Seuil d’Information et d’Alerte pour PM10

Seuil d’Information et Alerte par année
annee Seuil_Info Seuil_Alerte
2000 NA NA
2001 NA NA
2002 NA NA
2003 NA NA
2004 NA NA
2005 NA NA
2006 NA NA
2007 NA NA
2008 80 125
2009 80 125
2010 80 125
2011 80 125
2012 50 80
2013 50 80
2014 50 80
2015 50 80
2016 50 80
2017 50 80
Note:
Les couleurs indiquent les différentes périodes selon les changements de réglementation

The eligibility criterias to intervention for PM10 changed over the time. 3 periods can be identified :

 

Jours de Pics de Pollution déclarés par Airparif (2008 - 2017)

Nombre de jours de pic de pollution (2008-2017)
Pic Pollution Nombre de Jours
0 6432
1 143

143 jours ont été caracterisés par des pics de pollution de PM10 sur la période allant de 2008 à 2017: 117 (82%) rélevaient d’un dépassement du seuil d’Information, 26 (18%) d’un dépassement du seuil d’Alerte.

Niveau Seuil Frequence
Alerte 26
Information 117

 

Nombre de jours de pic de pollution par annéé

Nombre de jours de pic de pollution par année
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
0 366 365 365 365 366 365 365 365 366 357 362 352 326 332 352 353 351 359
1 0 0 0 0 0 0 0 0 0 8 3 13 40 33 13 12 15 6

 

Nombre de jours de pic de pollution par période

Periode 2 (janv 2008- oct 2011)
Nombre de jours de pic de pollution pendant la deuxième période (janv 2008- oct 2011)
Pic de Pollution Nombre de Jours
0 4328
1 23

 

Jours de pic de pollution au cours de la deuxième période et concentrations moyennes journalières de PM10 correspondantes:

Date PM10_Concentration1 PM10_Concentration2 Niveau_dépassement
2009-01-01 62.53194 63.43333 Information
2009-01-10 124.70972 119.12727 Information
2009-01-11 126.70556 131.75455 Alerte
2009-01-12 46.70707 54.24091 Information
2009-02-26 49.54630 55.77273 Information
2009-03-18 57.84850 63.02857 Information
2009-04-03 89.86674 91.85000 Information
2009-04-04 60.78316 63.97143 Information
2010-01-08 69.76929 70.41818 Information
2010-01-27 80.85467 84.15217 Information
2010-02-17 63.46296 68.02083 Information
2011-01-31 79.16214 83.15652 Information
2011-02-01 62.19196 67.23478 Information
2011-02-18 68.09370 73.26522 Information
2011-03-02 88.27394 91.75909 Information
2011-03-03 76.67396 78.24783 Information
2011-03-05 85.26042 89.48261 Information
2011-03-17 73.18637 75.12609 Information
2011-03-25 79.86979 80.65909 Information
2011-03-26 73.85371 77.04091 Information
2011-11-21 73.35938 70.85417 Information
2011-11-22 84.32292 78.80000 Information
2011-11-23 67.44271 71.34783 Information
Note:
La première colonne de niveau de concentration pour PM10 indique la valeur moyenne calculée par Santé Publique France, alors que la deuxième colonne indique la valeur calculée par moi directement à partir des données des stations fournies par Airparif

Pour cette période, le niveau d’Alerte est délanché uniquement une fois (le 11 janvier 2009). Encore beaucoup de jours où la moyenne des concentrations sur toutes les stations ne permet pas d’identifier les jours de pic de pollution.

 

Periode 3 (à partir de 2008)
Nombre de jours de pic de pollution pendant la trosième période (à partir de 2008)
Pic de pollution Nombre de Jours
0 2104
1 120

Parmi les jours déclarés pic de pollution par Aiparif pendant la période 3, 25 (~20%) constituaient un dépassement du niveau d’Alerte et 98 (~80%) comportaient un dépassement du niveau d’Information.

