D-R Curves for PM10 and respi 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(respi_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(respi_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(respi_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	0.9956	0.9917	0.9994	1.0004	1.0001	1.0007
clermont	0.9865	0.9799	0.9930	1.0013	1.0008	1.0019
grenoble	0.9861	0.9816	0.9906	1.0010	1.0006	1.0014
lehavre	0.9997	0.9944	1.0050	1.0000	0.9995	1.0004
lille	0.9968	0.9943	0.9992	1.0002	1.0000	1.0005
marseille	0.9954	0.9930	0.9979	1.0006	1.0004	1.0008
nantes	0.9871	0.9819	0.9923	1.0012	1.0008	1.0016
paris	1.0004	0.9992	1.0016	1.0001	1.0000	1.0001
rennes	0.9996	0.9924	1.0068	1.0001	0.9995	1.0007
rouen	1.0017	0.9976	1.0059	1.0003	1.0000	1.0006
strasbourg	0.9953	0.9909	0.9997	1.0009	1.0006	1.0012
toulouse	0.9941	0.9895	0.9987	1.0008	1.0004	1.0011

villes	Increase_2002	Increase_2015	Temp_change
bordeaux	0.762	5.862	5.100
clermont	2.372	19.445	17.073
grenoble	1.768	14.171	12.403
lehavre	-0.016	-0.122	-0.106
lille	0.480	3.658	3.178
marseille	1.137	8.863	7.726
nantes	2.133	17.322	15.189
paris	0.113	0.849	0.736
rennes	0.136	1.027	0.891
rouen	0.642	4.913	4.271
strasbourg	1.739	13.844	12.104
toulouse	1.461	11.528	10.067

Results For Lag1 exposure

Ville	Coefficient_B0	B0_CI95_Low	B0_CI95_High	Coefficient_B1	LB_CI95_Low	B1_CI95_High
bordeaux	0.9956	0.9917	0.9994	1.0004	1.0001	1.0007
clermont	0.9865	0.9799	0.9930	1.0013	1.0008	1.0019
grenoble	0.9861	0.9816	0.9906	1.0010	1.0006	1.0014
lehavre	0.9997	0.9944	1.0050	1.0000	0.9995	1.0004
lille	0.9968	0.9943	0.9992	1.0002	1.0000	1.0005
marseille	0.9954	0.9930	0.9979	1.0006	1.0004	1.0008
nantes	0.9871	0.9819	0.9923	1.0012	1.0008	1.0016
paris	1.0004	0.9992	1.0016	1.0001	1.0000	1.0001
rennes	0.9996	0.9924	1.0068	1.0001	0.9995	1.0007
rouen	1.0017	0.9976	1.0059	1.0003	1.0000	1.0006
strasbourg	0.9953	0.9909	0.9997	1.0009	1.0006	1.0012
toulouse	0.9941	0.9895	0.9987	1.0008	1.0004	1.0011

villes	Increase_2002	Increase_2015	Temp_change
bordeaux	0.908	7.022	6.114
clermont	2.384	19.590	17.206
grenoble	1.733	13.853	12.121
lehavre	0.099	0.742	0.643
lille	0.456	3.473	3.017
marseille	1.098	8.556	7.457
nantes	2.014	16.246	14.232
paris	0.125	0.943	0.818
rennes	-0.097	-0.728	-0.631
rouen	0.690	5.294	4.604
strasbourg	1.746	13.902	12.156
toulouse	1.350	10.599	9.249

Results For Lag2 exposure

Ville	Coefficient_B0	B0_CI95_Low	B0_CI95_High	Coefficient_B1	LB_CI95_Low	B1_CI95_High
bordeaux	0.9956	0.9917	0.9994	1.0004	1.0001	1.0007
clermont	0.9865	0.9799	0.9930	1.0013	1.0008	1.0019
grenoble	0.9861	0.9816	0.9906	1.0010	1.0006	1.0014
lehavre	0.9997	0.9944	1.0050	1.0000	0.9995	1.0004
lille	0.9968	0.9943	0.9992	1.0002	1.0000	1.0005
marseille	0.9954	0.9930	0.9979	1.0006	1.0004	1.0008
nantes	0.9871	0.9819	0.9923	1.0012	1.0008	1.0016
paris	1.0004	0.9992	1.0016	1.0001	1.0000	1.0001
rennes	0.9996	0.9924	1.0068	1.0001	0.9995	1.0007
rouen	1.0017	0.9976	1.0059	1.0003	1.0000	1.0006
strasbourg	0.9953	0.9909	0.9997	1.0009	1.0006	1.0012
toulouse	0.9941	0.9895	0.9987	1.0008	1.0004	1.0011

villes	Increase_2002	Increase_2015	Temp_change
bordeaux	0.935	7.238	6.303
clermont	2.110	17.111	15.001
grenoble	1.602	12.739	11.137
lehavre	0.182	1.370	1.189
lille	0.317	2.405	2.088
marseille	1.044	8.117	7.073
nantes	2.037	16.472	14.435
paris	0.128	0.963	0.835
rennes	0.460	3.503	3.043
rouen	0.711	5.467	4.756
strasbourg	1.852	14.815	12.963
toulouse	1.334	10.487	9.153

