Assignment 2 Revised
Anamika Kumar
2024-09-14
Key variables:
From the description of the exercise, we have the following key variables: agecensor: Age at last observation (death or censoring). died0121: Event status (1 = died, 0 = censored). Aageint: Age at baseline interview.
loading the libraries and data
library(survival)
library(ggsurvfit)## Loading required package: ggplot2library(gtsummary)
library(ggplot2)
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(readr)data2<-read_csv("C:\\Users\\anami\\OneDrive\\Documents\\EHA\\MHAS0121.csv")## Rows: 9636 Columns: 39
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (3): locsize01, died18, died21
## dbl (36): id, perwght01, mobirth, yrbirth, female, moint, yrint, schooling, ...
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.Creating the Survival Object and fitting Kaplan-Meier Model
surv_obj <- Surv(time = data2$agecensor, event = data2$died0121)
# Fit the Kaplan-Meier model
km_fit <- survfit(surv_obj ~ 1, data = data2)# Print summary to get survival function and standard errors
summary(km_fit)## Call: survfit(formula = surv_obj ~ 1, data = data2)
##
## 2071 observations deleted due to missingness
## time n.risk n.event survival std.err lower 95% CI upper 95% CI
## 51.2 7565 2 0.99974 0.000187 0.999369 1.0000
## 51.6 7563 1 0.99960 0.000229 0.999155 1.0000
## 52.1 7562 1 0.99947 0.000264 0.998953 1.0000
## 52.2 7561 1 0.99934 0.000295 0.998760 0.9999
## 52.3 7560 1 0.99921 0.000324 0.998573 0.9998
## 52.4 7559 2 0.99894 0.000374 0.998210 0.9997
## 52.7 7557 1 0.99881 0.000396 0.998034 0.9996
## 53.0 7556 3 0.99841 0.000458 0.997517 0.9993
## 53.1 7553 2 0.99815 0.000494 0.997181 0.9991
## 53.2 7551 1 0.99802 0.000511 0.997015 0.9990
## 53.2 7550 1 0.99788 0.000528 0.996850 0.9989
## 53.4 7549 1 0.99775 0.000544 0.996686 0.9988
## 53.6 7548 1 0.99762 0.000560 0.996523 0.9987
## 53.7 7547 1 0.99749 0.000575 0.996361 0.9986
## 53.8 7546 2 0.99722 0.000605 0.996039 0.9984
## 54.1 7544 1 0.99709 0.000619 0.995879 0.9983
## 54.2 7543 3 0.99670 0.000660 0.995403 0.9980
## 54.2 7540 1 0.99656 0.000673 0.995245 0.9979
## 54.3 7539 1 0.99643 0.000686 0.995088 0.9978
## 54.4 7538 1 0.99630 0.000698 0.994931 0.9977
## 54.8 7537 1 0.99617 0.000710 0.994775 0.9976
## 54.9 7536 1 0.99603 0.000723 0.994619 0.9975
## 55.0 7535 1 0.99590 0.000734 0.994464 0.9973
## 55.1 7534 1 0.99577 0.000746 0.994309 0.9972
## 55.2 7533 2 0.99551 0.000769 0.993999 0.9970
## 55.3 7531 1 0.99537 0.000780 0.993845 0.9969
## 55.4 7530 1 0.99524 0.000791 0.993692 0.9968
## 55.5 7529 1 0.99511 0.000802 0.993538 0.9967
## 55.6 7528 2 0.99484 0.000823 0.993232 0.9965
## 55.8 7526 1 0.99471 0.000834 0.993080 0.9963
## 55.8 7525 2 0.99445 0.000854 0.992775 0.9961
## 55.9 7523 3 0.99405 0.000884 0.992320 0.9958
## 56.1 7520 2 0.99379 0.000903 0.992018 0.9956
## 56.2 7518 3 0.99339 0.000932 0.991566 0.9952
## 56.2 7515 1 0.99326 0.000941 0.991416 0.9951
## 56.3 7514 4 0.99273 0.000977 0.990817 0.9946
## 56.5 7510 1 0.99260 0.000986 0.990668 0.9945
## 56.6 7509 1 0.99247 0.000994 0.990519 0.9944
## 56.7 7508 2 0.99220 0.001011 0.990221 0.9942
## 56.8 7506 2 0.99194 0.001028 0.989923 0.9940
## 56.8 7504 2 0.99167 0.001045 0.989626 0.9937
## 57.0 7502 2 0.99141 0.001061 0.989330 0.9935
## 57.2 7500 1 0.99128 0.001069 0.989182 0.9934
## 57.2 7499 1 0.99114 0.001077 0.989034 0.9933
## 57.3 7498 3 0.99075 0.001101 0.988592 0.9929
## 57.4 7495 4 0.99022 0.001132 0.988003 0.9924
## 57.5 7491 3 0.98982 0.001154 0.987562 0.9921
## 57.6 7488 1 0.98969 0.001161 0.987416 0.9920
## 57.7 7487 3 0.98929 0.001183 0.986976 0.9916
## 57.8 7484 4 0.98876 0.001212 0.986392 0.9911
## 57.9 7480 2 0.98850 0.001226 0.986100 0.9909
## 58.0 7478 1 0.98837 0.001233 0.985954 0.9908
## 58.1 7477 1 0.98824 0.001240 0.985809 0.9907
## 58.2 7476 2 0.98797 0.001253 0.985517 0.9904
## 58.3 7474 2 0.98771 0.001267 0.985227 0.9902
## 58.4 7472 2 0.98744 0.001280 0.984936 0.9900
## 58.5 7470 3 0.98705 0.001300 0.984501 0.9896
## 58.6 7467 3 0.98665 0.001320 0.984066 0.9892
## 58.7 7464 2 0.98638 0.001332 0.983777 0.9890
## 58.8 7462 4 0.98586 0.001358 0.983199 0.9885
## 58.8 7458 1 0.98572 0.001364 0.983054 0.9884
## 58.9 7457 3 0.98533 0.001382 0.982621 0.9880
## 59.0 7454 3 0.98493 0.001401 0.982189 0.9877
## 59.1 7451 2 0.98467 0.001413 0.981901 0.9874
## 59.2 7449 4 