SMART
市田 親正
2023-05-14
必要パッケージの読み込み
library(tidyverse)## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
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library(rms)## 要求されたパッケージ Hmisc をロード中です
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## format.pval, unitslibrary(tableone)
library(ggplot2)
library(gtsummary)
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## cbind, rbind# 第一部
(1)データの読み込み
SMARTo <- read.spss("SMARTs.sav",use.value.labels=F, to.data.frame=T) (2) 変数の確認
列名の取得
colnames(SMARTo)## [1] "TEVENT" "EVENT" "SEX" "AGE" "DIABETES" "CEREBRAL"
## [7] "CARDIAC" "AAA" "PERIPH" "STENOSIS" "SYSTBP" "DIASTBP"
## [13] "SYSTH" "DIASTH" "LENGTHO" "WEIGHTO" "BMIO" "CHOLO"
## [19] "HDLO" "LDLO" "TRIGO" "HOMOCO" "GLUTO" "CREATO"
## [25] "IMTO" "albumin" "SMOKING" "packyrs" "alcohol"データの確認
dfSummary(SMARTo) %>% view()## Switching method to 'browser'## Output file written: /var/folders/n9/tf_wmwpn3gl2t7l1cz4tqk000000gn/T//Rtmp8KYBC2/file118b621b7485.html因子・連続変数でそれぞれ抽出
col_cont = c("TEVENT", "AGE", "SYSTBP", "DIASTBP", "SYSTH", "DIASTH","LENGTHO", "WEIGHTO", "BMIO", "CHOLO", "HDLO", "LDLO", "TRIGO", "HOMOCO", "GLUTO", "CREATO", "IMTO", "packyrs" )
col_fact = c("EVENT", "SEX", "DIABETES", "CEREBRAL", "CARDIAC","AAA", "PERIPH", "STENOSIS", "albumin", "SMOKING", "alcohol")連続変数以外をfactor化
for (col_name in colnames(SMARTo)) {
if (!(col_name %in% col_cont)) {
SMARTo[[col_name]] <- as.factor(SMARTo[[col_name]])
}
}変換した変数の確認
str(SMARTo)## 'data.frame': 3873 obs. of 29 variables:
## $ TEVENT : num 3466 3465 3465 2445 3463 ...
## $ EVENT : Factor w/ 2 levels "0","1": 1 1 1 2 1 1 2 2 2 2 ...
## $ SEX : Factor w/ 2 levels "1","2": 1 2 1 1 1 2 1 1 1 1 ...
## $ AGE : num 71 46 59 76 57 52 66 72 75 53 ...
## $ DIABETES: Factor w/ 2 levels "0","1": 2 1 1 1 1 2 1 1 1 2 ...
## $ CEREBRAL: Factor w/ 2 levels "0","1": 1 1 1 1 1 1 2 1 1 1 ...
## $ CARDIAC : Factor w/ 2 levels "0","1": 2 1 2 2 2 1 1 2 2 1 ...
## $ AAA : Factor w/ 2 levels "0","1": 1 1 1 2 1 1 2 2 1 1 ...
## $ PERIPH : Factor w/ 2 levels "0","1": 2 2 2 2 2 2 1 1 2 2 ...
## $ STENOSIS: Factor w/ 2 levels "0","1": 1 1 1 1 1 1 2 1 2 1 ...
## $ SYSTBP : num 185 135 149 140 177 164 166 131 175 174 ...
## $ DIASTBP : num 86 82 97 74 96 73 70 76 68 89 ...
## $ SYSTH : num NA NA NA NA NA NA NA NA NA NA ...
## $ DIASTH : num NA NA NA NA NA NA NA NA NA NA ...
## $ LENGTHO : num 1.7 1.72 1.77 1.82 1.9 1.73 1.65 1.6 1.7 1.83 ...
## $ WEIGHTO : num 69 71 82 98 107 103 66 80 80 75 ...
## $ BMIO : num 23.9 24 26.2 29.6 29.6 ...
## $ CHOLO : num 6 4 4.9 5.3 5.2 4.6 5.8 6.1 4.4 6 ...
## $ HDLO : num 0.94 1.26 1.28 1 0.81 0.95 0.87 1.32 0.55 0.95 ...
## $ LDLO : num 4.03 2.23 3.17 3.4 NA 2.38 3.33 4.39 2.26 3.82 ...
## $ TRIGO : num 2.29 1.13 1.01 2.01 4.76 2.82 3.55 0.87 3.54 2.74 ...
## $ HOMOCO : num NA 8.7 NA NA NA NA NA NA NA NA ...
## $ GLUTO : num 6.3 4.7 6.1 5 6.1 10.2 5.4 5.3 5.9 10.8 ...
## $ CREATO : num 95 66 93 79 91 180 81 101 157 86 ...
## $ IMTO : num 0.82 0.57 0.83 1.45 1.07 0.97 1.15 0.7 1.48 0.87 ...
## $ albumin : Factor w/ 3 levels "1","2","3": 1 1 1 NA 1 3 1 2 1 1 ...
## $ SMOKING : Factor w/ 3 levels "1","2","3": 2 1 2 2 2 2 2 2 2 2 ...
## $ packyrs : num 22.5 0 33.3 49 53.2 54.6 72.8 28.6 16.5 29.7 ...
## $ alcohol : Factor w/ 3 levels "1","2","3": 3 1 3 3 3 1 3 2 1 3 ...
## - attr(*, "variable.labels")= Named chr [1:29] "FU-duur tot vasculaire complicatie (klinisch) EP (in dagen)" "Niet/wel vasculaire complicatie (klinisch) EP" "Geslacht" "Leeftijd (aantal voltooide jaren)" ...
## ..- attr(*, "names")= chr [1:29] "TEVENT" "EVENT" "SEX" "AGE" ...table1の作成、欠測の確認
# 順序に従って変数を並べ替え
ordered_vars <- c( "SEX","AGE","SMOKING","packyrs","alcohol","BMIO","DIABETES","SYSTH", "SYSTBP", "DIASTH","DIASTBP","CHOLO","HDLO", "LDLO","TRIGO","CEREBRAL", "CARDIAC","PERIPH","AAA","HOMOCO","GLUTO","CREATO","albumin","IMTO","STENOSIS")
CreateTableOne(vars = ordered_vars, factorVars = col_fact, data = SMARTo) -> tableone
print(tableone, missing =T , test = F, explain = T) ##
## Overall Missing
## n 3873
## SEX = 2 (%) 976 (25.2) 0.0
## AGE (mean (SD)) 59.56 (10.53) 0.0
## SMOKING (%) 0.6
## 1 693 (18.0)
## 2 2711 (70.5)
## 3 444 (11.5)
## packyrs (mean (SD)) 22.62 (20.31) 0.5
## alcohol (%) 0.6
## 1 751 (19.5)
## 2 408 (10.6)
## 3 2689 (69.9)
## BMIO (mean (SD)) 26.70 (3.92) 0.1
## DIABETES = 1 (%) 846 (22.1) 1.0
## SYSTH (mean (SD)) 142.16 (22.44) 38.7
## SYSTBP (mean (SD)) 141.32 (19.97) 31.6
## DIASTH (mean (SD)) 82.44 (11.82) 38.7
## DIASTBP (mean (SD)) 79.70 (9.92) 31.5
## CHOLO (mean (SD)) 5.20 (1.19) 0.5
## HDLO (mean (SD)) 1.23 (0.38) 0.8
## LDLO (mean (SD)) 3.14 (1.04) 5.6
## TRIGO (mean (SD)) 1.88 (1.58) 0.7
## CEREBRAL = 1 (%) 1147 (29.6) 0.0
## CARDIAC = 1 (%) 2160 (55.8) 0.0
## PERIPH = 1 (%) 940 (24.3) 0.0
## AAA = 1 (%) 416 (10.7) 0.0
## HOMOCO (mean (SD)) 14.06 (8.49) 12.0
## GLUTO (mean (SD)) 6.33 (2.01) 0.5
## CREATO (mean (SD)) 98.93 (71.84) 0.4
## albumin (%) 5.3
## 1 2897 (79.0)
## 2 655 (17.9)
## 3 114 ( 3.1)
## IMTO (mean (SD)) 0.94 (0.30) 2.5
## STENOSIS = 1 (%) 722 (19.1) 2.4(3)連続変数間の相関を確認
# 数値でない変数を数値に変換
numeric_columns <- SMARTo %>% select_if(is.numeric)
# 相関行列を計算
cor_matrix <- cor(numeric_columns, use = "complete.obs")
print(cor_matrix)## TEVENT AGE SYSTBP DIASTBP SYSTH
## TEVENT 1.00000000 -0.09621686 -0.124073663 -0.08540482 -0.118609425
## AGE -0.09621686 1.00000000 0.322483629 0.03056756 0.287855887
## SYSTBP -0.12407366 0.32248363 1.000000000 0.66538915 0.693043358
## DIASTBP -0.08540482 0.03056756 0.665389149 1.00000000 0.453772560
## SYSTH -0.11860943 0.28785589 0.693043358 0.45377256 1.000000000
## DIASTH -0.11645460 -0.06241188 0.407879393 0.59846969 0.682387646
## LENGTHO -0.06556916 -0.16342672 -0.117848520 0.05318287 -0.132727232
## WEIGHTO -0.07062578 -0.14873593 -0.028946092 0.12489484 -0.062218010
## BMIO -0.04265904 -0.05841828 0.047282864 0.10770971 0.018261561
## CHOLO 0.21624896 0.02531610 0.053907319 0.05913513 0.040930413
## HDLO -0.12145385 0.08914296 0.121026719 0.06153852 0.096577221
## LDLO 0.25368317 0.01710164 0.005088533 0.02258706 -0.001755867
## TRIGO 0.05766716 -0.07383878 0.021414176 0.05298330 0.028277456
## HOMOCO -0.13709856 0.22498490 0.151598418 0.11432454 0.139759179
## GLUTO -0.06960593 0.09869500 0.163560817 0.06324568 0.117465055
## CREATO -0.18533132 0.01515817 0.051364794 0.04572938 0.066649039
## IMTO -0.16476002 0.35679129 0.247167551 0.04215499 0.294147750
## packyrs -0.05072402 0.06033905 0.019387670 0.01313393 0.025128836
## DIASTH LENGTHO WEIGHTO BMIO CHOLO
## TEVENT -0.1164546013 -0.0655691571 -0.07062578 -0.04265904 0.21624896
## AGE -0.0624118801 -0.1634267169 -0.14873593 -0.05841828 0.02531610
## SYSTBP 0.4078793927 -0.1178485199 -0.02894609 0.04728286 0.05390732
## DIASTBP 0.5984696898 0.0531828658 0.12489484 0.10770971 0.05913513
## SYSTH 0.6823876455 -0.1327272320 -0.06221801 0.01826156 0.04093041
## DIASTH 1.0000000000 -0.0004257752 0.08531124 0.09966158 0.06619315
## LENGTHO -0.0004257752 1.0000000000 0.53924294 -0.08074846 -0.11708765
## WEIGHTO 0.0853112362 0.5392429400 1.00000000 0.79077170 -0.10409484
## BMIO 0.0996615800 -0.0807484551 0.79077170 1.00000000 -0.04258839
## CHOLO 0.0661931506 -0.1170876453 -0.10409484 -0.04258839 1.00000000
## HDLO 0.0685558504 -0.1628020661 -0.28559689 -0.21811418 0.12001085
## LDLO 0.0349872181 -0.0715197551 -0.05995716 -0.02168964 0.93517797
## TRIGO 0.0286337053 0.0273645225 0.17643647 0.18081853 0.22270781
## HOMOCO 0.0902599256 -0.0168522129 -0.04416554 -0.03608708 -0.02677297
## GLUTO -0.0145215489 -0.0353456174 0.14595640 0.19938905 -0.05340739
## CREATO 0.0581366534 0.0167923121 -0.07376534 -0.09443189 -0.13030079
## IMTO 0.0361263322 -0.0048271355 0.05650168 0.06909276 -0.01250730
## packyrs -0.0079079188 0.0992097141 0.14176022 0.09303720 0.03929526
## HDLO LDLO TRIGO HOMOCO GLUTO
## TEVENT -0.12145385 0.253683172 0.05766716 -0.13709856 -0.06960593
## AGE 0.08914296 0.017101638 -0.07383878 0.22498490 0.09869500
## SYSTBP 0.12102672 0.005088533 0.02141418 0.15159842 0.16356082
## DIASTBP 0.06153852 0.022587059 0.05298330 0.11432454 0.06324568
## SYSTH 0.09657722 -0.001755867 0.02827746 0.13975918 0.11746505
## DIASTH 0.06855585 0.034987218 0.02863371 0.09025993 -0.01452155
## LENGTHO -0.16280207 -0.071519755 0.02736452 -0.01685221 -0.03534562
## WEIGHTO -0.28559689 -0.059957161 0.17643647 -0.04416554 0.14595640
## BMIO -0.21811418 -0.021689640 0.18081853 -0.03608708 0.19938905
## CHOLO 0.12001085 0.935177970 0.22270781 -0.02677297 -0.05340739
## HDLO 1.00000000 -0.108230834 -0.42475364 -0.01685660 -0.11417457
## LDLO -0.10823083 1.000000000 0.07134857 -0.02821454 -0.06780419
## TRIGO -0.42475364 0.071348569 1.00000000 0.02003178 0.16899594
## HOMOCO -0.01685660 -0.028214536 0.02003178 1.00000000 -0.01772754
## GLUTO -0.11417457 -0.067804189 0.16899594 -0.01772754 1.00000000
## CREATO -0.04418908 -0.123857562 0.01031394 0.32058758 -0.01568331
## IMTO -0.05783082 -0.010416064 0.05848692 0.10733135 0.14021851
## packyrs -0.03854332 0.020599456 0.10970250 0.05874190 0.04580722
## CREATO IMTO packyrs
## TEVENT -0.18533132 -0.164760015 -0.050724018
## AGE 0.01515817 0.356791288 0.060339050
## SYSTBP 0.05136479 0.247167551 0.019387670
## DIASTBP 0.04572938 0.042154988 0.013133932
## SYSTH 0.06664904 0.294147750 0.025128836
## DIASTH 0.05813665 0.036126332 -0.007907919
## LENGTHO 0.01679231 -0.004827135 0.099209714
## WEIGHTO -0.07376534 0.056501678 0.141760223
## BMIO -0.09443189 0.069092759 0.093037203
## CHOLO -0.13030079 -0.012507298 0.039295257
## HDLO -0.04418908 -0.057830822 -0.038543323
## LDLO -0.12385756 -0.010416064 0.020599456
## TRIGO 0.01031394 0.058486917 0.109702503
## HOMOCO 0.32058758 0.107331346 0.058741903
## GLUTO -0.01568331 0.140218506 0.045807218
## CREATO 1.00000000 0.029616593 -0.054998042
## IMTO 0.02961659 1.000000000 0.130013708
## packyrs -0.05499804 0.130013708 1.000000000血圧は収縮相手動と収縮期自動 の相関係数は0.7未満であり、明らかな相関ありとまではいえない。 他の変数では体重とBMIの相関は0.8程度と高い相関あり。どちらかの投入がよさそう。 総コレステロールとLDLに関しも相関係数0.9超とかなり高いためこちらもどちらかの投入とすべき。
(4) 欠測パターンの確認
推奨
#Hmiscパッケージ naclus関数が便利です
na.patterns <- naclus(SMARTo)
plot(na.patterns, ylab="Fraction of NAs in common") 
naplot(na.patterns, which=c('na per var')) 
naplot(na.patterns, which=c('na per obs')) 
vis_miss(SMARTo,cluster = T)## Warning: `gather_()` was deprecated in tidyr 1.2.0.
