Modelos de sobrevivência, A Análise de Sobrevivência compreende os estudos em que o interesse principal é avaliar o tempo até a ocorrência de um evento pré-determinado. Esses tempos, chamados de tempos de falha, podem, então, ser explicados por outras variáveis a partir de modelos de regressão paramétricos ou semi-paramétricos. Uma característica fundamental desse tipo de estudo é a presença de censura, definida como a observação parcial do tempo de falha.
dados<- read.table("C:/Users/Gustavo/Downloads/sobrevivencia2.csv",header = T, sep = ",")
head(dados)
## Bike_id Publish_period End_Date Departure_Date
## 1 XL3-1095127 10 1.301357e+18 1.305590e+18
## 3 XL3-1123648 28 1.302307e+18 1.307923e+18
## 4 XL3-1139930 17 1.302826e+18 1.308096e+18
## 6 XL3-1277412 17 1.301616e+18 1.310170e+18
## 8 XL3-1513147 4 1.302221e+18 1.312848e+18
## 10 XL3-1146406 48 1.307318e+18 1.317427e+18
## Distance_travelled Color Country_Sold N_Photos Price N_Inquires
## 1 123525 Silver Vietnam 27 110000 34
## 3 120000 Silver Vietnam 28 110000 53
## 4 149374 Silver Vietnam 27 130000 34
## 6 112167 Black Vietnam 26 150000 58
## 8 126000 Black Vietnam 29 150000 20
## 10 154117 Silver Laos 28 150000 73
## is_sold
## 1 0
## 3 1
## 4 0
## 6 0
## 8 0
## 10 0
dados$Color<- as.factor(dados$Color)
dados$Country_Sold<- as.factor(dados$Country_Sold)
attach(dados)
Análise descritiva dos dados
Algumas estatísticas
dad<-dados[,c(-1,-6,-7,-11)]
basicStats(dad)
## Publish_period End_Date Departure_Date Distance_travelled
## nobs 2660.000000 2.660000e+03 2.660000e+03 2.660000e+03
## NAs 0.000000 0.000000e+00 0.000000e+00 0.000000e+00
## Minimum 0.000000 1.301357e+18 1.305590e+18 6.560000e+03
## Maximum 66.000000 1.402358e+18 1.409702e+18 1.813260e+05
## 1. Quartile 5.000000 1.364947e+18 1.369267e+18 7.151825e+04
## 3. Quartile 17.000000 1.390262e+18 1.395792e+18 1.080158e+05
## Mean 11.968421 1.375150e+18 1.379954e+18 9.012179e+04
## Median 9.000000 1.381277e+18 1.384819e+18 9.051150e+04
## Sum 31836.000000 3.657898e+21 3.670677e+21 2.397240e+08
## SE Mean 0.194594 3.872566e+14 3.876686e+14 5.281289e+02
## LCL Mean 11.586850 1.374390e+18 1.379193e+18 8.908621e+04
## UCL Mean 12.349992 1.375909e+18 1.380714e+18 9.115738e+04
## Variance 100.725591 3.989140e+32 3.997634e+32 7.419276e+08
## Stdev 10.036214 1.997283e+16 1.999408e+16 2.723835e+04
## Skewness 1.482170 -1.173550e+00 -1.024769e+00 2.545200e-02
## Kurtosis 2.995359 1.034617e+00 6.429600e-01 -1.159300e-01
## N_Photos Price N_Inquires
## nobs 2660.000000 2.660000e+03 2660.000000
## NAs 0.000000 0.000000e+00 0.000000
## Minimum 4.000000 6.000000e+04 1.000000
## Maximum 45.000000 2.100000e+05 306.000000
## 1. Quartile 28.000000 9.000000e+04 4.000000
## 3. Quartile 30.000000 1.000000e+05 15.000000
## Mean 29.622180 