0.98414 0.001437 0.981326 0.9870
## 59.2 7445 3 0.98374 0.001454 0.980895 0.9866
## 59.3 7442 3 0.98334 0.001471 0.980465 0.9862
## 59.5 7439 1 0.98321 0.001477 0.980321 0.9861
## 59.6 7438 1 0.98308 0.001483 0.980178 0.9860
## 59.7 7437 2 0.98282 0.001494 0.979891 0.9857
## 59.8 7435 2 0.98255 0.001505 0.979605 0.9855
## 59.9 7433 3 0.98215 0.001522 0.979176 0.9851
## 60.0 7430 3 0.98176 0.001539 0.978747 0.9848
## 60.1 7427 4 0.98123 0.001560 0.978176 0.9843
## 60.2 7423 5 0.98057 0.001587 0.977463 0.9837
## 60.2 7418 4 0.98004 0.001608 0.976893 0.9832
## 60.3 7414 6 0.97925 0.001639 0.976039 0.9825
## 60.5 7408 6 0.97845 0.001669 0.975187 0.9817
## 60.6 7402 6 0.97766 0.001699 0.974336 0.9810
## 60.7 7396 3 0.97726 0.001714 0.973910 0.9806
## 60.8 7393 2 0.97700 0.001724 0.973627 0.9804
## 60.8 7391 4 0.97647 0.001743 0.973061 0.9799
## 60.9 7387 5 0.97581 0.001766 0.972354 0.9793
## 61.0 7382 4 0.97528 0.001785 0.971788 0.9788
## 61.1 7378 3 0.97488 0.001799 0.971365 0.9784
## 61.2 7375 1 0.97475 0.001804 0.971223 0.9783
## 61.2 7374 2 0.97449 0.001813 0.970941 0.9780
## 61.3 7372 7 0.97356 0.001845 0.969954 0.9772
## 61.4 7365 4 0.97303 0.001862 0.969390 0.9767
## 61.5 7361 4 0.97250 0.001880 0.968827 0.9762
## 61.6 7357 3 0.97211 0.001893 0.968405 0.9758
## 61.7 7354 3 0.97171 0.001906 0.967983 0.9755
## 61.8 7351 4 0.97118 0.001923 0.967421 0.9750
## 61.8 7347 6 0.97039 0.001949 0.966578 0.9742
## 61.9 7341 2 0.97013 0.001957 0.966297 0.9740
## 62.0 7339 1 0.96999 0.001962 0.966157 0.9738
## 62.1 7338 6 0.96920 0.001986 0.965315 0.9731
## 62.2 7332 4 0.96867 0.002003 0.964754 0.9726
## 62.2 7328 5 0.96801 0.002023 0.964053 0.9720
## 62.3 7323 3 0.96761 0.002035 0.963633 0.9716
## 62.4 7320 8 0.96656 0.002067 0.962514 0.9706
## 62.5 7312 6 0.96576 0.002091 0.961675 0.9699
## 62.6 7306 3 0.96537 0.002102 0.961255 0.9695
## 62.7 7303 4 0.96484 0.002118 0.960696 0.9690
## 62.8 7299 1 0.96471 0.002122 0.960557 0.9689
## 62.8 7298 6 0.96391 0.002144 0.959719 0.9681
## 62.9 7292 4 0.96338 0.002159 0.959161 0.9676
## 63.0 7288 5 0.96272 0.002178 0.958464 0.9670
## 63.1 7283 9 0.96153 0.002211 0.957209 0.9659
## 63.2 7274 13 0.95981 0.002258 0.955400 0.9643
## 63.2 7261 6 0.95902 0.002279 0.954565 0.9635
## 63.3 7255 3 0.95863 0.002290 0.954148 0.9631
## 63.4 7252 1 0.95849 0.002293 0.954009 0.9630
## 63.5 7251 7 0.95757 0.002318 0.953036 0.9621
## 63.6 7244 7 0.95664 0.002342 0.952064 0.9612
## 63.7 7237 5 0.95598 0.002359 0.951370 0.9606
## 63.8 7232 2 0.95572 0.002365 0.951093 0.9604
## 63.8 7230 8 0.95466 0.002392 0.949983 0.9594
## 63.9 7222 3 0.95426 0.002402 0.949567 0.9590
## 64.0 7219 1 0.95413 0.002405 0.949428 0.9589
## 64.1 7218 2 0.95387 0.002412 0.949151 0.9586
## 64.2 7216 3 0.95347 0.002422 0.948735 0.9582
## 64.2 7213 7 0.95254 0.002444 0.947766 0.9573
## 64.3 7206 3 0.95215 0.002454 0.947350 0.9570
## 64.4 7203 7 0.95122 0.002477 0.946381 0.9561
## 64.5 7196 5 0.95056 0.002492 0.945689 0.9555
## 64.6 7191 4 0.95003 0.002505 0.945136 0.9550
## 64.7 7187 4 0.94950 0.002518 0.944583 0.9545
## 64.8 7183 9 0.94831 0.002545 0.943339 0.9533
## 64.8 7174 7 0.94739 0.002567 0.942372 0.9524
## 64.9 7167 4 0.94686 0.002579 0.941819 0.9519
## 65.0 7163 13 0.94514 0.002618 0.940025 0.9503
## 65.1 7150 12 0.94356 0.002653 0.938370 0.9488
## 65.2 7137 7 0.94263 0.002674 0.937405 0.9479
## 65.2 7129 6 0.94184 0.002691 0.936578 0.9471
## 65.3 7123 3 0.94144 0.002700 0.936164 0.9467
## 65.4 7120 7 0.94051 0.002719 0.935200 0.9459
## 65.5 7113 5 0.93985 0.002734 0.934511 0.9452
## 65.6 7106 6 0.93906 0.002750 0.933685 0.9445
## 65.7 7100 11 0.93761 0.002781 0.932171 0.9431
## 65.8 7089 7 0.93668 0.002800 0.931207 0.9422
## 65.8 7082 8 0.93562 0.002822 0.930107 0.9412
## 65.9 7074 6 0.93483 0.002838 0.929282 0.9404
## 66.0 7068 4 0.93430 0.002849 0.928732 0.9399
## 66.1 7064 5 0.93364 0.002862 0.928045 0.9393
## 66.2 7058 7 0.93271 0.002880 0.927083 0.9384
## 66.2 7051 6 0.93192 0.002896 0.926259 0.9376
## 66.3 7044 8 0.93086 0.002917 0.925160 0.9366
## 66.4 7035 11 0.92940 0.002945 0.923649 0.9352
## 66.5 7023 6 0.92861 0.002960 0.922825 0.9344
## 66.6 7014 6 0.92782 0.002976 0.922002 0.9337
## 66.7 7008 7 0.92689 0.002993 0.921041 0.9328
## 66.8 7000 3 0.92649 0.003001 0.920629 0.9324
## 66.8 6997 3 0.92609 0.003008 0.920217 0.9320
## 66.9 6994 6 0.92530 0.003023 