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

Descriptive Statistics for O3

Descriptive Statistics for o3
Ville	Minimum	X1st.Qu	Median	Mean	X3rd.Qu	Max	NA.s
bordeaux	1.9154062	51.33333	70.95833	70.70046	89.16369	169.5000	NA
clermont	1.7321429	54.12500	72.68750	72.06568	90.12500	178.5625	138
grenoble	0.4375000	35.51116	65.96875	65.82133	91.66518	185.8750	NA
lehavre	2.1250000	57.25000	70.62500	69.51529	82.12500	184.5000	59
lille	0.1666667	41.00000	59.00000	58.91898	74.75000	207.1250	239
marseille	3.1250000	54.75000	79.59742	77.44850	99.62500	185.6250	16
nantes	3.1250000	55.00000	70.37500	71.71581	87.62500	216.5000	71
paris	0.8592206	37.65048	57.72942	59.16113	77.16338	216.3857	NA
rennes	1.5625000	52.12500	65.93750	66.48971	80.25005	213.5625	17
rouen	1.2972346	46.96354	63.34375	63.70247	79.04688	178.6607	NA
strasbourg	0.0000000	36.75000	62.87500	64.30176	87.75000	206.5000	99
toulouse	1.6250000	57.31250	76.27500	76.08195	94.61250	180.9594	NA

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(respi_tot~o3.x+o3.x: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(respi_tot~o3_L1+o3_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(respi_tot~o3_L2+o3_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	0.9983	0.9960	1.0006	1.0002	1.0001	1.0003
clermont	0.9984	0.9952	1.0015	1.0003	1.0002	1.0005
grenoble	0.9996	0.9972	1.0021	1.0003	1.0002	1.0005
lehavre	0.9994	0.9961	1.0028	1.0000	0.9998	1.0002
lille	1.0008	0.9993	1.0022	1.0001	1.0000	1.0001
marseille	0.9997	0.9982	1.0012	1.0002	1.0001	1.0002
nantes	1.0005	0.9979	1.0032	1.0003	1.0002	1.0004
paris	1.0001	0.9993	1.0009	1.0000	0.9999	1.0000
rennes	1.0004	0.9968	1.0039	1.0000	0.9998	1.0002
rouen	0.9989	0.9962	1.0015	1.0001	0.9999	1.0002
strasbourg	0.9984	0.9961	1.0006	1.0003	1.0002	1.0005
toulouse	0.9997	0.9972	1.0021	1.0002	1.0001	1.0003

villes	Increase_2002	Increase_2015	Temp_change
bordeaux	0.320	2.428	2.107
clermont	0.689	5.283	4.595
grenoble	0.623	4.771	4.148
lehavre	-0.011	-0.081	-0.070
lille	0.122	0.920	0.798
marseille	0.347	2.636	2.288
nantes	0.610	4.668	4.058
paris	-0.016	-0.119	-0.103
rennes	0.021	0.161	0.139
rouen	0.155	1.172	1.017
strasbourg	0.644	4.936	4.292
toulouse	0.342	2.595	2.253

Results For Lag1 exposure

Ville	Coefficient_B0	B0_CI95_Low	B0_CI95_High	Coefficient_B1	LB_CI95_Low	B1_CI95_High
bordeaux	0.9983	0.9960	1.0006	1.0002	1.0001	1.0003
clermont	0.9984	0.9952	1.0015	1.0003	1.0002	1.0005
grenoble	0.9996	0.9972	1.0021	1.0003	1.0002	1.0005
lehavre	0.9994	0.9961	1.0028	1.0000	0.9998	1.0002
lille	1.0008	0.9993	1.0022	1.0001	1.0000	1.0001
marseille	0.9997	0.9982	1.0012	1.0002	1.0001	1.0002
nantes	1.0005	0.9979	1.0032	1.0003	1.0002	1.0004
paris	1.0001	0.9993	1.0009	1.0000	0.9999	1.0000
rennes	1.0004	0.9968	1.0039	1.0000	0.9998	1.0002
rouen	0.9989	0.9962	1.0015	1.0001	0.9999	1.0002
strasbourg	0.9984	0.9961	1.0006	1.0003	1.0002	1.0005
toulouse	0.9997	0.9972	1.0021	1.0002	1.0001	1.0003