9.292707e+04 12.218045
## Median 30.000000 9.000000e+04 8.000000
## Sum 78795.000000 2.471860e+08 32500.000000
## SE Mean 0.040813 2.585055e+02 0.311374
## LCL Mean 29.542152 9.242018e+04 11.607485
## UCL Mean 29.702209 9.343396e+04 12.828605
## Variance 4.430723 1.777547e+08 257.897531
## Stdev 2.104928 1.333247e+04 16.059188
## Skewness -3.158401 1.638957e+00 6.851322
## Kurtosis 50.685277 6.119893e+00 87.903827
dad<- dados[,c(6,7,11)]
dad$is_sold<- as.factor(dad$is_sold)
summary(dad)
## Color Country_Sold is_sold
## Silver :649 Laos :1472 0:2321
## Blue :608 Philippine: 404 1: 339
## Red :592 Vietnam : 275
## Pearl :209 Cambodia : 245
## Black :196 Malaysia : 57
## Pink :107 Chile : 41
## (Other):299 (Other) : 166
par(mfrow=c(2,2))
boxplot(dados$Price, las= 2, main = "BoxPlot da variável Preço")
boxplot(dados$N_Inquires, las= 2, main = "BoxPlot da variável Número de conversas")
boxplot(dados$N_Photos, las= 2, main = "BoxPlot da variável N de Fotos")
boxplot(dados$Distance_travelled, las= 2, main = "BoxPlot da variável Distância percorrida")
Teste de normalidade
ad.test(Price)
##
## Anderson-Darling normality test
##
## data: Price
## A = 126.19, p-value < 2.2e-16
ad.test(Publish_period)
##
## Anderson-Darling normality test
##
## data: Publish_period
## A = 72.349, p-value < 2.2e-16
ad.test(N_Inquires)
##
## Anderson-Darling normality test
##
## data: N_Inquires
## A = 261.77, p-value < 2.2e-16
ad.test(N_Photos)
##
## Anderson-Darling normality test
##
## data: N_Photos
## A = 115.53, p-value < 2.2e-16
ad.test(Distance_travelled)
##
## Anderson-Darling normality test
##
## data: Distance_travelled
## A = 0.48731, p-value = 0.224
Gráficos
par(mfrow=c(2,2))
histPlot(as.timeSeries(Price))
histPlot(as.timeSeries(Publish_period))
histPlot(as.timeSeries(N_Inquires))
histPlot(as.timeSeries(N_Photos))
histPlot(as.timeSeries(Distance_travelled))
Correlação
dad<-dados[,c(-1,-3,-4,-6,-7,-11)]
corrplot(cor(dad), order = "hclust",tl.col = 'black', tl.cex = 0.75)
R <- round(cor(dad), 2);R
## Publish_period Distance_travelled N_Photos Price
## Publish_period 1.00 0.06 0.08 0.16
## Distance_travelled 0.06 1.00 -0.10 -0.12
## N_Photos 0.08 -0.10 1.00 0.03
## Price 0.16 -0.12 0.03 1.00
## N_Inquires 0.26 0.10 -0.12 0.10
## N_Inquires
## Publish_period 0.26
## Distance_travelled 0.10
## N_Photos -0.12
## Price 0.10
## N_Inquires 1.00
Métodos não parametricos
Kaplan-Meier e LogRank
Curva de sobrevivência para os dados Completos
ekm1<- survfit(Surv(tempos,cens)~1, data= dados);ekm1
## Call: survfit(formula = Surv(tempos, cens) ~ 1, data = dados)
##
## n events median 0.95LCL 0.95UCL
## 2660 339 NA NA NA
summary(ekm1)
## Call: survfit(formula = Surv(tempos, cens) ~ 1, data = dados)
##
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 0.1 2660 10 0.996 0.00119 0.994 0.999
