SlideShare a Scribd company logo
University of Toronto | 1
Cox Proportional Hazards Model:
Modeling Overall Survival Rates with Multi-Covariates
Supervisor: Lisa Wang (Biostatistician)
Presentation at Dlsph – Yisen Lin (MSc Candidate)
April 7th 2016
University of Toronto | 2
Content
• Research Site: Princess Margaret Cancer Centre
• General Outline
• Model Development:
- Overview of The Data
- Coxph Model Introduction
- Covariates Selection
- Model Validation
• Conclusion
• Acknowledgement
University of Toronto | 3
Princess Margaret Cancer Centre:
• Largest Cancer Centre in Canada
• One of 5 Largest Cancer Centre in the world
Biostatistics Department at PMCC:
• Supporting approx. 150 biostatisticial request
• Closely affiliated with DLSPH of utoronto
University of Toronto | 4
General Outline
1. Read/Understand Completed Clinical Trial Protocol
2. Reproduce the result of Data Analysis Part of
Completed Clinical Trial Study
3. Model Development and Validation on the Given
Datasets
My second term work is mainly focusing on
Part 3
University of Toronto | 5
Model Development
Overview of the data
2 Datasets for one model development
Covariates Listing:
1. Hb – Male 140-180g/L, Female 120-160g/L
(Looking for the effect below lower limit normal, LLN)
2. Plt 150-400g/L (Looking for ULN)
3. Na 135-145mmol/L (Looking for LLN)
4. Albumin 38-50g/L (Looking for LLN)
5. LD 125-220U/L (Looking for ULN)
Note: Above continuous covariates would be convert to binary outcome in model
6. Age
7. Gender
8. ECOG
9. No. of Metastatic Sites
10. No. of systematic therapies
Looking for Predictors for Overall Survival Using Cox ph model
University of Toronto | 6
Model Development
Overview of the data
Study. No. Start Date DOB
Gender(1=M,
0=F) ECOG Hb Platelet Neutrophil Lymphocyte NLR Na Albumin LDH
Metastatic
sites no
No.
Systemic Tx Start Date Stop date
Best
response by
RECIST
Date of
progression
Last date
of follow-
up Death
1 02-Apr-14 27-Aug-55 1 1 128 226 2.6 1.2 2.17 137 43 173 2 0 02-Apr-14 Ongoing PR NA
15-Dec-15
Alive
2 02-Apr-14 10-May-47 1 1 135 187 5.3 1.8 2.94 141 41 230 3 1 02-Apr-14 19-Aug-14 SD 19-Aug-14
15-Dec-15
Alive
3 03-Apr-14 21-Sep-54 0 1 98 306 7.9 0.2 39.50 133 32 338 4 1 03-Apr-14 23-Apr-14 PD 22-Apr-15
05-May-14
Deceased
4 03-Apr-14 19-Mar-55 1 1 132 173 3 0.4 7.50 139 44 228 2 2 03-Apr-14 24-Jul-14 SD 24-Jul-14
09-Sep-14
Deceased
5 07-Apr-14 19-Feb-60 0 1 105 367 6.4 1.3 4.92 135 38 248 2 1 07-Apr-14 08-Jul-14 SD 08-Jul-14
14-Apr-15
Deceased
6 08-Apr-14 06-Dec-61 0 1 120 345 5.2 0.8 6.50 132 37 230 4 6 08-Apr-14 11-Aug-14 SD 11-Aug-14
04-Sep-14
Deceased
7 16-Apr-14 13-May-52 0 1 103 144 3.2 0.7 4.57 137 36 318 3 2 16-Apr-14 22-Sep-14 PR NA
15-Dec-15
Alive
8 22-Apr-14 08-Mar-66 1 0 110 104 1.5 0.4 3.75 139 39 206 4 2 22-Apr-14 23-Jul-14 PD 23-Jul-14
15-Dec-15
Alive
9 23-Apr-14 20-Mar-51 0 1 97 332 4.5 0.3 15.00 137 34 594 4 2 23-Apr-14 03-Jul-14 PD 03-Jul-14
27-Sep-14
Deceased
10 24-Apr-14 11-Dec-45 0 1 122 243 5 1.6 3.13 134 39 401 1 1 24-Apr-14 23-Jun-14 PD 23-Jun-14
06-Jul-14
Deceased
11 28-Apr-14 10-Apr-71 1 1 106 246 9.5 1 9.50 142 35 436 3 2 28-Apr-14 21-May-14 NE 21-May-14
10-Jun-14
Deceased
12 09-May-14 10-Jan-73 0 1 122 247 4.7 0.8 5.88 137 44 413 2 0 09-May-14 27-Oct-14 PD 27-Oct-14
29-Oct-14
Alive
13 15-May-14 16-Aug-57 0 0 112 235 2.8 0.9 3.11 138 44 476 5 4 15-May-14 08-Aug-14 PD 08-Aug-14
05-May-15
Alive
14 27-May-14 06-Apr-69 1 1 123 178 4.1 1.6 2.56 142 43 178 0 3 27-May-14 09-Mar-15 SD 09-Mar-15
13-Apr-15
Alive
15 27-May-14 18-Feb-66 1 1 154 163 2.3 1.2 1.92 149 44 194 3 1 27-May-14 13-Jan-15 SD 13-Jan-15
15-Dec-15
Alive
16 03-Jun-14 09-Jan-43 0 1 92 212 3.5 2 1.75 137 36 479 1 1 03-Jun-14 01-Aug-14 PD 01-Aug-14
20-Sep-15
Alive
