ACKNOWLDGEMENT
* The dashboard is for educational purpose only and it should be used for understanding the survival analysis technique. The outputs and analysis displayed in the flexdashboard should not strictly be considered for medical related advice or judgement.
DISCLAIMER
* > Authors don’t bear any responsibility for any consequences emnating from the content covered in the dashboard, the web url and links.
Introduction: SURVIVAL ANALYSIS
AUTHORS BEAR NO RESPONSIBLITY OF ANY DAMAGE OR HARM EMNATING FROM THE ONLINE DOWNLAODS AND LINKS MENTIONED IN THE FLEXDASHBOARD
Survival Analysis is a branch of statistics for analyzing the expected duration of time until one or more events happen, such as death in biological organisms and failure in mechanical systems. This topic is called reliability theory or reliability analysis in engineering, duration analysis or duration modelling in economics, and event history analysis in sociology. Survival analysis attempts to answer questions such as: what is the proportion of a population which will survive past a certain time? Of those that survive, at what rate will they die or fail? Can multiple causes of death or failure be taken into account? How do particular circumstances or characteristics increase or decrease the probability of survival?
More generally, survival analysis involves the modelling of time to event data; in this context, death or failure is considered an “event” in the survival analysis literature – traditionally only a single event occurs for each subject, after which the organism or mechanism is dead or broken. Recurring event or repeated event models relax that assumption. The study of recurring events is relevant in systems reliability, and in many areas of social sciences and medical research. Source:https://en.wikipedia.org/wiki/Survival_analysis
All the datasets used in this Flexdashboard can be accessed from the following link— http://www.stat.rice.edu/~sneeley/STAT553/Datasets/survivaldata.txt
DATASETS USED IN THE STUDY
Survival of the a patient after heart transplant
Source: Data on 69 patients receiving heart transplants. Taken from “The Statistical Analysis of Failure Time Data” by Kalbfleisch and Prentice, Appendix I, pages 230-232.
Survival of the ovarian cancer patients after chemotherapy
Source:D. Collett, Modelling Survival Data in Medical Research, Chapman & Hall, 1994 (pg 141).
Survival of cervical cancer patients with radiotherapy and without radiosanitizer
Source:MRC Working Party on Advanced Carcinoma of the Cervix, Radiotherapy Oncology 26:93-103, 1993. Analyzed in and obtained from MKB Parmar, D Machin, Survival Analysis: A Practical Approach, Wiley, 1995.
Survival of brain cancer patients with radiotherapy and without radiosanitizer
Source:MRC Working Party on Misonidazole in Gliomas, 1983. Analyzed in and obtained from MKB Parmar, D Machin, Survival Analysis: A Practical Approach, Wiley, 1995.
Survival of bladder cancer patients after surgery assigned to placebo or chemotherapy
Source:M Pagano and K Gauvreau, "Principles of Biostatistics, 2nd Ed. Duxbury 2000. Chapter 21, exercise 9, page 512.
Survival of lupus nephritis patients after renal biopsy
Source:Introduction to Abrahamowicz, MacKenzie and Esdaile (December 1996 issue, JASA).
Survival primary biliary cirrhosis
Source:Mayo Clinic trial in primary biliary cirrhosis (PBC) of the liver conducted between 1974 and 1984.
Dickson, et al., Hepatology 10:1-7 (1989) and in Markus, et al., N Eng J of Med 320:1709-13 (1989)
Survival of VA lung cancer patients
Source:Veteran’s Administration Lung Cancer Trial Taken from Kalbfleisch and Prentice, pages 223-224.