## ℹ Please use `gather()` instead.
## ℹ The deprecated feature was likely used in the visdat package.
## Please report the issue at <]8;;https://github.com/ropensci/visdat/issueshttps://github.com/ropensci/visdat/issues]8;;>.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
gg_miss_var(SMARTo,show_pct = T)## Warning: The `guide` argument in `scale_*()` cannot be `FALSE`. This was deprecated in
## ggplot2 3.3.4.
## ℹ Please use "none" instead.
## ℹ The deprecated feature was likely used in the naniar package.
## Please report the issue at <]8;;https://github.com/njtierney/naniar/issueshttps://github.com/njtierney/naniar/issues]8;;>.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
明らかな意図的な欠測とはいえずMARでよさそう。
第2部(Cox比例ハザードモデルによる予測モデルの構築と検証)
(1) TEVENT（観察時間）の情報を用いて、ヒストグラム、総追跡人年、追跡期間の平均と中央値と求めましょう。
# ヒストグラムの作成
hist(SMARTo$TEVENT, main="Histogram of TEVENT", xlab="TEVENT", col="lightblue", border="black")
# 総追跡人年の計算
total_person_years <- sum(SMARTo$TEVENT) / 365.25
cat("Total person-years:", total_person_years, "\n")## Total person-years: 14530.62# 追跡期間の平均および中央値の計算
mean_follow_up <- mean(SMARTo$TEVENT) / 365.25
median_follow_up <- median(SMARTo$TEVENT) / 365.25
cat("Mean follow-up period:", mean_follow_up, "years\n")## Mean follow-up period: 3.751773 yearscat("Median follow-up period:", median_follow_up, "years\n")## Median follow-up period: 3.321013 years(2) EVENTとTEVENTの情報から、カプランマイヤーカーブを描きましょう。追跡期間を無視した累積罹患率とカプランマイヤー法による累積罹患率を比べる。
# EVENT変数を数値型に変換
SMARTo$EVENT <- as.numeric(as.character(SMARTo$EVENT))
# カプランマイヤー法の適用
fit1 <- survfit(Surv(TEVENT,EVENT) ~ 1, data = SMARTo)
summary(fit1) ## Call: survfit(formula = Surv(TEVENT, EVENT) ~ 1, data = SMARTo)
##
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 0.1 3873 2 0.999 0.000365 0.999 1.000
## 1.0 3871 9 0.997 0.000855 0.995 0.999
## 2.0 3857 2 0.997 0.000930 0.995 0.998
## 3.0 3853 3 0.996 0.001031 0.994 0.998
## 4.0 3850 1 0.996 0.001063 0.994 0.998
## 12.0 3843 1 0.995 0.001094 0.993 0.997
## 16.0 3835 2 0.995 0.001153 0.993 0.997
## 20.0 3833 2 0.994 0.001209 0.992 0.997
## 21.0 3829 1 0.994 0.001237 0.992 0.996
## 27.0 3817 1 0.994 0.001264 0.991 0.996
## 29.0 3810 1 0.994 0.001290 0.991 0.996
## 31.0 3805 1 0.993 0.001316 0.991 0.996
## 32.0 3804 1 0.993 0.001341 0.990 0.996
## 37.0 3798 1 0.993 0.001366 0.990 0.995
## 40.0 3796 3 0.992 0.001438 0.989 0.995
## 49.0 3777 1 0.992 0.001461 0.989 0.995
## 52.0 3765 1 0.991 0.001485 0.989 0.994
## 54.0 3764 1 0.991 0.001507 0.988 0.994
## 56.0 3760 1 0.991 0.001530 0.988 0.994
## 58.0 3752 1 0.991 0.001552 0.988 0.994
## 59.0 3747 1 0.990 0.001574 0.987 0.993
## 60.0 3745 1 0.990 0.001596 0.987 0.993
## 65.0 3744 1 0.990 0.001617 0.987 0.993
## 69.0 3743 1 0.990 0.001638 0.986 0.993
## 73.0 3730 1 0.989 0.001659 0.986 0.993
## 75.0 3729 1 0.989 0.001680 0.986 0.992
## 77.0 3726 1 0.989 0.001700 0.985 0.992
## 86.0 3708 1 0.989 0.001720 0.985 0.992
## 87.0 3705 1 0.988 0.001740 0.985 0.992
## 92.0 3701 2 0.988 0.001780 0.984 0.991
## 94.0 3697 1 0.987 0.001799 0.984 0.991
## 96.0 3696 1 0.987 0.001819 0.984 0.991
## 97.0 3692 3 0.986 0.001875 0.983 0.990
## 102.0 3675 1 0.986 0.001894 0.982 0.990
## 104.0 3674 1 0.986 0.001912 0.982 0.990
## 105.0 3671 3 0.985 0.001966 0.981 0.989
## 106.0 3667 1 0.985 0.001984 0.981 0.989
## 113.0 3659 2 0.984 0.002019 0.980 0.988
## 114.0 3655 1 0.984 0.002037 0.980 0.988
## 115.0 3653 2 0.983 0.002071 0.979 0.987
## 118.0 3651 1 0.983 0.002088 0.979 0.987
## 119.0 3645 1 0.983 0.002104 0.979 0.987
## 120.0 3643 1 0.983 0.002121 0.978 0.987
## 125.0 3636 1 0.982 0.002138 0.978 0.987
## 126.0 3634 1 0.982 0.002154 0.978 0.986
## 128.0 3627 2 0.982 0.002187 0.977 0.986
## 132.0 3622 1 0.981 0.002203 0.977 0.986
## 133.0 3619 1 0.981 0.002219 0.977 0.985
## 138.0 3609 1 0.981 0.002235 0.976 0.985
## 142.0 3599 1 0.980 0.002251 0.976 0.985
## 144.0 3597 1 0.980 0.002266 0.976 0.985
## 146.0 3596 1 0.980 0.002282 0.975 0.984
## 150.0 3585 1 0.980 0.002298 0.975 0.984
## 151.0 3584 1 0.979 0.002313 0.975 0.984
## 162.0 3569 1 0.979 0.002329 0.975 0.984
## 167.0 3563 1 0.979 0.002344 0.974 0.983
## 168.0 3559 2 0.978 0.002375 0.974 0.983
## 170.0 3552 1 0.978 0.002390 0.973 0.983
## 172.0 3547 1 0.978 0.002406 0.973 0.982
## 177.0 3534 1 0.977 0.002421 0.973 0.982
## 178.0 3532 1 0.977 0.002436 0.972 0.982
## 181.0 3531 1 0.977 0.002451 0.972 0.982
## 182.0 3529 1 0.977 0.002466 0.972 0.981
## 183.0 3527 2 0.976 0.002495 0.971 0.981
## 185.0 3519 1 0.976 0.002510 0.971 0.981
## 190.0 3512 2 0.975 0.002539 0.970 0.980
## 191.0 3507 1 0.975 0.002554 0.970 0.980
## 194.0 3502 2 0.974 0.002582 0.969 0.979
## 196.0 3495 1 0.974 0.002597 0.969 0.979
## 199.0 3484 1 0.974 0.002611 0.969 0.979
## 203.0 3480 1 0.974 0.002625 0.968 0.979
## 205.0 3476 1 0.973 0.002639 0.968 0.978
## 214.0 3461 2 0.973 0.002667 0.967 0.978
## 215.0 3459 1 0.972 0.002681 0.967 0.978
## 217.0 3456 1 0.972 0.002695 0.967 0.977
## 220.0 3447 1 0.972 0.002709 0.967 0.977
## 230.0 3438 2 0.971 0.002737 0.966 0.977
## 232.0 3431 1 0.971 0.002751 0.966 0.976
## 236.0 3421 2 0.970 0.002778 0.965 0.976
## 237.0 3418 1 0.970 0.002792 0.965 0.976
## 245.0 3404 1 0.970 0.002806 0.964 0.975
## 248.0 3397 1 0.970 0.002819 0.964 0.975
## 249.0 3395 1 0.969 0.002833 0.964 0.975
## 253.0 3389 1 0.969 0.002847 0.963 0.975
## 254.0 3385 1 0.969 0.002860 0.963 0.974
## 256.0 3383 1 0.968 0.002874 0.963 0.974
## 259.0 3382 2 0.968 0.002900 0.962 0.974
## 261.0 3375 1 0.968 0.002913 0.962 0.973
## 268.0 3364 1 0.967 0.002927 0.962 0.973
## 277.0 3343 1 0.967 0.002940 0.961 0.973
## 279.0 3341 1 0.967 0.002954 0.961 0.973
## 281.0 3334 1 0.966 0.002967 0.961 0.972
## 285.0 3327 1 0.966 0.002980 0.960 0.972
## 291.0 3318 1 0.966 0.002993 0.960 0.972
## 294.0 3313 3 0.965 0.003033 0.959 0.971
## 295.0 3306 1 0.965 0.003046 0.959 0.971
## 296.0 3303 1 0.964 0.003059 0.958 0.970
## 299.0 3298 1 0.964 0.003072 0.958 0.970
## 300.0 3297 1 0.964 0.003085 0.958 0.970
## 309.0 3279 1 0.964 0.003098 0.957 0.970
## 315.0 3267 1 0.963 0.003111 0.957 0.969
## 322.0 3255 1 0.963 0.003124 0.957 0.969
## 333.0 3233 1 0.963 0.003137 0.956 0.969
## 336.0 3229 1 0.962 0.003151 0.956 0.969
## 337.0 3225 1 0.962 0.003164 0.956 0.968
## 345.0 3215 1 0.962 0.003177 0.956 0.968
## 357.0 3199 2 0.961 0.003203 0.955 0.967
## 359.0 3190 1 0.961 0.003216 0.955 0.967
## 360.0 3187 1 0.961 0.003229 0.954 0.967
## 363.0 3186 2 0.960 0.003255 0.954 0.966
## 366.0 3174 1 0.960 0.003268 0.953 0.966
## 367.0 3172 1 0.959 0.003281 0.953 0.966
