D-R Curves for PM10 and mortality over the time with two-stage modeling

Descriptive Statistics for PM10

Descriptive Statistics for pm10
Ville	Minimum	X1st.Qu	Median	Mean	X3rd.Qu	Max	NA.s
bordeaux	0.0000000	17.00000	22.33333	24.68781	29.49141	101.66667	128
clermont	2.0000000	12.50000	17.25000	19.75139	24.00000	105.75000	1
grenoble	3.3333333	17.17448	24.09375	27.45367	34.00000	110.50000	172
lehavre	5.0416667	16.66667	21.66667	24.81355	29.66667	123.66667	20
lille	0.0000000	16.50000	22.00000	25.53733	30.50000	131.00000	132
marseille	4.8229167	22.33333	30.33333	32.00210	39.33333	120.00000	66
nantes	4.5000000	15.00000	19.33333	21.77588	25.79027	112.00000	55
paris	8.0000000	23.00000	29.00000	31.88335	37.57474	153.50000	3
rennes	0.0000000	12.50000	17.00000	19.34861	23.00000	101.50000	67
rouen	0.3958333	17.50000	22.50000	25.40337	29.50000	116.50000	39
strasbourg	2.0000000	16.18750	22.66667	25.66733	31.66667	167.00000	106
toulouse	3.2000000	14.40000	19.60000	21.18753	26.00000	95.33333	30

Descriptive Statistics for pm10 by period (to be completed…)

Linear Interaction Model

Models For Lag0, Lag1 and La2 exposure

## change year variable with numeric ordinal number
for (i in 1:length(villes)){
  villes[[i]]$year<-as.numeric(villes[[i]]$annee)
} 

# define model objects
tot <- matrix(NA, nrow = 12, ncol = 7)
colnames(tot) <- c("Ville","Coefficient_B0","B0_CI95_Low","B0_CI95_High", "Coefficient_B1","LB_CI95_Low","B1_CI95_High")
modtot<-list()
st_errb0<-c()
st_errb1<-c()


# Linear Model for Lag0

for(i in 1:length(villes)) {
   modtot[[i]]<-gam(cv_tot~pm10+pm10:year+ns(time,df=round(8*length(time)/365))+ns(tempmoy,df=6)+ns(temp3,df=6)+Jours++Vacances,data=villes[[i]],family=quasipoisson)
  est<-summary(modtot[[i]])
  tot[i, 1] <- as.character(villes_name[[i]])
  ll<-length(modtot[[i]]$coefficients)
  tot[i, 2] <- modtot[[i]]$coefficients[2]
  tot[i, 3] <- modtot[[i]]$coefficients[2]-(1.96*est$se[2])
  tot[i, 4] <- modtot[[i]]$coefficients[2]+(1.96*est$se[2])
  tot[i, 5] <- modtot[[i]]$coefficients[ll]
  tot[i, 6] <- modtot[[i]]$coefficients[ll]-(1.96*est$se[ll])
  tot[i, 7] <- modtot[[i]]$coefficients[ll]+(1.96*est$se[ll])
  st_errb0[i]<- est$se[2]
  st_errb1[i]<- est$se[ll]
}


# Linear Model for Lag1

# define model objects
tot_L1 <- matrix(NA, nrow = 12, ncol = 7)
colnames(tot_L1) <- c("Ville","Coefficient_B0","B0_CI95_Low","B0_CI95_High", "Coefficient_B1","LB_CI95_Low","B1_CI95_High")
modtot_L1<-list()
st_errb0_L1<-c()
st_errb1_L1<-c()


for(i in 1:length(villes)) {
   modtot_L1[[i]]<-gam(cv_tot~pm10_L1+pm10_L1:year+ns(time,df=round(8*length(time)/365))+ns(tempmoy,df=6)+ns(temp3,df=6)+Jours++Vacances,data=villes[[i]],family=quasipoisson)
  est<-summary(modtot_L1[[i]])
  tot_L1[i, 1] <- as.character(villes_name[[i]])
  ll<-length(modtot_L1[[i]]$coefficients)
  tot_L1[i, 2] <- modtot_L1[[i]]$coefficients[2]
  tot_L1[i, 3] <- modtot_L1[[i]]$coefficients[2]-(1.96*est$se[2])
  tot_L1[i, 4] <- modtot_L1[[i]]$coefficients[2]+(1.96*est$se[2])
  tot_L1[i, 5] <- modtot_L1[[i]]$coefficients[ll]
  tot_L1[i, 6] <- modtot_L1[[i]]$coefficients[ll]-(1.96*est$se[ll])
  tot_L1[i, 7] <- modtot_L1[[i]]$coefficients[ll]+(1.96*est$se[ll])
  st_errb0_L1[i]<- est$se[2]
  st_errb1_L1[i]<- est$se[ll]
}