LINKS OF BOOKS FOR SURVIVAL ANALYSIS (Free PDF Downloads)
http://dl.booktolearn.com/ebooks2/science/statistics/9781466555662_handbook_of_survival_analysis_6afa.pdf
https://www.researchgate.net/publication/237067177_Survival_Analysis_Event_History_Analysis
https://epdf.pub/survival-analysis-a-self-learning-text-third-edition.html
HEART TRANSPLANT DATASET: Explainer
Data is on 69 patients receiving heart transplants. Taken from “The Statistical Analysis of Failure Time Data” by Kalbfleisch and Prentice, Appendix I, pages 230-232 from stalib data depository. http://lib.stat.cmu.edu/datasets/stanford
Following are the variables in the dataset—
Age = Age at transplant in years
Status = Survival Status 1=dead 0=alive
Time = Survival Time after transplant in days
Call: survfit(formula = Surv(time = Time, event = Status) ~ 1, data = df_heart)
time n.risk n.event survival std.err lower 95% CI upper 95% CI
5 69 1 0.986 0.0144 0.9577 1.000
16 68 2 0.957 0.0246 0.9096 1.000
17 66 1 0.942 0.0281 0.8885 0.999
28 65 1 0.928 0.0312 0.8683 0.991
30 64 1 0.913 0.0339 0.8489 0.982
39 63 1 0.899 0.0363 0.8301 0.973
43 61 1 0.884 0.0386 0.8113 0.963
45 60 1 0.869 0.0407 0.7929 0.953
51 59 1 0.854 0.0426 0.7748 0.942
53 58 1 0.840 0.0443 0.7571 0.931
58 57 1 0.825 0.0459 0.7396 0.920
61 56 1 0.810 0.0474 0.7224 0.909
66 55 1 0.795 0.0488 0.7053 0.897
68 54 2 0.766 0.0512 0.6719 0.873
72 52 2 0.737 0.0533 0.6391 0.849
77 50 1 0.722 0.0543 0.6229 0.836
78 49 1 0.707 0.0551 0.6069 0.824
80 48 1 0.692 0.0559 0.5910 0.811
81 47 1 0.678 0.0566 0.5752 0.798
90 46 1 0.663 0.0573 0.5596 0.785
96 45 1 0.648 0.0579 0.5441 0.772
100 44 1 0.633 0.0584 0.5287 0.759
110 42 1 0.618 0.0589 0.5130 0.745
153 40 1 0.603 0.0594 0.4969 0.731
165 39 1 0.587 0.0599 0.4810 0.717
186 37 1 0.572 0.0603 0.4647 0.703
188 36 1 0.556 0.0607 0.4485 0.688
207 35 1 0.540 0.0610 0.4325 0.674
219 34 1 0.524 0.0613 0.4166 0.659
285 32 2 0.491 0.0616 0.3840 0.628
308 30 1 0.475 0.0617 0.3680 0.613
334 29 1 0.458 0.0617 0.3521 0.597
342 27 1 0.441 0.0617 0.3356 0.581
583 20 1 0.419 0.0625 0.3132 0.562
675 16 1 0.393 0.0638 0.2860 0.540
733 15 1 0.367 0.0647 0.2597 0.519
852 13 1 0.339 0.0656 0.2317 0.495
979 10 1 0.305 0.0672 0.1979 0.470
995 9 1 0.271 0.0678 0.1660 0.442
1032 8 1 0.237 0.0672 0.1360 0.413
1386 5 1 0.190 0.0685 0.0935 0.385
Call:
coxph(formula = Surv(time = Time, event = Status) ~ Age, data = df_heart)
n= 69, number of events= 45
coef exp(coef) se(coef) z Pr(>|z|)
Age 0.05711 1.05877 0.02279 2.506 0.0122 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
Age 1.059 0.9445 1.013 1.107
Concordance= 0.602 (se = 0.053 )
Likelihood ratio test= 7.2 on 1 df, p=0.007
Wald test = 6.28 on 1 df, p=0.01
Score (logrank) test = 6.22 on 1 df, p=0.01
OVARIAN CANCER DATASET: Explainer
The dataset contains ovarian cancer patient data treated with chemotherapy after surgical treatment. 26 women with minimal residual disease were randomized to cyclophosphamide with or without adriamycin. Survival time in days, status (0 = censored), treatment (2 = combined), age in years. Example 4.9 in D. Collett, Modelling Survival Data in Medical Research, Chapman & Hall, 1994 (pg 141)