## 369.0 3171 1 0.959 0.003294 0.953 0.965
## 372.0 3164 1 0.959 0.003307 0.952 0.965
## 374.0 3158 1 0.958 0.003320 0.952 0.965
## 379.0 3149 1 0.958 0.003333 0.952 0.965
## 380.0 3144 1 0.958 0.003346 0.951 0.964
## 385.0 3137 2 0.957 0.003371 0.951 0.964
## 391.0 3133 1 0.957 0.003384 0.950 0.964
## 401.0 3119 1 0.957 0.003397 0.950 0.963
## 413.0 3103 1 0.956 0.003410 0.950 0.963
## 421.0 3089 1 0.956 0.003423 0.949 0.963
## 428.0 3088 1 0.956 0.003435 0.949 0.962
## 435.0 3080 1 0.955 0.003448 0.949 0.962
## 447.0 3062 3 0.954 0.003487 0.948 0.961
## 452.0 3057 1 0.954 0.003500 0.947 0.961
## 453.0 3056 1 0.954 0.003513 0.947 0.961
## 454.0 3055 1 0.953 0.003525 0.947 0.960
## 456.0 3047 1 0.953 0.003538 0.946 0.960
## 461.0 3040 1 0.953 0.003551 0.946 0.960
## 462.0 3038 1 0.953 0.003563 0.946 0.960
## 465.0 3033 1 0.952 0.003576 0.945 0.959
## 471.0 3027 1 0.952 0.003589 0.945 0.959
## 475.0 3023 1 0.952 0.003601 0.945 0.959
## 481.0 3007 1 0.951 0.003614 0.944 0.958
## 484.0 3003 1 0.951 0.003627 0.944 0.958
## 487.0 2997 1 0.951 0.003639 0.944 0.958
## 498.0 2982 1 0.950 0.003652 0.943 0.957
## 501.0 2978 1 0.950 0.003665 0.943 0.957
## 503.0 2975 1 0.950 0.003677 0.942 0.957
## 504.0 2973 1 0.949 0.003690 0.942 0.957
## 515.0 2961 1 0.949 0.003703 0.942 0.956
## 516.0 2960 1 0.949 0.003715 0.941 0.956
## 522.0 2949 1 0.948 0.003728 0.941 0.956
## 523.0 2948 1 0.948 0.003740 0.941 0.955
## 525.0 2944 1 0.948 0.003753 0.940 0.955
## 538.0 2932 1 0.947 0.003766 0.940 0.955
## 553.0 2908 1 0.947 0.003778 0.940 0.955
## 558.0 2901 1 0.947 0.003791 0.939 0.954
## 559.0 2900 1 0.946 0.003804 0.939 0.954
## 568.0 2878 1 0.946 0.003817 0.939 0.954
## 570.0 2871 1 0.946 0.003830 0.938 0.953
## 576.0 2862 1 0.945 0.003842 0.938 0.953
## 579.0 2858 1 0.945 0.003855 0.938 0.953
## 586.0 2851 1 0.945 0.003868 0.937 0.952
## 587.0 2850 1 0.944 0.003881 0.937 0.952
## 588.0 2848 1 0.944 0.003894 0.937 0.952
## 589.0 2847 1 0.944 0.003907 0.936 0.951
## 603.0 2831 1 0.943 0.003919 0.936 0.951
## 606.0 2827 1 0.943 0.003932 0.935 0.951
## 609.0 2822 1 0.943 0.003945 0.935 0.951
## 619.0 2801 1 0.942 0.003958 0.935 0.950
## 663.0 2740 1 0.942 0.003971 0.934 0.950
## 676.0 2724 1 0.942 0.003985 0.934 0.950
## 683.0 2708 1 0.941 0.003999 0.934 0.949
## 687.0 2703 2 0.941 0.004026 0.933 0.949
## 689.0 2700 1 0.940 0.004039 0.932 0.948
## 691.0 2699 1 0.940 0.004053 0.932 0.948
## 698.0 2689 1 0.940 0.004066 0.932 0.948
## 702.0 2683 1 0.939 0.004080 0.931 0.947
## 712.0 2667 1 0.939 0.004094 0.931 0.947
## 717.0 2664 1 0.939 0.004107 0.931 0.947
## 738.0 2630 1 0.938 0.004121 0.930 0.946
## 752.0 2609 1 0.938 0.004135 0.930 0.946
## 757.0 2600 2 0.937 0.004163 0.929 0.945
## 763.0 2589 1 0.937 0.004178 0.929 0.945
## 765.0 2583 1 0.936 0.004192 0.928 0.945
## 766.0 2581 1 0.936 0.004206 0.928 0.944
## 768.0 2580 1 0.936 0.004220 0.927 0.944
## 770.0 2575 1 0.935 0.004234 0.927 0.944
## 780.0 2548 2 0.935 0.004262 0.926 0.943
## 781.0 2546 1 0.934 0.004276 0.926 0.943
## 782.0 2544 1 0.934 0.004290 0.926 0.942
## 784.0 2538 1 0.934 0.004304 0.925 0.942
## 788.0 2531 1 0.933 0.004318 0.925 0.942
## 810.0 2512 1 0.933 0.004333 0.924 0.941
## 823.0 2489 1 0.932 0.004347 0.924 0.941
## 826.0 2480 1 0.932 0.004361 0.924 0.941
## 832.0 2471 1 0.932 0.004376 0.923 0.940
## 841.0 2463 1 0.931 0.004391 0.923 0.940
## 847.0 2457 1 0.931 0.004405 0.922 0.940
## 851.0 2447 1 0.931 0.004420 0.922 0.939
## 852.0 2446 1 0.930 0.004434 0.921 0.939
## 856.0 2441 1 0.930 0.004449 0.921 0.939
## 858.0 2438 1 0.929 0.004463 0.921 0.938
## 863.0 2428 1 0.929 0.004478 0.920 0.938
## 873.0 2421 1 0.929 0.004492 0.920 0.937
## 888.0 2397 1 0.928 0.004507 0.919 0.937
## 913.0 2364 1 0.928 0.004522 0.919 0.937
## 914.0 2363 1 0.927 0.004537 0.919 0.936
## 939.0 2324 1 0.927 0.004553 0.918 0.936
## 947.0 2307 1 0.927 0.004569 0.918 0.936
## 949.0 2306 1 0.926 0.004584 0.917 0.935
## 950.0 2305 1 0.926 0.004600 0.917 0.935
## 952.0 2304 1 0.925 0.004615 0.916 0.935
## 958.0 2294 2 0.925 0.004647 0.916 0.934
## 966.0 2285 1 0.924 0.004662 0.915 0.933
## 972.0 2279 1 0.924 0.004678 0.915 0.933
## 973.0 2278 1 0.923 0.004693 0.914 0.933
## 981.0 2273 2 0.923 0.004724 0.913 0.932
## 982.0 2269 2 0.922 0.004755 0.913 0.931
## 984.0 2263 1 0.921 0.004770 0.912 0.931
## 991.0 2247 1 0.921 0.004786 0.912 0.930
## 994.0 2243 1 0.921 0.004801 0.911 0.930
## 1002.0 2231 1 0.920 0.004817 0.911 0.930
## 1006.0 2225 1 0.920 0.004832 0.910 0.929
## 1009.0 2223 1 0.919 0.004848 0.910 0.929
## 1021.0 2204 1 0.919 0.004863 0.909 0.928
## 1022.0 2199 1 0.918 0.004879 0.909 0.928
## 1035.0 2182 1 0.918 0.004895 0.909 0.928
## 1037.0 2177 1 0.918 0.004911 0.908 0.927
## 1042.0 2171 1 0.917 0.004927 0.908 0.927
## 1045.0 2164 1 0.917 0.004943 0.907 0.927
## 1047.0 2162 1 0.916 0.004958 0.907 0.926
## 1056.0 2149 1 0.916 0.004974 0.906 0.926
## 1069.0 2136 1 0.916 0.004991 0.906 0.925
## 1079.0 2124 1 0.915 0.005007 0.905 0.925
## 1080.0 2122 1 0.915 0.005023 0.905 0.925
## 1081.0 2117 1 0.914 0.005039 0.904 0.924
## 1084.0 2115 1 0.914 0.005055 0.904 0.924
## 1099.0 2098 1 0.913 0.005072 0.903 0.923
## 1102.0 2092 1 0.913 0.005088 0.903 0.923
## 1106.0 2085 1 0.912 0.005104 0.903 0.923
## 1119.0 2067 1 0.912 0.005121 0.902 0.922
## 1121.0 2064 1 0.912 0.005137 0.902 0.922
## 1123.0 2058 1 0.911 0.005154 0.901 0.921
## 1136.0 2046 1 0.911 0.005171 0.901 0.921
## 1161.0 2012 1 0.910 0.005188 0.900 0.920
## 1165.0 2009 1 0.910 0.005205 0.900 0.920
## 1170.0 1997 1 0.909 0.005222 0.899 0.920
## 1173.0 1993 1 0.909 0.005240 0.899 0.919
## 1178.0 1987 1 0.908 0.005257 0.898 0.919
## 1179.0 1985 1 0.908 0.005274 0.898 0.918
## 1183.0 1980 1 0.908 0.005291 0.897 0.918
## 1185.0 1976 1 0.907 0.005309 0.897 0.918
## 1200.0 1957 1 0.907 0.005326 0.896 0.917
## 1203.0 1955 1 0.906 0.005344 0.896 0.917
## 1204.0 1952 1 0.906 0.005361 0.895 0.916
## 1207.0 1944 1 0.905 0.005378 0.895 0.916
## 1216.0 1934 1 0.905 0.005396 0.894 0.915
## 1222.0 1919 1 0.904 0.005414 0.894 0.915
## 1227.0 1908 1 0.904 0.005432 0.893 0.914
## 1244.0 1893 1 0.903 0.005450 0.893 0.914
## 1253.0 1881 1 0.903 0.005468 0.892 0.914
## 1258.0 1875 1 0.902 0.005486 0.892 0.913
## 1263.0 1867 1 0.902 0.005504 0.891 0.913
## 1267.0 1863 1 0.901 0.005523 0.891 0.912
## 1274.0 1859 1 0.901 0.005541 0.890 0.912
## 1297.0 1830 1 0.900 0.005560 0.890 0.911
## 1301.0 1825 1 0.900 0.005579 0.889 0.911
## 1315.0 1807 1 0.899 0.005598 0.889 0.910
## 1317.0 1804 1 0.899 0.005617 0.888 0.910
## 1319.0 1800 