# Linear Model for Lag2

# define model objects
tot_L2 <- matrix(NA, nrow = 12, ncol = 7)
colnames(tot_L2) <- c("Ville","Coefficient_B0","B0_CI95_Low","B0_CI95_High", "Coefficient_B1","LB_CI95_Low","B1_CI95_High")
modtot_L2<-list()
st_errb0_L2<-c()
st_errb1_L2<-c()


for(i in 1:length(villes)) {
   modtot_L2[[i]]<-gam(cv_tot~pm10_L2+pm10_L2:year+ns(time,df=round(8*length(time)/365))+ns(tempmoy,df=6)+ns(temp3,df=6)+Jours++Vacances,data=villes[[i]],family=quasipoisson)
  est<-summary(modtot_L2[[i]])
  tot_L2[i, 1] <- as.character(villes_name[[i]])
  ll<-length(modtot_L2[[i]]$coefficients)
  tot_L2[i, 2] <- modtot_L2[[i]]$coefficients[2]
  tot_L2[i, 3] <- modtot_L2[[i]]$coefficients[2]-(1.96*est$se[2])
  tot_L2[i, 4] <- modtot_L2[[i]]$coefficients[2]+(1.96*est$se[2])
  tot_L2[i, 5] <- modtot_L2[[i]]$coefficients[ll]
  tot_L2[i, 6] <- modtot_L2[[i]]$coefficients[ll]-(1.96*est$se[ll])
  tot_L2[i, 7] <- modtot_L2[[i]]$coefficients[ll]+(1.96*est$se[ll])
  st_errb0_L2[i]<- est$se[2]
  st_errb1_L2[i]<- est$se[ll]
}

Results For Lag0 exposure

Ville	Coefficient_B0	B0_CI95_Low	B0_CI95_High	Coefficient_B1	LB_CI95_Low	B1_CI95_High
bordeaux	1.0065	1.0046	1.0084	0.9993	0.9991	0.9994
clermont	1.0046	1.0017	1.0075	0.9994	0.9992	0.9997
grenoble	1.0001	0.9980	1.0021	1.0000	0.9998	1.0001
lehavre	1.0020	0.9995	1.0045	1.0000	0.9998	1.0002
lille	1.0054	1.0041	1.0067	0.9994	0.9993	0.9995
marseille	1.0044	1.0032	1.0056	0.9994	0.9993	0.9995
nantes	1.0015	0.9991	1.0040	0.9999	0.9997	1.0001
paris	1.0053	1.0047	1.0060	0.9994	0.9993	0.9994
rennes	0.9993	0.9955	1.0030	1.0001	0.9998	1.0004
rouen	1.0023	1.0003	1.0043	0.9997	0.9995	0.9998
strasbourg	1.0038	1.0018	1.0058	0.9996	0.9994	0.9997
toulouse	1.0079	1.0057	1.0100	0.9990	0.9988	0.9992

villes	Increase_2002	Increase_2015	Temp_change
bordeaux	-1.560	-11.162	-9.601
clermont	-1.219	-8.803	-7.584
grenoble	-0.047	-0.349	-0.302
lehavre	0.049	0.366	0.317
lille	-1.239	-8.949	-7.709
marseille	-1.169	-8.452	-7.283
nantes	-0.185	-1.379	-1.194
paris	-1.315	-9.473	-8.158
rennes	0.263	1.988	1.725
rouen	-0.692	-5.077	-4.385
strasbourg	-0.910	-6.631	-5.722
toulouse	-2.128	-14.976	-12.848