0.919394 0.9312
## 67.0 6988 8 0.92424 0.003043 0.918296 0.9302
## 67.1 6980 7 0.92331 0.003060 0.917336 0.9293
## 67.2 6973 10 0.92199 0.003084 0.915965 0.9281
## 67.2 6963 8 0.92093 0.003103 0.914868 0.9270
## 67.3 6955 8 0.91987 0.003122 0.913772 0.9260
## 67.4 6947 9 0.91868 0.003143 0.912539 0.9249
## 67.5 6938 8 0.91762 0.003162 0.911444 0.9238
## 67.6 6930 10 0.91630 0.003185 0.910075 0.9226
## 67.7 6920 12 0.91471 0.003212 0.908433 0.9210
## 67.8 6908 9 0.91352 0.003232 0.907202 0.9199
## 67.8 6899 7 0.91259 0.003248 0.906244 0.9190
## 67.9 6892 5 0.91193 0.003259 0.905561 0.9183
## 68.0 6886 8 0.91087 0.003277 0.904467 0.9173
## 68.1 6877 10 0.90954 0.003299 0.903100 0.9160
## 68.2 6866 13 0.90782 0.003327 0.901323 0.9144
## 68.2 6853 11 0.90636 0.003350 0.899820 0.9130
## 68.3 6842 10 0.90504 0.003372 0.898454 0.9117
## 68.4 6832 10 0.90371 0.003393 0.897089 0.9104
## 68.5 6821 14 0.90186 0.003422 0.895177 0.9086
## 68.6 6807 13 0.90014 0.003448 0.893403 0.9069
## 68.7 6794 11 0.89868 0.003471 0.891902 0.9055
## 68.8 6783 19 0.89616 0.003509 0.889311 0.9031
## 68.8 6764 12 0.89457 0.003532 0.887675 0.9015
## 68.9 6751 8 0.89351 0.003548 0.886585 0.9005
## 69.0 6742 9 0.89232 0.003565 0.885358 0.8993
## 69.1 6732 9 0.89113 0.003583 0.884131 0.8982
## 69.2 6723 19 0.88861 0.003619 0.881543 0.8957
## 69.2 6702 13 0.88688 0.003643 0.879772 0.8941
## 69.3 6687 9 0.88569 0.003660 0.878546 0.8929
## 69.4 6676 19 0.88317 0.003695 0.875957 0.8904
## 69.5 6657 7 0.88224 0.003708 0.875004 0.8895
## 69.6 6650 10 0.88091 0.003726 0.873642 0.8882
## 69.7 6639 15 0.87892 0.003753 0.871599 0.8863
## 69.8 6621 12 0.87733 0.003774 0.869965 0.8848
## 69.8 6607 12 0.87574 0.003795 0.868331 0.8832
## 69.9 6594 11 0.87428 0.003814 0.866833 0.8818
## 70.0 6583 13 0.87255 0.003837 0.865063 0.8801
## 70.1 6569 12 0.87096 0.003857 0.863429 0.8785
## 70.2 6552 11 0.86949 0.003876 0.861931 0.8771
## 70.2 6540 11 0.86803 0.003894 0.860432 0.8757
## 70.3 6528 13 0.86630 0.003916 0.858662 0.8740
## 70.4 6514 15 0.86431 0.003941 0.856619 0.8721
## 70.5 6496 11 0.86284 0.003959 0.855120 0.8706
## 70.6 6485 7 0.86191 0.003970 0.854167 0.8697
## 70.7 6477 11 0.86045 0.003988 0.852669 0.8683
## 70.8 6466 6 0.85965 0.003997 0.851852 0.8675
## 70.8 6459 13 0.85792 0.004018 0.850082 0.8658
## 70.9 6445 15 0.85592 0.004041 0.848039 0.8639
## 71.0 6430 14 0.85406 0.004063 0.846133 0.8621
## 71.1 6410 9 0.85286 0.004077 0.844907 0.8609
## 71.2 6388 5 0.85219 0.004085 0.844225 0.8602
## 71.2 6361 5 0.85152 0.004093 0.843540 0.8596
## 71.3 6331 11 0.85004 0.004110 0.842027 0.8581
## 71.4 6296 8 0.84896 0.004122 0.840923 0.8571
## 71.5 6255 7 0.84801 0.004133 0.839951 0.8562
## 71.6 6218 8 0.84692 0.004146 0.838836 0.8551
## 71.7 6180 12 0.84528 0.004165 0.837155 0.8535
## 71.8 6156 9 0.84404 0.004179 0.835891 0.8523
## 71.8 6123 11 0.84253 0.004197 0.834341 0.8508
## 71.9 6091 14 0.84059 0.004219 0.832362 0.8489
## 72.0 6039 7 0.83962 0.004230 0.831366 0.8479
## 72.1 5989 12 0.83793 0.004249 0.829646 0.8463
## 72.2 5943 14 0.83596 0.004272 0.827628 0.8444
## 72.2 5894 14 0.83397 0.004294 0.825599 0.8424
## 72.3 5849 12 0.83226 0.004314 0.823850 0.8408
## 72.4 5827 15 0.83012 0.004338 0.821661 0.8387
## 72.5 5795 13 0.82826 0.004359 0.819758 0.8368
## 72.6 5752 12 0.82653 0.004378 0.817993 0.8352
## 72.7 5722 8 0.82537 0.004391 0.816812 0.8340
## 72.8 5697 10 0.82393 0.004407 0.815332 0.8326
## 72.8 5657 11 0.82232 0.004425 0.813696 0.8310
## 72.9 5629 12 0.82057 0.004445 0.811905 0.8293
## 73.0 5590 11 0.81896 0.004463 0.810256 0.8277
## 73.1 5561 10 0.81748 0.004479 0.808752 0.8263
## 73.2 5526 9 0.81615 0.004493 0.807392 0.8250
## 73.2 5495 10 0.81467 0.004510 0.805875 0.8236
## 73.3 5463 12 0.81288 0.004529 0.804048 0.8218
## 73.4 5426 8 0.81168 0.004542 0.802824 0.8206
## 73.5 5396 5 0.81093 0.004551 0.802056 0.8199
## 73.6 5364 9 0.80957 0.004566 0.800667 0.8186
## 73.7 5325 14 0.80744 0.004589 0.798493 0.8165
## 73.8 5288 17 0.80484 0.004617 0.795843 0.8139
## 73.8 5248 16 0.80239 0.004644 0.793338 0.8115
## 73.9 5210 6 0.80146 0.004653 0.792395 0.8106
## 74.0 5192 21 0.79822 0.004688 0.789086 0.8075
## 74.1 5147 7 0.79714 0.004700 0.787978 0.8064
## 74.2 5115 5 0.79636 0.004708 0.787183 0.8056
## 74.2 5082 12 0.79448 0.004728 0.785264 0.8038
## 74.3 5037 8 0.79321 0.004742 0.783976 