17 05-Jun-14 08-Sep-70 0 1 118 141 3 0.6 5.00 142 41 214 2 3 05-Jun-14 13-Aug-14 PD 13-Aug-14
19-Jan-15
Deceased
18 05-Jun-14 02-Apr-59 0 0 123 161 2.4 3 0.80 143 43 353 3 1 05-Jun-14 10-Nov-14 PD 10-Nov-14
14-Apr-15
Deceased
19 05-Jun-14 21-Jul-79 0 0 129 154 3 0.3 10.00 139 38 138 0 1 05-Jun-14 07-Aug-14 SD 07-Aug-14
27-Aug-14
Deceased
20 11-Jun-14 29-Jan-60 1 0 138 184 4.2 2 2.10 146 43 226 2 1 11-Jun-14 23-Jul-14 PD 23-Jul-14
30-Aug-15
Alive
21 19-Jun-14 08-Jan-70 1 0 151 286 2.3 1.2 1.92 137 42 210 2 3 19-Jun-14 Ongoing PR NA
15-Dec-15
Alive
Major Data Manipulation: Convert original continuous covariates to be
binary covariates
For example: Albumin 38-50g/L (Looking for LLN) means assign 1 to those albumin
level < 38g/L, assign 0 otherwise.
University of Toronto | 7
Kaplan Meier Plot for the OS
General look about the survival proportion without any model fitting
University of Toronto | 8
Cox Proportional Hazard Model
Introduction
Why this model?
1. Since we want to assess the effect of multiple covariates on overall Survival.
And Cox-proportional hazards is the most commonly used multivariable
survival method (we got 10)
2. Robustness: safe choice for many situation
3. The estimated hazard is always non-negative
4. Hazard rate and survival rate can be estimated under minimum assumptions
5. For example: Comparing with logistic model, it considers censoring info and
survival time. ( we are going to use logistic model for 90 day mortality for score
testing)
University of Toronto | 9
Covariates Selection
1. Using univariate analysis:
(with p-vlaue < 0.05 criteria to exclude non-significant covariates)
Hb Plt Na Albumin Ld
P-
value
0.0527 0.011 0.0779 2.07e^-5 0.0122
Age Gender Meta.no. Terapy.no. Ecog
P-
value
0.766 0.746 0.00237 0.0158
4.09e^
-9
(Hb, Na, Gender and Age have been removed from the model, and fit
Multivariate model with all the covariates p < 0.05)
University of Toronto | 10
Covariates Selection
2. Applied both forward and backward selection method:
(with the selection criteria smaller AIC and p-value < 0.05)
We get the same result (model is stable)
Covariates in Final Model
Albumin 38-50 g/L (LLN)
Number of Metastatic Sites
ECOG
For the final Model the C-index is 0.724
University of Toronto | 11
Covariates Selection
Model Diagnostics
The residual plot is almost symmetric around 0, which
indicates appropriate linearity assumption
University of Toronto | 12
Covariates Selection
Model Diagnostics
Testing For the Proportionality of all 3 covariates:
p value are all big enough implies there is no evidence for having
a non-proportional hazard. So the coxph we proposed is quite right
University of Toronto | 13
Model Validation On the 90 day
mortality
Using the same covariates as the coxph model on Overall Survival
Same dataset
Area under the curve is 0.6764,which is acceptable.
University of Toronto | 14
Model Validation On the 90 day
mortality
1. Note that the c-index for the logistic model is 0.724,which is already
quite close to 0.8 (we consider 0.8 as the boundary of the model having good
prediction ability .
2. In order to eliminate the effect of over optimism, we use bootstrap to find the modified c-index
(0.731), clearly even better
University of Toronto | 15
Conclusion
Current work
In addition to the work presented before, I also use the covariates
and the estimation of parameters generated from dataset1, and validate
the model in the dataset2.
(Since, from my view I am doing very similar thing as what I did on dataset1)
Result would be presented in the Report
A glance of the dataset 2
In order to make the definition of covariates consistent
We need to adjust the corresponding covariates from dataset 2
University of Toronto | 1