Results For Lag1 exposure

Ville	Coefficient_B0	B0_CI95_Low	B0_CI95_High	Coefficient_B1	LB_CI95_Low	B1_CI95_High
bordeaux	1.0065	1.0046	1.0084	0.9993	0.9991	0.9994
clermont	1.0046	1.0017	1.0075	0.9994	0.9992	0.9997
grenoble	1.0001	0.9980	1.0021	1.0000	0.9998	1.0001
lehavre	1.0020	0.9995	1.0045	1.0000	0.9998	1.0002
lille	1.0054	1.0041	1.0067	0.9994	0.9993	0.9995
marseille	1.0044	1.0032	1.0056	0.9994	0.9993	0.9995
nantes	1.0015	0.9991	1.0040	0.9999	0.9997	1.0001
paris	1.0053	1.0047	1.0060	0.9994	0.9993	0.9994
rennes	0.9993	0.9955	1.0030	1.0001	0.9998	1.0004
rouen	1.0023	1.0003	1.0043	0.9997	0.9995	0.9998
strasbourg	1.0038	1.0018	1.0058	0.9996	0.9994	0.9997
toulouse	1.0079	1.0057	1.0100	0.9990	0.9988	0.9992

villes	Increase_2002	Increase_2015	Temp_change
bordeaux	-1.570	-11.233	-9.663
clermont	-1.201	-8.683	-7.482
grenoble	-0.190	-1.414	-1.225
lehavre	0.119	0.898	0.779
lille	-1.173	-8.485	-7.312
marseille	-1.187	-8.577	-7.391
nantes	-0.165	-1.229	-1.064
paris	-1.317	-9.484	-8.168
rennes	0.255	1.927	1.672
rouen	-0.654	-4.806	-4.152
strasbourg	-0.907	-6.612	-5.705
toulouse	-2.180	-15.321	-13.141

Results For Lag2 exposure

Ville	Coefficient_B0	B0_CI95_Low	B0_CI95_High	Coefficient_B1	LB_CI95_Low	B1_CI95_High
bordeaux	1.0065	1.0046	1.0084	0.9993	0.9991	0.9994
clermont	1.0046	1.0017	1.0075	0.9994	0.9992	0.9997
grenoble	1.0001	0.9980	1.0021	1.0000	0.9998	1.0001
lehavre	1.0020	0.9995	1.0045	1.0000	0.9998	1.0002
lille	1.0054	1.0041	1.0067	0.9994	0.9993	0.9995
marseille	1.0044	1.0032	1.0056	0.9994	0.9993	0.9995
nantes	1.0015	0.9991	1.0040	0.9999	0.9997	1.0001
paris	1.0053	1.0047	1.0060	0.9994	0.9993	0.9994
rennes	0.9993	0.9955	1.0030	1.0001	0.9998	1.0004
rouen	1.0023	1.0003	1.0043	0.9997	0.9995	0.9998
strasbourg	1.0038	1.0018	1.0058	0.9996	0.9994	0.9997
toulouse	1.0079	1.0057	1.0100	0.9990	0.9988	0.9992

villes	Increase_2002	Increase_2015	Temp_change
bordeaux	-1.509	-10.810	-9.301
clermont	-1.138	-8.241	-7.102
grenoble	-0.284	-2.113	-1.829
lehavre	0.038	0.286	0.248
lille	-1.170	-8.465	-7.295
marseille	-1.206	-8.715	-7.509
nantes	-0.181	-1.346	-1.166
paris	-1.302	-9.383	-8.081
rennes	0.229	1.729	1.500
rouen	-0.741	-5.427	-4.686
strasbourg	-0.771	-5.644	-4.873
toulouse	-2.029	-14.321	-12.292