0.8026
## 74.4 5009 16 0.79068 0.004769 0.781390 0.8001
## 74.5 4970 9 0.78925 0.004784 0.779929 0.7987
## 74.6 4942 17 0.78653 0.004812 0.777159 0.7960
## 74.7 4909 8 0.78525 0.004826 0.775851 0.7948
## 74.8 4878 15 0.78284 0.004851 0.773387 0.7924
## 74.8 4847 7 0.78171 0.004863 0.772234 0.7913
## 74.9 4808 15 0.77927 0.004888 0.769746 0.7889
## 75.0 4767 9 0.77780 0.004904 0.768246 0.7875
## 75.1 4735 14 0.77550 0.004927 0.765900 0.7852
## 75.2 4705 11 0.77368 0.004946 0.764051 0.7834
## 75.2 4677 16 0.77104 0.004973 0.761352 0.7808
## 75.3 4639 9 0.76954 0.004989 0.759826 0.7794
## 75.4 4606 10 0.76787 0.005006 0.758123 0.7777
## 75.5 4580 11 0.76603 0.005024 0.756242 0.7759
## 75.6 4547 13 0.76384 0.005047 0.754009 0.7738
## 75.7 4509 14 0.76147 0.005071 0.751591 0.7715
## 75.8 4474 9 0.75993 0.005086 0.750030 0.7700
## 75.8 4451 9 0.75840 0.005102 0.748464 0.7685
## 75.9 4429 8 0.75703 0.005115 0.747067 0.7671
## 76.0 4394 14 0.75461 0.005139 0.744609 0.7648
## 76.1 4363 8 0.75323 0.005153 0.743198 0.7634
## 76.2 4336 17 0.75028 0.005183 0.740189 0.7605
## 76.2 4302 14 0.74784 0.005207 0.737701 0.7581
## 76.3 4273 7 0.74661 0.005219 0.736453 0.7569
## 76.4 4241 10 0.74485 0.005236 0.734659 0.7552
## 76.5 4214 9 0.74326 0.005252 0.733038 0.7536
## 76.6 4179 5 0.74237 0.005260 0.732132 0.7528
## 76.7 4158 16 0.73951 0.005288 0.729222 0.7500
## 76.8 4123 8 0.73808 0.005302 0.727760 0.7485
## 76.8 4097 8 0.73664 0.005316 0.726291 0.7471
## 76.9 4073 11 0.73465 0.005336 0.724265 0.7452
## 77.0 4037 11 0.73265 0.005355 0.722226 0.7432
## 77.1 4003 12 0.73045 0.005377 0.719988 0.7411
## 77.2 3970 5 0.72953 0.005386 0.719051 0.7402
## 77.2 3947 11 0.72750 0.005405 0.716980 0.7382
## 77.3 3920 11 0.72546 0.005425 0.714901 0.7362
## 77.4 3888 11 0.72340 0.005445 0.712810 0.7342
## 77.5 3855 16 0.72040 0.005474 0.709752 0.7312
## 77.6 3821 12 0.71814 0.005495 0.707448 0.7290
## 77.7 3797 9 0.71644 0.005512 0.705715 0.7273
## 77.8 3765 9 0.71472 0.005528 0.703971 0.7256
## 77.8 3737 18 0.71128 0.005561 0.700466 0.7223
## 77.9 3697 11 0.70916 0.005580 0.698311 0.7202
## 78.0 3667 13 0.70665 0.005604 0.695752 0.7177
## 78.1 3631 7 0.70529 0.005617 0.694365 0.7164
## 78.2 3601 14 0.70255 0.005643 0.691574 0.7137
## 78.2 3567 10 0.70058 0.005661 0.689569 0.7118
## 78.3 3539 16 0.69741 0.005691 0.686345 0.7087
## 78.4 3505 11 0.69522 0.005711 0.684117 0.7065
## 78.5 3480 9 0.69342 0.005727 0.682287 0.7047
## 78.6 3454 6 0.69222 0.005739 0.681062 0.7036
## 78.7 3429 10 0.69020 0.005757 0.679007 0.7016
## 78.8 3400 10 0.68817 0.005776 0.676941 0.6996
## 78.8 3369 6 0.68694 0.005787 0.675694 0.6984
## 78.9 3349 17 0.68346 0.005819 0.672146 0.6950
## 79.0 3318 17 0.67996 0.005851 0.668583 0.6915
## 79.1 3285 9 0.67809 0.005868 0.666688 0.6897
## 79.2 3265 12 0.67560 0.005890 0.664153 0.6872
## 79.2 3236 14 0.67268 0.005917 0.661180 0.6844
## 79.3 3211 8 0.67100 0.005931 0.659476 0.6827
## 79.4 3182 13 0.66826 0.005956 0.656688 0.6800
## 79.5 3149 13 0.66550 0.005980 0.653883 0.6773
## 79.6 3121 10 0.66337 0.005999 0.651715 0.6752
## 79.7 3091 17 0.65972 0.006031 0.648006 0.6716
## 79.8 3054 11 0.65734 0.006051 0.645590 0.6693
## 79.8 3033 10 0.65518 0.006070 0.643387 0.6672
## 79.9 3003 25 0.64972 0.006117 0.637844 0.6618
## 80.0 2965 8 0.64797 0.006132 0.636062 0.6601
## 80.1 2945 11 0.64555 0.006152 0.633603 0.6577
## 80.2 2923 14 0.64246 0.006178 0.630462 0.6547
## 80.2 2888 13 0.63957 0.006202 0.627525 0.6518
## 80.3 2862 7 0.63800 0.006215 0.625936 0.6503
## 80.4 2846 7 0.63643 0.006228 0.624342 0.6488
## 80.5 2830 11 0.63396 0.006248 0.621830 0.6463
## 80.6 2810 8 0.63215 0.006263 0.619997 0.6445
## 80.7 2794 11 0.62966 0.006283 0.617470 0.6421
## 80.8 2770 10 0.62739 0.006301 0.615162 0.6399
## 80.8 2746 9 0.62533 0.006318 0.613074 0.6378
## 80.9 2726 12 0.62258 0.006340 0.610280 0.6351
## 81.0 2703 14 0.61936 0.006365 0.607007 0.6320
## 81.1 2679 13 0.61635 0.006389 0.603957 0.6290
## 81.2 2649 13 0.61333 0.006412 0.600888 0.6260
## 81.2 2625 15 0.60982 0.006439 0.597332 0.6226
## 81.3 2590 16 0.60606 0.006468 0.593510 0.6189
## 81.4 2565 9 0.60393 0.006484 0.591354 0.6168
## 81.5 2543 10 0.60155 0.006502 0.588945 0.6144
## 81.6 2522 10 0.59917 0.006519 0.586526 0.6121
## 81.7 2496 9 0.59701 0.006536 0.584335 0.6100
## 81.8 2474 11 0.59435 0.006555 0.581643 