More Related Content

Viewers also liked

Systematic Review Of Observational Studies By Yusuf Abdu Misau
Systematic Review Of Observational Studies By Yusuf Abdu MisauSystematic Review Of Observational Studies By Yusuf Abdu Misau
Systematic Review Of Observational Studies By Yusuf Abdu MisauYusuf Misau
 
Classification and Regression Tree Analysis in Biomedical Research
Classification and Regression Tree Analysis in Biomedical Research Classification and Regression Tree Analysis in Biomedical Research
Classification and Regression Tree Analysis in Biomedical Research Salford Systems
 
Antiretroviral Treatment of Adult with HIV Infection The guidelines of Inter...
Antiretroviral Treatment of Adult with HIV Infection The guidelines of Inter...Antiretroviral Treatment of Adult with HIV Infection The guidelines of Inter...
Antiretroviral Treatment of Adult with HIV Infection The guidelines of Inter...
King Abdualziz Medical City -National Guard Health Affairs
 
Kshivets O. Esophageal Cancer Surgery
Kshivets O. Esophageal Cancer SurgeryKshivets O. Esophageal Cancer Surgery
Kshivets O. Esophageal Cancer Surgery
Oleg Kshivets
 
HIV epidemiology and pathogenesis
HIV epidemiology and pathogenesis HIV epidemiology and pathogenesis
HIV epidemiology and pathogenesis
prakashtu
 
HIV AIDS
HIV AIDSHIV AIDS
HIV AIDS
Malini Rajan
 

Viewers also liked (8)

Systematic Review Of Observational Studies By Yusuf Abdu Misau
Systematic Review Of Observational Studies By Yusuf Abdu MisauSystematic Review Of Observational Studies By Yusuf Abdu Misau
Systematic Review Of Observational Studies By Yusuf Abdu Misau
 
Classification and Regression Tree Analysis in Biomedical Research
Classification and Regression Tree Analysis in Biomedical Research Classification and Regression Tree Analysis in Biomedical Research
Classification and Regression Tree Analysis in Biomedical Research
 
Antiretroviral Treatment of Adult with HIV Infection The guidelines of Inter...
Antiretroviral Treatment of Adult with HIV Infection The guidelines of Inter...Antiretroviral Treatment of Adult with HIV Infection The guidelines of Inter...
Antiretroviral Treatment of Adult with HIV Infection The guidelines of Inter...
 
Part 2 Cox Regression
Part 2 Cox RegressionPart 2 Cox Regression
Part 2 Cox Regression
 
Hiv&aids in kenya
Hiv&aids in kenyaHiv&aids in kenya
Hiv&aids in kenya
 
Kshivets O. Esophageal Cancer Surgery
Kshivets O. Esophageal Cancer SurgeryKshivets O. Esophageal Cancer Surgery
Kshivets O. Esophageal Cancer Surgery
 
HIV epidemiology and pathogenesis
HIV epidemiology and pathogenesis HIV epidemiology and pathogenesis
HIV epidemiology and pathogenesis
 