## 1.0 2548 15 0.990 0.00192 0.987 0.994
## 2.0 2430 20 0.982 0.00263 0.977 0.987
## 3.0 2284 36 0.967 0.00364 0.960 0.974
## 4.0 2145 20 0.958 0.00413 0.950 0.966
## 5.0 2004 22 0.947 0.00465 0.938 0.956
## 6.0 1877 40 0.927 0.00554 0.916 0.938
## 7.0 1728 56 0.897 0.00666 0.884 0.910
## 8.0 1561 26 0.882 0.00716 0.868 0.896
## 9.0 1445 16 0.872 0.00749 0.858 0.887
## 10.0 1329 13 0.864 0.00778 0.849 0.879
## 11.0 1209 8 0.858 0.00799 0.843 0.874
## 12.0 1110 11 0.850 0.00831 0.833 0.866
## 13.0 1019 6 0.845 0.00851 0.828 0.861
## 14.0 932 13 0.833 0.00899 0.815 0.851
## 15.0 832 2 0.831 0.00908 0.813 0.849
## 16.0 752 4 0.826 0.00930 0.808 0.845
## 17.0 691 2 0.824 0.00942 0.806 0.843
## 18.0 633 5 0.817 0.00979 0.798 0.837
## 20.0 505 1 0.816 0.00990 0.797 0.835
## 21.0 461 5 0.807 0.01056 0.787 0.828
## 22.0 401 2 0.803 0.01088 0.782 0.825
## 24.0 324 1 0.800 0.01113 0.779 0.823
## 25.0 284 2 0.795 0.01174 0.772 0.818
## 28.0 210 1 0.791 0.01228 0.767 0.815
## 29.0 186 1 0.787 0.01293 0.762 0.813
## 38.0 65 1 0.775 0.01750 0.741 0.810
plot(ekm1, ylab = "S(t)", xlab = "Dias", main = "Curva de Sobrevivencia")
Curvas de sobrevivência para as variáveis independentes
Cor
KMcor <- survfit(Surv(tempos, cens)~ Color, data = dados)
KMcor
## Call: survfit(formula = Surv(tempos, cens) ~ Color, data = dados)
##
## n events median 0.95LCL 0.95UCL
## Color=Beige 2 0 NA NA NA
## Color=Black 196 20 NA NA NA
## Color=Blue 608 78 NA NA NA
## Color=Brown 1 0 NA NA NA
## Color=Gray 73 11 NA NA NA
## Color=Green 49 5 NA NA NA
## Color=Maroon 26 9 16 10 NA
## Color=Pearl 209 29 38 38 NA
## Color=Pink 107 4 NA NA NA
## Color=Purple 1 0 NA NA NA
## Color=Red 592 73 NA NA NA
## Color=Silver 649 93 NA NA NA
## Color=White 106 15 NA NA NA
## Color=Yellow 41 2 NA NA NA
plot(KMcor, lty = 1:14, col = 1:14, ylab = "S(t)", xlab = "Dias",
conf.int = F, main ="Curva de Sobrevivência pelas cores das motos")
Preço
#separando o preco em dois(mediana) grupos temos q
summary(Price)#mediana= 90000
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 60000 90000 90000 92927 100000 210000
idapreco<- cut(dados$Price, breaks=c(21000,80000,171000),labels=c("1","2"), right=F)
KMpreco2<- survfit(Surv(tempos, cens) ~idapreco, data= dados)
KMpreco2
## Call: survfit(formula = Surv(tempos, cens) ~ idapreco, data = dados)
##
## 1 observation deleted due to missingness
## n events median 0.95LCL 0.95UCL
## idapreco=1 98 34 21 14 25
## idapreco=2 2561 305 NA NA NA
plot(KMpreco2, lty = 1:2, col = 2:3, ylab = "S(t)", xlab = "Dias",
conf.int = F, main = "Curvas de sobrevivências com base no preço")
legend(1,0.3,lty = 1:2, col = 2:3,c("1 < mediana","2 >= mediana"),lwd=1, bty="n")
survdiff(Surv(tempos,cens)~idapreco, data = dados, rho= 0)