0.6073
## 81.8 2454 7 0.59266 0.006568 0.579924 0.6057
## 81.9 2432 10 0.59022 0.006586 0.577453 0.6033
## 82.0 2407 7 0.58851 0.006599 0.575713 0.6016
## 82.1 2387 11 0.58579 0.006619 0.572963 0.5989
## 82.2 2360 15 0.58207 0.006646 0.569188 0.5952
## 82.2 2333 11 0.57933 0.006666 0.566406 0.5925
## 82.3 2310 21 0.57406 0.006704 0.561069 0.5873
## 82.4 2276 11 0.57128 0.006723 0.558257 0.5846
## 82.5 2259 14 0.56774 0.006748 0.554671 0.5811
## 82.6 2233 16 0.56368 0.006776 0.550551 0.5771
## 82.7 2207 10 0.56112 0.006793 0.547964 0.5746
## 82.8 2186 12 0.55804 0.006814 0.544845 0.5716
## 82.8 2165 9 0.55572 0.006829 0.542497 0.5693
## 82.9 2147 15 0.55184 0.006855 0.538566 0.5654
## 83.0 2114 12 0.54871 0.006875 0.535396 0.5623
## 83.1 2088 15 0.54476 0.006901 0.531406 0.5585
## 83.2 2060 14 0.54106 0.006924 0.527660 0.5548
## 83.2 2035 8 0.53894 0.006938 0.525508 0.5527
## 83.3 2017 10 0.53626 0.006955 0.522804 0.5501
## 83.4 1999 15 0.53224 0.006980 0.518734 0.5461
## 83.5 1976 7 0.53035 0.006991 0.516827 0.5442
## 83.6 1956 11 0.52737 0.007010 0.513810 0.5413
## 83.7 1937 11 0.52438 0.007028 0.510782 0.5383
## 83.8 1914 18 0.51945 0.007057 0.505796 0.5335
## 83.8 1888 12 0.51614 0.007076 0.502459 0.5302
## 83.9 1868 7 0.51421 0.007087 0.500504 0.5283
## 84.0 1853 6 0.51254 0.007097 0.498822 0.5266
## 84.1 1834 16 0.50807 0.007123 0.494303 0.5222
## 84.2 1814 5 0.50667 0.007130 0.492888 0.5208
## 84.2 1802 14 0.50274 0.007152 0.488912 0.5170
## 84.3 1780 11 0.49963 0.007169 0.485774 0.5139
## 84.4 1767 12 0.49624 0.007187 0.482348 0.5105
## 84.5 1745 14 0.49226 0.007208 0.478329 0.5066
## 84.6 1724 10 0.48940 0.007222 0.475447 0.5038
## 84.7 1705 6 0.48768 0.007231 0.473709 0.5021
## 84.8 1692 10 0.48480 0.007245 0.470800 0.4992
## 84.8 1673 12 0.48132 0.007263 0.467292 0.4958
## 84.9 1654 9 0.47870 0.007275 0.464650 0.4932
## 85.0 1636 14 0.47460 0.007295 0.460518 0.4891
## 85.1 1610 8 0.47224 0.007306 0.458139 0.4868
## 85.2 1594 15 0.46780 0.007327 0.453658 0.4824
## 85.2 1571 10 0.46482 0.007341 0.450655 0.4794
## 85.3 1558 9 0.46214 0.007353 0.447949 0.4768
## 85.4 1536 10 0.45913 0.007366 0.444916 0.4738
## 85.5 1516 12 0.45549 0.007382 0.441253 0.4702
## 85.6 1487 7 0.45335 0.007392 0.439092 0.4681
## 85.7 1474 16 0.44843 0.007413 0.434132 0.4632
## 85.8 1450 14 0.44410 0.007431 0.429771 0.4589
## 85.8 1425 17 0.43880 0.007453 0.424434 0.4537
## 85.9 1403 14 0.43442 0.007470 0.420026 0.4493
## 86.0 1380 14 0.43002 0.007486 0.415590 0.4449
## 86.1 1360 9 0.42717 0.007497 0.412726 0.4421
## 86.2 1343 8 0.42463 0.007506 0.410166 0.4396
## 86.2 1328 7 0.42239 0.007514 0.407914 0.4374
## 86.3 1312 10 0.41917 0.007525 0.404675 0.4342
## 86.4 1295 5 0.41755 0.007531 0.403047 0.4326
## 86.5 1279 8 0.41494 0.007540 0.400419 0.4300
## 86.6 1262 8 0.41231 0.007549 0.397773 0.4274
## 86.7 1245 6 0.41032 0.007557 0.395774 0.4254
## 86.8 1234 8 0.40766 0.007566 0.393098 0.4228
## 86.8 1220 7 0.40532 0.007574 0.390745 0.4204
## 86.9 1208 7 0.40297 0.007582 0.388383 0.4181
## 87.0 1196 11 0.39927 0.007594 0.384656 0.4144
## 87.1 1180 17 0.39351 0.007612 0.378875 0.4087
## 87.2 1160 1 0.39317 0.007613 0.378534 0.4084
## 87.2 1152 10 0.38976 0.007623 0.375104 0.4050
## 87.3 1129 10 0.38631 0.007633 0.371635 0.4016
## 87.4 1113 7 0.38388 0.007640 0.369194 0.3991
## 87.5 1099 3 0.38283 0.007643 0.368141 0.3981
## 87.6 1090 6 0.38072 0.007649 0.366024 0.3960
## 87.7 1075 6 0.37860 0.007656 0.363888 0.3939
## 87.8 1064 3 0.37753 0.007659 0.362816 0.3928
## 87.8 1055 9 0.37431 0.007668 0.359580 0.3896
## 87.9 1035 10 0.37069 0.007679 0.355946 0.3861
## 88.0 1017 4 0.36924 0.007683 0.354481 0.3846
## 88.1 1009 11 0.36521 0.007695 0.350437 0.3806
## 88.2 992 6 0.36300 0.007701 0.348218 0.3784
## 88.2 980 8 0.36004 0.007709 0.345243 0.3755
## 88.3 964 13 0.35518 0.007722 0.340367 0.3706
## 88.4 948 11 0.35106 0.007732 0.336232 0.3665
## 88.5 932 12 0.34654 0.007741 0.331697 0.3621
## 88.6 916 5 0.34465 0.007745 0.329800 0.3602
## 88.7 901 15 0.33891 0.007757 0.324046 0.3545
## 88.8 881 4 0.33737 0.007759 0.322504 0.3529
## 88.8 873 7 0.33467 0.007764 0.319792 0.3502
## 88.9 861 7 0.33195 0.007769 0.317065 0.3475
## 89.0 846 10 0.32802 0.007776 0.313133 0.3436
## 89.1 830 4 0.32644 0.007778 0.311549 0.3421
## 89.2 824 4 0.32486 0.007781 0.309962 0.3405
## 89.2 815 15 0.31888 