villes	Increase_2002	Increase_2015	Temp_change
bordeaux	0.326	2.468	2.142
clermont	0.698	5.358	4.660
grenoble	0.503	3.833	3.331
lehavre	-0.046	-0.346	-0.300
lille	0.113	0.851	0.738
marseille	0.361	2.742	2.380
nantes	0.614	4.695	4.081
paris	-0.001	-0.010	-0.009
rennes	0.002	0.017	0.015
rouen	0.165	1.245	1.080
strasbourg	0.643	4.927	4.284
toulouse	0.317	2.405	2.087

Results For Lag2 exposure

Ville	Coefficient_B0	B0_CI95_Low	B0_CI95_High	Coefficient_B1	LB_CI95_Low	B1_CI95_High
bordeaux	0.9983	0.9960	1.0006	1.0002	1.0001	1.0003
clermont	0.9984	0.9952	1.0015	1.0003	1.0002	1.0005
grenoble	0.9996	0.9972	1.0021	1.0003	1.0002	1.0005
lehavre	0.9994	0.9961	1.0028	1.0000	0.9998	1.0002
lille	1.0008	0.9993	1.0022	1.0001	1.0000	1.0001
marseille	0.9997	0.9982	1.0012	1.0002	1.0001	1.0002
nantes	1.0005	0.9979	1.0032	1.0003	1.0002	1.0004
paris	1.0001	0.9993	1.0009	1.0000	0.9999	1.0000
rennes	1.0004	0.9968	1.0039	1.0000	0.9998	1.0002
rouen	0.9989	0.9962	1.0015	1.0001	0.9999	1.0002
strasbourg	0.9984	0.9961	1.0006	1.0003	1.0002	1.0005
toulouse	0.9997	0.9972	1.0021	1.0002	1.0001	1.0003

villes	Increase_2002	Increase_2015	Temp_change
bordeaux	0.302	2.290	1.987
clermont	0.696	5.347	4.651
grenoble	0.507	3.869	3.361
lehavre	-0.118	-0.879	-0.762
lille	0.112	0.840	0.729
marseille	0.354	2.684	2.330
nantes	0.665	5.100	4.435
paris	-0.009	-0.069	-0.060
rennes	0.012	0.089	0.077
rouen	0.152	1.148	0.996
strasbourg	0.673	5.160	4.487
toulouse	0.332	2.519	2.186

