ACKNOWELDGEMENT & DISCLAIMER



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.

Survival Analysis: Explainer

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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

Survival Analysis of Patients after Heart Transplant

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OVERVIEW OF THE DATASET

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

DATASET IN TABLE VIEW

KAPLAN MEIER MODEL

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

PLOT OF KM MODEL

AGE GROUP WISE PLOT OF KM MODEL

COX PROP. HAZARD MODEL

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

PLOT OF CHP MODEL

RANDOM FOREST MODEL

KM,CPH,RF COMPARISON

Survival Analysis of Ovarian Cancer Patients

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OVERVIEW OF THE DATASET

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

DATASET IN TABLE VIEW

KAPLAN MEIER MODEL

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

PLOT OF KM MODEL

AGE GROUP WISE PLOT OF KM MODEL

COX PROP. HAZARD MODEL

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

PLOT OF CHP MODEL

RANDOM FOREST MODEL

KM,CPH,RF COMPARISON

Survival Analysis of Cervical Cancer Patients

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OVERVIEW OF THE DATASET

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

DATASET IN TABLE VIEW

KAPLAN MEIER MODEL

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

PLOT OF KM MODEL

GROUP WISE PLOT OF KM MODEL

COX PROP. HAZARD MODEL

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

PLOT OF CHP MODEL

RANDOM FOREST MODEL

KM,CPH,RF COMPARISON

Survival Analysis of Primary Biliary Cirrhosis Patients

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OVERVIEW OF THE DATASET

PRIMARY BILIARY CIRRHOSIS DATASET: Explainer

The dayse contains the trial in primary biliary cirrhosis (PBC) of the liver conducted between 1974 and 1984.
A total of 424 PBC patients, referred to Mayo Clinic during that ten-year interval, met eligibility criteria for the randomized placebo controlled trial of the drug D-penicillamine. The first 312 cases in the data set participated in the randomized trial and contain largely complete data. Missing data items are denoted by “.”

Following variables are in the dataset:

Case_Number: case number Time: number of days status: 1=Earlier Death, 2=Transplantation and 0=No Death in study time Drug: 1= D-penicillamine, 2=placebo Age: age in days sex: 0=male, 1=female ascites: presence of ascites: 0=no 1=yes hepatomegaly: presence of hepatomegaly 0=no 1=yes spiders: presence of spiders 0=no 1=yes edema: presence of edema 0=no edema and no diuretic therapy for edema; .5 = edema present without diuretics, or edema resolved by diuretics; 1 = edema despite diuretic therapy bilirubin: serum bilirubin in mg/dl cholesterol: serum cholesterol in mg/dl albumin: albumin in gm/dl urine_copper: urine copper in ug/day alkaline_phosphate: alkaline phosphatase in U/liter SGOT: SGOT in U/ml tryglicerdes: triglicerides in mg/dl platelets: platelets per cubic ml / 1000 prothrombin: prothrombin time in seconds Disease_Stage: histologic stage of disease


DATASET IN TABLE VIEW

KAPLAN MEIER MODEL

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

PLOT OF KM MODEL

DRUG WISE PLOT OF KM MODEL

COX PROP. HAZARD MODEL

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

PLOT OF CHP MODEL

RANDOM FOREST MODEL

KM,CPH,RF COMPARISON

About Us

DASHBOARD PREPARED BY (CONTACT FOR MACHINE LEARNING TRAINING, COACHING & CONSULTING)

* 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: Tel:9468567418