HIV AIDS
HIV AIDSHIV AIDS
HIV AIDS
 

Similar to Yisen Lin's Term 2 Presentation

Proteomics_Chapter 3 Protein Identification.ppt
Proteomics_Chapter 3 Protein Identification.pptProteomics_Chapter 3 Protein Identification.ppt
Proteomics_Chapter 3 Protein Identification.ppt
ZaldaaZaldaa
 
High Throughput Screening for ARV Drugs in HIV Prevention Studies
High Throughput Screening for ARV Drugs in HIV Prevention StudiesHigh Throughput Screening for ARV Drugs in HIV Prevention Studies
High Throughput Screening for ARV Drugs in HIV Prevention Studies
HopkinsCFAR
 
Luigi Atzori Metabolomica: Introduzione e review di alcune applicazioni in am...
Luigi Atzori Metabolomica: Introduzione e review di alcune applicazioni in am...Luigi Atzori Metabolomica: Introduzione e review di alcune applicazioni in am...
Luigi Atzori Metabolomica: Introduzione e review di alcune applicazioni in am...
CRS4 Research Center in Sardinia
 
Application of Multivariate Regression Analysis and Analysis of Variance
Application of Multivariate Regression Analysis and Analysis of VarianceApplication of Multivariate Regression Analysis and Analysis of Variance
Application of Multivariate Regression Analysis and Analysis of Variance
Kalaivanan Murthy
 
Maldi tof-ms analysis in identification of prostate cancer
Maldi tof-ms analysis in identification of prostate cancerMaldi tof-ms analysis in identification of prostate cancer
Maldi tof-ms analysis in identification of prostate cancer
Moustafa Rezk
 
Ct lecture 20. survival analysis (part 2)
Ct lecture 20. survival analysis (part 2)Ct lecture 20. survival analysis (part 2)
Ct lecture 20. survival analysis (part 2)
Hau Pham
 
Wan Muhamad Amir et al., 2015
Wan Muhamad Amir et al., 2015Wan Muhamad Amir et al., 2015
Wan Muhamad Amir et al., 2015Min Pau Tan
 
Parametric Statistics
Parametric StatisticsParametric Statistics
Parametric Statistics
jennytuazon01630
 
GC-MS (Gas chromatography–mass spectrometry )
GC-MS (Gas chromatography–mass spectrometry )GC-MS (Gas chromatography–mass spectrometry )
GC-MS (Gas chromatography–mass spectrometry )
Parixit Prajapati
 
Determination of Elemental Impurities – Challenges of a Screening Method
Determination of Elemental Impurities – Challenges of a Screening MethodDetermination of Elemental Impurities – Challenges of a Screening Method
Determination of Elemental Impurities – Challenges of a Screening Method
SGS
 
2014 abstracs.pdf
2014 abstracs.pdf2014 abstracs.pdf
2014 abstracs.pdf
leroleroero1
 
EXPERIMENTAL IMPLEMENTATION OF EMBARRASINGLY PARALLEL PROCESS IN ANALYSIS OF ...
EXPERIMENTAL IMPLEMENTATION OF EMBARRASINGLY PARALLEL PROCESS IN ANALYSIS OF ...EXPERIMENTAL IMPLEMENTATION OF EMBARRASINGLY PARALLEL PROCESS IN ANALYSIS OF ...
EXPERIMENTAL IMPLEMENTATION OF EMBARRASINGLY PARALLEL PROCESS IN ANALYSIS OF ...
ijesajournal
 
Validation of bevacizumab elisa ich q2 ver3,0 dt14.03
Validation of bevacizumab elisa   ich q2 ver3,0 dt14.03Validation of bevacizumab elisa   ich q2 ver3,0 dt14.03
Validation of bevacizumab elisa ich q2 ver3,0 dt14.03
krishgen
 
Size-Exclusion Chromatography with On-Line Light-Scattering, Absorbance, and ...
Size-Exclusion Chromatography with On-Line Light-Scattering, Absorbance, and ...Size-Exclusion Chromatography with On-Line Light-Scattering, Absorbance, and ...
Size-Exclusion Chromatography with On-Line Light-Scattering, Absorbance, and ...
KBI Biopharma
 
Rodriguez_Ullmayer_Rojo_RUSIS@UNR_REU_Technical_Report
Rodriguez_Ullmayer_Rojo_RUSIS@UNR_REU_Technical_ReportRodriguez_Ullmayer_Rojo_RUSIS@UNR_REU_Technical_Report
Rodriguez_Ullmayer_Rojo_RUSIS@UNR_REU_Technical_Report​Iván Rodríguez
 