Following are the variables in the dataset—
Patient= ID number of ovarian cancer patient
Age = Age at transplant in years
Status = Survival Status 1=dead 0=alive
Time = Survival Time in days
Treatment= Treatment
Call: survfit(formula = Surv(time = Time, event = Status) ~ 1, data = df_ovarian)
time n.risk n.event survival std.err lower 95% CI upper 95% CI
59 26 1 0.962 0.0377 0.890 1.000
115 25 1 0.923 0.0523 0.826 1.000
156 24 1 0.885 0.0627 0.770 1.000
268 23 1 0.846 0.0708 0.718 0.997
329 22 1 0.808 0.0773 0.670 0.974
353 21 1 0.769 0.0826 0.623 0.949
365 20 1 0.731 0.0870 0.579 0.923
431 17 1 0.688 0.0919 0.529 0.894
464 15 1 0.642 0.0965 0.478 0.862
475 14 1 0.596 0.0999 0.429 0.828
563 12 1 0.546 0.1032 0.377 0.791
638 11 1 0.497 0.1051 0.328 0.752
Call:
coxph(formula = Surv(time = Time, event = Status) ~ Age, data = df_ovarian)
n= 26, number of events= 12
coef exp(coef) se(coef) z Pr(>|z|)
Age 0.16115 1.17487 0.04945 3.259 0.00112 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
Age 1.175 0.8512 1.066 1.294
Concordance= 0.773 (se = 0.086 )
Likelihood ratio test= 14.27 on 1 df, p=2e-04
Wald test = 10.62 on 1 df, p=0.001
Score (logrank) test = 12.27 on 1 df, p=5e-04
CERVICAL CANCER DATASET: Explainer
This dataset contains the sample of 30 patients from a randomized study of radiotherapy with and without a new radiosensitiser. Based on data from MRC Working Party on Advanced Carcinoma of the Cervix, Radiotherapy Oncology 26:93-103, 1993. Analyzed in and obtained from MKB Parmar, D Machin, Survival Analysis: A Practical Approach, Wiley, 1995. Group = treatment (2 = radiosensitiser),
Following are the variables in the dataset—
Age = Age at transplant in years
Status = Survival Status 1=dead 0=alive
Time = Survival Time in days
Group= Group 1= Radiotherapy with new radiosensitizer and 0= Radiotherapy without new radiosensitizer
Call: survfit(formula = Surv(time = Time, event = Status) ~ 1, data = df_cervical)
time n.risk n.event survival std.err lower 95% CI upper 95% CI
90 30 1 0.967 0.0328 0.9045 1.000
142 29 1 0.933 0.0455 0.8482 1.000
150 28 1 0.900 0.0548 0.7988 1.000
269 27 1 0.867 0.0621 0.7532 0.997
272 26 1 0.833 0.0680 0.7101 0.978
291 25 1 0.800 0.0730 0.6689 0.957
362 24 1 0.767 0.0772 0.6293 0.934
373 23 1 0.733 0.0807 0.5910 0.910
680 17 1 0.690 0.0867 0.5395 0.883
827 16 1 0.647 0.0914 0.4905 0.854
837 15 1 0.604 0.0950 0.4437 0.822
1037 11 1 0.549 0.1010 0.3829 0.787
1153 7 1 0.471 0.1130 0.2940 0.753
1297 6 1 0.392 0.1183 0.2171 0.708
1307 5 1 0.314 0.1178 0.1503 0.655
1429 3 1 0.209 0.1160 0.0705 0.620
Call:
coxph(formula = Surv(time = Time, event = Status) ~ Age, data = df_cervical)
n= 30, number of events= 16
coef exp(coef) se(coef) z Pr(>|z|)
Age -0.02074 0.97947 0.02168 -0.957 0.339
exp(coef) exp(-coef) lower .95 upper .95
Age 0.9795 1.021 0.9387 1.022
Concordance= 0.596 (se = 0.07 )