Date PM10_Concentration1 PM10_Concentration2 Niveau_dépassement
2011-12-27 41.47917 42.00417 Information
2012-01-17 55.05729 62.52609 Information
2012-01-18 46.35938 50.60476 Information
2012-01-31 54.82677 59.60000 Information
2012-02-01 64.32003 67.54762 Information
2012-02-06 58.76388 64.08261 Information
2012-02-07 53.70257 56.56522 Information
2012-02-08 53.21882 60.83333 Information
2012-02-09 74.21354 80.54091 Information
2012-02-11 52.08990 55.12727 Information
2012-02-12 70.89583 75.49091 Information
2012-02-13 54.51373 57.68182 Information
2012-02-21 40.39583 47.86957 Information
2012-02-22 52.90195 58.28182 Information
2012-02-27 45.95833 51.40435 Information
2012-02-29 45.21354 50.22174 Information
2012-03-09 47.78646 53.47391 Information
2012-03-12 49.05655 52.21304 Information
2012-03-13 66.80443 70.43182 Information
2012-03-14 63.63021 69.76957 Information
2012-03-15 75.18018 80.13913 Alerte
2012-03-16 75.84598 81.01739 Alerte
2012-03-17 57.25473 61.13043 Information
2012-03-21 48.81581 52.76364 Information
2012-03-22 54.72869 61.95652 Information
2012-03-23 72.80208 78.19565 Alerte
2012-03-24 69.81771 74.17727 Information
2012-03-25 67.71591 73.75455 Information
2012-03-28 65.01373 69.95455 Information
2012-03-29 70.10938 73.28636 Alerte
2012-03-30 54.26979 59.18182 Information
2012-03-31 46.38791 49.21818 Information
2012-04-03 53.20947 56.70455 Information
2012-04-05 65.55208 68.69000 Information
2012-04-06 59.74481 64.03333 Information
2012-05-24 59.57292 63.54545 Information
2012-10-25 45.93229 50.07391 Information
2012-11-09 40.69271 42.78636 Information
2012-11-15 44.42377 50.30870 Information
2012-11-16 47.11685 47.41304 Information
2012-12-12 40.36756 47.40000 Information
2013-01-17 61.39015 69.52917 Information
2013-01-18 51.10938 56.40000 Information
2013-01-24 61.06250 65.77083 Information
2013-01-25 46.10417 52.75000 Information
2013-02-19 53.21210 63.85000 Information
2013-02-20 47.57707 55.98750 Information
2013-02-23 50.51468 54.67500 Information
2013-02-27 50.41456 54.61304 Information
2013-03-03 61.50663 66.67391 Information
2013-03-04 58.57008 67.46250 Information
2013-03-06 42.98913 51.36667 Information
2013-03-21 51.14017 59.18333 Information
2013-03-24 48.85938 52.66400 Information
2013-03-26 49.58333 56.83333 Information
2013-03-27 54.75340 62.83200 Information
2013-03-28 64.58333 71.01667 Information
2013-03-29 61.09896 69.18800 Information
2013-03-30 74.00000 80.85000 Information
2013-04-03 47.04214 53.85600 Information
2013-04-04 50.66146 56.83750 Information
2013-04-05 58.32292 64.74583 Information
2013-04-06 46.40625 52.04800 Information
2013-05-03 41.03397 48.54348 Information
2013-09-25 43.72781 41.30000 Information
2013-09-26 45.27972 48.14762 Information
2013-11-28 52.22024 58.01304 Information
2013-12-03 58.86905 62.01364 Alerte
2013-12-04 43.56926 52.19130 Information
2013-12-09 58.94643 64.79565 Alerte
2013-12-10 64.89286 71.67391 Alerte
2013-12-11 68.30357 74.33478 Alerte
2013-12-12 77.91071 86.43478 Alerte
2013-12-13 67.07143 74.15652 Alerte
2014-03-06 49.78646 54.87000 Information
2014-03-07 54.58333 62.57273 Information
2014-03-08 53.59375 59.78182 Information
2014-03-10 63.03125 65.78571 Information
2014-03-11 88.55729 92.22381 Alerte
2014-03-12 88.44271 92.76667 Alerte
2014-03-13 99.36458 100.23810 Alerte
2014-03-14 112.03172 120.48182 Alerte
2014-03-15 60.07292 64.11818 Information
2014-03-28 41.36905 48.79048 Information
2014-03-31 42.34624 48.01429 Information
2014-04-01 43.09951 51.24091 Information
2014-12-31 42.79167 54.15217 Information
2015-01-01 64.88542 62.21304 Alerte
2015-01-22 50.55051 54.51429 Information
2015-01-23 50.65712 57.26190 Information
2015-02-12 75.49705 78.15000 Alerte
2015-02-13 46.20947 49.35000 Information
2015-02-18 46.10038 50.91739 Information
2015-03-07 42.35938 51.03043 Information
2015-03-17 65.82528 70.15455 Information
2015-03-18 85.93676 91.31739 Alerte
2015-03-20 89.46117 100.20435 Alerte
2015-03-21 57.75000 61.07391 Information
2015-04-09 44.58985 52.17727 Information
2016-01-20 58.27242 61.72609 Information
2016-01-21 47.61979 57.29565 Information
2016-03-11 56.96354 63.98182 Information
2016-03-12 50.56250 55.27391 Information
2016-03-18 64.50000 68.31304 Information
2016-05-13 50.37184 54.92609 Information
2016-11-30 65.85119 67.02857 Information
2016-12-01 109.92857 103.51364 Alerte
2016-12-02 83.25000 84.69545 Alerte
2016-12-05 55.57143 61.34545 Information
2016-12-06 73.04762 77.64545 Alerte
2016-12-07 65.71429 71.41818 Alerte
2016-12-08 51.65395 57.73333 Information
2016-12-15 48.22412 54.01364 Information
2016-12-30 51.00000 48.94348 Information
2017-01-21 79.22500 83.27826 Alerte
2017-01-22 85.35000 86.19565 Alerte
2017-01-23 80.61250 81.18261 Alerte
2017-01-24 52.37363 52.13913 Information
2017-01-26 65.82361 69.15217 Information
2017-02-11 65.78750 66.52273 Information
Note:
La première colonne de niveau de concentration pour PM10 indique la valeur moyenne calculée par Santé Publique France, alors que la deuxième colonne indique la valeur calculée par moi directement à partir des données des stations fournies par Airparif

 

Variable d’éligibilité aux mesures anti-pic de pollution pour la 1er période, avant fin 2007

Nombre de jours de pic de pollution pendant la première période (2000-2007)
Pic de Pollution Nombre de Jours
0 2906
1 15

Les 15 Jours éligibles aux mesures antipic de pollution au cours de la première période et leurs concentrations moyennes journalières de PM10 correspondantes:

Date PM10_Concentration1 PM10_Concentration2 Niveau_dépassement
2000-01-27 NA 90.40000 Information
2002-01-06 NA 78.05000 Information
2002-10-31 NA 68.28750 Information
2006-02-01 NA 99.12941 Alerte
2006-03-20 NA 75.44444 Information
2006-11-05 NA 66.31579 Information
2007-04-15 94.35000 94.96842 Information
2007-04-16 77.05741 78.84118 Information
2007-11-17 67.06713 66.11053 Information
2007-11-28 61.99028 62.87895 Information
2007-12-20 82.84306 83.47895 Information
2007-12-21 87.81991 89.60526 Information
2007-12-22 99.84444 94.54737 Information
2007-12-23 140.78889 135.24737 Alerte
2007-12-24 125.12870 127.02105 Alerte
Note:
La première colonne de niveau de concentration pour PM10 indique la valeur moyenne calculée par Santé Publique France, alors que la deuxième colonne indique la valeur calculée par moi directement à partir des données des stations fournies par Airparif

Des 15 jours éligibles aux mesures anti pic de pollution, 3 étaient des jours de dépassement du seuil d’alerte et les autres étaient des jours de déassement du seuil d’Information.

Creation d’une variable indicatrice de période:

data$annee<-as.numeric(as.character(data$annee))
data$period<-NA
for (i in 1:nrow(data)) {
  data$period[i]<-if (data$Dates[i]<"2008-01-01") "1" 
  else if (data$Dates[i]>="2008-01-01" & data$Dates[i]<"2011-11-30") "2" 
  else if (data$Dates[i]>="2011-11-30") "3"
}

for (i in 1:nrow(data)) {
  data$Period[i]<-if (data$Dates[i]<"2008-01-01") "1" 
  else "2"
  }

Les données de mortalité étant disponible uniquement jusqu’à l’année 2015, la base de données est restrainte et selectionée uniquement pour la période 2000-2015.

The number of pollution episode for each period

##              
##                  1    2    3
##   Alerte         3    1   18
##   Information   12   22   81
##   <NA>        2907 1406 1394

The number of deaths for each mortality cause and each period

During the whole study period, for non accidental, cardiovascular and respiratory, respectively:

## [1] 622268
## [1] 154894
## [1] 39899

During the Period 1, for non accidental, cardiovascular and respiratory, respectively:

## [1] 316306
## [1] 84184
## [1] 20012

During the Period 2, for non accidental, cardiovascular and respiratory, respectively:

## [1] 148527
## [1] 36181
## [1] 9379

During the Period 3, for non accidental, cardiovascular and respiratory, respectively:

## [1] 157435
## [1] 34529
## [1] 10508

 

