D-R Curves for Ozone and mortality over the time with two-stage modeling - Linear and Non linear interaction Models
Anna Alari
25 février, 2021
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(cv_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$se[ll]
}
# Linear Model for Lag1
# define model objects
tot_L1 <- matrix(NA, nrow = 12, ncol = 7)
colnames(tot_L1) <- c("Ville","Coefficient_B0","B0_CI95_Low","B0_CI95_High", "Coefficient_B1","LB_CI95_Low","B1_CI95_High")
modtot_L1<-list()
st_errb0_L1<-c()
st_errb1_L1<-c()
for(i in 1:length(villes)) {
modtot_L1[[i]]<-gam(cv_tot~o3_L1+o3_L1:year+ns(time,df=round(8*length(time)/365))+ns(tempmoy,df=6)+ns(temp3,df=6)+Jours++Vacances,data=villes[[i]],family=quasipoisson)
est<-summary(modtot_L1[[i]])
tot_L1[i, 1] <- as.character(villes_name[[i]])
ll<-length(modtot_L1[[i]]$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(cv_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 | 1.0008 | 0.9997 | 1.0018 | 0.9997 | 0.9997 | 0.9998 |
| clermont | 1.0008 | 0.9994 | 1.0022 | 0.9998 | 0.9998 | 0.9999 |
| grenoble | 1.0002 | 0.9991 | 1.0013 | 1.0000 | 0.9999 | 1.0000 |
| lehavre | 0.9999 | 0.9982 | 1.0015 | 1.0000 | 0.9999 | 1.0001 |
| lille | 1.0016 | 1.0009 | 1.0024 | 0.9998 | 0.9997 | 0.9998 |
| marseille | 1.0021 | 1.0014 | 1.0029 | 0.9998 | 0.9997 | 0.9998 |
| nantes | 1.0000 | 0.9988 | 1.0012 | 1.0000 | 0.9999 | 1.0000 |
| paris | 1.0022 | 1.0018 | 1.0026 | 0.9997 | 0.9997 | 0.9997 |
| rennes | 1.0003 | 0.9985 | 1.0021 | 1.0000 | 0.9999 | 1.0001 |
| rouen | 1.0009 | 0.9997 | 1.0021 | 0.9999 | 0.9998 | 0.9999 |
| strasbourg | 1.0008 | 0.9998 | 1.0018 | 0.9998 | 0.9998 | 0.9999 |
| toulouse | 1.0027 | 1.0016 | 1.0039 | 0.9997 | 0.9997 | 0.9997 |
| villes | Increase_2002 | Increase_2015 | Temp_change |
|---|---|---|---|
| bordeaux | -0.551 | -4.061 | -3.510 |
| clermont | -0.341 | -2.526 | -2.186 |
| grenoble | -0.042 | -0.316 | -0.274 |
| lehavre | -0.002 | -0.016 | -0.014 |
| lille | -0.467 | -3.448 | -2.981 |
| marseille | -0.463 | -3.423 | -2.960 |
| nantes | -0.097 | -0.729 | -0.631 |
| paris | -0.608 | -4.474 | -3.866 |
| rennes | 0.035 | 0.260 | 0.226 |
| rouen | -0.250 | -1.861 | -1.611 |
| strasbourg | -0.313 | -2.326 | -2.013 |
| toulouse | -0.614 | -4.518 | -3.904 |
Results For Lag1 exposure
| Ville | Coefficient_B0 | B0_CI95_Low | B0_CI95_High | Coefficient_B1 | LB_CI95_Low | B1_CI95_High |
|---|---|---|---|---|---|---|
| bordeaux | 1.0008 | 0.9997 | 1.0018 | 0.9997 | 0.9997 | 0.9998 |
| clermont | 1.0008 | 0.9994 | 1.0022 | 0.9998 | 0.9998 | 0.9999 |
| grenoble | 1.0002 | 0.9991 | 1.0013 | 1.0000 | 0.9999 | 1.0000 |
| lehavre | 0.9999 | 0.9982 | 1.0015 | 1.0000 | 0.9999 | 1.0001 |
| lille | 1.0016 | 1.0009 | 1.0024 | 0.9998 | 0.9997 | 0.9998 |