Likelihood ratio test= 0.89 on 1 df, p=0.3
Wald test = 0.92 on 1 df, p=0.3
Score (logrank) test = 0.92 on 1 df, p=0.3
PRIMARY BILIARY CIRRHOSIS DATASET: Explainer
Call: survfit(formula = Surv(time = Time, event = Status) ~ 1, data = df_pbc)
time n.risk n.event survival std.err lower 95% CI upper 95% CI
41 312 1 0.997 0.00320 0.991 1.000
51 311 1 0.994 0.00452 0.985 1.000
71 310 1 0.990 0.00552 0.980 1.000
77 309 1 0.987 0.00637 0.975 1.000
110 308 1 0.984 0.00711 0.970 0.998
130 307 1 0.981 0.00778 0.966 0.996
131 306 1 0.978 0.00838 0.961 0.994
140 305 1 0.974 0.00895 0.957 0.992
179 304 1 0.971 0.00948 0.953 0.990
186 303 1 0.968 0.00997 0.949 0.988
191 302 1 0.965 0.01044 0.944 0.985
198 301 1 0.962 0.01089 0.940 0.983
207 300 1 0.958 0.01131 0.936 0.981
216 299 1 0.955 0.01172 0.932 0.978
223 298 1 0.952 0.01211 0.928 0.976
264 297 2 0.946 0.01285 0.921 0.971
304 295 1 0.942 0.01320 0.917 0.969
321 294 1 0.939 0.01354 0.913 0.966
326 293 1 0.936 0.01387 0.909 0.963
334 292 1 0.933 0.01418 0.905 0.961
348 291 1 0.929 0.01449 0.902 0.958
388 290 1 0.926 0.01479 0.898 0.956
400 289 1 0.923 0.01509 0.894 0.953
460 288 1 0.920 0.01537 0.890 0.950
515 287 1 0.917 0.01565 0.887 0.948
533 286 1 0.913 0.01592 0.883 0.945
549 285 1 0.910 0.01618 0.879 0.943
552 284 1 0.907 0.01644 0.875 0.940
597 283 1 0.904 0.01669 0.872 0.937
611 282 1 0.901 0.01694 0.868 0.934
673 281 1 0.897 0.01718 0.864 0.932
694 280 1 0.894 0.01741 0.861 0.929
708 279 1 0.891 0.01764 0.857 0.926
732 278 1 0.888 0.01787 0.853 0.924
733 277 1 0.885 0.01809 0.850 0.921
737 276 1 0.881 0.01830 0.846 0.918
750 275 1 0.878 0.01852 0.843 0.915
762 274 1 0.875 0.01872 0.839 0.912
769 273 1 0.872 0.01893 0.835 0.910
786 272 1 0.869 0.01913 0.832 0.907
790 270 1 0.865 0.01932 0.828 0.904
797 269 1 0.862 0.01952 0.825 0.901
799 268 1 0.859 0.01971 0.821 0.898
824 267 1 0.856 0.01990 0.818 0.896
837 266 1 0.853 0.02008 0.814 0.893
850 264 1 0.849 0.02026 0.810 0.890
853 263 1 0.846 0.02044 0.807 0.887
859 262 1 0.843 0.02062 0.803 0.884
877 261 1 0.840 0.02079 0.800 0.881
890 260 1 0.836 0.02096 0.796 0.878
901 259 1 0.833 0.02112 0.793 0.876
904 258 1 0.830 0.02129 0.789 0.873
930 257 1 0.827 0.02145 0.786 0.870
943 255 1 0.823 0.02161 0.782 0.867
971 254 1 0.820 0.02176 0.779 0.864
974 253 1 0.817 0.02192 0.775 0.861
980 252 1 0.814 0.02207 0.772 0.858
999 250 1 0.810 0.02222 0.768 0.855
1000 249 1 0.807 0.02237 0.765 0.852
1012 248 1 0.804 0.02251 0.761 0.849
1037 246 1 0.801 0.02266 0.757 0.846
1067 245 1 0.797 0.02280 0.754 0.843
1077 244 1 0.794 0.02294 0.750 0.840
1080 243 1 0.791 0.02308 0.747 0.837
1083 242 1 0.788 0.02321 0.743 0.834
1084 241 1 0.784 0.02334 0.740 0.831
1152 239 1 0.781 0.02348 0.736 0.828
1165 237 1 0.778 0.02361 0.733 0.825
1170 236 1 0.774 0.02374 0.729 0.822
1191 235 2 0.768 0.02399 0.722 0.816
1212 233 1 0.765 0.02411 0.719 0.813
1217 230 1 0.761 0.02423 0.715 0.810
1235 227 1 0.758 0.02436 0.712 0.807
1297 222 1 0.754 0.02449 0.708 0.804
1301 220 1 0.751 0.02461 0.704 0.801
1350 214 1 0.748 0.02475 0.701 0.798