## Call:
## survdiff(formula = Surv(tempos, cens) ~ idapreco, data = dados,
## rho = 0)
##
## n=2659, 1 observation deleted due to missingness.
##
## N Observed Expected (O-E)^2/E (O-E)^2/V
## idapreco=1 98 34 10.3 54.2 56.7
## idapreco=2 2561 305 328.7 1.7 56.7
##
## Chisq= 56.7 on 1 degrees of freedom, p= 5e-14
N_fotos
summary((N_Photos))#30 mediana
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 4.00 28.00 30.00 29.62 30.00 45.00
idafotos<- cut(dados$N_Photos, breaks=c(4,30,46),labels=c("1","2"), right=F)
length(idafotos)
## [1] 2660
KMfoto <- survfit(Surv(tempos, cens) ~ idafotos, data = dados)
KMfoto
## Call: survfit(formula = Surv(tempos, cens) ~ idafotos, data = dados)
##
## n events median 0.95LCL 0.95UCL
## idafotos=1 1284 209 NA NA NA
## idafotos=2 1376 130 NA NA NA
plot(KMfoto, lty = 1:2, col = 2:3, ylab = "S(t)", xlab = "Dias",
conf.int = F, main ="Curva de Sobrevivência pelo número de fotos")
legend(1,0.3,lty = 1:2, col = 2:3,c("1 < mediana","2 >= mediana"),lwd=1, bty="n")
survdiff(Surv(tempos,cens)~idafotos, data = dados, rho= 0)
## Call:
## survdiff(formula = Surv(tempos, cens) ~ idafotos, data = dados,
## rho = 0)
##
## N Observed Expected (O-E)^2/E (O-E)^2/V
## idafotos=1 1284 209 157 17.2 32.5
## idafotos=2 1376 130 182 14.8 32.5
##
## Chisq= 32.5 on 1 degrees of freedom, p= 1e-08
N_Dialogos
#---------------------------------------------N_inquires
summary(N_Inquires)#8 mediana
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.00 4.00 8.00 12.22 15.00 306.00
idainqui<- cut(dados$N_Inquires, breaks=c(1,8,307),labels=c("1","2"), right=F)
KMinqui <- survfit(Surv(tempos, cens) ~ idainqui, data = dados)
KMinqui
## Call: survfit(formula = Surv(tempos, cens) ~ idainqui, data = dados)
##
## n events median 0.95LCL 0.95UCL
## idainqui=1 1279 261 NA NA NA
## idainqui=2 1381 78 NA NA NA
plot(KMinqui, lty = 1:2, col = 2:3, ylab = "S(t)", xlab = "Dias",
conf.int = F, main ="Curva de Sobrevida pelo número de Inqueritos")
legend(1,0.3,lty = 1:2, col = 2:3,c("1 < mediana","2 >= mediana"),lwd=1, bty="n")
survdiff(Surv(tempos,cens)~idainqui, data = dados, rho= 0)
## Call:
## survdiff(formula = Surv(tempos, cens) ~ idainqui, data = dados,
## rho = 0)
##
## N Observed Expected (O-E)^2/E (O-E)^2/V
## idainqui=1 1279 261 145 92.6 166
## idainqui=2 1381 78 194 69.3 166
##
## Chisq= 166 on 1 degrees of freedom, p= <2e-16
Distância percorrida
summary(Distance_travelled)#90512 mediana
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 6560 71518 90512 90122 108016 181326
idadist<- cut(dados$Distance_travelled, breaks=c(6560,90512,181326),labels=c("1","2"), right=F)
KMdist <- survfit(Surv(tempos, cens) ~ idainqui, data = dados)
KMdist
## Call: survfit(formula = Surv(tempos, cens) ~ idainqui, data = dados)
##
## n events median 0.95LCL 0.95UCL
## idainqui=1 1279 261 NA NA NA
## idainqui=2 1381 78 NA NA NA
plot(KMdist, lty = 1:2, col = 2:3, ylab = "S(t)", xlab = "Dias",
conf.int = F, main ="Curva de Sobrevida pela distáncia percorrida")
legend(1,0.3,lty = 1:2, col = 2:3,c("1 < mediana","2 >= mediana"),lwd=1, bty="n")
survdiff(Surv(tempos,cens)~idadist, data = dados, rho= 0)