2 0.898 0.005655 0.887 0.909
## 1327.0 1792 1 0.897 0.005674 0.886 0.909
## 1361.0 1765 1 0.897 0.005693 0.886 0.908
## 1386.0 1741 1 0.896 0.005713 0.885 0.908
## 1414.0 1713 1 0.896 0.005734 0.885 0.907
## 1421.0 1703 1 0.895 0.005754 0.884 0.907
## 1425.0 1699 1 0.895 0.005775 0.884 0.906
## 1427.0 1696 1 0.894 0.005796 0.883 0.906
## 1431.0 1693 1 0.894 0.005816 0.882 0.905
## 1436.0 1689 1 0.893 0.005837 0.882 0.905
## 1437.0 1688 2 0.892 0.005878 0.881 0.904
## 1442.0 1683 1 0.892 0.005898 0.880 0.903
## 1446.0 1677 1 0.891 0.005919 0.880 0.903
## 1447.0 1676 1 0.891 0.005939 0.879 0.902
## 1451.0 1667 1 0.890 0.005959 0.878 0.902
## 1466.0 1653 2 0.889 0.006001 0.877 0.901
## 1472.0 1646 1 0.888 0.006021 0.877 0.900
## 1481.0 1638 1 0.888 0.006042 0.876 0.900
## 1488.0 1628 1 0.887 0.006063 0.876 0.899
## 1491.0 1625 1 0.887 0.006084 0.875 0.899
## 1495.0 1619 1 0.886 0.006104 0.874 0.898
## 1506.0 1611 1 0.886 0.006125 0.874 0.898
## 1512.0 1603 1 0.885 0.006146 0.873 0.897
## 1513.0 1598 1 0.885 0.006167 0.873 0.897
## 1520.0 1593 1 0.884 0.006189 0.872 0.896
## 1522.0 1592 1 0.883 0.006210 0.871 0.896
## 1523.0 1590 1 0.883 0.006230 0.871 0.895
## 1533.0 1587 1 0.882 0.006251 0.870 0.895
## 1541.0 1581 1 0.882 0.006272 0.870 0.894
## 1547.0 1574 1 0.881 0.006293 0.869 0.894
## 1556.0 1564 1 0.881 0.006314 0.868 0.893
## 1558.0 1558 1 0.880 0.006336 0.868 0.893
## 1562.0 1555 1 0.880 0.006357 0.867 0.892
## 1567.0 1547 1 0.879 0.006378 0.867 0.892
## 1569.0 1543 1 0.878 0.006399 0.866 0.891
## 1571.0 1540 1 0.878 0.006420 0.865 0.891
## 1590.0 1520 1 0.877 0.006442 0.865 0.890
## 1593.0 1514 2 0.876 0.006486 0.863 0.889
## 1595.0 1510 1 0.876 0.006507 0.863 0.888
## 1634.0 1464 1 0.875 0.006530 0.862 0.888
## 1635.0 1462 2 0.874 0.006576 0.861 0.887
## 1638.0 1455 1 0.873 0.006599 0.860 0.886
## 1647.0 1444 1 0.873 0.006622 0.860 0.886
## 1649.0 1441 1 0.872 0.006645 0.859 0.885
## 1651.0 1439 1 0.871 0.006668 0.858 0.884
## 1666.0 1423 1 0.871 0.006691 0.858 0.884
## 1669.0 1418 1 0.870 0.006714 0.857 0.883
## 1677.0 1409 1 0.869 0.006738 0.856 0.883
## 1682.0 1404 1 0.869 0.006762 0.856 0.882
## 1688.0 1396 1 0.868 0.006785 0.855 0.882
## 1695.0 1390 1 0.868 0.006809 0.854 0.881
## 1701.0 1385 1 0.867 0.006833 0.854 0.880
## 1735.0 1357 1 0.866 0.006858 0.853 0.880
## 1747.0 1346 1 0.866 0.006883 0.852 0.879
## 1751.0 1343 1 0.865 0.006908 0.852 0.879
## 1755.0 1337 1 0.864 0.006933 0.851 0.878
## 1779.0 1321 1 0.864 0.006958 0.850 0.877
## 1782.0 1319 1 0.863 0.006984 0.850 0.877
## 1797.0 1316 1 0.862 0.007009 0.849 0.876
## 1798.0 1315 1 0.862 0.007035 0.848 0.876
## 1801.0 1314 1 0.861 0.007060 0.847 0.875
## 1804.0 1312 1 0.860 0.007085 0.847 0.874
## 1811.0 1304 1 0.860 0.007110 0.846 0.874
## 1822.0 1296 1 0.859 0.007135 0.845 0.873
## 1826.0 1293 1 0.858 0.007161 0.845 0.873
## 1833.0 1290 1 0.858 0.007186 0.844 0.872
## 1866.0 1255 1 0.857 0.007213 0.843 0.871
## 1873.0 1244 1 0.856 0.007240 0.842 0.871
## 1877.0 1239 1 0.856 0.007267 0.842 0.870
## 1879.0 1234 1 0.855 0.007294 0.841 0.869
## 1915.0 1209 1 0.854 0.007322 0.840 0.869
## 1924.0 1196 1 0.854 0.007351 0.839 0.868
## 1927.0 1192 1 0.853 0.007380 0.839 0.868
## 1970.0 1146 1 0.852 0.007411 0.838 0.867
## 1973.0 1145 1 0.851 0.007441 0.837 0.866
## 1981.0 1136 1 0.851 0.007472 0.836 0.865
## 1982.0 1135 1 0.850 0.007503 0.835 0.865
## 1986.0 1130 1 0.849 0.007534 0.835 0.864
## 1991.0 1124 1 0.848 0.007565 0.834 0.863
## 2005.0 1108 1 0.848 0.007597 0.833 0.863
## 2009.0 1106 1 0.847 0.007629 0.832 0.862
## 2033.0 1077 1 0.846 0.007662 0.831 0.861
## 2045.0 1071 1 0.845 0.007696 0.830 0.861
## 2051.0 1063 1 0.845 0.007729 0.830 0.860
## 2053.0 1058 1 0.844 0.007763 0.829 0.859
## 2080.0 1037 1 0.843 0.007798 0.828 0.858
## 2083.0 1036 1 0.842 0.007833 0.827 0.858
## 2084.0 1035 1 0.841 0.007868 0.826 0.857
## 2114.0 1014 2 0.840 0.007939 0.824 0.855
## 2118.0 1006 1 0.839 0.007975 0.823 0.855
## 2142.0 987 1 0.838 0.008012 0.822 0.854
## 2152.0 982 1 0.837 0.008049 0.821 0.853
## 2165.0 969 1 0.836 0.008087 0.821 0.852
## 2178.0 953 2 0.834 0.008165 0.819 0.851
## 2194.0 933 1 0.834 0.008205 0.818 0.850
## 2208.0 916 1 0.833 0.008246 0.817 0.849
## 2214.0 910 1 0.832 0.008288 0.816 0.848
## 2224.0 899 1 0.831 0.008330 0.815 0.847
## 2239.0 889 1 0.830 0.008373 0.814 0.846
## 2257.0 871 1 0.829 0.008417 0.813 0.846
## 2266.0 868 1 0.828 0.008462 0.812 0.845
## 2269.0 864 1 0.827 0.008506 0.811 0.844
## 2288.0 839 1 0.826 0.008553 0.809 0.843
## 2305.0 816 1 0.825 0.008602 0.808 0.842
## 2321.0 799 1 0.824 0.008653 0.807 0.841
## 2330.0 788 1 0.823 0.008705 0.806 0.840
## 2334.0 781 1 0.822 0.008757 0.805 0.839
## 2342.0 776 1 0.821 0.008810 0.804 0.838
## 2378.0 735 1 0.820 0.008868 0.803 0.837
## 2387.0 729 1 0.819 0.008927 0.801 0.836
## 2413.0 708 2 0.816 0.009051 0.799 0.834
## 2429.0 688 1 0.815 0.009115 0.797 0.833
## 2445.0 668 1 0.814 0.009182 0.796 0.832
## 2447.0 665 1 0.813 0.009250 0.795 0.831
## 2449.0 664 1 0.811 0.009317 0.793 0.830
## 2455.0 658 1 0.810 0.009384 0.792 0.829
## 2470.0 646 1 0.809 0.009453 0.791 0.828
## 2486.0 633 1 0.808 0.009524 0.789 0.827
## 2530.0 591 1 0.806 0.009605 0.788 0.825
## 2551.0 568 1 0.805 0.009692 0.786 0.824
## 2554.0 566 1 0.803 0.009779 0.785 0.823
## 2555.0 564 1 0.802 0.009865 0.783 0.822
## 2581.0 537 1 0.801 0.009959 0.781 0.820
## 2582.0 536 1 0.799 0.010052 0.780 0.819
## 2623.0 499 1 0.797 0.010158 0.778 0.818
## 2633.0 492 1 0.796 0.010266 0.776 0.816
## 2636.0 489 1 0.794 0.010373 0.774 0.815
## 2662.0 468 1 0.792 0.010489 0.772 0.813
## 2676.0 453 1 0.791 0.010611 0.770 0.812
## 2686.0 446 1 0.789 0.010734 0.768 0.810
## 2718.0 416 1 0.787 0.010875 0.766 0.809
## 2790.0 367 1 0.785 0.011055 0.764 0.807
## 2813.0 344 1 0.783 0.011255 0.761 0.805
## 2848.0 300 1 0.780 0.011516 0.758 0.803
## 2849.0 297 1 0.777 0.011773 0.755 0.801
## 2861.0 285 1 0.775 0.012044 0.751 0.799
## 2875.0 263 1 0.772 0.012353 0.748 0.796
## 3011.0 204 1 0.768 0.012859 0.743 0.794
## 3017.0 198 1 0.764 0.013366 0.738 0.791
## 3020.0 193 1 0.760 0.013870 0.733 0.788
## 3085.0 167 1 0.756 0.014515 0.728 0.785
## 3109.0 152 1 0.751 0.015247 0.721 0.781
## 3131.0 140 1 0.745 0.016053 0.714 0.777
## 3244.0 85 1 0.736 0.018101 0.702 0.773
## 3282.0 65 1 0.725 0.021072 0.685 0.768# カプランマイヤーカーブの描画
ggsurvplot(fit1, data = SMARTo, pval = TRUE) ## Warning in .pvalue(fit, data = data, method = method, pval = pval, pval.coord = pval.coord, : There are no survival curves to be compared.