1356 213 1 0.744 0.02488 0.697 0.794
1360 212 1 0.741 0.02501 0.693 0.791
1413 206 1 0.737 0.02514 0.689 0.788
1427 203 1 0.733 0.02528 0.685 0.785
1434 201 1 0.730 0.02542 0.681 0.781
1435 199 1 0.726 0.02555 0.678 0.778
1444 198 1 0.722 0.02568 0.674 0.774
1447 197 1 0.719 0.02581 0.670 0.771
1487 193 1 0.715 0.02595 0.666 0.768
1492 192 1 0.711 0.02608 0.662 0.764
1504 191 1 0.707 0.02621 0.658 0.761
1536 189 1 0.704 0.02633 0.654 0.757
1542 188 1 0.700 0.02646 0.650 0.754
1576 184 1 0.696 0.02659 0.646 0.750
1657 178 1 0.692 0.02672 0.642 0.747
1682 175 1 0.688 0.02686 0.638 0.743
1690 174 2 0.680 0.02713 0.629 0.736
1741 169 1 0.676 0.02727 0.625 0.732
1786 162 1 0.672 0.02742 0.621 0.728
1827 159 1 0.668 0.02757 0.616 0.724
1847 156 1 0.664 0.02772 0.612 0.720
1925 151 1 0.659 0.02788 0.607 0.716
2033 143 1 0.655 0.02807 0.602 0.712
2055 141 1 0.650 0.02825 0.597 0.708
2081 140 1 0.645 0.02843 0.592 0.704
2090 139 1 0.641 0.02860 0.587 0.699
2105 138 1 0.636 0.02877 0.582 0.695
2224 127 1 0.631 0.02897 0.577 0.691
2241 125 1 0.626 0.02918 0.571 0.686
2256 123 1 0.621 0.02938 0.566 0.681
2288 121 1 0.616 0.02958 0.561 0.677
2297 119 1 0.611 0.02978 0.555 0.672
2350 114 1 0.605 0.03000 0.549 0.667
2386 110 1 0.600 0.03023 0.543 0.662
2400 109 1 0.594 0.03045 0.538 0.657
2419 108 1 0.589 0.03066 0.532 0.652
2466 103 1 0.583 0.03089 0.526 0.647
2468 102 1 0.577 0.03111 0.519 0.642
2475 101 1 0.572 0.03132 0.513 0.636
2503 100 1 0.566 0.03153 0.507 0.631
2540 96 1 0.560 0.03175 0.501 0.626
2583 88 1 0.554 0.03202 0.494 0.620
2598 87 1 0.547 0.03227 0.488 0.614
2689 80 1 0.540 0.03259 0.480 0.608
2769 76 1 0.533 0.03293 0.473 0.602
2796 74 1 0.526 0.03326 0.465 0.596
2847 71 1 0.519 0.03361 0.457 0.589
3086 60 1 0.510 0.03414 0.447 0.582
3090 59 1 0.501 0.03464 0.438 0.574
3092 58 1 0.493 0.03511 0.429 0.567
3170 53 1 0.484 0.03565 0.418 0.559
3222 52 1 0.474 0.03616 0.408 0.551
3244 50 1 0.465 0.03666 0.398 0.542
3282 48 1 0.455 0.03715 0.388 0.534
3358 45 1 0.445 0.03768 0.377 0.525
3395 43 1 0.435 0.03820 0.366 0.516
3428 41 1 0.424 0.03871 0.355 0.507
3445 40 1 0.413 0.03916 0.343 0.498
3574 37 1 0.402 0.03967 0.332 0.488
3584 34 1 0.390 0.04023 0.319 0.478
3762 30 1 0.377 0.04094 0.305 0.467
3839 27 1 0.363 0.04174 0.290 0.455
3853 25 1 0.349 0.04252 0.275 0.443
4079 17 1 0.328 0.04470 0.251 0.429
4191 13 1 0.303 0.04787 0.222 0.413
Start: AIC=1315.84
Surv(time = Time, event = Status) ~ Case_Number + Drug + Age +
Sex + ascites + hepatomegaly + spider + edema + bilirubin +
chelesterol + albumin + urine_copper + alkaline_phosphate +
SGOT + triglicerides + platelets + prothrombin + Disease_Stage
Step: AIC=1315.84
Surv(time = Time, event = Status) ~ Case_Number + Drug + Age +
Sex + ascites + hepatomegaly + spider + edema + bilirubin +
chelesterol + albumin + urine_copper + alkaline_phosphate +
SGOT + triglicerides + platelets + Disease_Stage
Df AIC
- spider 1 1314.0
- Case_Number 1 1314.0
- ascites 1 1314.2
- Drug 1 1314.4
- Age 1 1314.8
- Sex 1 1314.9