## Call:
## survdiff(formula = Surv(tempos, cens) ~ idadist, data = dados,
## rho = 0)
##
## n=2659, 1 observation deleted due to missingness.
##
## N Observed Expected (O-E)^2/E (O-E)^2/V
## idadist=1 1330 206 166 9.57 19.1
## idadist=2 1329 133 173 9.20 19.1
##
## Chisq= 19.1 on 1 degrees of freedom, p= 1e-05
Métodos Parametricos
Escolha da Distribuição
ajust1<-survreg(Surv(tempos,cens)~1,dist="exponential")
alpha1<-exp(ajust1$coefficients[1])
ajust2<-survreg(Surv(tempos,cens)~1,dist="weibull")
alpha2<-exp(ajust2$coefficients[1]);
gama<-1/ajust2$scale
ajust3<-survreg(Surv(tempos,cens)~1,dist="lognorm")
#S(T) KAPLA VS ESTIMATIVAS
ekm<- survfit(Surv(tempos,cens)~1, data= dados)
time<-ekm$time
st<-ekm$surv
ste<- exp(-time/alpha1)
stw<- exp(-(time/alpha2)^gama)
stln<- pnorm((-log(time)+ 4.778)/2.0347)
cbind(time,st,ste,stw,stln)
## time st ste stw stln
## [1,] 0.1 0.9962406 0.9989361 0.9984058 0.9997492
## [2,] 1.0 0.9903758 0.9894119 0.9868017 0.9905693
## [3,] 2.0 0.9822245 0.9789359 0.9751655 0.9776568
## [4,] 3.0 0.9667429 0.9685708 0.9641332 0.9647216
## [5,] 4.0 0.9577290 0.9583154 0.9535150 0.9522360
## [6,] 5.0 0.9472150 0.9481687 0.9432214 0.9402959
## [7,] 6.0 0.9270292 0.9381293 0.9331998 0.9289012
## [8,] 7.0 0.8969866 0.9281963 0.9234151 0.9180230
## [9,] 8.0 0.8820464 0.9183684 0.9138422 0.9076246
## [10,] 9.0 0.8722798 0.9086446 0.9044619 0.8976691
## [11,] 10.0 0.8637474 0.8990238 0.8952592 0.8881217
## [12,] 11.0 0.8580319 0.8895048 0.8862221 0.8789506
## [13,] 12.0 0.8495289 0.8800866 0.8773404 0.8701274
## [14,] 13.0 0.8445268 0.8707682 0.8686055 0.8616262
## [15,] 14.0 0.8327469 0.8615484 0.8600101 0.8534241
## [16,] 15.0 0.8307451 0.8524262 0.8515477 0.8455004
## [17,] 16.0 0.8263262 0.8434006 0.8432126 0.8378366
## [18,] 17.0 0.8239345 0.8344706 0.8349999 0.8304159
## [19,] 18.0 0.8174264 0.8256351 0.8269050 0.8232231
## [20,] 19.0 0.8174264 0.8168931 0.8189237 0.8162446
## [21,] 20.0 0.8158077 0.8082438 0.8110523 0.8094677
## [22,] 21.0 0.8069595 0.7996860 0.8032873 0.8028811
## [23,] 22.0 0.8029347 0.7912188 0.7956256 0.7964744
## [24,] 23.0 0.8029347 0.7828413 0.7880642 0.7902379
## [25,] 24.0 0.8004565 0.7745525 0.7806004 0.7841630
## [26,] 25.0 0.7948195 0.7663514 0.7732316 0.7782414
## [27,] 26.0 0.7948195 0.7582372 0.7659555 0.7724656
## [28,] 27.0 0.7948195 0.7502089 0.7587697 0.7668288
## [29,] 28.0 0.7910347 0.7422656 0.7516722 0.7613244
## [30,] 29.0 0.7867818 0.7344064 0.7446609 0.7559465
## [31,] 30.0 0.7867818 0.7266304 0.7377339 0.7506895
## [32,] 31.0 0.7867818 0.7189367 0.7308894 0.7455482