Tableau Descriptif

Descriptive Statistics before and after the measures implementation
Before PM10 Regulation
First PM10 Regulation
Last PM10 Regulation
Non-Polluted days Polluted days Non-Polluted days Polluted days Non-Polluted days Polluted days
Non acc Deaths 108.2064 116.6667 103.7603 114.7826 104.8852 113.3838
Cardio Deaths 28.79670 31.46667 25.24182 30.04348 22.99857 24.93939
Respi Deaths 6.843137 7.933333 6.546230 7.608696 6.960545 8.131313
Minimum Temperature 9.310079 1.766667 9.145021 2.234783 9.699498 3.354545
Maximum Temperature 16.226144 9.586667 16.391038 8.860870 16.898924 11.333333
Mean Temperature 12.683331 5.248056 12.707882 5.536051 13.299211 7.343939

According to Alert Type (informational or Warning Alert)

Descriptive Statistics before and after the measures implementation
Before PM10 Regulation
First PM10 Regulation
Last PM10 Regulation
WA Polluted days IA Polluted days Non-Polluted days WA Polluted days IA Polluted days Non-Polluted days WA Polluted days IA Polluted days Non-Polluted days
Non acc Deaths 122.0000 115.3333 108.2064 132.0000 114.0000 103.7603 108.4444 114.4815 104.8852
Cardio Deaths 32.33333 31.25000 28.79670 31.00000 30.00000 25.24182 22.88889 25.39506 22.99857
Respi Deaths 9.000000 7.666667 6.843137 17.000000 7.181818 6.546230 8.222222 8.111111 6.960545
Minimum Temperature -1.266667 2.525000 9.310079 -6.100000 2.613636 9.145021 4.255556 3.154321 9.699498
Maximum Temperature 6.766667 10.291667 16.226144 3.500000 9.104545 16.391038 13.788889 10.787654 16.898924
Mean Temperature 1.979167 6.065278 12.683331 -1.633333 5.861932 12.707882 9.022222 6.970988 13.299211
Note:
WA=Warning Alert, IA=Informational Alert

 

Calcul Score de Propension

Une trentaine de modèles pour calculer le score de propension ont été comparés. Plusieurs combinaisons des variables quantitatives ont été testés et chaque variable quantitative a été inserée dans les differents versions du modèle en linéaire ou avec differents types de splines. Le modèle avec l’AIC plus petit a été retenu.

mod<-gam(elipic ~ s(tempmax,k=7,bs="tp") + s(tempmoy,k=7, bs="tp") +s(lag_tempmax,k=7,bs="tp") + s(lag_tempmoy,k=7, bs="tp")+ s(lag2_tempmax,k=7,bs="tp") + s(lag2_tempmoy,k=7, bs="tp") + s(lag3_tempmax,k=7,bs="tp") + s(lag3_tempmoy,k=7, bs="tp") + Jours + mois  + jours_fériés + Vacances + annee + s(lag_O3,k=6) + s(lag2_O3,k=6) + s(lag3_O3,k=6) + s(lag_PM10,k=6) + s(lag2_PM10,k=6) + s(lag3_PM10,k=6), family="binomial", data=data)


data$SP<-NA
data$SP[4:nrow(data)]<-mod$fitted
data<-data[-c(1:3),]
data$nrow<-c(1:nrow(data))

 

Résultats du Modèle retenu

## 
## Family: binomial 
## Link function: logit 
## 
## Formula:
## elipic ~ s(tempmax, k = 7, bs = "tp") + s(tempmoy, k = 7, bs = "tp") + 
##     s(lag_tempmax, k = 7, bs = "tp") + s(lag_tempmoy, k = 7, 
##     bs = "tp") + s(lag2_tempmax, k = 7, bs = "tp") + s(lag2_tempmoy, 
##     k = 7, bs = "tp") + s(lag3_tempmax, k = 7, bs = "tp") + s(lag3_tempmoy, 
##     k = 7, bs = "tp") + Jours + mois + jours_fériés + Vacances + 
##     annee + s(lag_O3, k = 6) + s(lag2_O3, k = 6) + s(lag3_O3, 
##     k = 6) + s(lag_PM10, k = 6) + s(lag2_PM10, k = 6) + s(lag3_PM10, 
##     k = 6)
## 
## Parametric coefficients:
##                 Estimate Std. Error z value Pr(>|z|)    
## (Intercept)   -1.187e+01  2.176e+00  -5.457 4.83e-08 ***
## Joursjeudi     1.891e+00  5.823e-01   3.248  0.00116 ** 
## Jourslundi     1.904e+00  6.390e-01   2.980  0.00288 ** 
## Joursmardi     1.490e+00  6.169e-01   2.415  0.01575 *  
## Joursmercredi  2.407e+00  6.028e-01   3.992 6.54e-05 ***
## Jourssamedi    8.979e-01  5.920e-01   1.517  0.12933    
## Joursvendredi  1.585e+00  5.965e-01   2.658  0.00786 ** 
## mois10        -1.287e+00  9.700e-01  -1.327  0.18459    
## mois11         9.258e-01  6.275e-01   1.475  0.14011    
## mois12         2.037e-01  5.853e-01   0.348  0.72780    
## mois2         -7.299e-01  5.325e-01  -1.371  0.17048    
## mois3         -7.193e-01  7.008e-01  -1.026  0.30471    
## mois4         -1.161e+00  9.089e-01  -1.278  0.20131    
## mois5         -1.755e+00  1.242e+00  -1.413  0.15768    
## mois6         -4.840e+01  3.105e+06   0.000  0.99999    
## mois7         -4.920e+01  3.056e+06   0.000  0.99999    
## mois8         -4.833e+01  3.056e+06   0.000  0.99999    
## mois9         -1.967e+00  1.231e+00  -1.598  0.11004    
## jours_fériés  -1.393e+00  1.076e+00  -1.294  0.19557    
## Vacances       9.502e-01  3.696e-01   2.571  0.01014 *  
## annee2001     -4.673e+01  3.543e+06   0.000  0.99999    
## annee2002      1.559e+00  1.623e+00   0.961  0.33676    
## annee2003     -4.941e+01  3.543e+06   0.000  0.99999    
## annee2004     -4.723e+01  3.538e+06   0.000  0.99999    
## annee2005     -4.699e+01  3.543e+06   0.000  0.99999    
## annee2006      4.471e-01  1.580e+00   0.283  0.77721    
## annee2007      9.478e-01  1.553e+00   0.610  0.54160    
## annee2008     -4.889e+01  3.538e+06   0.000  0.99999    
## annee2009      8.524e-01  1.514e+00   0.563  0.57332    
## annee2010     -3.627e-02  1.590e+00  -0.023  0.98179    
## annee2011      1.894e+00  1.503e+00   1.260  0.20774    
## annee2012      4.370e+00  1.496e+00   2.920  0.00350 ** 
## annee2013      3.974e+00  1.506e+00   2.639  0.00832 ** 
## annee2014      3.434e+00  1.527e+00   2.248  0.02455 *  
## annee2015      2.881e+00  1.499e+00   1.922  0.05455 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                   edf Ref.df Chi.sq  p-value    
## s(tempmax)      1.000  1.001 29.389 5.94e-08 ***
## s(tempmoy)      2.468  3.112 44.706 1.64e-09 ***
## s(lag_tempmax)  1.000  1.000  0.024   0.8778    
## s(lag_tempmoy)  1.001  1.001  5.086   0.0241 *  
## s(lag2_tempmax) 1.000  1.000  0.016   0.8989    
## s(lag2_tempmoy) 1.000  1.000  0.023   0.8796    
## s(lag3_tempmax) 1.000  1.000  0.453   0.5011    
## s(lag3_tempmoy) 1.000  1.000  0.149   0.6993    
## s(lag_O3)       3.855  4.283  9.359   0.0687 .  
## s(lag2_O3)      1.743  2.214  1.881   0.4508    
## s(lag3_O3)      1.000  1.000  0.367   0.5450    
## s(lag_PM10)     4.608  4.862 83.622 2.33e-16 ***
## s(lag2_PM10)    1.003  1.005  2.797   0.0957 .  
## s(lag3_PM10)    1.000  1.001  0.505   0.4777    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.528   Deviance explained = 67.5%
## UBRE = -0.90795  Scale est. = 1         n = 5841