- hepatomegaly 1 1314.9
- chelesterol 1 1315.1
- triglicerides 1 1315.2
<none> 1315.8
- alkaline_phosphate 1 1316.1
- platelets 1 1317.3
- SGOT 1 1317.7
- edema 1 1319.0
- albumin 1 1321.9
- Disease_Stage 1 1323.6
- urine_copper 1 1325.2
- bilirubin 1 1326.0
Step: AIC=1314
Surv(time = Time, event = Status) ~ Case_Number + Drug + Age +
Sex + ascites + hepatomegaly + edema + bilirubin + chelesterol +
albumin + urine_copper + alkaline_phosphate + SGOT + triglicerides +
platelets + Disease_Stage
Df AIC
- Case_Number 1 1312.2
- ascites 1 1312.3
- Drug 1 1312.5
- hepatomegaly 1 1312.9
- Age 1 1313.0
- Sex 1 1313.2
- chelesterol 1 1313.3
- triglicerides 1 1313.4
<none> 1314.0
- alkaline_phosphate 1 1314.1
- platelets 1 1315.3
- SGOT 1 1315.8
- edema 1 1317.1
- albumin 1 1320.0
- Disease_Stage 1 1321.6
- urine_copper 1 1323.4
- bilirubin 1 1324.0
Step: AIC=1312.16
Surv(time = Time, event = Status) ~ Drug + Age + Sex + ascites +
hepatomegaly + edema + bilirubin + chelesterol + albumin +
urine_copper + alkaline_phosphate + SGOT + triglicerides +
platelets + Disease_Stage
Df AIC
- ascites 1 1310.5
- Drug 1 1310.7
- Age 1 1311.0
- hepatomegaly 1 1311.1
- Sex 1 1311.3
- chelesterol 1 1311.4
- triglicerides 1 1311.5
- alkaline_phosphate 1 1312.2
<none> 1312.2
- SGOT 1 1313.9
- platelets 1 1314.0
- edema 1 1315.8
- albumin 1 1318.0
- Disease_Stage 1 1319.8
- urine_copper 1 1321.4
- bilirubin 1 1322.1
Step: AIC=1310.54
Surv(time = Time, event = Status) ~ Drug + Age + Sex + hepatomegaly +
edema + bilirubin + chelesterol + albumin + urine_copper +
alkaline_phosphate + SGOT + triglicerides + platelets + Disease_Stage
Df AIC
- Drug 1 1309.0
- hepatomegaly 1 1309.4
- triglicerides 1 1309.5
- Age 1 1309.6
- chelesterol 1 1309.8
- Sex 1 1309.9
<none> 1310.5
- alkaline_phosphate 1 1310.9
- SGOT 1 1312.1
- platelets 1 1312.7
- edema 1 1314.8
- Disease_Stage 1 1318.4
- albumin 1 1318.6
- bilirubin 1 1320.7
- urine_copper 1 1321.3
Step: AIC=1309.04
Surv(time = Time, event = Status) ~ Age + Sex + hepatomegaly +
edema + bilirubin + chelesterol + albumin + urine_copper +
alkaline_phosphate + SGOT + triglicerides + platelets + Disease_Stage
Df AIC
- triglicerides 1 1307.7
- hepatomegaly 1 1308.0
- chelesterol 1 1308.2
- Sex 1 1308.4
- Age 1 1308.4
<none> 1309.0
- alkaline_phosphate 1 1309.3
- SGOT 1 1310.6
- platelets 1 1311.2
- edema 1 1313.3
- Disease_Stage 1 1316.7
- albumin 1 1317.3
- bilirubin 1 1318.8
- urine_copper 1 1319.6
Step: AIC=1307.73
Surv(time = Time, event = Status) ~ Age + Sex + hepatomegaly +
edema + bilirubin + chelesterol + albumin + urine_copper +
alkaline_phosphate + SGOT + platelets + Disease_Stage
Df AIC
- hepatomegaly 1 1306.8
- chelesterol 1 1306.8
- Sex 1 1307.0
- Age 1 1307.4
<none> 1307.7
- alkaline_phosphate 1 1308.0
- SGOT 1 1309.8
- platelets 1 1310.3
- edema 1 1312.4
- Disease_Stage 1 1315.0
- albumin 1 1315.4
- bilirubin 1 1317.4
- urine_copper 1 1317.8
Step: AIC=1306.77
Surv(time = Time, event = Status) ~ Age + Sex + edema + bilirubin +
chelesterol + albumin + urine_copper + alkaline_phosphate +