Ct lecture 17. introduction to logistic regression
Ct lecture 17. introduction to logistic regressionCt lecture 17. introduction to logistic regression
Ct lecture 17. introduction to logistic regression
Hau Pham
 
Complex sampling design & analysis
Complex sampling design & analysisComplex sampling design & analysis
Complex sampling design & analysis
International Islamic University Malaysia
 
36433 Topic HA W9 R1Number of Pages 1 (Double Spaced)N.docx
36433 Topic HA W9 R1Number of Pages 1 (Double Spaced)N.docx36433 Topic HA W9 R1Number of Pages 1 (Double Spaced)N.docx
36433 Topic HA W9 R1Number of Pages 1 (Double Spaced)N.docx
rhetttrevannion
 

Similar to Yisen Lin's Term 2 Presentation (20)

Proteomics_Chapter 3 Protein Identification.ppt
Proteomics_Chapter 3 Protein Identification.pptProteomics_Chapter 3 Protein Identification.ppt
Proteomics_Chapter 3 Protein Identification.ppt
 
High Throughput Screening for ARV Drugs in HIV Prevention Studies
High Throughput Screening for ARV Drugs in HIV Prevention StudiesHigh Throughput Screening for ARV Drugs in HIV Prevention Studies
High Throughput Screening for ARV Drugs in HIV Prevention Studies
 
Luigi Atzori Metabolomica: Introduzione e review di alcune applicazioni in am...
Luigi Atzori Metabolomica: Introduzione e review di alcune applicazioni in am...Luigi Atzori Metabolomica: Introduzione e review di alcune applicazioni in am...
Luigi Atzori Metabolomica: Introduzione e review di alcune applicazioni in am...
 
Chenomx
ChenomxChenomx
Chenomx
 
Application of Multivariate Regression Analysis and Analysis of Variance
Application of Multivariate Regression Analysis and Analysis of VarianceApplication of Multivariate Regression Analysis and Analysis of Variance
Application of Multivariate Regression Analysis and Analysis of Variance
 
Maldi tof-ms analysis in identification of prostate cancer
Maldi tof-ms analysis in identification of prostate cancerMaldi tof-ms analysis in identification of prostate cancer
Maldi tof-ms analysis in identification of prostate cancer
 
Ct lecture 20. survival analysis (part 2)
Ct lecture 20. survival analysis (part 2)Ct lecture 20. survival analysis (part 2)
Ct lecture 20. survival analysis (part 2)
 
Wan Muhamad Amir et al., 2015
Wan Muhamad Amir et al., 2015Wan Muhamad Amir et al., 2015
Wan Muhamad Amir et al., 2015
 
Parametric Statistics
Parametric StatisticsParametric Statistics
Parametric Statistics
 
GC-MS (Gas chromatography–mass spectrometry )
GC-MS (Gas chromatography–mass spectrometry )GC-MS (Gas chromatography–mass spectrometry )
GC-MS (Gas chromatography–mass spectrometry )
 
Determination of Elemental Impurities – Challenges of a Screening Method
Determination of Elemental Impurities – Challenges of a Screening MethodDetermination of Elemental Impurities – Challenges of a Screening Method
Determination of Elemental Impurities – Challenges of a Screening Method
 
2014 abstracs.pdf
2014 abstracs.pdf2014 abstracs.pdf
2014 abstracs.pdf
 
EXPERIMENTAL IMPLEMENTATION OF EMBARRASINGLY PARALLEL PROCESS IN ANALYSIS OF ...
EXPERIMENTAL IMPLEMENTATION OF EMBARRASINGLY PARALLEL PROCESS IN ANALYSIS OF ...EXPERIMENTAL IMPLEMENTATION OF EMBARRASINGLY PARALLEL PROCESS IN ANALYSIS OF ...
EXPERIMENTAL IMPLEMENTATION OF EMBARRASINGLY PARALLEL PROCESS IN ANALYSIS OF ...
 