AIC du modèle:

## [1] 537.6434

 

Statistiques Descriptives pour le Score de Propension:

Summary Statistics for the propensity score (PS):

##      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
## 0.0000000 0.0000000 0.0000000 0.0234549 0.0003828 0.9916062

Summary Statistics for the variable eligibility to intervention (polluted days):

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## 0.00000 0.00000 0.00000 0.02345 0.00000 1.00000

 

Test moyenne Score de Propension Test de Student pour difference moyenne entre variable Score de Propension (x) et variable pic de pollution (y):

## 
##  Welch Two Sample t-test
## 
## data:  data$SP and data$elipic
## t = 5.9406e-14, df = 10694, p-value = 1
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.004808168  0.004808168
## sample estimates:
##  mean of x  mean of y 
## 0.02345489 0.02345489

La moyenne du score de propension predit par le modèle est statistiquement pas differente de la moyenne de la variable éligibilité.

Comparaison de la moyenne du score de propension entre jours éligibles et pas éligibles avec test de Student.

## 
##  Welch Two Sample t-test
## 
## data:  SP by elipic
## t = -20.046, df = 136.24, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.5861339 -0.4808755
## sample estimates:
## mean in group 0 mean in group 1 
##      0.01094159      0.54444630

Les jours éligibles ont une moyenne du SP statistiquement différente de la moyenne du SP des jours non éligibles.

 

Standard Deviation de la variable SP et Eligibilité:

## data$elipic: 0
## [1] 0.05950014
## ------------------------------------------------------------ 
## data$elipic: 1
## [1] 0.3113678

La Standard deviation de la variable SP est assez différente de celle de la variable éligibilité.

Propensity score Matching

Several types of matching were compared. Differents matches were determined by following parameters:

The matching minimazing the standardized mean difference for numerical variables included in the SP predictions was retained. The selected matching include M=3, no caliper requirement and it handles ties deterministically, that means that ties are randomly broken.

var.match<-cbind(data$SP,data$period)
App<-Match(Tr = data$elipic,X=var.match, M=3, ties=FALSE)

summary(App)
## 
## Estimate...  0 
## SE.........  0 
## T-stat.....  NaN 
## p.val......  NA 
## 
## Original number of observations..............  5841 
## Original number of treated obs...............  137 
## Matched number of observations...............  137 
## Matched number of observations  (unweighted).  411
control=data.frame(App$index.control)
treated=data.frame(App$index.treated)


colnames(control) <- c("nrow")
colnames(treated) <- c("nrow")

cas<-unique(treated)

cas$PAIR<-c(1:nrow(cas))

treated<-merge(treated,cas,by="nrow")

control$PAIR <- treated$PAIR

casm<-merge(cas,data,by="nrow")
controlm<- merge(control,data, by ="nrow")

datam<-rbind(casm,controlm)

datam<-datam[order(datam[,"PAIR"]),]

table(datam$PAIR,datam$period)
##      
##       1 2 3
##   1   4 0 0
##   2   4 0 0
##   3   4 0 0
##   4   4 0 0
##   5   4 0 0
##   6   4 0 0
##   7   4 0 0
##   8   3 1 0
##   9   4 0 0
##   10  3 1 0
##   11  4 0 0
##   12  3 1 0
##   13  3 1 0
##   14  3 1 0
##   15  2 1 1
##   16  0 4 0
##   17  0 2 2
##   18  1 2 1
##   19  1 2 1
##   20  0 4 0
##   21  1 2 1
##   22  0 4 0
##   23  0 4 0
##   24  0 4 0
##   25  0 4 0
##   26  0 4 0
##   27  0 2 2
##   28  0 1 3
##   29  0 4 0
##   30  0 4 0
##   31  0 2 2
##   32  0 4 0
##   33  0 4 0
##   34  0 4 0
##   35  0 4 0
##   36  0 4 0
##   37  0 4 0
##   38  0 3 1
##   39  0 0 4
##   40  0 0 4
##   41  0 0 4
##   42  0 0 4
##   43  0 0 4
##   44  0 0 4
##   45  0 0 4
##   46  0 0 4
##   47  0 0 4
##   48  0 0 4
##   49  0 0 4
##   50  0 0 4
##   51  0 0 4
##   52  0 0 4
##   53  0 0 4
##   54  0 0 4
##   55  0 0 4
##   56  0 0 4
##   57  0 0 4
##   58  0 0 4
##   59  0 0 4
##   60  0 0 4
##   61  0 0 4
##   62  0 0 4
##   63  0 0 4
##   64  0 0 4
##   65  0 0 4
##   66  0 0 4
##   67  0 0 4
##   68  0 0 4
##   69  0 0 4
##   70  0 0 4
##   71  0 0 4
##   72  0 0 4
##   73  0 0 4
##   74  0 0 4
##   75  0 0 4
##   76  0 0 4
##   77  0 0 4
##   78  0 0 4
##   79  0 0 4
##   80  0 0 4
##   81  0 0 4
##   82  0 0 4
##   83  0 0 4
##   84  0 0 4
##   85  0 0 4
##   86  0 0 4
##   87  0 0 4
##   88  0 0 4
##   89  0 0 4
##   90  0 0 4
##   91  0 0 4
##   92  0 0 4
##   93  0 0 4
##   94  0 0 4
##   95  0 0 4
##   96  0 0 4
##   97  0 0 4
##   98  0 0 4
##   99  0 0 4
##   100 0 0 4
##   101 0 0 4
##   102 0 0 4
##   103 0 0 4
##   104 0 0 4
##   105 0 0 4
##   106 0 0 4
##   107 0 0 4
##   108 0 0 4
##   109 0 0 4
##   110 0 0 4
##   111 0 0 4
##   112 0 0 4
##   113 0 0 4
##   114 0 0 4
##   115 0 0 4
##   116 0 0 4
##   117 0 0 4
##   118 0 0 4
##   119 0 0 4
##   120 0 0 4
##   121 0 0 4
##   122 0 0 4
##   123 0 0 4
##   124 0 0 4
##   125 0 0 4
##   126 0 0 4
##   127 0 0 4
##   128 0 0 4
##   129 0 0 4
##   130 0 0 4
##   131 0 0 4
##   132 0 0 4
##   133 0 0 4
##   134 0 0 4
##   135 0 0 4
##   136 0 0 4
##   137 0 0 4

Les matchs de 8 à 19 et 21 mélangent des observations sur des périodes différentes.