SGOT + platelets + Disease_Stage
Df AIC
- chelesterol 1 1306.0
- Sex 1 1306.1
- Age 1 1306.3
<none> 1306.8
- alkaline_phosphate 1 1307.0
- SGOT 1 1309.0
- platelets 1 1309.6
- edema 1 1311.7
- albumin 1 1315.2
- bilirubin 1 1316.8
- urine_copper 1 1317.1
- Disease_Stage 1 1319.5
Step: AIC=1306.05
Surv(time = Time, event = Status) ~ Age + Sex + edema + bilirubin +
albumin + urine_copper + alkaline_phosphate + SGOT + platelets +
Disease_Stage
Df AIC
- Age 1 1305.2
- Sex 1 1305.4
<none> 1306.0
- alkaline_phosphate 1 1306.2
- platelets 1 1308.4
- SGOT 1 1309.0
- edema 1 1310.0
- albumin 1 1314.9
- urine_copper 1 1315.7
- Disease_Stage 1 1318.1
- bilirubin 1 1322.3
Step: AIC=1305.21
Surv(time = Time, event = Status) ~ Sex + edema + bilirubin +
albumin + urine_copper + alkaline_phosphate + SGOT + platelets +
Disease_Stage
Df AIC
<none> 1305.2
- Sex 1 1305.6
- alkaline_phosphate 1 1305.9
- SGOT 1 1307.3
- platelets 1 1308.0
- edema 1 1308.8
- albumin 1 1315.7
- urine_copper 1 1315.7
- Disease_Stage 1 1318.3
- bilirubin 1 1321.5
Call:
coxph(formula = Surv(time = Time, event = Status) ~ Sex + edema +
bilirubin + albumin + urine_copper + alkaline_phosphate +
SGOT + platelets + Disease_Stage, data = df_pbc)
n= 312, number of events= 144
coef exp(coef) se(coef) z Pr(>|z|)
Sex -3.922e-01 6.756e-01 2.451e-01 -1.600 0.109557
edema 7.218e-01 2.058e+00 2.960e-01 2.439 0.014739 *
bilirubin 8.544e-02 1.089e+00 1.839e-02 4.645 3.4e-06 ***
albumin -8.490e-01 4.278e-01 2.352e-01 -3.610 0.000306 ***
urine_copper 3.461e-03 1.003e+00 9.245e-04 3.743 0.000181 ***
alkaline_phosphate -5.443e-05 9.999e-01 3.448e-05 -1.579 0.114430
SGOT 3.208e-03 1.003e+00 1.508e-03 2.127 0.033445 *
platelets 2.141e-01 1.239e+00 9.369e-02 2.285 0.022293 *
Disease_Stage 4.658e-01 1.593e+00 1.259e-01 3.701 0.000215 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
Sex 0.6756 1.4802 0.4179 1.0922
edema 2.0582 0.4859 1.1522 3.6766
bilirubin 1.0892 0.9181 1.0506 1.1292
albumin 0.4278 2.3373 0.2698 0.6784
urine_copper 1.0035 0.9965 1.0017 1.0053
alkaline_phosphate 0.9999 1.0001 0.9999 1.0000
SGOT 1.0032 0.9968 1.0003 1.0062
platelets 1.2388 0.8073 1.0310 1.4885
Disease_Stage 1.5932 0.6276 1.2450 2.0390
Concordance= 0.833 (se = 0.016 )
Likelihood ratio test= 190.5 on 9 df, p=<2e-16
Wald test = 209.4 on 9 df, p=<2e-16
Score (logrank) test = 290.3 on 9 df, p=<2e-16
* Dr AMITA SHARMA Post Doc from Erasmus University, Rotterdam, the Netherlands Assistant Professor Institute of Agri Business Management, Swami Keshwanand Rajasthan Agricultural University, Bikaner (Raj),India Blog: www.thinkingai.in
* ARUN KUMAR SHARMA Machine Learning Enthusiast 13 Years of Financial Services Marketing Exp Blogger, Writer and Machine Learning Consutlant Certified Business Analytics Professional Certified in Predictive Analytics, Indian Institute of Mnamagement,IIMx Bangalore Certified in Macroeconomic Forecasting, International Monetary Fund(IMFx) Certified in Text Analytics, openSAP Email: aks10000@gmail.com Tel:9468567418