## This is a null model.
# 追跡期間を無視した累積罹患率の計算
cumulative_incidence_ignored <- sum(SMARTo$EVENT) / length(SMARTo$EVENT)
cat("Cumulative incidence (ignoring follow-up time):", cumulative_incidence_ignored, "\n")## Cumulative incidence (ignoring follow-up time): 0.118771# カプランマイヤー法による累積罹患率の計算
km_cumulative_incidence <- 1 - fit1$surv[which.min(abs(fit1$time - max(SMARTo$TEVENT)))]
cat("Cumulative incidence (Kaplan-Meier method):", km_cumulative_incidence, "\n")## Cumulative incidence (Kaplan-Meier method): 0.2748606(3) 次に性別毎のカプランマイヤーカーブを描きましょう。
fit2 <- survfit(Surv(TEVENT,EVENT) ~ SEX, data = SMARTo)
summary(fit2) ## Call: survfit(formula = Surv(TEVENT, EVENT) ~ SEX, data = SMARTo)
##
## SEX=1
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 0.1 2897 2 0.999 0.000488 0.998 1.000
## 1.0 2895 9 0.996 0.001143 0.994 0.998
## 2.0 2882 2 0.996 0.001242 0.993 0.998
## 3.0 2879 2 0.995 0.001334 0.992 0.997
## 12.0 2873 1 0.994 0.001378 0.992 0.997
## 16.0 2868 1 0.994 0.001420 0.991 0.997
## 20.0 2867 2 0.993 0.001501 0.990 0.996
## 29.0 2851 1 0.993 0.001541 0.990 0.996
## 31.0 2847 1 0.993 0.001579 0.990 0.996
## 32.0 2846 1 0.992 0.001617 0.989 0.996
## 37.0 2841 1 0.992 0.001654 0.989 0.995
## 40.0 2839 2 0.991 0.001725 0.988 0.995
## 52.0 2815 1 0.991 0.001760 0.988 0.994
## 54.0 2814 1 0.991 0.001794 0.987 0.994
## 56.0 2810 1 0.990 0.001828 0.987 0.994
## 59.0 2800 1 0.990 0.001861 0.986 0.994
## 65.0 2798 1 0.990 0.001893 0.986 0.993
## 69.0 2797 1 0.989 0.001926 0.985 0.993
## 73.0 2787 1 0.989 0.001957 0.985 0.993
## 75.0 2786 1 0.989 0.001989 0.985 0.992
## 77.0 2784 1 0.988 0.002019 0.984 0.992
## 86.0 2769 1 0.988 0.002050 0.984 0.992
## 87.0 2767 1 0.987 0.002080 0.983 0.992
## 92.0 2763 2 0.987 0.002139 0.983 0.991
## 96.0 2760 1 0.986 0.002168 0.982 0.991
## 97.0 2757 3 0.985 0.002252 0.981 0.990
## 102.0 2742 1 0.985 0.002280 0.980 0.989
## 104.0 2741 1 0.985 0.002307 0.980 0.989
## 105.0 2739 2 0.984 0.002361 0.979 0.988
## 106.0 2736 1 0.983 0.002387 0.979 0.988
## 113.0 2729 2 0.983 0.002439 0.978 0.988
## 114.0 2726 1 0.982 0.002465 0.978 0.987
## 115.0 2724 2 0.982 0.002515 0.977 0.987
## 119.0 2718 1 0.981 0.002540 0.976 0.986
## 120.0 2717 1 0.981 0.002565 0.976 0.986
## 125.0 2712 1 0.981 0.002589 0.976 0.986
## 126.0 2710 1 0.980 0.002614 0.975 0.985
## 128.0 2705 2 0.980 0.002661 0.974 0.985
## 132.0 2700 1 0.979 0.002685 0.974 0.984
## 138.0 2690 1 0.979 0.002709 0.974 0.984
## 142.0 2683 1 0.978 0.002732 0.973 0.984
## 144.0 2681 1 0.978 0.002755 0.973 0.983
## 150.0 2674 1 0.978 0.002778 0.972 0.983
## 151.0 2673 1 0.977 0.002801 0.972 0.983
## 162.0 2664 1 0.977 0.002824 0.971 0.983
## 168.0 2658 2 0.976 0.002870 0.971 0.982
## 170.0 2653 1 0.976 0.002892 0.970 0.982
## 172.0 2649 1 0.975 0.002914 0.970 0.981
## 177.0 2640 1 0.975 0.002936 0.969 0.981
## 178.0 2638 1 0.975 0.002958 0.969 0.981
## 181.0 2637 1 0.974 0.002980 0.969 0.980
## 182.0 2635 1 0.974 0.003002 0.968 0.980
## 183.0 2633 2 0.973 0.003045 0.967 0.979
## 185.0 2626 1 0.973 0.003066 0.967 0.979
## 190.0 2623 2 0.972 0.003109 0.966 0.978
## 191.0 2619 1 0.972 0.003129 0.966 0.978
## 194.0 2616 2 0.971 0.003171 0.965 0.977
## 203.0 2600 1 0.971 0.003192 0.964 0.977
## 205.0 2597 1 0.970 0.003212 0.964 0.977
## 214.0 2585 1 0.970 0.003233 0.964 0.976
## 215.0 2584 1 0.970 0.003253 0.963 0.976
## 220.0 2577 1 0.969 0.003274 0.963 0.976
## 230.0 2570 2 0.968 0.003314 0.962 0.975
## 232.0 2567 1 0.968 0.003334 0.962 0.975
## 236.0 2557 1 0.968 0.003354 0.961 0.974
## 245.0 2546 1 0.967 0.003375 0.961 0.974
## 248.0 2541 1 0.967 0.003395 0.960 0.974
## 253.0 2536 1 0.967 0.003415 0.960 0.973
## 256.0 2534 1 0.966 0.003435 0.959 0.973
## 261.0 2531 1 0.966 0.003454 0.959 0.973
## 268.0 2520 1 0.965 0.003474 0.959 0.972
## 277.0 2502 1 0.965 0.003494 0.958 0.972
## 281.0 2496 1 0.965 0.003514 0.958 0.972
## 285.0 2492 1 0.964 0.003534 0.957 0.971
## 291.0 2485 1 0.964 0.003554 0.957 0.971
## 294.0 2480 2 0.963 0.003593 0.956 0.970
## 295.0 2475 1 0.963 0.003613 0.956 0.970
## 296.0 2474 1 0.962 0.003632 0.955 0.969
## 300.0 2470 1 0.962 0.003652 0.955 0.969
## 309.0 2459 1 0.961 0.003671 0.954 0.969
## 315.0 2451 1 0.961 0.003690 0.954 0.968
## 322.0 2444 1 0.961 0.003710 0.953 0.968
## 333.0 2427 1 0.960 0.003729 0.953 0.968
## 336.0 2424 1 0.960 0.003749 0.953 0.967
## 337.0 2421 1 0.960 0.003768 0.952 0.967
## 345.0 2413 1 0.959 0.003787 0.952 0.967
## 357.0 2398 2 0.958 0.003826 0.951 0.966
## 363.0 2390 2 0.958 0.003865 0.950 0.965
## 366.0 2379 1 0.957 0.003884 0.950 0.965
## 367.0 2377 1 0.957 0.003903 0.949 0.964
## 369.0 2376 1 0.956 0.003922 0.949 0.964
## 372.0 2373 1 0.956 0.003941 0.948 0.964
## 374.0 2367 1 0.956 0.003960 0.948 0.963
## 379.0 2361 1 0.955 0.003979 0.947 0.963
## 380.0 2357 1 0.955 0.003998 0.947 0.963
## 385.0 2351 2 0.954 0.004036 0.946 0.962
## 391.0 2347 1 0.953 0.004055 0.946 0.961
## 401.0 2335 1 0.953 0.004073 0.945 0.961
## 421.0 2313 1 0.953 0.004092 0.945 0.961
## 428.0 2312 1 0.952 0.004111 0.944 0.960
## 435.0 2307 1 0.952 0.004130 0.944 0.960
## 447.0 2294 3 0.951 0.004187 0.942 0.959
## 452.0 2290 1 0.950 0.004205 0.942 0.958
## 454.0 2289 1 0.950 0.004224 0.942 0.958
## 456.0 2283 1 0.949 0.004243 0.941 0.958
## 462.0 2277 1 0.949 0.004261 0.941 0.957
## 471.0 2270 1 0.949 0.004280 0.940 0.957
## 475.0 2267 1 0.948 0.004298 0.940 0.957
## 484.0 2257 1 0.948 0.004317 0.939 0.956
## 487.0 2253 1 0.947 0.004335 0.939 0.956
## 498.0 2245 1 0.947 0.004354 0.938 0.955
## 501.0 2242 1 0.946 0.004372 0.938 0.955
## 503.0 2241 1 0.946 0.004391 0.937 0.955
## 504.0 2239 1 0.946 0.004409 0.937 0.954
## 515.0 2230 1 0.945 0.004428 0.936 0.954
## 516.0 2229 1 0.945 0.004446 0.936 0.953
## 522.0 2220 1 0.944 0.004464 0.936 0.953
## 523.0 2219 1 0.944 0.004482 0.935 0.953
## 525.0 2216 1 0.943 0.004501 0.935 0.952
## 553.0 2192 1 0.943 0.004519 0.934 0.952
## 558.0 2186 1 0.943 0.004537 0.934 0.952
## 559.0 2185 1 0.942 0.004556 0.933 0.951
## 576.0 2157 1 0.942 0.004575 0.933 0.951
## 586.0 2150 1 0.941 0.004593 0.932 0.950
## 587.0 2149 1 0.941 0.004612 0.932 0.950
## 588.0 2147 1 0.940 0.004631 0.931 0.950
## 603.0 2135 1 0.940 0.004650 0.931 0.949
## 606.0 2131 1 0.940 0.004668 0.930 0.949
## 609.0 2127 1 0.939 0.004687 0.930 0.948
## 619.0 2111 1 0.939 0.004706 0.929 0.948
## 663.0 2072 1 0.938 0.004725 0.929 0.947
## 687.0 2046 2 0.937 0.004765 0.928 0.947
## 689.0 2043 1 0.937 0.004785 0.927 0.946
## 691.0 2042 1 0.936 0.004804 0.927 0.946
## 698.0 2035 1 0.936 0.004824 0.926 0.945
## 712.0 2018 1 0.935 0.004844 0.926 0.945
## 717.0 2016 1 0.935 0.004863 0.925 0.945
## 738.0 1991 1 0.934 0.004884 0.925 0.944
## 752.0 1979 1 0.934 0.004904 0.924 0.944
## 757.0 1971 2 0.933 0.004944 0.923 0.943
## 763.0 1964 1 0.933 0.004965 0.923 0.942
## 765.0 1958 1 0.932 0.004985 0.922 0.942
## 766.0 1956 1 0.932 0.005005 0.922 0.941
## 768.0 1955 1 0.931 0.005025 0.921 0.941
## 770.0 1952 1 0.931 0.005045 0.921 0.941
## 780.0 1931 2 0.930 0.005086 0.920 0.940
## 781.0 1929 1 0.929 0.005106 0.919 0.939
## 782.0 1928 1 0.929 0.005126 0.919 0.939
## 784.0 1923 1 0.928 0.005146 0.918 0.938
## 810.0 1905 1 0.928 0.005166 0.918 0.938
## 823.0 1887 1 0.927 0.005187 0.917 0.938
## 826.0 1881 1 0.927 0.005208 0.917 0.937
## 832.0 1872 1 0.926 0.005228 0.916 0.937
## 841.0 1865 1 0.926 0.005249 0.916 0.936
## 851.0 1854 1 0.925 0.005270 0.915 0.936
## 852.0 1853 1 0.925 0.005291 0.914 0.935
## 863.0 1842 1 0.924 0.005312 0.914 0.935
## 873.0 1836 1 0.924 0.005333 0.913 0.934
## 888.0 1821 1 0.923 0.005354 0.913 0.934
## 914.0 1799 1 0.923 0.005375 0.912 0.933
## 947.0 1759 1 0.922 0.005398 0.912 0.933
## 949.0 1758 1 0.922 0.005420 0.911 0.932
## 950.0 1757 1 0.921 0.005442 0.911 0.932
## 952.0 1756 1 0.921 0.005464 0.910 0.931
## 958.0 1748 2 0.920 0.005509 0.909 0.930
## 966.0 1742 1 0.919 0.005531 0.908 0.930
## 972.0 1738 1 0.919 0.005553 0.908 0.930
## 981.0 1733 2 0.918 0.005597 0.907 0.929
## 982.0 1730 2 0.916 