 

Comparing SP for eligible days and not eligible days before and after matching:

 

Comparing PS average for eligible days and not eligible days after matching through Student test:

## 
##  Welch Two Sample t-test
## 
## data:  SP by elipic
## t = -0.13635, df = 234.19, p-value = 0.8917
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.06478698  0.05640012
## sample estimates:
## mean in group 0 mean in group 1 
##       0.5402529       0.5444463

 

Mean PS values for eligible days and not eligible days after matching are not statistically different.

Balance statistics for matching

 

Standardized mean differences for continuos variables after matching:
temp max LAG temp max LAG2 temp max LAG3 temp max temp moy LAG temp moy LAG2 temp moy LAG3 temp moy lag_O3 lag2_O3 lag3_O3 lag_PM10 lag2_PM10 lag3_PM10 tot_SMD
Before Matching 0.14597 0.14830 0.15839 0.16898 0.23269 0.23084 0.23784 0.24514 0.18180 0.15816 0.14690 0.45948 0.37585 0.30622 3.19656
After Matching 0.03159 0.02771 0.03344 0.02376 0.04254 0.02610 0.02536 0.02644 0.06128 0.04272 0.05201 0.03468 0.04498 0.03121 0.50383

 

Love Plot for standardized mean difference

 

Stars indicates variables with mean differences that have been standardized

 

Comparing average number of non accidental, cardiovascular and respiratory deaths per month for eligible days and not eligible days before intervention in the after-matching data:

Descriptive Statistics before and after the measures implementation
Before PM10 Regulation
First PM10 Regulation
Last PM10 Regulation
Non-Polluted days Polluted days Non-Polluted days Polluted days Non-Polluted days Polluted days
Non acc Deaths 121.1463 116.6667 112.8136 114.7826 112.5756 113.3838
Cardio Deaths 33.78049 31.46667 27.64407 30.04348 26.85531 24.93939
Respi Deaths 7.951220 7.933333 6.677966 7.608696 8.729904 8.131313
Minimum Temperature 2.134146 1.766667 3.940678 2.234783 3.452412 3.354545
Maximum Temperature 10.060976 9.586667 12.983051 8.860870 10.623151 11.333333
Mean Temperature 5.924695 5.248056 8.337853 5.536051 7.037781 7.343939 
##    
##       1   2   3
##   0  41  59 311
##   1  15  23  99

 

Differences in Differences

### Model to study effect on PM10 concentration
fixPM10<-plm(moyPM10 ~ Period + elipic + Period*elipic, data=datam, model="within")


### Model to study effect on mortality

## Linear Version
# Non accidental mortality
nocc<-plm(nocc_tot ~ Period + elipic + Period*elipic, data=datam, model="within")

# Cardiovascual causes mortality
cardio<-plm(cv_tot ~ Period + elipic + Period*elipic, data=datam, model="within")

# Respiratory causes mortality
respi<-plm(respi_tot ~ Period + elipic + Period*elipic, data=datam, model="within")


## Poisson Version
# Non accidental mortality
noccP<-pglm(nocc_tot ~ Period + elipic + Period*elipic, data=datam, family=poisson(link = "log"), model="within")

# Cardiovascual causes mortality
cardioP<-pglm(cv_tot ~ Period + elipic + Period*elipic, data=datam, family=poisson(link = "log"), model="within")

# Respiratory causes mortality
respiP<-pglm(respi_tot ~ Period + elipic + Period*elipic, data=datam, family=poisson(link = "log"), model="within")

Effet sur le niveau de concentration de PM10 de la période post-mésures par rapport à la période avant l’entrée de la réglementation des PM10:

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = moyPM10 ~ Period + elipic + Period * elipic, data = datam, 
##     model = "within")
## 
## Balanced Panel: n = 137, T = 4, N = 548
## 
## Residuals:
##       Min.    1st Qu.     Median    3rd Qu.       Max. 
## -29.402579  -6.292435   0.027076   5.641602  40.553695 
## 
## Coefficients:
##                Estimate Std. Error t-value  Pr(>|t|)    
## Period2         -7.5892     4.1690 -1.8204  0.069429 .  
## elipic          33.9797     3.2871 10.3374 < 2.2e-16 ***
## Period2:elipic  -9.6117     3.4824 -2.7601  0.006039 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    116010
## Residual Sum of Squares: 47664
## R-Squared:      0.58916
## Adj. R-Squared: 0.44919
## F-statistic: 195.025 on 3 and 408 DF, p-value: < 2.22e-16

Effet sur la mortalité de la période post-mésures par rapport à la période avant l’entrée de la réglementation des PM10:

Modèle Linéaire:

Non accidental mortality

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = nocc_tot ~ Period + elipic + Period * elipic, data = datam, 
##     model = "within")
## 
## Balanced Panel: n = 137, T = 4, N = 548
## 
## Residuals:
##       Min.    1st Qu.     Median    3rd Qu.       Max. 
## -41.221723  -7.588867   0.096723   8.028277  49.778277 
## 
## Coefficients:
##                Estimate Std. Error t-value Pr(>|t|)
## Period2         -6.1323     5.5010 -1.1148   0.2656
## elipic          -4.9095     4.3374 -1.1319   0.2583
## Period2:elipic   6.0226     4.5951  1.3107   0.1907
## 
## Total Sum of Squares:    83521
## Residual Sum of Squares: 82989
## R-Squared:      0.0063715
## Adj. R-Squared: -0.33214
## F-statistic: 0.872079 on 3 and 408 DF, p-value: 0.45555

Cardiovascular causes mortality

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = cv_tot ~ Period + elipic + Period * elipic, data = datam, 
##     model = "within")
## 
## Balanced Panel: n = 137, T = 4, N = 548
## 
## Residuals:
##      Min.   1st Qu.    Median   3rd Qu.      Max. 
## -15.01468  -2.95597  -0.26468   3.04403  18.79403 
## 
## Coefficients:
##                Estimate Std. Error t-value Pr(>|t|)   
## Period2         -6.1718     2.1651 -2.8506 0.004585 **
## elipic          -2.4267     1.7071 -1.4216 0.155916   
## Period2:elipic   1.3680     1.8085  0.7564 0.449825   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    13248
## Residual Sum of Squares: 12855
## R-Squared:      0.029652
## Adj. R-Squared: -0.30093
## F-statistic: 4.1559 on 3 and 408 DF, p-value: 0.0064351