Metanalysis of the results

For Lag0 exposure

##         Increase_2002 Increase_2015 Temp_change
## intrcpt     0.3174538       2.40565    2.088196

Results For Lag1 exposure

##         Increase_2002 Increase_2015 Temp_change
## intrcpt     0.3059602        2.3178     2.01184

Results For Lag2 exposure

##         Increase_2002 Increase_2015 Temp_change
## intrcpt     0.3068711      2.324763    2.017892

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]]$year,"ns",knots=c(4,7,11))
  yr<-year[[i]]
  nl_modtot[[i]]<-gam(respi_tot~o3+o3:yr+ns(time,df=round(8*length(time)/365))+ns(tempmoy,df=6)+ns(temp3,df=6)+Jours++Vacances,data=villes[[i]],family=quasipoisson)
  est<-summary(nl_modtot[[i]])
  nl_coeffB0[i,1] <- as.character(villes_name[[i]])
  nl_coeffB1[i,1] <- as.character(villes_name[[i]])
  ll<-length(nl_modtot[[i]]$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]]$year,"ns",knots=c(4,7,11))
  yr<-year[[i]]
  nl_modtot_L1[[i]]<-gam(respi_tot~o3_L1+o3_L1:yr+ns(time,df=round(8*length(time)/365))+ns(tempmoy,df=6)+ns(temp3,df=6)+Jours++Vacances,data=villes[[i]],family=quasipoisson)
  est<-summary(nl_modtot_L1[[i]])
  nl_coeffB0_L1[i,1] <- as.character(villes_name[[i]])
  nl_coeffB1_L1[i,1] <- as.character(villes_name[[i]])
  ll<-length(nl_modtot_L1[[i]]$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]]$year,"ns",knots=c(4,7,11))
  yr<-year[[i]]
  nl_modtot_L2[[i]]<-gam(respi_tot~o3_L2+o3_L2:yr+ns(time,df=round(8*length(time)/365))+ns(tempmoy,df=6)+ns(temp3,df=6)+Jours++Vacances,data=villes[[i]],family=quasipoisson)
  est<-summary(nl_modtot_L2[[i]])
  nl_coeffB0_L2[i,1] <- as.character(villes_name[[i]])
  nl_coeffB1_L2[i,1] <- as.character(villes_name[[i]])
  ll<-length(nl_modtot_L2[[i]]$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   -0.0014      0.0007  -2.1596    0.0308   -0.0028   -0.0001    *
## y2    0.0005      0.0006   0.8023    0.4224   -0.0007    0.0016     
## y3    0.0008      0.0011   0.7522    0.4519   -0.0013    0.0029     
## y4    0.0041      0.0009   4.5968    0.0000    0.0023    0.0058  ***
## ---
## 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    0.0017        y1        y2        y3
## y2    0.0012  -0.17685                    
## y3    0.0026  -0.20308   0.87793          
## y4    0.0025   0.63583   0.06172   0.38011
## 
## Multivariate Cochran Q-test for heterogeneity:
## Q = 126.5203 (df = 44), p-value = 0.0000
## I-square statistic = 65.2%
## 
## 12 studies, 48 observations, 4 fixed and 10 random-effects parameters
##    logLik        AIC        BIC  
##  219.1554  -410.3108  -384.1140

## 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   -0.0012      0.0004  -2.6510    0.0080   -0.0020   -0.0003   **
## y2    0.0003      0.0005   0.5105    0.6097   -0.0007    0.0012     
## y3    0.0005      0.0008   0.6361    0.5247   -0.0010    0.0020     
## y4    0.0030      0.0006   4.6781    0.0000    0.0017    0.0042  ***
## ---
## 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    0.0010        y1        y2        y3
## y2    0.0013   0.09163                    
## y3    0.0019  -0.27064   0.82487          
## y4    0.0018   0.46127  -0.03728   0.20091
## 
## Multivariate Cochran Q-test for heterogeneity:
## Q = 137.7102 (df = 44), p-value = 0.0000
## I-square statistic = 68.0%
## 
## 12 studies, 48 observations, 4 fixed and 10 random-effects parameters
##    logLik        AIC        BIC  
##  234.4894  -440.9788  -414.7819

## 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   -0.0013      0.0005  -2.7671    0.0057   -0.0022   -0.0004   **
## y2    0.0004      0.0005   0.7653    0.4441   -0.0007    0.0015     
## y3    0.0006      0.0009   0.6914    0.4893   -0.0011    0.0023     
## y4    0.0028      0.0007   4.0365    0.0001    0.0015    0.0042  ***
## ---
## 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    0.0011        y1        y2        y3
## y2    0.0015   0.12040                    
## y3    0.0023  -0.27852   0.81554          
## y4    0.0020   0.61429  -0.07473   0.02831
## 
## Multivariate Cochran Q-test for heterogeneity:
## Q = 152.6785 (df = 44), p-value = 0.0000
## I-square statistic = 71.2%
## 
## 12 studies, 48 observations, 4 fixed and 10 random-effects parameters
##    logLik        AIC        BIC  
##  231.3374  -434.6748  -408.4780

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

Anna Alari

25 février, 2021

Descriptive Statistics for O3

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