0.005640 0.905 0.928
## 984.0 1724 1 0.916 0.005662 0.905 0.927
## 991.0 1708 1 0.915 0.005684 0.904 0.927
## 1006.0 1694 1 0.915 0.005706 0.904 0.926
## 1009.0 1692 1 0.914 0.005729 0.903 0.926
## 1021.0 1676 1 0.914 0.005751 0.903 0.925
## 1035.0 1660 1 0.913 0.005774 0.902 0.925
## 1037.0 1656 1 0.913 0.005797 0.901 0.924
## 1042.0 1650 1 0.912 0.005819 0.901 0.924
## 1045.0 1645 1 0.912 0.005842 0.900 0.923
## 1047.0 1643 1 0.911 0.005865 0.900 0.923
## 1069.0 1625 1 0.910 0.005888 0.899 0.922
## 1079.0 1616 1 0.910 0.005911 0.898 0.922
## 1080.0 1614 1 0.909 0.005935 0.898 0.921
## 1084.0 1609 1 0.909 0.005958 0.897 0.920
## 1099.0 1596 1 0.908 0.005981 0.897 0.920
## 1102.0 1592 1 0.908 0.006005 0.896 0.919
## 1119.0 1576 1 0.907 0.006028 0.895 0.919
## 1121.0 1575 1 0.906 0.006052 0.895 0.918
## 1123.0 1572 1 0.906 0.006075 0.894 0.918
## 1136.0 1561 1 0.905 0.006099 0.893 0.917
## 1161.0 1532 1 0.905 0.006124 0.893 0.917
## 1170.0 1521 1 0.904 0.006149 0.892 0.916
## 1173.0 1518 1 0.904 0.006173 0.891 0.916
## 1179.0 1511 1 0.903 0.006198 0.891 0.915
## 1183.0 1506 1 0.902 0.006223 0.890 0.915
## 1185.0 1502 1 0.902 0.006248 0.890 0.914
## 1200.0 1486 1 0.901 0.006273 0.889 0.913
## 1203.0 1485 1 0.900 0.006298 0.888 0.913
## 1204.0 1482 1 0.900 0.006323 0.888 0.912
## 1207.0 1476 1 0.899 0.006348 0.887 0.912
## 1216.0 1467 1 0.899 0.006373 0.886 0.911
## 1222.0 1453 1 0.898 0.006399 0.886 0.911
## 1227.0 1445 1 0.897 0.006424 0.885 0.910
## 1244.0 1433 1 0.897 0.006450 0.884 0.910
## 1253.0 1424 1 0.896 0.006477 0.884 0.909
## 1258.0 1422 1 0.896 0.006503 0.883 0.908
## 1263.0 1414 1 0.895 0.006529 0.882 0.908
## 1267.0 1411 1 0.894 0.006555 0.882 0.907
## 1274.0 1408 1 0.894 0.006581 0.881 0.907
## 1297.0 1385 1 0.893 0.006608 0.880 0.906
## 1301.0 1380 1 0.892 0.006635 0.879 0.905
## 1317.0 1365 1 0.892 0.006662 0.879 0.905
## 1319.0 1361 1 0.891 0.006689 0.878 0.904
## 1327.0 1357 1 0.890 0.006716 0.877 0.904
## 1386.0 1319 1 0.890 0.006745 0.877 0.903
## 1414.0 1294 1 0.889 0.006775 0.876 0.902
## 1421.0 1285 1 0.888 0.006805 0.875 0.902
## 1427.0 1281 1 0.888 0.006835 0.874 0.901
## 1431.0 1279 1 0.887 0.006864 0.874 0.900
## 1436.0 1275 1 0.886 0.006894 0.873 0.900
## 1446.0 1270 1 0.886 0.006924 0.872 0.899
## 1447.0 1269 1 0.885 0.006954 0.871 0.899
## 1451.0 1261 1 0.884 0.006983 0.871 0.898
## 1472.0 1246 1 0.883 0.007014 0.870 0.897
## 1481.0 1241 1 0.883 0.007044 0.869 0.897
## 1488.0 1236 1 0.882 0.007075 0.868 0.896
## 1495.0 1229 1 0.881 0.007105 0.867 0.895
## 1506.0 1223 1 0.881 0.007136 0.867 0.895
## 1512.0 1217 1 0.880 0.007166 0.866 0.894
## 1513.0 1213 1 0.879 0.007197 0.865 0.893
## 1520.0 1208 1 0.878 0.007228 0.864 0.893
## 1522.0 1207 1 0.878 0.007258 0.864 0.892
## 1523.0 1205 1 0.877 0.007289 0.863 0.891
## 1533.0 1202 1 0.876 0.007319 0.862 0.891
## 1547.0 1190 1 0.875 0.007350 0.861 0.890
## 1556.0 1180 1 0.875 0.007381 0.860 0.889
## 1558.0 1175 1 0.874 0.007412 0.860 0.889
## 1567.0 1168 1 0.873 0.007444 0.859 0.888
## 1569.0 1164 1 0.872 0.007475 0.858 0.887
## 1571.0 1161 1 0.872 0.007506 0.857 0.887
## 1590.0 1144 1 0.871 0.007538 0.856 0.886
## 1593.0 1139 2 0.869 0.007602 0.855 0.884
## 1595.0 1135 1 0.869 0.007634 0.854 0.884
## 1634.0 1097 1 0.868 0.007668 0.853 0.883
## 1635.0 1095 1 0.867 0.007702 0.852 0.882
## 1638.0 1090 1 0.866 0.007736 0.851 0.882
## 1647.0 1081 1 0.865 0.007770 0.850 0.881
## 1649.0 1079 1 0.865 0.007804 0.850 0.880
## 1651.0 1077 1 0.864 0.007838 0.849 0.879
## 1669.0 1060 1 0.863 0.007873 0.848 0.879
## 1677.0 1053 1 0.862 0.007908 0.847 0.878
## 1682.0 1049 1 0.861 0.007943 0.846 0.877
## 1695.0 1037 1 0.861 0.007979 0.845 0.876
## 1701.0 1032 1 0.860 0.008014 0.844 0.876
## 1735.0 1009 1 0.859 0.008052 0.843 0.875
## 1747.0 999 1 0.858 0.008089 0.842 0.874
## 1755.0 992 1 0.857 0.008127 0.841 0.873
## 1779.0 979 1 0.856 0.008166 0.840 0.872
## 1782.0 977 1 0.855 0.008205 0.840 0.872
## 1798.0 974 1 0.855 0.008243 0.839 0.871
## 1801.0 973 1 0.854 0.008281 0.838 0.870
## 1804.0 972 1 0.853 0.008319 0.837 0.869
## 1811.0 968 1 0.852 0.008357 0.836 0.868
## 1822.0 961 1 0.851 0.008395 0.835 0.868
## 1826.0 958 1 0.850 0.008433 0.834 0.867
## 1833.0 955 1 0.849 0.008471 0.833 0.866
## 1866.0 929 1 0.848 0.008511 0.832 0.865
## 1873.0 919 1 0.847 0.008552 0.831 0.864
## 1877.0 914 1 0.846 0.008593 0.830 0.864
## 1924.0 883 1 0.846 0.008636 0.829 0.863
## 1927.0 879 1 0.845 0.008680 0.828 0.862
## 1970.0 851 1 0.844 0.008726 0.827 0.861
## 1973.0 850 1 0.843 0.008772 0.826 0.860
## 1981.0 842 1 0.842 0.008819 0.824 0.859
## 1982.0 841 1 0.841 0.008865 0.823 0.858
## 1986.0 837 1 0.840 0.008911 0.822 0.857
## 2005.0 818 1 0.839 0.008959 0.821 0.856
## 2009.0 816 1 0.838 0.009007 0.820 0.855
## 2033.0 793 1 0.836 0.009057 0.819 0.854
## 2045.0 788 1 0.835 0.009108 0.818 0.853
## 2080.0 765 1 0.834 0.009161 0.817 0.852
## 2083.0 764 1 0.833 0.009214 0.815 0.851
## 2084.0 763 1 0.832 0.009266 0.814 0.850
## 2114.0 745 2 0.830 0.009375 0.812 0.848
## 2118.0 739 1 0.829 0.009429 0.811 0.847
## 2142.0 724 1 0.828 0.009486 0.809 0.846
## 2165.0 711 1 0.826 0.009543 0.808 0.845
## 2178.0 702 2 0.824 0.009660 0.805 0.843
## 2194.0 687 1 0.823 0.009721 0.804 0.842
## 2208.0 673 1 0.822 0.009783 0.803 0.841
## 2214.0 668 1 0.820 0.009845 0.801 0.840
## 2239.0 652 1 0.819 0.009910 0.800 0.839
## 2257.0 641 1 0.818 0.009977 0.799 0.838
## 2266.0 639 1 0.817 0.010043 0.797 0.837
## 2288.0 617 1 0.815 0.010113 0.796 0.835
## 2305.0 597 1 0.814 0.010188 0.794 0.834
## 2321.0 581 1 0.813 0.010267 0.793 0.833
## 2330.0 573 1 0.811 0.010346 0.791 0.832
## 2334.0 567 1 0.810 0.010426 0.790 0.830
## 2342.0 563 1 0.808 0.010507 0.788 0.829
## 2378.0 530 1 0.807 0.010597 0.786 0.828
## 2387.0 528 1 0.805 0.010686 0.785 0.826
## 2413.0 516 1 0.804 0.010779 0.783 0.825
## 2429.0 503 1 0.802 0.010875 0.781 0.824
## 2445.0 486 1 0.800 0.010977 0.779 0.822
## 2447.0 483 1 0.799 0.011079 0.777 0.821
## 2449.0 482 1 0.797 0.011179 0.775 0.819
## 2455.0 476 1 0.795 0.011281 0.774 0.818
## 2470.0 467 1 0.794 0.011384 0.772 0.816
## 2486.0 456 1 0.792 0.011492 0.770 0.815
## 2551.0 407 1 0.790 0.011627 0.768 0.813
## 2554.0 405 1 0.788 0.011761 0.765 0.811
## 2555.0 404 1 0.786 0.011892 0.763 0.810
## 2581.0 380 1 0.784 0.012040 0.761 0.808
## 2582.0 379 1 0.782 0.012184 0.758 0.806
## 2623.0 355 1 0.780 0.012348 0.756 0.804
## 2633.0 349 1 0.778 0.012513 0.753 0.802
## 2636.0 346 1 0.775 0.012677 0.751 0.801
## 2662.0 331 1 0.773 0.012853 0.748 0.799
## 2676.0 321 1 0.771 0.013037 0.745 0.797
## 2686.0 315 1 0.768 0.013223 0.743 0.794
## 2718.0 293 1 0.765 0.013435 0.740 0.792
## 2790.0 255 1 0.762 0.013713 0.736 0.790
## 2813.0 239 1 0.759 0.014022 0.732 0.787
## 2848.0 204 1 0.756 0.014439 0.728 0.784
## 2849.0 202 1 0.752 0.014844 0.723 0.781
## 2861.0 195 1 0.748 0.015261 0.719 0.778
## 2875.0 178 1 0.744 0.015743 0.714 0.775
## 3011.0 137 1 0.738 0.016538 0.707 0.771
## 3017.0 131 1 0.733 0.017345 0.699 0.768
## 3085.0 111 1 0.726 0.018402 0.691 0.763
## 3109.0 101 1 0.719 0.019574 0.682 0.758
## 3131.0 90 1 0.711 0.020923 0.671 0.753
## 3244.0 52 1 0.697 0.024585 0.651 0.747
## 3282.0 37 1 0.678 0.030294 0.622 0.740
##
## SEX=2
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 3 974 1 0.999 0.00103 0.997 1.000