Metanalysis of the results

For Lag0 exposure

##         Increase_2002 Increase_2015 Temp_change
## intrcpt    -0.8533283     -6.231571   -5.378243

Results For Lag1 exposure

##         Increase_2002 Increase_2015 Temp_change
## intrcpt    -0.8546975     -6.241711   -5.387014

Results For Lag2 exposure

##         Increase_2002 Increase_2015 Temp_change
## intrcpt    -0.8507206     -6.213144   -5.362423

Non-Linear Interaction Model

Models For Lag0, Lag1 and La2 exposure

# Non-Linear Model for Lag0

for(i in 1:length(villes)) {
  year[[i]] <- onebasis(villes[[i]]$year,"ns",knots=c(4,7,11))
  yr<-year[[i]]
  nl_modtot[[i]]<-gam(cv_tot~pm10+pm10:yr+ns(time,df=round(8*length(time)/365))+ns(tempmoy,df=6)+ns(temp3,df=6)+Jours++Vacances,data=villes[[i]],family=quasipoisson)
  est<-summary(nl_modtot[[i]])
  nl_coeffB0[i,1] <- as.character(villes_name[[i]])
  nl_coeffB1[i,1] <- as.character(villes_name[[i]])
  ll<-length(nl_modtot[[i]]$coefficients)
  nl_coeffB0[i, 2] <- nl_modtot[[i]]$coefficients[2]
  nl_coeffB0[i, 3] <- nl_modtot[[i]]$coefficients[2]-(1.96*est$se[2])
  nl_coeffB0[i, 4] <- nl_modtot[[i]]$coefficients[2]+(1.96*est$se[2])
  nl_coeffB1[i, 2] <- nl_modtot[[i]]$coefficients[ll-3]
  nl_coeffB1[i, 3] <- nl_modtot[[i]]$coefficients[ll-3]-(1.96*est$se[ll-3])
  nl_coeffB1[i, 4] <- nl_modtot[[i]]$coefficients[ll-3]+(1.96*est$se[ll-3])
  nl_coeffB1[i, 5] <- nl_modtot[[i]]$coefficients[ll-2]
  nl_coeffB1[i, 6] <- nl_modtot[[i]]$coefficients[ll-2]-(1.96*est$se[ll-2])
  nl_coeffB1[i, 7] <- nl_modtot[[i]]$coefficients[ll-2]+(1.96*est$se[ll-2])
  nl_coeffB1[i, 8] <- nl_modtot[[i]]$coefficients[ll-1]
  nl_coeffB1[i, 9] <- nl_modtot[[i]]$coefficients[ll-1]-(1.96*est$se[ll-1])
  nl_coeffB1[i, 10] <- nl_modtot[[i]]$coefficients[ll]+(1.96*est$se[ll-1])
  nl_coeffB1[i, 11] <- nl_modtot[[i]]$coefficients[ll]
  nl_coeffB1[i, 12] <- nl_modtot[[i]]$coefficients[ll]-(1.96*est$se[ll])
  nl_coeffB1[i, 13] <- nl_modtot[[i]]$coefficients[ll]+(1.96*est$se[ll])
  # nl_st_errb0[i]<- est$se[2]
  # nl_st_errb11[i]<- est$se[ll-3]
  # nl_st_errb12[i]<- est$se[ll-2]
  # nl_st_errb13[i]<- est$se[ll-1]
  # nl_st_errb14[i]<- est$se[ll]
  pred_nnlin[[i]]<-crosspred(yr,nl_modtot[[i]],cen=0)
  y_nl[i,] <- pred_nnlin[[i]]$coef
  S_nl[[i]] <- pred_nnlin[[i]]$vcov
}

# Non-Linear Model for Lag1

for(i in 1:length(villes)) {
  year[[i]] <- onebasis(villes[[i]]$year,"ns",knots=c(4,7,11))
  yr<-year[[i]]
  nl_modtot_L1[[i]]<-gam(cv_tot~pm10_L1+pm10_L1:yr+ns(time,df=round(8*length(time)/365))+ns(tempmoy,df=6)+ns(temp3,df=6)+Jours++Vacances,data=villes[[i]],family=quasipoisson)
  est<-summary(nl_modtot_L1[[i]])
  nl_coeffB0_L1[i,1] <- as.character(villes_name[[i]])
  nl_coeffB1_L1[i,1] <- as.character(villes_name[[i]])
  ll<-length(nl_modtot_L1[[i]]$coefficients)
  nl_coeffB0_L1[i, 2] <- nl_modtot_L1[[i]]$coefficients[2]
  nl_coeffB0_L1[i, 3] <- nl_modtot_L1[[i]]$coefficients[2]-(1.96*est$se[2])
  nl_coeffB0_L1[i, 4] <- nl_modtot_L1[[i]]$coefficients[2]+(1.96*est$se[2])
  nl_coeffB1_L1[i, 2] <- nl_modtot_L1[[i]]$coefficients[ll-3]
  nl_coeffB1_L1[i, 3] <- nl_modtot_L1[[i]]$coefficients[ll-3]-(1.96*est$se[ll-3])
  nl_coeffB1_L1[i, 4] <- nl_modtot_L1[[i]]$coefficients[ll-3]+(1.96*est$se[ll-3])
  nl_coeffB1_L1[i, 5] <- nl_modtot_L1[[i]]$coefficients[ll-2]
  nl_coeffB1_L1[i, 6] <- nl_modtot_L1[[i]]$coefficients[ll-2]-(1.96*est$se[ll-2])
  nl_coeffB1_L1[i, 7] <- nl_modtot_L1[[i]]$coefficients[ll-2]+(1.96*est$se[ll-2])
  nl_coeffB1_L1[i, 8] <- nl_modtot_L1[[i]]$coefficients[ll-1]
  nl_coeffB1_L1[i, 9] <- nl_modtot_L1[[i]]$coefficients[ll-1]-(1.96*est$se[ll-1])
  nl_coeffB1_L1[i, 10] <- nl_modtot_L1[[i]]$coefficients[ll]+(1.96*est$se[ll-1])
  nl_coeffB1_L1[i, 11] <- nl_modtot_L1[[i]]$coefficients[ll]
  nl_coeffB1_L1[i, 12] <- nl_modtot_L1[[i]]$coefficients[ll]-(1.96*est$se[ll])
  nl_coeffB1_L1[i, 13] <- nl_modtot_L1[[i]]$coefficients[ll]+(1.96*est$se[ll])
  pred_nnlin_L1[[i]]<-crosspred(yr,nl_modtot_L1[[i]],cen=0)
  y_nl_L1[i,] <- pred_nnlin_L1[[i]]$coef
  S_nl_L1[[i]] <- pred_nnlin_L1[[i]]$vcov
}