Respiratory causes mortality

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = respi_tot ~ Period + elipic + Period * elipic, 
##     data = datam, model = "within")
## 
## Balanced Panel: n = 137, T = 4, N = 548
## 
## Residuals:
##     Min.  1st Qu.   Median  3rd Qu.     Max. 
## -6.84519 -2.34519 -0.59519  1.65481  9.40481 
## 
## Coefficients:
##                 Estimate Std. Error t-value Pr(>|t|)
## Period2         0.451198   1.474584  0.3060   0.7598
## elipic          0.070186   1.162657  0.0604   0.9519
## Period2:elipic -0.450934   1.231744 -0.3661   0.7145
## 
## Total Sum of Squares:    5977.5
## Residual Sum of Squares: 5963.1
## R-Squared:      0.0024051
## Adj. R-Squared: -0.33746
## F-statistic: 0.327884 on 3 and 408 DF, p-value: 0.8052

Modèle de Poisson:

Non accidental mortality

## --------------------------------------------
## Maximum Likelihood estimation
## Newton-Raphson maximisation, 2 iterations
## Return code 1: gradient close to zero
## Log-Likelihood: -1623.52 
## 3  free parameters
## Estimates:
##                Estimate Std. error t value Pr(> t)  
## Period2        -0.05041    0.03489  -1.445  0.1485  
## elipic         -0.04131    0.02803  -1.474  0.1405  
## Period2:elipic  0.05116    0.02976   1.719  0.0855 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## --------------------------------------------

Cardiovascular causes mortality

## --------------------------------------------
## Maximum Likelihood estimation
## Newton-Raphson maximisation, 2 iterations
## Return code 1: gradient close to zero
## Log-Likelihood: -1193.814 
## 3  free parameters
## Estimates:
##                Estimate Std. error t value Pr(> t)   
## Period2        -0.18886    0.06787  -2.783 0.00539 **
## elipic         -0.07415    0.05377  -1.379 0.16783   
## Period2:elipic  0.03413    0.05765   0.592 0.55379   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## --------------------------------------------

Respiratory causes mortality

## --------------------------------------------
## Maximum Likelihood estimation
## Newton-Raphson maximisation, 2 iterations
## Return code 1: gradient close to zero
## Log-Likelihood: -1030.765 
## 3  free parameters
## Estimates:
##                 Estimate Std. error t value Pr(> t)
## Period2         0.057481   0.137539   0.418   0.676
## elipic          0.008715   0.107934   0.081   0.936
## Period2:elipic -0.055056   0.114206  -0.482   0.630
## --------------------------------------------

 

Alternative analysis with three periods: 1) before PM10 concentration regulation 2) first PM10 regulation 3) more recent PM10 regulation

Après création de 2 dataframes par type d’appariement et par période 1 ou 2, analyse diff in diff via regression linéaire pour évaluer l’effet des mesures sur le niveau de PM10 et via regression de Poisson pour évaluer effet sur mortalité non accidentelle:

# Periode 1:

## Create panel data dataframe 
#datam_p1<-pdata.frame(datam_p1,index="PAIR")
#datam_p2<-pdata.frame(datam_p2,index="PAIR")


### Model to study effect on PM10 concentration
fixPM10_P1<-plm(moyPM10 ~ period + elipic + period*elipic, data=datam_p1, model="within")

fixPM10_P2<-plm(moyPM10 ~ period + elipic + period*elipic, data=datam_p2, model="within")


### Model to study effect on mortality

## Non accidental causes 
# Gaussian Version
nocc_P1<-plm(nocc_tot ~ period + elipic + period*elipic, data=datam_p1, model="within")

nocc_P2<-plm(nocc_tot ~ period + elipic + period*elipic, data=datam_p2, model="within")

# Poisson Version
noccP_P1<-pglm(nocc_tot ~ period + elipic + period*elipic, data=datam_p1, family=poisson(link = "log"), model="within")

noccP_P2<-pglm(nocc_tot ~ period + elipic + period*elipic, data=datam_p2, family=poisson(link = "log"), model="within")


## Cardiovascular causes 
# Gaussian Version
cv_P1<-plm(cv_tot ~ period + elipic + period*elipic, data=datam_p1, model="within")

cv_P2<-plm(cv_tot ~ period + elipic + period*elipic, data=datam_p2, model="within")

# Poisson Version
cvP_P1<-pglm(cv_tot ~ period + elipic + period*elipic, data=datam_p1, family=poisson(link = "log"), model="within")

cvP_P2<-pglm(cv_tot ~ period + elipic + period*elipic, data=datam_p2, family=poisson(link = "log"), model="within")


## Respiratory causes 
# Gaussian Version
respi_P1<-plm(respi_tot ~ period + elipic + period*elipic, data=datam_p1, model="within")

respi_P2<-plm(respi_tot ~ period + elipic + period*elipic, data=datam_p2, model="within")

# Poisson Version
respiP_P1<-pglm(respi_tot ~ period + elipic + period*elipic, data=datam_p1, family=poisson(link = "log"), model="within")

respiP_P2<-pglm(respi_tot ~ period + elipic + period*elipic, data=datam_p2, family=poisson(link = "log"), model="within")

Première Période:

PM10 Concentration

Effet sur niveau de concentration de PM10 période 1 vs. Période 2 :

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = moyPM10 ~ period + elipic + period * elipic, data = datam_p1, 
##     model = "within")
## 
## Unbalanced Panel: n = 38, T = 1-4, N = 138
## 
## Residuals:
##      Min.   1st Qu.    Median   3rd Qu.      Max. 
## -28.53461  -7.52177  -0.70442   7.57479  30.88311 
## 
## Coefficients:
##                Estimate Std. Error t-value  Pr(>|t|)    
## period2         -3.2859     5.7263 -0.5738    0.5674    
## elipic          34.2569     4.3188  7.9321 3.741e-12 ***
## period2:elipic  -9.4101     5.6943 -1.6525    0.1017    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    42374
## Residual Sum of Squares: 19489
## R-Squared:      0.54007
## Adj. R-Squared: 0.3504
## F-statistic: 37.9666 on 3 and 97 DF, p-value: 2.5664e-16

Non accidental mortality

Effet sur mortalité non accidentelle période 1 vs. Période 2 :