## [33,] 32.0 0.7867818 0.7113245 0.7241257 0.7405177
## [34,] 33.0 0.7867818 0.7037930 0.7174412 0.7355934
## [35,] 34.0 0.7867818 0.6963411 0.7108342 0.7307712
## [36,] 35.0 0.7867818 0.6889682 0.7043033 0.7260468
## [37,] 36.0 0.7867818 0.6816733 0.6978470 0.7214167
## [38,] 37.0 0.7867818 0.6744556 0.6914639 0.7168771
## [39,] 38.0 0.7746775 0.6673144 0.6851528 0.7124248
## [40,] 39.0 0.7746775 0.6602488 0.6789122 0.7080566
## [41,] 40.0 0.7746775 0.6532580 0.6727410 0.7037696
## [42,] 41.0 0.7746775 0.6463412 0.6666380 0.6995607
## [43,] 42.0 0.7746775 0.6394977 0.6606020 0.6954275
## [44,] 43.0 0.7746775 0.6327266 0.6546320 0.6913673
## [45,] 44.0 0.7746775 0.6260272 0.6487267 0.6873777
## [46,] 45.0 0.7746775 0.6193988 0.6428853 0.6834564
## [47,] 46.0 0.7746775 0.6128405 0.6371066 0.6796013
## [48,] 47.0 0.7746775 0.6063517 0.6313897 0.6758102
## [49,] 48.0 0.7746775 0.5999315 0.6257336 0.6720812
## [50,] 49.0 0.7746775 0.5935794 0.6201375 0.6684123
## [51,] 50.0 0.7746775 0.5872945 0.6146003 0.6648019
## [52,] 51.0 0.7746775 0.5810761 0.6091212 0.6612481
## [53,] 52.0 0.7746775 0.5749236 0.6036994 0.6577493
## [54,] 54.0 0.7746775 0.5628134 0.5930243 0.6509106
## [55,] 56.0 0.7746775 0.5509582 0.5825686 0.6442738
## [56,] 57.0 0.7746775 0.5451246 0.5774210 0.6410278
## [57,] 59.0 0.7746775 0.5336420 0.5672828 0.6346740
## [58,] 60.0 0.7746775 0.5279917 0.5622908 0.6315639
## [59,] 61.0 0.7746775 0.5224013 0.5573492 0.6284967
## [60,] 63.0 0.7746775 0.5113973 0.5476148 0.6224870
## [61,] 66.0 0.7746775 0.4953245 0.5333751 0.6137689
Escolhendo a melhor distribuição para o modelo de sobrevivencia pelo teste TRV
x1<-survreg(Surv(tempos,cens)~1, data= dados, dist="lognormal") #lognormal tem 2 parametros
x2<-survreg(Surv(tempos,cens)~1, data= dados, dist="exponential") #exponencial tem 1 parametros
x3<-survreg(Surv(tempos,cens)~1, data= dados, dist="weibull") #tem 2 parametros
alpha.e<-exp(x2$coefficients[1])
alpha.w<-exp(x3$coefficients[1])
gama<-1/x3$scale
x4<-flexsurvreg(Surv(tempos,cens)~1, data= dados, dist="gengamma")# gama generalizada tem 3 parametros
TRV1=2*(x4$loglik-x1$loglik[2])
modelo1=1-pchisq(TRV1,1)
TRV2=2*(x4$loglik-x2$loglik[2])
modelo2=1-pchisq(TRV2,2)
TRV3=2*(x4$loglik-x3$loglik[2])
modelo3=1-pchisq(TRV3,1)
distri<- c("exp","weibull","lognormal");distri
## [1] "exp" "weibull" "lognormal"
modelos=c(modelo1,modelo2,modelo3);modelos
## [1] 8.939157e-01 8.088587e-07 7.059712e-07
Gráfico de Kaplan-Meier vs distribuições
par(mfrow=c(1,1))
plot(ekm, conf.int=F, xlab="Tempos", ylab="S(t)", main= "Kaplan-Meier vs exponencial" )