# Non-Linear Model for Lag2

for(i in 1:length(villes)) {
  year[[i]] <- onebasis(villes[[i]]$year,"ns",knots=c(4,7,11))
  yr<-year[[i]]
  nl_modtot_L2[[i]]<-gam(cv_tot~pm10_L2+pm10_L2:yr+ns(time,df=round(8*length(time)/365))+ns(tempmoy,df=6)+ns(temp3,df=6)+Jours++Vacances,data=villes[[i]],family=quasipoisson)
  est<-summary(nl_modtot_L2[[i]])
  nl_coeffB0_L2[i,1] <- as.character(villes_name[[i]])
  nl_coeffB1_L2[i,1] <- as.character(villes_name[[i]])
  ll<-length(nl_modtot_L2[[i]]$coefficients)
  nl_coeffB0_L2[i, 2] <- nl_modtot_L2[[i]]$coefficients[2]
  nl_coeffB0_L2[i, 3] <- nl_modtot_L2[[i]]$coefficients[2]-(1.96*est$se[2])
  nl_coeffB0_L2[i, 4] <- nl_modtot_L2[[i]]$coefficients[2]+(1.96*est$se[2])
  nl_coeffB1_L2[i, 2] <- nl_modtot_L2[[i]]$coefficients[ll-3]
  nl_coeffB1_L2[i, 3] <- nl_modtot_L2[[i]]$coefficients[ll-3]-(1.96*est$se[ll-3])
  nl_coeffB1_L2[i, 4] <- nl_modtot_L2[[i]]$coefficients[ll-3]+(1.96*est$se[ll-3])
  nl_coeffB1_L2[i, 5] <- nl_modtot_L2[[i]]$coefficients[ll-2]
  nl_coeffB1_L2[i, 6] <- nl_modtot_L2[[i]]$coefficients[ll-2]-(1.96*est$se[ll-2])
  nl_coeffB1_L2[i, 7] <- nl_modtot_L2[[i]]$coefficients[ll-2]+(1.96*est$se[ll-2])
  nl_coeffB1_L2[i, 8] <- nl_modtot_L2[[i]]$coefficients[ll-1]
  nl_coeffB1_L2[i, 9] <- nl_modtot_L2[[i]]$coefficients[ll-1]-(1.96*est$se[ll-1])
  nl_coeffB1_L2[i, 10] <- nl_modtot_L2[[i]]$coefficients[ll]+(1.96*est$se[ll-1])
  nl_coeffB1_L2[i, 11] <- nl_modtot_L2[[i]]$coefficients[ll]
  nl_coeffB1_L2[i, 12] <- nl_modtot_L2[[i]]$coefficients[ll]-(1.96*est$se[ll])
  nl_coeffB1_L2[i, 13] <- nl_modtot_L2[[i]]$coefficients[ll]+(1.96*est$se[ll])
  pred_nnlin_L2[[i]]<-crosspred(yr,nl_modtot_L2[[i]],cen=0)
  y_nl_L2[i,] <- pred_nnlin_L2[[i]]$coef
  S_nl_L2[[i]] <- pred_nnlin_L2[[i]]$vcov
}