Linear Normal Regression

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = nocc_tot ~ period + elipic + period * elipic, data = datam_p1, 
##     model = "within")
## 
## Unbalanced Panel: n = 38, T = 1-4, N = 138
## 
## Residuals:
##      Min.   1st Qu.    Median   3rd Qu.      Max. 
## -35.11404  -8.64276  -0.66039   8.75000  32.88596 
## 
## Coefficients:
##                Estimate Std. Error t-value Pr(>|t|)
## period2         -4.4675     6.2161 -0.7187   0.4741
## elipic          -4.6036     4.6882 -0.9820   0.3286
## period2:elipic   4.1474     6.1814  0.6710   0.5038
## 
## Total Sum of Squares:    23272
## Residual Sum of Squares: 22966
## R-Squared:      0.013186
## Adj. R-Squared: -0.39375
## F-statistic: 0.432054 on 3 and 97 DF, p-value: 0.73052

Poisson Regression

## --------------------------------------------
## Maximum Likelihood estimation
## Newton-Raphson maximisation, 3 iterations
## Return code 1: gradient close to zero
## Log-Likelihood: -403.4435 
## 3  free parameters
## Estimates:
##                Estimate Std. error t value Pr(> t)
## period2        -0.03632    0.03644  -0.997   0.319
## elipic         -0.03871    0.02808  -1.378   0.168
## period2:elipic  0.03476    0.03738   0.930   0.352
## --------------------------------------------

Cardiovascular causes mortality

Effet sur mortalité par causes cardiovasculaires période 1 vs. Période 2 :

Linear Normal Regression

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = cv_tot ~ period + elipic + period * elipic, data = datam_p1, 
##     model = "within")
## 
## Unbalanced Panel: n = 38, T = 1-4, N = 138
## 
## Residuals:
##      Min.   1st Qu.    Median   3rd Qu.      Max. 
## -14.46380  -2.94457  -0.30582   3.11923  15.14141 
## 
## Coefficients:
##                Estimate Std. Error t-value Pr(>|t|)  
## period2         -6.2322     2.7258 -2.2863  0.02441 *
## elipic          -2.4284     2.0558 -1.1813  0.24039  
## period2:elipic   3.5732     2.7106  1.3182  0.19053  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    4689.2
## Residual Sum of Squares: 4416.1
## R-Squared:      0.058238
## Adj. R-Squared: -0.33012
## F-statistic: 1.99947 on 3 and 97 DF, p-value: 0.11914

Poisson Regression

## --------------------------------------------
## Maximum Likelihood estimation
## Newton-Raphson maximisation, 3 iterations
## Return code 1: gradient close to zero
## Log-Likelihood: -311.3459 
## 3  free parameters
## Estimates:
##                Estimate Std. error t value Pr(> t)   
## period2        -0.19223    0.07157  -2.686 0.00723 **
## elipic         -0.07440    0.05387  -1.381 0.16724   
## period2:elipic  0.11517    0.07280   1.582 0.11368   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## --------------------------------------------

Respiratory causes mortality

Effet sur mortalité par causes respiratoires période 1 vs. Période 2 :

Linear Normal Regression

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = respi_tot ~ period + elipic + period * elipic, 
##     data = datam_p1, model = "within")
## 
## Unbalanced Panel: n = 38, T = 1-4, N = 138
## 
## Residuals:
##     Min.  1st Qu.   Median  3rd Qu.     Max. 
## -6.17434 -1.72208 -0.30165  1.26464  8.72478 
## 
## Coefficients:
##                Estimate Std. Error t-value Pr(>|t|)
## period2        -0.52815    1.28438 -0.4112   0.6818
## elipic          0.11168    0.96868  0.1153   0.9085
## period2:elipic  0.78744    1.27721  0.6165   0.5390
## 
## Total Sum of Squares:    994.08
## Residual Sum of Squares: 980.45
## R-Squared:      0.01371
## Adj. R-Squared: -0.39301
## F-statistic: 0.449469 on 3 and 97 DF, p-value: 0.71824

Poisson Regression

## --------------------------------------------
## Maximum Likelihood estimation
## Newton-Raphson maximisation, 3 iterations
## Return code 1: gradient close to zero
## Log-Likelihood: -222.3134 
## 3  free parameters
## Estimates:
##                Estimate Std. error t value Pr(> t)
## period2        -0.07568    0.15025  -0.504   0.614
## elipic          0.01422    0.10813   0.132   0.895
## period2:elipic  0.11130    0.14499   0.768   0.443
## --------------------------------------------

Deuxième Période:

PM10 Concentration

Effet sur niveau de concentration de PM10 période 2 vs. Période 3 :

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = moyPM10 ~ period + elipic + period * elipic, data = datam_p2, 
##     model = "within")
## 
## Unbalanced Panel: n = 128, T = 1-4, N = 492
## 
## Residuals:
##       Min.    1st Qu.     Median    3rd Qu.       Max. 
## -23.110000  -6.054287  -0.090112   5.257165  37.735533 
## 
## Coefficients:
##                Estimate Std. Error t-value  Pr(>|t|)    
## period3        -22.1535     3.8718 -5.7217 2.217e-08 ***
## elipic          24.8848     2.4845 10.0160 < 2.2e-16 ***
## period3:elipic  -1.5940     2.7278 -0.5843    0.5594    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    92082
## Residual Sum of Squares: 33983
## R-Squared:      0.63095
## Adj. R-Squared: 0.49805
## F-statistic: 205.731 on 3 and 361 DF, p-value: < 2.22e-16

Non accidental mortality

Effet sur mortalité non accidentelle période 2 vs. Période 3 :

Linear Normal Regression

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = nocc_tot ~ period + elipic + period * elipic, data = datam_p2, 
##     model = "within")
## 
## Unbalanced Panel: n = 128, T = 1-4, N = 492
## 
## Residuals:
##     Min.  1st Qu.   Median  3rd Qu.     Max. 
## -41.2862  -7.2862   0.0000   7.9645  49.7138 
## 
## Coefficients:
##                Estimate Std. Error t-value Pr(>|t|)
## period3        -8.81460    5.74565 -1.5341   0.1259
## elipic          0.68033    3.68692  0.1845   0.8537
## period3:elipic  0.17489    4.04787  0.0432   0.9656
## 
## Total Sum of Squares:    75483
## Residual Sum of Squares: 74835
## R-Squared:      0.0085852
## Adj. R-Squared: -0.34843
## F-statistic: 1.04203 on 3 and 361 DF, p-value: 0.37395

Poisson Regression

## --------------------------------------------
## Maximum Likelihood estimation
## Newton-Raphson maximisation, 3 iterations
## Return code 2: successive function values within tolerance limit
## Log-Likelihood: -1444.768 
## 3  free parameters
## Estimates:
##                 Estimate Std. error t value Pr(> t)  
## period3        -0.075398   0.037097  -2.032  0.0421 *
## elipic          0.005871   0.024052   0.244  0.8071  
## period3:elipic  0.001700   0.026410   0.064  0.9487  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## --------------------------------------------