lines(c(0,time),c(1,ste), lty=2)
legend(3,0.4,lty=c(1,2),c("Kaplan-Meier", "exponencial"),bty="n",cex=0.8)
plot(ekm, conf.int=F, xlab="Tempos", ylab="S(t)", main= "Kaplan-Meier vs Weibull" )
lines(c(0,time),c(1,stw), lty=2)
legend(3,0.4,lty=c(1,2),c("Kaplan-Meier", "Weibull"),bty="n",cex=0.8)
plot(ekm, conf.int=F, xlab="Tempos", ylab="S(t)", main= "Kaplan-Meiervs log-normal")
lines(c(0,time),c(1,stln), lty=2)
legend(3,0.4,lty=c(1,2),c("Kaplan-Meier", "Log-normal"),bty="n",cex=0.8)
Collet para escolha do melhor modelo
Passo 1
1. Ajustar todos os modelos contendo uma unica covariável. Incluir
todas as covariáveis que forem significativas ao nível de 0; 10.
É aconselhável utilizar o teste da razão deverossimilhanças neste passo.
ajuste1<-survreg(Surv(tempos,cens)~1, data= dados, dist="lognorm")
ajuste2<-survreg(Surv(tempos,cens)~Distance_travelled, data= dados, dist="lognorm")
summary(ajust2)
##
## Call:
## survreg(formula = Surv(tempos, cens) ~ 1, dist = "weibull")
## Value Std. Error z p
## (Intercept) 4.6941 0.1055 44.49 <2e-16
## Log(scale) 0.0828 0.0454 1.82 0.068
##
## Scale= 1.09
##
## Weibull distribution
## Loglik(model)= -1877.2 Loglik(intercept only)= -1877.2
## Number of Newton-Raphson Iterations: 10
## n= 2660
ajuste3<-survreg(Surv(tempos,cens)~N_Photos, data= dados, dist="lognorm")
summary(ajuste3)
##
## Call:
## survreg(formula = Surv(tempos, cens) ~ N_Photos, data = dados,
## dist = "lognorm")
## Value Std. Error z p
## (Intercept) -0.7709 0.7631 -1.01 0.31
## N_Photos 0.1862 0.0264 7.05 1.8e-12
## Log(scale) 0.6783 0.0423 16.03 < 2e-16
##
## Scale= 1.97
##
## Log Normal distribution
## Loglik(model)= -1839.5 Loglik(intercept only)= -1865
## Chisq= 50.99 on 1 degrees of freedom, p= 9.3e-13
## Number of Newton-Raphson Iterations: 5
## n= 2660
ajuste4<-survreg(Surv(tempos,cens)~N_Inquires, data= dados, dist="lognorm")
summary(ajuste4)
##
## Call:
## survreg(formula = Surv(tempos, cens) ~ N_Inquires, data = dados,
## dist = "lognorm")
## Value Std. Error z p
## (Intercept) 3.49654 0.10763 32.5 <2e-16
## N_Inquires 0.10473 0.00891 11.8 <2e-16
## Log(scale) 0.55693 0.04185 13.3 <2e-16
##
## Scale= 1.75
##
## Log Normal distribution
## Loglik(model)= -1758.2 Loglik(intercept only)= -1865
## Chisq= 213.47 on 1 degrees of freedom, p= 2.4e-48
## Number of Newton-Raphson Iterations: 5
## n= 2660
ajuste5<-survreg(Surv(tempos,cens)~Price, data= dados, dist="lognorm")
summary(ajuste5)