14.2 Wahlen
14.2 Wahlen14.2 Wahlen
14.2 Wahlen
 
Validation of bevacizumab elisa ich q2 ver3,0 dt14.03
Validation of bevacizumab elisa   ich q2 ver3,0 dt14.03Validation of bevacizumab elisa   ich q2 ver3,0 dt14.03
Validation of bevacizumab elisa ich q2 ver3,0 dt14.03
 
Size-Exclusion Chromatography with On-Line Light-Scattering, Absorbance, and ...
Size-Exclusion Chromatography with On-Line Light-Scattering, Absorbance, and ...Size-Exclusion Chromatography with On-Line Light-Scattering, Absorbance, and ...
Size-Exclusion Chromatography with On-Line Light-Scattering, Absorbance, and ...
 
Rodriguez_Ullmayer_Rojo_RUSIS@UNR_REU_Technical_Report
Rodriguez_Ullmayer_Rojo_RUSIS@UNR_REU_Technical_ReportRodriguez_Ullmayer_Rojo_RUSIS@UNR_REU_Technical_Report
Rodriguez_Ullmayer_Rojo_RUSIS@UNR_REU_Technical_Report
 
Ct lecture 17. introduction to logistic regression
Ct lecture 17. introduction to logistic regressionCt lecture 17. introduction to logistic regression
Ct lecture 17. introduction to logistic regression
 
Complex sampling design & analysis
Complex sampling design & analysisComplex sampling design & analysis
Complex sampling design & analysis
 
36433 Topic HA W9 R1Number of Pages 1 (Double Spaced)N.docx
36433 Topic HA W9 R1Number of Pages 1 (Double Spaced)N.docx36433 Topic HA W9 R1Number of Pages 1 (Double Spaced)N.docx
36433 Topic HA W9 R1Number of Pages 1 (Double Spaced)N.docx
 