0.007789 0.303973 0.3345
## 89.3 793 9 0.31526 0.007794 0.300350 0.3309
## 89.4 781 9 0.31163 0.007797 0.296714 0.3273
## 89.5 770 8 0.30839 0.007800 0.293476 0.3241
## 89.6 757 13 0.30309 0.007803 0.288180 0.3188
## 89.7 740 5 0.30105 0.007804 0.286133 0.3167
## 89.8 729 9 0.29733 0.007805 0.282419 0.3130
## 89.8 716 6 0.29484 0.007806 0.279929 0.3105
## 89.9 703 4 0.29316 0.007806 0.278253 0.3089
## 90.0 696 6 0.29063 0.007807 0.275728 0.3063
## 90.1 689 11 0.28599 0.007807 0.271095 0.3017
## 90.2 677 5 0.28388 0.007806 0.268987 0.2996
## 90.2 667 5 0.28175 0.007805 0.266863 0.2975
## 90.3 660 11 0.27706 0.007802 0.262179 0.2928
## 90.4 646 6 0.27448 0.007800 0.259613 0.2902
## 90.5 636 8 0.27103 0.007797 0.256172 0.2868
## 90.6 622 11 0.26624 0.007792 0.251396 0.2820
## 90.7 607 6 0.26361 0.007789 0.248774 0.2793
## 90.8 597 7 0.26052 0.007785 0.245696 0.2762
## 90.8 588 7 0.25741 0.007780 0.242609 0.2731
## 90.9 577 4 0.25563 0.007777 0.240833 0.2713
## 91.0 569 6 0.25293 0.007772 0.238151 0.2686
## 91.1 559 2 0.25203 0.007771 0.237250 0.2677
## 91.2 554 4 0.25021 0.007768 0.235439 0.2659
## 91.2 543 13 0.24422 0.007757 0.229479 0.2599
## 91.3 525 5 0.24189 0.007753 0.227165 0.2576
## 91.4 518 6 0.23909 0.007747 0.224380 0.2548
## 91.5 509 7 0.23580 0.007740 0.221112 0.2515
## 91.6 498 7 0.23249 0.007731 0.217819 0.2481
## 91.7 487 5 0.23010 0.007725 0.215448 0.2458
## 91.8 481 4 0.22819 0.007720 0.213548 0.2438
## 91.8 475 7 0.22483 0.007710 0.210210 0.2405
## 91.9 466 11 0.21952 0.007693 0.204948 0.2351
## 92.0 454 5 0.21710 0.007683 0.202552 0.2327
## 92.1 446 5 0.21467 0.007674 0.200141 0.2302
## 92.2 435 10 0.20973 0.007655 0.195253 0.2253
## 92.2 422 4 0.20774 0.007646 0.193285 0.2233
## 92.3 416 7 0.20425 0.007631 0.189827 0.2198
## 92.4 408 3 0.20275 0.007624 0.188341 0.2183
## 92.5 402 4 0.20073 0.007615 0.186346 0.2162
## 92.6 396 8 0.19667 0.007595 0.182339 0.2121
## 92.7 385 5 0.19412 0.007581 0.179815 0.2096
## 92.8 379 9 0.18951 0.007555 0.175266 0.2049
## 92.8 369 3 0.18797 0.007546 0.173746 0.2034
## 92.9 362 4 0.18589 0.007534 0.171698 0.2013
## 93.0 355 6 0.18275 0.007515 0.168600 0.1981
## 93.1 347 6 0.17959 0.007495 0.165486 0.1949
## 93.2 339 6 0.17641 0.007474 0.162356 0.1917
## 93.2 332 4 0.17429 0.007459 0.160264 0.1895
## 93.3 326 3 0.17268 0.007447 0.158686 0.1879
## 93.4 322 3 0.17107 0.007436 0.157104 0.1863
## 93.5 318 2 0.17000 0.007428 0.156046 0.1852
## 93.6 313 9 0.16511 0.007391 0.151241 0.1803
## 93.7 303 5 0.16239 0.007369 0.148567 0.1775
## 93.8 296 3 0.16074 0.007355 0.146952 0.1758
## 93.8 290 4 0.15852 0.007337 0.144776 0.1736
## 93.9 285 3 0.15685 0.007322 0.143139 0.1719
## 94.0 281 7 0.15295 0.007287 0.139310 0.1679
## 94.1 273 5 0.15015 0.007261 0.136568 0.1651
## 94.2 268 4 0.14790 0.007238 0.134377 0.1628
## 94.2 264 4 0.14566 0.007215 0.132187 0.1605
## 94.3 259 3 0.14398 0.007197 0.130540 0.1588
## 94.4 255 2 0.14285 0.007184 0.129437 0.1576
## 94.5 253 3 0.14115 0.007166 0.127785 0.1559
## 94.6 248 4 0.13888 0.007140 0.125565 0.1536
## 94.7 241 2 0.13772 0.007127 0.124440 0.1524
## 94.8 237 2 0.13656 0.007114 0.123307 0.1512
## 94.8 235 7 0.13249 0.007066 0.119343 0.1471
## 94.9 227 9 0.12724 0.007000 0.114235 0.1417
## 95.0 215 8 0.12251 0.006936 0.109638 0.1369
## 95.1 206 3 0.12072 0.006912 0.107908 0.1351
## 95.2 203 6 0.11715 0.006859 0.104453 0.1314
## 95.2 196 3 0.11536 0.006832 0.102719 0.1296
## 95.3 191 3 0.11355 0.006804 0.100966 0.1277
## 95.4 188 3 0.11174 0.006775 0.099216 0.1258
## 95.5 184 1 0.11113 0.006766 0.098630 0.1252
## 95.6 183 1 0.11052 0.006756 0.098043 0.1246
## 95.7 181 2 0.10930 0.006736 0.096864 0.1233
## 95.8 177 5 0.10621 0.006686 0.093885 0.1202
## 95.8 171 3 0.10435 0.006655 0.092089 0.1182
## 95.9 168 3 0.10249 0.006622 0.090296 0.1163
## 96.0 165 3 0.10062 0.006589 0.088504 0.1144
## 96.1 162 3 0.09876 0.006554 0.086715 0.1125
## 96.2 158 2 0.09751 0.006530 0.085515 0.1112
## 96.2 156 4 0.09501 0.006481 0.083119 0.1086
## 96.3 152 1 0.09438 0.006469 0.082520 0.1080
## 96.5 148 1 0.09375 0.006456 0.081909 0.1073
## 96.6 144 2 0.09244 0.006432 0.080660 0.1060
## 96.7 139 5 0.08912 0.006370 0.077469 0.1025
## 97.0 132 2 0.08777 0.006345 0.076174 0.1011
## 97.1 129 1 0.08709 0.006332 0.075522 0.1004
## 97.2 127 2 0.08572 0.006306 0.074207 0.0990
## 97.2 122 1 0.08501 0.006294 