Cardiovascular causes mortality

Effet sur mortalité par causes cardiovasculaires période 2 vs. Période 3 :

Linear Normal Regression

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = cv_tot ~ period + elipic + period * elipic, data = datam_p2, 
##     model = "within")
## 
## Unbalanced Panel: n = 128, T = 1-4, N = 492
## 
## Residuals:
##      Min.   1st Qu.    Median   3rd Qu.      Max. 
## -14.98064  -2.75522  -0.23064   3.19084  15.21721 
## 
## Coefficients:
##                Estimate Std. Error t-value Pr(>|t|)  
## period3         -4.4465     2.2311 -1.9930  0.04701 *
## elipic           1.8689     1.4317  1.3054  0.19260  
## period3:elipic  -3.7914     1.5718 -2.4121  0.01636 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    11814
## Residual Sum of Squares: 11284
## R-Squared:      0.044894
## Adj. R-Squared: -0.29905
## F-statistic: 5.65619 on 3 and 361 DF, p-value: 0.00085215

Poisson Regression

## --------------------------------------------
## Maximum Likelihood estimation
## Newton-Raphson maximisation, 3 iterations
## Return code 2: successive function values within tolerance limit
## Log-Likelihood: -1054.883 
## 3  free parameters
## Estimates:
##                Estimate Std. error t value Pr(> t)   
## period3        -0.15570    0.07563  -2.059 0.03952 * 
## elipic          0.06405    0.04765   1.344 0.17886   
## period3:elipic -0.13831    0.05292  -2.614 0.00896 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## --------------------------------------------

Respiratory causes mortality

Effet sur mortalité par causes respiratoires période 2 vs. Période 3 :

Linear Normal Regression

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = respi_tot ~ period + elipic + period * elipic, 
##     data = datam_p2, model = "within")
## 
## Unbalanced Panel: n = 128, T = 1-4, N = 492
## 
## Residuals:
##     Min.  1st Qu.   Median  3rd Qu.     Max. 
## -6.88384 -2.29713 -0.59848  1.74369  9.36616 
## 
## Coefficients:
##                Estimate Std. Error t-value Pr(>|t|)  
## period3         2.94145    1.56934  1.8743  0.06169 .
## elipic          0.81148    1.00703  0.8058  0.42088  
## period3:elipic -1.34683    1.10562 -1.2182  0.22396  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    5659.2
## Residual Sum of Squares: 5582.9
## R-Squared:      0.013488
## Adj. R-Squared: -0.34177
## F-statistic: 1.64523 on 3 and 361 DF, p-value: 0.17858

Poisson Regression

## --------------------------------------------
## Maximum Likelihood estimation
## Newton-Raphson maximisation, 2 iterations
## Return code 2: successive function values within tolerance limit
## Log-Likelihood: -928.1845 
## 3  free parameters
## Estimates:
##                Estimate Std. error t value Pr(> t)  
## period3         0.34510    0.13632   2.531  0.0114 *
## elipic          0.11199    0.09462   1.184  0.2366  
## period3:elipic -0.17575    0.10288  -1.708  0.0876 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## --------------------------------------------

Alternative analysis for comparing period 1 with period 3: 1) before PM10 concentration regulation 3) more recent PM10 regulation

### Model to study effect on PM10 concentration
fixPM10_P13<-plm(moyPM10 ~ period + elipic + period*elipic, data=datam13, model="within")


### Model to study effect on mortality

## Non accidental causes 
# Poisson Version
noccP_P13<-pglm(nocc_tot ~ period + elipic + period*elipic, data=datam13, family=poisson(link = "log"), model="within")



## Cardiovascular causes 
# Poisson Version
cvP_P13<-pglm(cv_tot ~ period + elipic + period*elipic, data=datam13, family=poisson(link = "log"), model="within")


## Respiratory causes 
# Poisson Version
respiP_P13<-pglm(respi_tot ~ period + elipic + period*elipic, data=datam13, family=poisson(link = "log"), model="within")

Results

PM10 Concentration

Effet sur niveau de concentration de PM10 période 1 vs. Période 3 :

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = moyPM10 ~ period + elipic + period * elipic, data = datam13, 
##     model = "within")
## 
## Unbalanced Panel: n = 122, T = 1-4, N = 466
## 
## Residuals:
##      Min.   1st Qu.    Median   3rd Qu.      Max. 
## -25.10474  -6.02854   0.14793   5.36840  37.73553 
## 
## Coefficients:
##                Estimate Std. Error t-value  Pr(>|t|)    
## period3        -31.0434     6.5921 -4.7092 3.625e-06 ***
## elipic          34.1880     2.9595 11.5520 < 2.2e-16 ***
## period3:elipic -10.8972     3.1655 -3.4424 0.0006482 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    87592
## Residual Sum of Squares: 31954
## R-Squared:      0.6352
## Adj. R-Squared: 0.50254
## F-statistic: 197.917 on 3 and 341 DF, p-value: < 2.22e-16

Non accidental mortality

Effet sur mortalité non accidentelle période 1 vs. Période 3 :

Poisson Regression

## --------------------------------------------
## Maximum Likelihood estimation
## Newton-Raphson maximisation, 2 iterations
## Return code 2: successive function values within tolerance limit
## Log-Likelihood: -1341.8 
## 3  free parameters
## Estimates:
##                Estimate Std. error t value Pr(> t)  
## period3        -0.12885    0.06193  -2.081  0.0375 *
## elipic         -0.04117    0.02819  -1.461  0.1441  
## period3:elipic  0.04874    0.03022   1.613  0.1068  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## --------------------------------------------

Cardiovascular causes mortality

Effet sur mortalité par causes cardiovasculaires période 1 vs. Période 3 :

Poisson Regression

## --------------------------------------------
## Maximum Likelihood estimation
## Newton-Raphson maximisation, 2 iterations
## Return code 1: gradient close to zero
## Log-Likelihood: -963.6563 
## 3  free parameters
## Estimates:
##                 Estimate Std. error t value Pr(> t)  
## period3        -0.252299   0.120643  -2.091  0.0365 *
## elipic         -0.073217   0.054068  -1.354  0.1757  
## period3:elipic -0.001045   0.058768  -0.018  0.9858  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## --------------------------------------------

Respiratory causes mortality

Effet sur mortalité par causes respiratoires période 1 vs. Période 3 :

Poisson Regression

## --------------------------------------------
## Maximum Likelihood estimation
## Newton-Raphson maximisation, 3 iterations
## Return code 1: gradient close to zero
## Log-Likelihood: -868.7599 
## 3  free parameters
## Estimates:
##                Estimate Std. error t value Pr(> t)  
## period3         0.51866    0.23242   2.232  0.0256 *
## elipic         -0.01307    0.10811  -0.121  0.9037  
## period3:elipic -0.05069    0.11540  -0.439  0.6605  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## --------------------------------------------