| marseille | 1.0021 | 1.0014 | 1.0029 | 0.9998 | 0.9997 | 0.9998 |
| nantes | 1.0000 | 0.9988 | 1.0012 | 1.0000 | 0.9999 | 1.0000 |
| paris | 1.0022 | 1.0018 | 1.0026 | 0.9997 | 0.9997 | 0.9997 |
| rennes | 1.0003 | 0.9985 | 1.0021 | 1.0000 | 0.9999 | 1.0001 |
| rouen | 1.0009 | 0.9997 | 1.0021 | 0.9999 | 0.9998 | 0.9999 |
| strasbourg | 1.0008 | 0.9998 | 1.0018 | 0.9998 | 0.9998 | 0.9999 |
| toulouse | 1.0027 | 1.0016 | 1.0039 | 0.9997 | 0.9997 | 0.9997 |
| villes | Increase_2002 | Increase_2015 | Temp_change |
|---|---|---|---|
| bordeaux | -0.565 | -4.161 | -3.596 |
| clermont | -0.334 | -2.479 | -2.145 |
| grenoble | -0.033 | -0.249 | -0.215 |
| lehavre | -0.020 | -0.153 | -0.132 |
| lille | -0.495 | -3.653 | -3.158 |
| marseille | -0.469 | -3.466 | -2.997 |
| nantes | -0.108 | -0.806 | -0.698 |
| paris | -0.607 | -4.464 | -3.857 |
| rennes | -0.010 | -0.078 | -0.067 |
| rouen | -0.249 | -1.856 | -1.606 |
| strasbourg | -0.319 | -2.367 | -2.048 |
| toulouse | -0.629 | -4.627 | -3.998 |
Results For Lag2 exposure
| Ville | Coefficient_B0 | B0_CI95_Low | B0_CI95_High | Coefficient_B1 | LB_CI95_Low | B1_CI95_High |
|---|---|---|---|---|---|---|
| bordeaux | 1.0008 | 0.9997 | 1.0018 | 0.9997 | 0.9997 | 0.9998 |
| clermont | 1.0008 | 0.9994 | 1.0022 | 0.9998 | 0.9998 | 0.9999 |
| grenoble | 1.0002 | 0.9991 | 1.0013 | 1.0000 | 0.9999 | 1.0000 |
| lehavre | 0.9999 | 0.9982 | 1.0015 | 1.0000 | 0.9999 | 1.0001 |
| lille | 1.0016 | 1.0009 | 1.0024 | 0.9998 | 0.9997 | 0.9998 |
| marseille | 1.0021 | 1.0014 | 1.0029 | 0.9998 | 0.9997 | 0.9998 |
| nantes | 1.0000 | 0.9988 | 1.0012 | 1.0000 | 0.9999 | 1.0000 |
| paris | 1.0022 | 1.0018 | 1.0026 | 0.9997 | 0.9997 | 0.9997 |
| rennes | 1.0003 | 0.9985 | 1.0021 | 1.0000 | 0.9999 | 1.0001 |
| rouen | 1.0009 | 0.9997 | 1.0021 | 0.9999 | 0.9998 | 0.9999 |
| strasbourg | 1.0008 | 0.9998 | 1.0018 | 0.9998 | 0.9998 | 0.9999 |
| toulouse | 1.0027 | 1.0016 | 1.0039 | 0.9997 | 0.9997 | 0.9997 |
| villes | Increase_2002 | Increase_2015 | Temp_change |
|---|---|---|---|
| bordeaux | -0.544 | -4.008 | -3.464 |
| clermont | -0.353 | -2.616 | -2.264 |
| grenoble | -0.012 | -0.093 | -0.080 |
| lehavre | -0.026 | -0.196 | -0.170 |
| lille | -0.484 | -3.572 | -3.088 |
| marseille | -0.481 | -3.550 | -3.069 |
| nantes | -0.114 | -0.854 | -0.740 |
| paris | -0.609 | -4.480 | -3.871 |
| rennes | 0.004 | 0.028 | 0.024 |
| rouen | -0.214 | -1.591 | -1.378 |
| strasbourg | -0.338 | -2.510 | -2.171 |
| toulouse | -0.618 | -4.549 | -3.931 |
Metanalysis of the results
For Lag0 exposure