##
## Call:
## survreg(formula = Surv(tempos, cens) ~ Price, data = dados, dist = "lognorm")
## Value Std. Error z p
## (Intercept) 1.85e+00 4.59e-01 4.03 5.5e-05
## Price 3.13e-05 5.08e-06 6.16 7.1e-10
## Log(scale) 6.88e-01 4.24e-02 16.25 < 2e-16
##
## Scale= 1.99
##
## Log Normal distribution
## Loglik(model)= -1844 Loglik(intercept only)= -1865
## Chisq= 41.91 on 1 degrees of freedom, p= 9.6e-11
## Number of Newton-Raphson Iterations: 5
## n= 2660
ajuste6<-survreg(Surv(tempos,cens)~Color, data= dados, dist="lognorm")
summary(ajuste6)
##
## Call:
## survreg(formula = Surv(tempos, cens) ~ Color, data = dados, dist = "lognorm")
## Value Std. Error z p
## (Intercept) 12.8322 813.3194 0.02 0.99
## ColorBlack -7.9480 813.3194 -0.01 0.99
## ColorBlue -8.0969 813.3194 -0.01 0.99
## ColorBrown -4.7233 1429.9126 0.00 1.00
## ColorGray -7.9780 813.3195 -0.01 0.99
## ColorGreen -7.6169 813.3195 -0.01 0.99
## ColorMaroon -9.6240 813.3196 -0.01 0.99
## ColorPearl -8.1915 813.3194 -0.01 0.99
## ColorPink -6.5785 813.3195 -0.01 0.99
## ColorPurple -1.0345 1429.9126 0.00 1.00
## ColorRed -8.0493 813.3194 -0.01 0.99
## ColorSilver -8.2466 813.3194 -0.01 0.99
## ColorWhite -8.3344 813.3194 -0.01 0.99
## ColorYellow -7.0512 813.3197 -0.01 0.99
## Log(scale) 0.6959 0.0424 16.41 <2e-16
##
## Scale= 2.01
##
## Log Normal distribution
## Loglik(model)= -1850.6 Loglik(intercept only)= -1865
## Chisq= 28.79 on 13 degrees of freedom, p= 0.007
## Number of Newton-Raphson Iterations: 12
## n= 2660
ajuste7<-survreg(Surv(tempos,cens)~Country_Sold, data= dados, dist="lognorm")
summary(ajuste7)
##
## Call:
## survreg(formula = Surv(tempos, cens) ~ Country_Sold, data = dados,
## dist = "lognorm")
## Value Std. Error z p
## (Intercept) 3.10e+00 6.82e-01 4.54 5.5e-06
## Country_SoldAruba 1.06e+01 1.09e+03 0.01 0.9922
## Country_SoldBahamas 1.30e+00 1.31e+00 1.00 0.3190
## Country_SoldBotswana 1.03e+01 1.57e+03 0.01 0.9948
## Country_SoldBrunei 1.02e+00 1.07e+00 0.95 0.3408
## Country_SoldBurundi -5.04e-01 1.63e+00 -0.31 0.7576
## Country_SoldCambodia 9.65e-01 7.02e-01 1.38 0.1690
## Country_SoldCayman Islands -2.00e+00 2.02e+00 -0.99 0.3213
## Country_SoldChile 3.38e-01 7.83e-01 0.43 0.6665
## Country_SoldCommonwealth Of Dominica 9.14e+00 0.00e+00 Inf < 2e-16
## Country_SoldD.R.Congo 1.05e+01 1.58e+03 0.01 0.9947
## Country_SoldGuatemala 5.00e-01 1.11e+00 0.45 0.6515
## Country_SoldIndonesia 3.15e-01 8.10e-01 0.39 0.6978
## Country_SoldKazakhstan 5.23e+00 0.00e+00 Inf < 2e-16
## Country_SoldLaos 2.02e+00 6.87e-01 2.93 0.0033
## Country_SoldLiberia 9.93e+00 0.00e+00 Inf < 2e-16
## Country_SoldMalawi 9.22e-01 8.55e-01 1.08 0.2807
## Country_SoldMalaysia 1.17e+00 7.73e-01 1.51 0.1313
## Country_SoldMicro