0.073533 0.0983
## 97.3 120 3 0.08289 0.006255 0.071494 0.0961
## 97.4 117 3 0.08076 0.006214 0.069459 0.0939
## 97.5 113 3 0.07862 0.006171 0.067410 0.0917
## 97.6 108 3 0.07644 0.006127 0.065323 0.0894
## 97.7 103 1 0.07569 0.006112 0.064614 0.0887
## 97.8 101 4 0.07270 0.006051 0.061753 0.0856
## 97.8 97 3 0.07045 0.006001 0.059615 0.0832
## 98.1 91 1 0.06967 0.005985 0.058877 0.0824
## 98.2 89 3 0.06732 0.005935 0.056642 0.0800
## 98.2 86 4 0.06419 0.005862 0.053674 0.0768
## 98.3 80 1 0.06339 0.005843 0.052913 0.0759
## 98.4 79 2 0.06179 0.005805 0.051396 0.0743
## 98.6 77 1 0.06098 0.005784 0.050638 0.0734
## 98.7 76 2 0.05938 0.005742 0.049127 0.0718
## 98.8 74 2 0.05777 0.005698 0.047619 0.0701
## 98.8 72 2 0.05617 0.005652 0.046116 0.0684
## 98.9 70 1 0.05537 0.005628 0.045366 0.0676
## 99.1 68 1 0.05455 0.005604 0.044605 0.0667
## 99.2 67 2 0.05292 0.005553 0.043086 0.0650
## 99.2 65 1 0.05211 0.005527 0.042329 0.0642
## 99.6 61 1 0.05126 0.005502 0.041531 0.0633
## 99.8 60 2 0.04955 0.005450 0.039939 0.0615
## 100.0 57 2 0.04781 0.005395 0.038322 0.0596
## 100.1 54 1 0.04692 0.005368 0.037499 0.0587
## 100.2 53 1 0.04604 0.005339 0.036678 0.0578
## 100.2 52 1 0.04515 0.005309 0.035859 0.0569
## 100.3 51 1 0.04427 0.005278 0.035042 0.0559
## 100.7 48 1 0.04335 0.005248 0.034188 0.0550
## 100.8 47 1 0.04242 0.005217 0.033337 0.0540
## 101.1 46 1 0.04150 0.005185 0.032488 0.0530
## 101.2 44 2 0.03961 0.005118 0.030753 0.0510
## 101.3 41 3 0.03672 0.005009 0.028101 0.0480
## 101.4 38 1 0.03575 0.004970 0.027223 0.0469
## 101.6 36 1 0.03476 0.004930 0.026321 0.0459
## 101.7 34 1 0.03373 0.004890 0.025391 0.0448
## 101.8 33 1 0.03271 0.004847 0.024467 0.0437
## 101.9 31 2 0.03060 0.004759 0.022562 0.0415
## 102.0 29 2 0.02849 0.004659 0.020679 0.0393
## 102.1 27 3 0.02533 0.004485 0.017898 0.0358
## 102.3 24 1 0.02427 0.004421 0.016984 0.0347
## 102.4 23 2 0.02216 0.004281 0.015175 0.0324
## 102.7 20 1 0.02105 0.004208 0.014228 0.0311
## 103.0 18 1 0.01988 0.004133 0.013228 0.0299
## 103.1 17 1 0.01871 0.004052 0.012241 0.0286
## 103.4 16 1 0.01754 0.003964 0.011266 0.0273
## 103.5 15 1 0.01637 0.003869 0.010305 0.0260
## 104.2 14 1 0.01520 0.003765 0.009358 0.0247
## 105.0 10 1 0.01368 0.003683 0.008075 0.0232
## 106.1 9 1 0.01216 0.003574 0.006839 0.0216
## 106.2 8 1 0.01064 0.003435 0.005654 0.0200
## 106.3 7 1 0.00912 0.003264 0.004525 0.0184
## 107.0 4 1 0.00684 0.003145 0.002779 0.0168
## 109.9 3 1 0.00456 0.002804 0.001367 0.0152
## 113.0 2 1 0.00228 0.002137 0.000363 0.0143km_table <- summary(km_fit)cumulative hazard function
# Extract cumulative hazard from the Kaplan-Meier fit
km_summary <- summary(km_fit)
# Cumulative hazard can be computed as: -log(survival probability)
cum_hazard <- -log(km_summary$surv)
# Plot cumulative hazard
plot(km_summary$time, cum_hazard, type = "s",
xlab = "Time", ylab = "Cumulative Hazard",
main = "Cumulative Hazard Function")
### Plot Kaplan-Meier survival curve
library(survminer)## Loading required package: ggpubr##
## Attaching package: 'survminer'## The following object is masked from 'package:survival':
##
## myelomaggsurvplot(km_fit,
risk.table = TRUE,
conf.int = TRUE,
xlab = "Age",
ylab = "Survival Probability",
title = "Kaplan-Meier Survival Curve")
#### Smoothed hazard estimate
# Calculate the smoothed hazard function
# Hazard estimate: hazard = (n.event / n.risk)
km_summary <- summary(km_fit)
hazard <- km_summary$n.event / km_summary$n.risk
# Create a data frame for plotting
hazard_data <- data.frame(
time = km_summary$time,
hazard = hazard
)
# Plot the hazard function with a smooth line
ggplot(hazard_data, aes(x = time, y = hazard)) +
geom_line(color = "blue") + # Original hazard step line
geom_smooth(method = "loess", color = "red", se = FALSE) + # Smoothed line
labs(title = "Smoothed Hazard Function", x = "Time", y = "Hazard Rate")## `geom_smooth()` using formula = 'y ~ x'
### by Gender
# Kaplan-Meier by gender
km_fit_gender <- survfit(Surv(agecensor, died0121) ~ female, data = data2)
# Plot survival by gender
ggsurvplot(km_fit_gender,
conf.int = TRUE,
pval = TRUE, # Include p-value for statistical significance
legend.labs = c("Male", "Female"),
title = "Survival by Gender",
xlab = "Age",
ylab = "Survival Probability")
by locality size
km_fit_locsize <- survfit(Surv(agecensor, died0121) ~ locsize01, data = data2)