## Increase_2002 Increase_2015 Temp_change
## intrcpt -0.3152548 -2.340599 -2.025344Results For Lag1 exposure
## Increase_2002 Increase_2015 Temp_change
## intrcpt -0.3251724 -2.413511 -2.088339Results For Lag2 exposure
## Increase_2002 Increase_2015 Temp_change
## intrcpt -0.3204696 -2.378928 -2.058459Non-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~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(cv_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]]$year,"ns",knots=c(4,7,11))
yr<-year[[i]]
nl_modtot_L2[[i]]<-gam(cv_tot~o3_L2+o3_L2:yr+ns(time,df=round(8*length(time)/365))+ns(tempmoy,df=6)+ns(temp3,df=6)+Jours++Vacances,data=villes[[i]],family=quasipoisson)
est<-summary(nl_modtot_L2[[i]])
nl_coeffB0_L2[i,1] <- as.character(villes_name[[i]])
nl_coeffB1_L2[i,1] <- as.character(villes_name[[i]])
ll<-length(nl_modtot_L2[[i]]$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 -0.0012 0.0003 -4.1080 0.0000 -0.0018 -0.0006 ***
## y2 -0.0031 0.0006 -5.0215 0.0000 -0.0043 -0.0019 ***
## y3 -0.0049 0.0008 -5.8909 0.0000 -0.0066 -0.0033 ***
## y4 -0.0015 0.0006 -2.6211 0.0088 -0.0026 -0.0004 **
## ---
## 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 0.0007 y1 y2 y3
## y2 0.0020 0.3357
## y3 0.0026 0.7160 0.8852
## y4 0.0017 0.9066 0.6300 0.8528
##
## Multivariate Cochran Q-test for heterogeneity:
## Q = 289.6345 (df = 44), p-value = 0.0000
## I-square statistic = 84.8%
##
## 12 studies, 48 observations, 4 fixed and 10 random-effects parameters
## logLik AIC BIC
## 249.7238 -471.4475 -445.2507
## 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 -0.0009 0.0002 -4.5068 0.0000 -0.0013 -0.0005 ***
## y2 -0.0023 0.0004 -5.5543 0.0000 -0.0031 -0.0015 ***
## y3 -0.0036 0.0005 -6.7712 0.0000 -0.0046 -0.0025 ***
## y4 -0.0011 0.0004 -2.6613 0.0078 -0.0018 -0.0003 **
## ---
## 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 0.0005 y1 y2 y3
## y2 0.0013 0.3220
## y3 0.0016 0.6906 0.8837
## y4 0.0012 0.9268 0.6119 0.8383
##
## Multivariate Cochran Q-test for heterogeneity:
## Q = 265.5387 (df = 44), p-value = 0.0000
## I-square statistic = 83.4%
##
## 12 studies, 48 observations, 4 fixed and 10 random-effects parameters
## logLik AIC BIC
## 267.1539 -506.3077 -480.1109
## 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 -0.0009 0.0002 -4.0598 0.0000 -0.0013 -0.0005 ***
## y2 -0.0023 0.0004 -5.4981 0.0000 -0.0031 -0.0015 ***
## y3 -0.0036 0.0005 -6.6626 0.0000 -0.0046 -0.0025 ***
## y4 -0.0010 0.0004 -2.5188 0.0118 -0.0018 -0.0002 *
## ---
## 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 0.0005 y1 y2 y3
## y2 0.0013 0.2073
## y3 0.0016 0.6072 0.8891
## y4 0.0012 0.9057 0.5960 0.8642
##
## Multivariate Cochran Q-test for heterogeneity:
## Q = 268.2916 (df = 44), p-value = 0.0000
## I-square statistic = 83.6%
##
## 12 studies, 48 observations, 4 fixed and 10 random-effects parameters
## logLik AIC BIC
## 267.8930 -507.7860 -481.5891