## 4 973 1 0.998 0.00145 0.995 1.000
## 16 967 1 0.997 0.00178 0.993 1.000
## 21 966 1 0.996 0.00205 0.992 1.000
## 27 962 1 0.995 0.00230 0.990 0.999
## 40 957 1 0.994 0.00252 0.989 0.999
## 49 953 1 0.993 0.00272 0.987 0.998
## 58 949 1 0.992 0.00292 0.986 0.997
## 60 947 1 0.991 0.00310 0.985 0.997
## 94 937 1 0.990 0.00327 0.983 0.996
## 105 932 1 0.989 0.00343 0.982 0.995
## 118 929 1 0.987 0.00359 0.980 0.995
## 133 922 1 0.986 0.00374 0.979 0.994
## 146 916 1 0.985 0.00389 0.978 0.993
## 167 902 1 0.984 0.00404 0.976 0.992
## 196 885 1 0.983 0.00418 0.975 0.991
## 199 881 1 0.982 0.00432 0.974 0.991
## 214 876 1 0.981 0.00446 0.972 0.990
## 217 874 1 0.980 0.00460 0.971 0.989
## 236 864 1 0.979 0.00473 0.969 0.988
## 237 863 1 0.978 0.00486 0.968 0.987
## 249 856 1 0.976 0.00498 0.967 0.986
## 254 851 1 0.975 0.00511 0.965 0.985
## 259 849 2 0.973 0.00535 0.962 0.983
## 279 841 1 0.972 0.00547 0.961 0.983
## 294 833 1 0.971 0.00558 0.960 0.982
## 299 828 1 0.969 0.00570 0.958 0.981
## 359 798 1 0.968 0.00582 0.957 0.980
## 360 797 1 0.967 0.00594 0.955 0.979
## 413 780 1 0.966 0.00606 0.954 0.978
## 453 767 1 0.964 0.00618 0.952 0.977
## 461 762 1 0.963 0.00630 0.951 0.976
## 465 760 1 0.962 0.00642 0.949 0.975
## 481 747 1 0.961 0.00654 0.948 0.974
## 538 723 1 0.959 0.00666 0.946 0.972
## 568 709 1 0.958 0.00679 0.945 0.971
## 570 708 1 0.957 0.00691 0.943 0.970
## 579 705 1 0.955 0.00703 0.942 0.969
## 589 701 1 0.954 0.00715 0.940 0.968
## 676 663 1 0.952 0.00729 0.938 0.967
## 683 659 1 0.951 0.00742 0.937 0.966
## 702 652 1 0.950 0.00755 0.935 0.964
## 788 613 1 0.948 0.00769 0.933 0.963
## 847 596 1 0.946 0.00784 0.931 0.962
## 856 591 1 0.945 0.00799 0.929 0.961
## 858 590 1 0.943 0.00814 0.927 0.959
## 913 565 1 0.942 0.00829 0.925 0.958
## 939 553 1 0.940 0.00845 0.923 0.957
## 973 541 1 0.938 0.00861 0.921 0.955
## 994 538 1 0.936 0.00877 0.919 0.954
## 1002 534 1 0.935 0.00893 0.917 0.952
## 1022 527 1 0.933 0.00908 0.915 0.951
## 1056 514 1 0.931 0.00925 0.913 0.949
## 1081 507 1 0.929 0.00941 0.911 0.948
## 1106 498 1 0.927 0.00957 0.909 0.946
## 1165 480 1 0.925 0.00975 0.907 0.945
## 1178 475 1 0.923 0.00992 0.904 0.943
## 1315 441 1 0.921 0.01011 0.902 0.941
## 1319 439 1 0.919 0.01031 0.899 0.940
## 1361 429 1 0.917 0.01050 0.897 0.938
## 1425 417 1 0.915 0.01071 0.894 0.936
## 1437 414 2 0.911 0.01110 0.889 0.933
## 1442 411 1 0.908 0.01129 0.886 0.931
## 1466 403 2 0.904 0.01168 0.881 0.927
## 1491 392 1 0.901 0.01187 0.879 0.925
## 1541 385 1 0.899 0.01207 0.876 0.923
## 1562 383 1 0.897 0.01227 0.873 0.921
## 1635 367 1 0.894 0.01247 0.870 0.919
## 1666 359 1 0.892 0.01269 0.867 0.917
## 1688 355 1 0.889 0.01290 0.864 0.915
## 1751 346 1 0.887 0.01311 0.861 0.913
## 1797 342 1 0.884 0.01333 0.858 0.911
## 1879 325 1 0.881 0.01356 0.855 0.908
## 1915 319 1 0.879 0.01380 0.852 0.906
## 1991 293 1 0.876 0.01407 0.849 0.904
## 2051 282 1 0.873 0.01436 0.845 0.901
## 2053 279 1 0.869 0.01465 0.841 0.899
## 2152 262 1 0.866 0.01496 0.837 0.896
## 2224 238 1 0.863 0.01534 0.833 0.893
## 2269 227 1 0.859 0.01573 0.828 0.890
## 2413 192 1 0.854 0.01627 0.823 0.887
## 2530 168 1 0.849 0.01695 0.817 0.883
## 3020 66 1 0.836 0.02102 0.796 0.879ggsurvplot(fit2, data = SMARTo, pval = TRUE) 
(4) いくつかの変数を使ってCoxモデルを当てはめてみましょう。
# 生存時間とイベント変数の設定
time <- SMARTo$TEVENT
event <- SMARTo$EVENT
# Coxモデルの適用
cox_model <- coxph(Surv(time, event) ~ AGE + SEX + DIABETES + CEREBRAL + CARDIAC + AAA + PERIPH + STENOSIS + albumin + SMOKING + alcohol, data = SMARTo)
# 結果の表示
summary(cox_model)## Call:
## coxph(formula = Surv(time, event) ~ AGE + SEX + DIABETES + CEREBRAL +
## CARDIAC + AAA + PERIPH + STENOSIS + albumin + SMOKING + alcohol,
## data = SMARTo)
##
## n= 3536, number of events= 410
## ( 337 個の観測値が欠損のため削除されました )
##
## coef exp(coef) se(coef) z Pr(>|z|)
## AGE 0.038227 1.038967 0.005845 6.540 6.16e-11 ***
## SEX2 -0.270955 0.762651 0.135828 -1.995 0.046060 *
## DIABETES1 0.148905 1.160562 0.115844 1.285 0.198658
## CEREBRAL1 0.336125 1.399514 0.133759 2.513 0.011974 *
## CARDIAC1 0.315171 1.370493 0.114633 2.749 0.005971 **
## AAA1 0.761805 2.142140 0.127411 5.979 2.24e-09 ***
## PERIPH1 0.402679 1.495827 0.120085 3.353 0.000799 ***
## STENOSIS1 0.274760 1.316215 0.123019 2.233 0.025517 *
## albumin2 0.426650 1.532116 0.119977 3.556 0.000376 ***
## albumin3 0.827608 2.287840 0.201406 4.109 3.97e-05 ***
## SMOKING2 0.098133 1.103110 0.148475 0.661 0.508652
## SMOKING3 -0.020667 0.979546 0.260873 -0.079 0.936857
## alcohol2 -0.074567 0.928146 0.178415 -0.418 0.675992
## alcohol3 -0.153965 0.857302 0.126613 -1.216 0.223973
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## AGE 1.0390 0.9625 1.0271 1.0509
## SEX2 0.7627 1.3112 0.5844 0.9953
## DIABETES1 1.1606 0.8617 0.9248 1.4564
## CEREBRAL1 1.3995 0.7145 1.0768 1.8190
## CARDIAC1 1.3705 0.7297 1.0947 1.7157
## AAA1 2.1421 0.4668 1.6688 2.7498
## PERIPH1 1.4958 0.6685 1.1821 1.8928
## STENOSIS1 1.3162 0.7598 1.0342 1.6751
## albumin2 1.5321 0.6527 1.2111 1.9383
## albumin3 2.2878 0.4371 1.5417 3.3952
## SMOKING2 1.1031 0.9065 0.8246 1.4757
## SMOKING3 0.9795 1.0209 0.5874 1.6334
## alcohol2 0.9281 1.0774 0.6543 1.3167
## alcohol3 0.8573 1.1665 0.6689 1.0988
##
## Concordance= 0.673 (se = 0.015 )
## Likelihood ratio test= 198.9 on 14 df, p=<2e-16
## Wald test = 210.2 on 14 df, p=<2e-16
## Score (logrank) test = 229.4 on 14 df, p=<2e-16(5) Cox比例ハザード性が成り立っているか検討しましょう。
# Schoenfeld残差による比例ハザード性の評価
cox_zph_result <- cox.zph(cox_model)
# 結果の表示
print(cox_zph_result)## chisq df p
## AGE 6.133 1 0.01327
## SEX 1.950 1 0.16260
## DIABETES 0.163 1 0.68636
## CEREBRAL 2.173 1 0.14044
## CARDIAC 1.139 1 0.28588
## AAA 1.059 1 0.30340
## PERIPH 0.364 1 0.54650
## STENOSIS 2.005 1 0.15677
## albumin 1.574 2 0.45521
## SMOKING 14.375 2 0.00076
## alcohol 0.124 2 0.93994
## GLOBAL 30.719 14 0.00607# グラフの描画
plot(cox_zph_result)
AGE:0.01327、GLOBAL 0.00607のP値は0.05未満ちなっおり、比例ハザード性は満たしておらず、モデルを修正する必要がある。
第3部(欠測値の処理)
1) 多重代入を行ってみましょう。
imp <- mice(SMARTo,
m=5, #mは代入の結果として作成するデータセットの数
maxit =5, #maxitは反復回数
method="pmm",
seed = 10) ##
## iter imp variable
## 1 1 DIABETES STENOSIS SYSTBP DIASTBP SYSTH DIASTH LENGTHO WEIGHTO BMIO CHOLO HDLO LDLO TRIGO HOMOCO GLUTO CREATO IMTO albumin SMOKING packyrs alcohol
## 1 2 DIABETES STENOSIS SYSTBP DIASTBP SYSTH DIASTH LENGTHO WEIGHTO BMIO CHOLO HDLO LDLO TRIGO HOMOCO GLUTO CREATO IMTO albumin SMOKING packyrs alcohol
## 1 3 DIABETES STENOSIS SYSTBP DIASTBP SYSTH DIASTH LENGTHO WEIGHTO BMIO CHOLO HDLO LDLO TRIGO HOMOCO GLUTO CREATO IMTO albumin SMOKING packyrs alcohol
## 1 4 DIABETES STENOSIS SYSTBP DIASTBP SYSTH DIASTH LENGTHO WEIGHTO BMIO CHOLO HDLO LDLO TRIGO HOMOCO GLUTO CREATO IMTO albumin SMOKING packyrs alcohol
## 1 5 DIABETES STENOSIS SYSTBP DIASTBP SYSTH DIASTH LENGTHO WEIGHTO BMIO CHOLO HDLO LDLO TRIGO HOMOCO GLUTO CREATO IMTO albumin SMOKING packyrs alcohol
## 2 1 DIABETES STENOSIS SYSTBP DIASTBP SYSTH DIASTH LENGTHO WEIGHTO BMIO CHOLO HDLO LDLO TRIGO HOMOCO GLUTO CREATO IMTO albumin SMOKING packyrs alcohol
## 2 2 DIABETES STENOSIS SYSTBP DIASTBP SYSTH DIASTH LENGTHO WEIGHTO BMIO CHOLO HDLO LDLO TRIGO HOMOCO GLUTO CREATO IMTO albumin SMOKING packyrs alcohol
## 2 3 DIABETES STENOSIS SYSTBP DIASTBP SYSTH DIASTH LENGTHO WEIGHTO BMIO CHOLO HDLO LDLO TRIGO HOMOCO GLUTO CREATO IMTO albumin SMOKING packyrs alcohol
## 2 4 DIABETES STENOSIS SYSTBP DIASTBP SYSTH DIASTH LENGTHO WEIGHTO BMIO CHOLO HDLO LDLO TRIGO HOMOCO GLUTO CREATO IMTO albumin SMOKING packyrs alcohol
## 2 5 DIABETES STENOSIS SYSTBP DIASTBP SYSTH DIASTH LENGTHO WEIGHTO BMIO CHOLO HDLO LDLO TRIGO HOMOCO GLUTO CREATO IMTO albumin SMOKING packyrs alcohol
## 3 1 DIABETES STENOSIS SYSTBP DIASTBP SYSTH DIASTH LENGTHO WEIGHTO BMIO CHOLO HDLO LDLO TRIGO HOMOCO GLUTO CREATO IMTO albumin SMOKING packyrs alcohol
## 3 2 DIABETES STENOSIS SYSTBP DIASTBP SYSTH DIASTH LENGTHO WEIGHTO BMIO CHOLO HDLO LDLO TRIGO HOMOCO GLUTO CREATO IMTO albumin SMOKING packyrs alcohol
## 3 3 DIABETES STENOSIS SYSTBP DIASTBP SYSTH DIASTH LENGTHO WEIGHTO BMIO CHOLO HDLO LDLO TRIGO HOMOCO GLUTO CREATO IMTO albumin SMOKING packyrs alcohol
## 3 4 DIABETES STENOSIS SYSTBP DIASTBP SYSTH DIASTH LENGTHO WEIGHTO BMIO CHOLO HDLO LDLO TRIGO HOMOCO GLUTO CREATO IMTO albumin SMOKING packyrs alcohol
## 3 5 DIABETES STENOSIS SYSTBP DIASTBP SYSTH DIASTH LENGTHO WEIGHTO BMIO CHOLO HDLO LDLO TRIGO HOMOCO GLUTO CREATO IMTO albumin SMOKING packyrs alcohol
## 4 1 DIABETES STENOSIS SYSTBP DIASTBP SYSTH DIASTH LENGTHO WEIGHTO BMIO CHOLO HDLO LDLO TRIGO HOMOCO GLUTO CREATO IMTO albumin SMOKING packyrs alcohol
## 4 2 DIABETES STENOSIS SYSTBP DIASTBP SYSTH DIASTH LENGTHO WEIGHTO BMIO CHOLO