# Plot survival by locality size
ggsurvplot(km_fit_locsize,
conf.int = TRUE,
pval = TRUE,
legend.labs = c("100,000+", "15,000 - 99,999", "2,500 - 14,999", "<2,500"),
title = "Survival by Locality Size",
xlab = "Age",
ylab = "Survival Probability")
by schooling level
km_fit_schooling <- survfit(Surv(agecensor, died0121) ~ educlevel, data = data2)
# Plot survival by schooling level
ggsurvplot(km_fit_schooling,
conf.int = TRUE,
pval = TRUE,
legend.labs = c("No schooling", "1-5 years", "6-8 years", "9+ years"),
title = "Survival by Schooling Level",
xlab = "Age",
ylab = "Survival Probability")
### Statistical Test to Compare Survival Between Groups
# Log-rank test for gender
survdiff(Surv(agecensor, died0121) ~ female, data = data2)## Call:
## survdiff(formula = Surv(agecensor, died0121) ~ female, data = data2)
##
## n=7565, 2071 observations deleted due to missingness.
##
## N Observed Expected (O-E)^2/E (O-E)^2/V
## female=0 3450 1898 1645 39.0 67
## female=1 4115 2096 2349 27.3 67
##
## Chisq= 67 on 1 degrees of freedom, p= 3e-16Interpretation: For males, the observed number of deaths (1,898) exceeds the expected number (1,645), while for females, the observed deaths (2,096) fall below the expected count (2,349). This indicates that males have a higher-than-expected mortality rate, whereas females have a lower-than-expected rate. The Chi-square statistic of 67 shows a significant difference between the survival curves for males and females.The extremely small p-value (3e-16) confirms that this difference is highly statistically significant, far below the typical threshold of 0.05, suggesting a clear survival difference between genders in the dataset.
# Log-rank test for locality size
survdiff(Surv(agecensor, died0121) ~ locsize01, data = data2)## Call:
## survdiff(formula = Surv(agecensor, died0121) ~ locsize01, data = data2)
##
## n=7565, 2071 observations deleted due to missingness.
##
## N Observed Expected (O-E)^2/E (O-E)^2/V
## locsize01=< 2,500 1309 690 767 7.74 9.65
## locsize01=100,000 - + 4350 2266 2194 2.38 5.31
## locsize01=15,000 - 99,999 1167 627 599 1.35 1.59
## locsize01=2,500 - 14,999 739 411 435 1.28 1.44
##
## Chisq= 12.9 on 3 degrees of freedom, p= 0.005Interpretation: The log-rank test indicates a difference in survival across the four locality size groups (p = 0.005). Individuals in rural areas (< 2,500 inhabitants) and small urban areas (2,500-14,999 inhabitants) show slightly lower mortality rates than expected, while those in large urban areas (100,000+ inhabitants) exhibit a slightly higher mortality rate. In medium urban areas (15,000-99,999 inhabitants), the survival rates closely align with expectations. Overall, the results suggest that locality size influences mortality, with distinct survival patterns across rural, small urban, medium urban, and large urban areas.
# Log-rank test for schooling level
survdiff(Surv(agecensor, died0121) ~ educlevel, data = data2)## Call:
## survdiff(formula = Surv(agecensor, died0121) ~ educlevel, data = data2)
##
## n=7552, 2084 observations deleted due to missingness.
##
## N Observed Expected (O-E)^2/E (O-E)^2/V
## educlevel=0 2024 1275 1411 13.121 21.128
## educlevel=15 2676 1461 1439 0.344 0.542
## educlevel=68 1620 759 677 9.929 12.154
## educlevel=919 1232 488 456 2.223 2.557
##
## Chisq= 26.8 on 3 degrees of freedom, p= 6e-06Interpretation: The Chi-square statistic of 26.8 indicates a significant difference in survival rates across the four education levels. The p-value (6e-06) is exceptionally small, far below the standard significance threshold of 0.05, highlighting a highly statistically significant difference in survival among the education groups.
Longitudinal vs Synthetic cohort approach
The analysis is mainly longitudinal, tracking the same individuals over multiple waves (2001, 2003, 2012, 2015, 2018, and 2021) to collect data on their survival status over time. However, it also incorporates a synthetic cohort element by adding new individuals in subsequent waves to maintain representativeness of the 50+ population. Refresher samples were drawn in 2012 (ages 50-61) and 2018 (ages 50-56), introducing new participants, which mirrors the synthetic cohort approach. Therefore, the study can be considered a combination of both longitudinal and synthetic cohort methods.