Metanalysis of the results

For Lag0 exposure

##         Increase_2002 Increase_2015 Temp_change
## intrcpt      1.076127      8.373883    7.297756

Results For Lag1 exposure

##         Increase_2002 Increase_2015 Temp_change
## intrcpt      1.058639      8.231845    7.173206

Results For Lag2 exposure

##         Increase_2002 Increase_2015 Temp_change
## intrcpt      1.055356      8.207516     7.15216

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]]$year,"ns",knots=c(4,7,11))
  yr<-year[[i]]
  nl_modtot[[i]]<-gam(respi_tot~pm10+pm10:yr+ns(time,df=round(8*length(time)/365))+ns(tempmoy,df=6)+ns(temp3,df=6)+Jours++Vacances,data=villes[[i]],family=quasipoisson)
  est<-summary(nl_modtot[[i]])
  nl_coeffB0[i,1] <- as.character(villes_name[[i]])
  nl_coeffB1[i,1] <- as.character(villes_name[[i]])
  ll<-length(nl_modtot[[i]]$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]]$year,"ns",knots=c(4,7,11))
  yr<-year[[i]]
  nl_modtot_L1[[i]]<-gam(respi_tot~pm10_L1+pm10_L1:yr+ns(time,df=round(8*length(time)/365))+ns(tempmoy,df=6)+ns(temp3,df=6)+Jours++Vacances,data=villes[[i]],family=quasipoisson)
  est<-summary(nl_modtot_L1[[i]])
  nl_coeffB0_L1[i,1] <- as.character(villes_name[[i]])
  nl_coeffB1_L1[i,1] <- as.character(villes_name[[i]])
  ll<-length(nl_modtot_L1[[i]]$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]]$year,"ns",knots=c(4,7,11))
  yr<-year[[i]]
  nl_modtot_L2[[i]]<-gam(respi_tot~pm10_L2+pm10_L2:yr+ns(time,df=round(8*length(time)/365))+ns(tempmoy,df=6)+ns(temp3,df=6)+Jours++Vacances,data=villes[[i]],family=quasipoisson)
  est<-summary(nl_modtot_L2[[i]])
  nl_coeffB0_L2[i,1] <- as.character(villes_name[[i]])
  nl_coeffB1_L2[i,1] <- as.character(villes_name[[i]])
  ll<-length(nl_modtot_L2[[i]]$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   -0.0015      0.0009  -1.5432    0.1228   -0.0033    0.0004     
## y2    0.0013      0.0012   1.1044    0.2694   -0.0010    0.0036     
## y3    0.0041      0.0020   2.0910    0.0365    0.0003    0.0080    *
## y4    0.0108      0.0015   7.1996    0.0000    0.0078    0.0137  ***
## ---
## 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    0.0020       y1       y2       y3
## y2    0.0033   0.5270                  
## y3    0.0048  -0.2724   0.4722         
## y4    0.0042   0.3827   0.9584   0.6968
## 
## Multivariate Cochran Q-test for heterogeneity:
## Q = 178.5237 (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  
##  188.0033  -348.0066  -321.8098

## 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   -0.0019      0.0010  -2.0283    0.0425   -0.0038   -0.0001    *
## y2    0.0015      0.0012   1.2510    0.2109   -0.0009    0.0039     
## y3    0.0045      0.0021   2.1630    0.0305    0.0004    0.0085    *
## y4    0.0103      0.0014   7.5841    0.0000    0.0076    0.0129  ***
## ---
## 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    0.0019       y1       y2       y3
## y2    0.0033  0.38668                  
## y3    0.0047  0.12498  0.32632         
## y4    0.0037  0.07009  0.93333  0.46723
## 
## Multivariate Cochran Q-test for heterogeneity:
## Q = 173.6179 (df = 44), p-value = 0.0000
## I-square statistic = 74.7%
## 
## 12 studies, 48 observations, 4 fixed and 10 random-effects parameters
##    logLik        AIC        BIC  
##  186.8885  -345.7771  -319.5803

## 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   -0.0016      0.0009  -1.7502    0.0801   -0.0033    0.0002    .
## y2    0.0010      0.0012   0.8423    0.3996   -0.0013    0.0033     
## y3    0.0045      0.0020   2.2905    0.0220    0.0007    0.0084    *
## y4    0.0108      0.0016   6.6257    0.0000    0.0076    0.0140  ***
## ---
## 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    0.0029   0.33565                    
## y3    0.0044  -0.04287   0.23726          
## y4    0.0044   0.16962   0.48192   0.55411
## 
## Multivariate Cochran Q-test for heterogeneity:
## Q = 169.1722 (df = 44), p-value = 0.0000
## I-square statistic = 74.0%
## 
## 12 studies, 48 observations, 4 fixed and 10 random-effects parameters
##    logLik        AIC        BIC  
##  188.1874  -348.3748  -322.1780

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

Anna Alari

8/02/2021

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