Meta-analysis results

## Call:  mvmeta(formula = y_nl ~ 1, S = S_nl, method = "ml")
## 
## Multivariate random-effects meta-analysis
## Dimension: 4
## Estimation method: ML
## 
## Fixed-effects coefficients
##     Estimate  Std. Error        z  Pr(>|z|)  95%ci.lb  95%ci.ub     
## y1   -0.0029      0.0006  -5.2692    0.0000   -0.0040   -0.0018  ***
## y2   -0.0055      0.0011  -4.9205    0.0000   -0.0076   -0.0033  ***
## y3   -0.0095      0.0015  -6.3377    0.0000   -0.0125   -0.0066  ***
## y4   -0.0030      0.0012  -2.5475    0.0108   -0.0054   -0.0007    *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## 
## Between-study random-effects (co)variance components
## Structure: General positive-definite
##     Std. Dev    Corr                
## y1    0.0016      y1      y2      y3
## y2    0.0035  0.7905                
## y3    0.0048  0.9575  0.9335        
## y4    0.0036  0.9825  0.6625  0.8870
## 
## Multivariate Cochran Q-test for heterogeneity:
## Q = 202.1117 (df = 44), p-value = 0.0000
## I-square statistic = 78.2%
## 
## 12 studies, 48 observations, 4 fixed and 10 random-effects parameters
##    logLik        AIC        BIC  
##  220.4507  -412.9014  -386.7046

## Call:  mvmeta(formula = y_nl_L1 ~ 1, S = S_nl_L1, method = "ml")
## 
## Multivariate random-effects meta-analysis
## Dimension: 4
## Estimation method: ML
## 
## Fixed-effects coefficients
##     Estimate  Std. Error        z  Pr(>|z|)  95%ci.lb  95%ci.ub     
## y1   -0.0030      0.0006  -5.3705    0.0000   -0.0042   -0.0019  ***
## y2   -0.0055      0.0010  -5.2990    0.0000   -0.0075   -0.0035  ***
## y3   -0.0097      0.0015  -6.5720    0.0000   -0.0126   -0.0068  ***
## y4   -0.0030      0.0012  -2.3886    0.0169   -0.0054   -0.0005    *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## 
## Between-study random-effects (co)variance components
## Structure: General positive-definite
##     Std. Dev    Corr                
## y1    0.0016      y1      y2      y3
## y2    0.0032  0.7803                
## y3    0.0047  0.9658  0.9158        
## y4    0.0039  0.9911  0.6902  0.9227
## 
## Multivariate Cochran Q-test for heterogeneity:
## Q = 197.9010 (df = 44), p-value = 0.0000
## I-square statistic = 77.8%
## 
## 12 studies, 48 observations, 4 fixed and 10 random-effects parameters
##    logLik        AIC        BIC  
##  221.2760  -414.5519  -388.3551

## Call:  mvmeta(formula = y_nl_L2 ~ 1, S = S_nl_L2, method = "ml")
## 
## Multivariate random-effects meta-analysis
## Dimension: 4
## Estimation method: ML
## 
## Fixed-effects coefficients
##     Estimate  Std. Error        z  Pr(>|z|)  95%ci.lb  95%ci.ub     
## y1   -0.0029      0.0005  -5.3413    0.0000   -0.0040   -0.0019  ***
## y2   -0.0054      0.0010  -5.4234    0.0000   -0.0074   -0.0035  ***
## y3   -0.0095      0.0013  -7.1951    0.0000   -0.0121   -0.0069  ***
## y4   -0.0031      0.0012  -2.6642    0.0077   -0.0053   -0.0008   **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## 
## Between-study random-effects (co)variance components
## Structure: General positive-definite
##     Std. Dev    Corr                
## y1    0.0015      y1      y2      y3
## y2    0.0031  0.5240                
## y3    0.0040  0.8604  0.8849        
## y4    0.0035  0.9910  0.6335  0.9210
## 
## Multivariate Cochran Q-test for heterogeneity:
## Q = 178.9844 (df = 44), p-value = 0.0000
## I-square statistic = 75.4%
## 
## 12 studies, 48 observations, 4 fixed and 10 random-effects parameters
##    logLik        AIC        BIC  
##  221.4674  -414.9348  -388.7380

D-R Curves for PM10 and mortality over the time with two-stage modeling - Linear and Non linear interaction Models

Anna Alari

11 février, 2021

Descriptive Statistics for PM10

Descriptive Statistics for pm10 by period (to be completed…)

Linear Interaction Model

Models For Lag0, Lag1 and La2 exposure

Results For Lag0 exposure

Results For Lag1 exposure

Results For Lag2 exposure

Metanalysis of the results

For Lag0 exposure

Results For Lag1 exposure

Results For Lag2 exposure

Non-Linear Interaction Model

Models For Lag0, Lag1 and La2 exposure

Meta-analysis results