

a = 1.014 ± 0.005
b = (-26.8 ± 2.9) · 10^{-}

4

a = 1
b = (-19.9 ± 1.5) · 10^{-}

4

a = 1.180 ± 0.004
b = (-23.9 ± 0.3) · 10^{-3}

c = (4.7 ± 0.2) · 10^{-4}

a = 1
b = (-6.6 ± 0.2) · 10^{-3}

c = (1.5 ± 0.1) · 10^{-4}

without Cohen’s

and miners’ data^{x} a = 1.065 ± 0.045

a = 0.985 ± 0.146
b = (38.1 ± 40.8) · 10^{-}

4

a = 1
b = (33.2 ± 12.8) · 10^{-}

4

a = 0.931 ± 0.038
b = (9.3 ± 1.3) · 10^{-3}
c = (-0.9 ± 0.4) · 10^{-4}

a = 1
b = (3.4 ± 1.3) · 10^{-3}
c = (-0.1 ± 0.4) · 10^{-4}

**Partly pooled data**^{y}**– set 2**

major data a = 0.981 ± 0.003

a = 1.036 ± 0.005
b = (-40.0 ± 3.8) · 10^{-}

4

a = 1
b = (-19.8 ± 2.2) · 10^{-}

4

a = 1.176 ± 0.004
b = (-22.1 ± 0.4) · 10^{-3}

c = (4.1 ± 0.2) · 10^{-4}

a = 1
b = (-5.0 ± 0.3) · 10^{-3}

c = (1.1 ± 0.2) · 10^{-4}

without Cohen’s

and miners’ data^{x} a = 1.066 ± 0.028

a = 1.019 ± 0.116
b = (25.3 ± 40.7) · 10^{-}

4

a = 1
b = (31.7 ± 11.9) · 10^{-}

4

a = 1.011 ± 0.034
b = (3.4 ± 1.2) · 10^{-3}
c = (-0.1 ± 0.4) · 10^{-4}

a = 1
b = (4.4 ± 1.2) · 10^{-3}
c = (-0.3 ± 0.4) · 10^{-4}

### Krzysztof W. Fornalski

### Krzysztof W. Fornalski 28 28

### Analysis for the model 2, which assumes that the incidence of lu

### Analysis for the model 2, which assumes that the incidence of lung cancer is ng cancer is independent on the dose, gives the average of

### independent on the dose, gives the average of RR of 97.6 ± RR of 97.6 ± 0.3%. 0.3%. For the linear For the linear models 3 and 4, in all studied cases the risk decreases with inc

### models 3 and 4, in all studied cases the risk decreases with increasing dose. reasing dose. However, if **However, if ** **one forces in the model 5 the LNT assumption the value of the s**

**one forces in the model 5 the LNT assumption the value of the slope equals ** **lope equals b ** **b = ** **= ** **0.0011 **

**b =**

**0.0011 ** ± ± ± ± ± ± ± ± **0.0003 and increases to b ** **0.0003 and increases to ** **b = 0.0019 ** **= 0.0019 ** ± ± ± ± ± ± ± ± **0.0003 when Cohen** **0.0003 when Cohen** **’s and miner** **’** **s and miner’** **’s ** **s ** **data are excluded**

**b = 0.0019**

**data are excluded. For quadratic models, 6 and 7, inclusion of Cohen** . For quadratic models, 6 and 7, inclusion of Cohen’ ’s (Cohen, 1995) s (Cohen, 1995) and miners

### and miners ’s (Lubin et al., 1997a) data results in ’ s (Lubin et al., 1997a) data results in hormetic curve with the NOAEL point hormetic curve with the NOAEL point ( ( *No Observed Adverse Effect Level* *No Observed Adverse Effect Level* , see Calabrese and Baldwin, (1993)) at 140 mSv , see Calabrese and Baldwin, (1993)) at 140 mSv (782 Bq m

### (782 Bq m ^{-} ^{-3} ^{3} ) and the maximal reduction (13± ) and the maximal reduction (13 ± 7)% of lung cancer incidences at 73 mSv 7)% of lung cancer incidences at 73 mSv per year (408 Bq m

### per year (408 Bq m ^{-} ^{-} ^{3} ^{3} ). ). No significant increase of risk is observed below 8 mSv per year No significant increase of risk is observed below 8 mSv per yea r (45 Bq m

### (45 Bq m ^{-} ^{-3} ^{3} ). This result heavily relies on the Cohen’ ). This result heavily relies on the Cohen ’s and miners s and miners’ ’ data. Exclusion of data. Exclusion of these data from the analysis leads to non

### these data from the analysis leads to non- -physical behavior presented by an inverted physical behavior presented by an inverted parabola. This result can be expected if one notes that for Cohe

### parabola. This result can be expected if one notes that for Cohen n ’s and miners ’ s and miners ’ ’ set of set of data, model 3 (

### data, model 3 (“ “linear 1 linear 1” ”) produces RR > 100%. Because the risk is decreasing with the ) produces RR > 100%. Because the risk is decreasing with the dose, final result using quadratic models (6 and 7) cannot be di

### dose, final result using quadratic models (6 and 7) cannot be different. Obviously, fferent. Obviously, inverted parabola is just the mathematical result and has no phy

### inverted parabola is just the mathematical result and has no physical meaning. sical meaning.

### The Bayesian analysis of the LNT model (model 5, Appendix) produ

### The Bayesian analysis of the LNT model (model 5, Appendix) produces ces results of the

### results of the same order of magnitude as presented by UNSCEAR same order of magnitude as presented by UNSCEAR (2006, (2006, Annex E), where the slope, recalculated from the Fig. 18 in p. 2

### Annex E), where the slope, recalculated from the Fig. 18 in p. 2 91, is 91, is *b * *b *

### ≈ ≈ 0.0047. 0.0047. **Our analysis of model 5 for the annual dose range below ** **Our analysis of model 5 for the annual dose range below ** **150 mSv, gives **

**150 mSv, gives ** **b ** **b ** **= 0.0011 ** **= 0.0011 ** ± ± ± ± ± ± ± ± **0.0003 for the data set 1, and ** **0.0003 for the data set 1, and ** **b ** **b ** **= 0.0019 ** **= 0.0019 **

**b**

**b**

**b**

**b**

### ± ±

### ± ±

### ±

### ± ±

### ± **0.0003 when Cohen** **0.0003 when Cohen** **’** **’** **s and miner** **s and miner** **’** **’** **s data are excluded. Taking ** **s data are excluded. Taking ** **narrower range of annual doses, up to 70 mSv, the slope values a**

**narrower range of annual doses, up to 70 mSv, the slope values a** **re ** **re ** **b ** **b **

**b**

**b**

**= 0.0013 **

**= 0.0013 ** ± ± ± ± ± ± ± ± **0.0003 and ** **0.0003 and ** **b ** **b ** **= 0.0043 ** **= 0.0043 ** ± ± ± ± ± ± ± ± **0.0016, respectively. The latter ** **0.0016, respectively** . The latter value is practically the same as UNSCEAR estimate. The negative

**b**

**b**