HDLO LDLO TRIGO HOMOCO GLUTO CREATO IMTO albumin SMOKING packyrs alcohol
## 4 3 DIABETES STENOSIS SYSTBP DIASTBP SYSTH DIASTH LENGTHO WEIGHTO BMIO CHOLO HDLO LDLO TRIGO HOMOCO GLUTO CREATO IMTO albumin SMOKING packyrs alcohol
## 4 4 DIABETES STENOSIS SYSTBP DIASTBP SYSTH DIASTH LENGTHO WEIGHTO BMIO CHOLO HDLO LDLO TRIGO HOMOCO GLUTO CREATO IMTO albumin SMOKING packyrs alcohol
## 4 5 DIABETES STENOSIS SYSTBP DIASTBP SYSTH DIASTH LENGTHO WEIGHTO BMIO CHOLO HDLO LDLO TRIGO HOMOCO GLUTO CREATO IMTO albumin SMOKING packyrs alcohol
## 5 1 DIABETES STENOSIS SYSTBP DIASTBP SYSTH DIASTH LENGTHO WEIGHTO BMIO CHOLO HDLO LDLO TRIGO HOMOCO GLUTO CREATO IMTO albumin SMOKING packyrs alcohol
## 5 2 DIABETES STENOSIS SYSTBP DIASTBP SYSTH DIASTH LENGTHO WEIGHTO BMIO CHOLO HDLO LDLO TRIGO HOMOCO GLUTO CREATO IMTO albumin SMOKING packyrs alcohol
## 5 3 DIABETES STENOSIS SYSTBP DIASTBP SYSTH DIASTH LENGTHO WEIGHTO BMIO CHOLO HDLO LDLO TRIGO HOMOCO GLUTO CREATO IMTO albumin SMOKING packyrs alcohol
## 5 4 DIABETES STENOSIS SYSTBP DIASTBP SYSTH DIASTH LENGTHO WEIGHTO BMIO CHOLO HDLO LDLO TRIGO HOMOCO GLUTO CREATO IMTO albumin SMOKING packyrs alcohol
## 5 5 DIABETES STENOSIS SYSTBP DIASTBP SYSTH DIASTH LENGTHO WEIGHTO BMIO CHOLO HDLO LDLO TRIGO HOMOCO GLUTO CREATO IMTO albumin SMOKING packyrs alcohol2)多重代入後の確認
plot(imp) 
全然収束していない。本来ならばデータセットも繰り返し数ももっと増やす必要がある。
3) 多重代入後の一つのデータを抜き出してCox比例ハザードモデルを実施しましょう
# 欠損データを補完したデータセットの選択
completed_data_1 <- complete(imp, action = 1) # action=は選択するデータセットのインデックス、なしでも良い。
# Coxモデルの適用
cox_model_1 <- coxph(Surv(time, event) ~ AGE + SEX + DIABETES + CEREBRAL + CARDIAC + AAA + PERIPH + STENOSIS + albumin + SMOKING + alcohol, data = completed_data_1)
# 結果の表示
summary(cox_model_1)## Call:
## coxph(formula = Surv(time, event) ~ AGE + SEX + DIABETES + CEREBRAL +
## CARDIAC + AAA + PERIPH + STENOSIS + albumin + SMOKING + alcohol,
## data = completed_data_1)
##
## n= 3873, number of events= 460
##
## coef exp(coef) se(coef) z Pr(>|z|)
## AGE 0.035542 1.036181 0.005465 6.504 7.85e-11 ***
## SEX2 -0.269115 0.764055 0.128674 -2.091 0.036488 *
## DIABETES1 0.133679 1.143025 0.108546 1.232 0.218123
## CEREBRAL1 0.320773 1.378193 0.125316 2.560 0.010476 *
## CARDIAC1 0.346760 1.414477 0.107349 3.230 0.001237 **
## AAA1 0.743864 2.104049 0.120658 6.165 7.05e-10 ***
## PERIPH1 0.396019 1.485897 0.111756 3.544 0.000395 ***
## STENOSIS1 0.266689 1.305634 0.115853 2.302 0.021338 *
## albumin2 0.374186 1.453808 0.115003 3.254 0.001139 **
## albumin3 0.969153 2.635711 0.171922 5.637 1.73e-08 ***
## SMOKING2 0.165891 1.180444 0.144321 1.149 0.250367
## SMOKING3 0.136513 1.146270 0.234319 0.583 0.560166
## alcohol2 -0.109945 0.895883 0.164703 -0.668 0.504429
## alcohol3 -0.204890 0.814737 0.119253 -1.718 0.085777 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## AGE 1.0362 0.9651 1.0251 1.0473
## SEX2 0.7641 1.3088 0.5937 0.9832
## DIABETES1 1.1430 0.8749 0.9240 1.4140
## CEREBRAL1 1.3782 0.7256 1.0781 1.7619
## CARDIAC1 1.4145 0.7070 1.1461 1.7457
## AAA1 2.1040 0.4753 1.6609 2.6654
## PERIPH1 1.4859 0.6730 1.1936 1.8498
## STENOSIS1 1.3056 0.7659 1.0404 1.6385
## albumin2 1.4538 0.6878 1.1604 1.8214
## albumin3 2.6357 0.3794 1.8817 3.6918
## SMOKING2 1.1804 0.8471 0.8896 1.5664
## SMOKING3 1.1463 0.8724 0.7242 1.8144
## alcohol2 0.8959 1.1162 0.6487 1.2372
## alcohol3 0.8147 1.2274 0.6449 1.0293
##
## Concordance= 0.671 (se = 0.014 )
## Likelihood ratio test= 222 on 14 df, p=<2e-16
## Wald test = 242.4 on 14 df, p=<2e-16
## Score (logrank) test = 265.2 on 14 df, p=<2e-164)多重代入後のデータでCox比例ハザードモデルを実施しましょう
# Coxモデルを適用
fit_cox <- with(imp, coxph(Surv(time, event) ~ AGE + SEX + DIABETES + CEREBRAL + CARDIAC + AAA + PERIPH + STENOSIS + albumin + SMOKING + alcohol))
# 結果の統合
pooled_cox <- pool(fit_cox)
# 統合された結果の表示
summary(pooled_cox)## term estimate std.error statistic df p.value
## 1 AGE 0.03508699 0.005477038 6.4061983 438.2317 3.853947e-10
## 2 SEX2 -0.27225432 0.128942928 -2.1114327 442.3421 3.529544e-02
## 3 DIABETES1 0.14347841 0.108937630 1.3170693 431.2924 1.885147e-01
## 4 CEREBRAL1 0.30730375 0.125722066 2.4443104 438.9877 1.490542e-02
## 5 CARDIAC1 0.34537038 0.107481918 3.2132882 441.3350 1.408405e-03
## 6 AAA1 0.75150346 0.120778031 6.2221868 442.1694 1.138535e-09
## 7 PERIPH1 0.38932596 0.112582571 3.4581371 431.0070 5.980072e-04
## 8 STENOSIS1 0.28987828 0.116928423 2.4791087 413.2017 1.356914e-02
## 9 albumin2 0.40209433 0.119466853 3.3657397 235.6706 8.911847e-04
## 10 albumin3 0.99617496 0.173905299 5.7282611 415.8420 1.948732e-08
## 11 SMOKING2 0.14182277 0.144273444 0.9830137 432.4422 3.261503e-01
## 12 SMOKING3 0.13541559 0.235214707 0.5757105 414.6890 5.651231e-01
## 13 alcohol2 -0.13726578 0.168529840 -0.8144895 381.0519 4.158733e-01
## 14 alcohol3 -0.20638068 0.119771386 -1.7231218 433.1676 8.558015e-025)多重代入後のデータを用いて非線形性の確認をしましょう。
# Coxモデルを適用
fit_cox_2 <- with(imp, coxph(Surv(time, event) ~ rcs(AGE, 4) + SEX + DIABETES + CEREBRAL + CARDIAC + AAA + PERIPH + STENOSIS + albumin + SMOKING + alcohol))
# 結果の統合
pooled_cox <- pool(fit_cox_2)
# 統合された結果の表示
summary(pooled_cox)## term estimate std.error statistic df p.value
## 1 rcs(AGE, 4)AGE -0.004106661 0.01944091 -0.2112382 441.7535 8.327989e-01
## 2 rcs(AGE, 4)AGE' 0.026854069 0.04311759 0.6228100 441.3274 5.337310e-01
## 3 rcs(AGE, 4)AGE'' 0.069850293 0.19111601 0.3654863 441.2783 7.149235e-01
## 4 SEX2 -0.276805325 0.12942862 -2.1386717 440.3773 3.301179e-02
## 5 DIABETES1 0.160534399 0.10924554 1.4694824 431.2922 1.424310e-01
## 6 CEREBRAL1 0.302208839 0.12580824 2.4021386 436.9119 1.671600e-02
## 7 CARDIAC1 0.375494244 0.10772459 3.4856874 438.8555 5.402765e-04
## 8 AAA1 0.754137449 0.12198256 6.1823384 440.1384 1.442413e-09
## 9 PERIPH1 0.383963219 0.11291560 3.4004444 428.4621 7.358385e-04
## 10 STENOSIS1 0.314203811 0.11760689 2.6716445 407.8190 7.850416e-03
## 11 albumin2 0.384462042 0.12017252 3.1992510 225.8254 1.575653e-03
## 12 albumin3 0.976526774 0.17440301 5.5992541 416.2574 3.915152e-08
## 13 SMOKING2 0.189211818 0.14512377 1.3037962 429.8109 1.930009e-01
## 14 SMOKING3 0.164228519 0.23549313 0.6973814 414.7491 4.859549e-01
## 15 alcohol2 -0.116750376 0.16858447 -0.6925334 378.8071 4.890267e-01
## 16 alcohol3 -0.196730771 0.12004852 -1.6387604 431.4978 1.019921e-01# 非線形性の確認
#options(datadist='distribution')
#distribution <- datadist(SMARTo)
# 統合された結果を用いてPredictプロットを作成
#plot(Predict(pooled_cox, AGE))# フォーミュラを設定
formula_cox <- Surv(time, event) ~ rcs(AGE, 4) + SEX + DIABETES + CEREBRAL + CARDIAC + AAA + PERIPH + STENOSIS + albumin + SMOKING + alcohol
# fit.mult.impute を使用して Cox モデルを適用
fit_cox_mult_impute <- fit.mult.impute(formula_cox, fitter=coxph, xtrans=imp, data=SMARTo) # x=TRUE, y=TRUE, surv=TRUEこれがあると回らない。##
## Variance Inflation Factors Due to Imputation:
##
## rcs(AGE, 4)AGE rcs(AGE, 4)AGE' rcs(AGE, 4)AGE'' SEX2
## 1.00 1.00 1.00 1.00
## DIABETES1 CEREBRAL1 CARDIAC1 AAA1
## 1.01 1.01 1.00 1.00
## PERIPH1 STENOSIS1 albumin2 albumin3
## 1.01 1.02 1.10 1.02
## SMOKING2 SMOKING3 alcohol2 alcohol3
## 1.01 1.02 1.04 1.01
##
## Rate of Missing Information:
##
## rcs(AGE, 4)AGE rcs(AGE, 4)AGE' rcs(AGE, 4)AGE'' SEX2
## 0.00 0.00 0.00 0.00
## DIABETES1 CEREBRAL1 CARDIAC1 AAA1
## 0.01 0.01 0.00 0.00
## PERIPH1 STENOSIS1 albumin2 albumin3
## 0.01 0.02 0.09 0.02
## SMOKING2 SMOKING3 alcohol2 alcohol3
## 0.01 0.02 0.03 0.01
##
## d.f. for t-distribution for Tests of Single Coefficients:
##
## rcs(AGE, 4)AGE rcs(AGE, 4)AGE' rcs(AGE, 4)AGE'' SEX2
## 13022402.50 2191760.70 1939788.36 501139.38
## DIABETES1 CEREBRAL1 CARDIAC1 AAA1
## 32433.37 89420.04 179859.11 402576.94
## PERIPH1 STENOSIS1 albumin2 albumin3
## 23874.31 7367.97 513.65 10525.76
## SMOKING2 SMOKING3 alcohol2 alcohol3
## 27365.25 9797.55 3369.69 33273.50
##
## The following fit components were averaged over the 5 model fits:
##
## linear.predictors means# 統合された結果を用いて Predict プロットを作成
#plot(Predict(fit_cox_mult_impute, AGE))ここの plotからどうしてもエラーになる。x=TRUE, y=TRUE, surv=TRUEこれがあっても回らない。どうすればよいのか。。。