Yisen Lin's Term 2 Presentation

  • 1. University of Toronto | 1 Cox Proportional Hazards Model: Modeling Overall Survival Rates with Multi-Covariates Supervisor: Lisa Wang (Biostatistician) Presentation at Dlsph – Yisen Lin (MSc Candidate) April 7th 2016
  • 2. University of Toronto | 2 Content • Research Site: Princess Margaret Cancer Centre • General Outline • Model Development: - Overview of The Data - Coxph Model Introduction - Covariates Selection - Model Validation • Conclusion • Acknowledgement
  • 3. University of Toronto | 3 Princess Margaret Cancer Centre: • Largest Cancer Centre in Canada • One of 5 Largest Cancer Centre in the world Biostatistics Department at PMCC: • Supporting approx. 150 biostatisticial request • Closely affiliated with DLSPH of utoronto
  • 4. University of Toronto | 4 General Outline 1. Read/Understand Completed Clinical Trial Protocol 2. Reproduce the result of Data Analysis Part of Completed Clinical Trial Study 3. Model Development and Validation on the Given Datasets My second term work is mainly focusing on Part 3
  • 5. University of Toronto | 5 Model Development Overview of the data 2 Datasets for one model development Covariates Listing: 1. Hb – Male 140-180g/L, Female 120-160g/L (Looking for the effect below lower limit normal, LLN) 2. Plt 150-400g/L (Looking for ULN) 3. Na 135-145mmol/L (Looking for LLN) 4. Albumin 38-50g/L (Looking for LLN) 5. LD 125-220U/L (Looking for ULN) Note: Above continuous covariates would be convert to binary outcome in model 6. Age 7. Gender 8. ECOG 9. No. of Metastatic Sites 10. No. of systematic therapies Looking for Predictors for Overall Survival Using Cox ph model
  • 6. University of Toronto | 6 Model Development Overview of the data Study. No. Start Date DOB Gender(1=M, 0=F) ECOG Hb Platelet Neutrophil Lymphocyte NLR Na Albumin LDH Metastatic sites no No. Systemic Tx Start Date Stop date Best response by RECIST Date of progression Last date of follow- up Death 1 02-Apr-14 27-Aug-55 1 1 128 226 2.6 1.2 2.17 137 43 173 2 0 02-Apr-14 Ongoing PR NA 15-Dec-15 Alive 2 02-Apr-14 10-May-47 1 1 135 187 5.3 1.8 2.94 141 41 230 3 1 02-Apr-14 19-Aug-14 SD 19-Aug-14 15-Dec-15 Alive 3 03-Apr-14 21-Sep-54 0 1 98 306 7.9 0.2 39.50 133 32 338 4 1 03-Apr-14 23-Apr-14 PD 22-Apr-15 05-May-14 Deceased 4 03-Apr-14 19-Mar-55 1 1 132 173 3 0.4 7.50 139 44 228 2 2 03-Apr-14 24-Jul-14 SD 24-Jul-14 09-Sep-14 Deceased 5 07-Apr-14 19-Feb-60 0 1 105 367 6.4 1.3 4.92 135 38 248 2 1 07-Apr-14 08-Jul-14 SD 08-Jul-14 14-Apr-15 Deceased 6 08-Apr-14 06-Dec-61 0 1 120 345 5.2 0.8 6.50 132 37 230 4 6 08-Apr-14 11-Aug-14 SD 11-Aug-14 04-Sep-14 Deceased 7 16-Apr-14 13-May-52 0 1 103 144 3.2 0.7 4.57 137 36 318 3 2 16-Apr-14 22-Sep-14 PR NA 15-Dec-15 Alive 8 22-Apr-14 08-Mar-66 1 0 110 104 1.5 0.4 3.75 139 39 206 4 2 22-Apr-14 23-Jul-14 PD 23-Jul-14 15-Dec-15 Alive 9 23-Apr-14 20-Mar-51 0 1 97 332 4.5 0.3 15.00 137 34 594 4 2 23-Apr-14 03-Jul-14 PD 03-Jul-14 27-Sep-14 Deceased 10 24-Apr-14 11-Dec-45 0 1 122 243 5 1.6 3.13 134 39 401 1 1 24-Apr-14 23-Jun-14 PD 23-Jun-14 06-Jul-14 Deceased 11 28-Apr-14 10-Apr-71 1 1 106 246 9.5 1 9.50 142 35 436 3 2 28-Apr-14 21-May-14 NE 21-May-14 10-Jun-14 Deceased 12 09-May-14 10-Jan-73 0 1 122 247 4.7 0.8 5.88 137 44 413 2 0 09-May-14 27-Oct-14 PD 27-Oct-14 29-Oct-14 Alive 13 15-May-14 16-Aug-57 0 0 112 235 2.8 0.9 3.11 138 44 476 5 4 15-May-14 08-Aug-14 PD 08-Aug-14 05-May-15 Alive 14 27-May-14 06-Apr-69 1 1 123 178 4.1 1.6 2.56 142 43 178 0 3 27-May-14 09-Mar-15 SD 09-Mar-15 13-Apr-15 Alive 15 27-May-14 18-Feb-66 1 1 154 163 2.3 1.2 1.92 149 44 194 3 1 27-May-14 13-Jan-15 SD 13-Jan-15 15-Dec-15 Alive 16 03-Jun-14 09-Jan-43 0 1 92 212 3.5 2 1.75 137 36 479 1 1 03-Jun-14 01-Aug-14 PD 01-Aug-14 20-Sep-15 Alive 17 05-Jun-14 08-Sep-70 0 1 118 141 3 0.6 5.00 142 41 214 2 3 05-Jun-14 13-Aug-14 PD 13-Aug-14 19-Jan-15 Deceased 18 05-Jun-14 02-Apr-59 0 0 123 161 2.4 3 0.80 143 43 353 3 1 05-Jun-14 10-Nov-14 PD 10-Nov-14 14-Apr-15 Deceased 19 05-Jun-14 21-Jul-79 0 0 129 154 3 0.3 10.00 139 38 138 0 1 05-Jun-14 07-Aug-14 SD 07-Aug-14 27-Aug-14 Deceased 20 11-Jun-14 29-Jan-60 1 0 138 184 4.2 2 2.10 146 43 226 2 1 11-Jun-14 23-Jul-14 PD 23-Jul-14 30-Aug-15 Alive 21 19-Jun-14 08-Jan-70 1 0 151 286 2.3 1.2 1.92 137 42 210 2 3 19-Jun-14 Ongoing PR NA 15-Dec-15 Alive Major Data Manipulation: Convert original continuous covariates to be binary covariates For example: Albumin 38-50g/L (Looking for LLN) means assign 1 to those albumin level < 38g/L, assign 0 otherwise.
  • 7. University of Toronto | 7 Kaplan Meier Plot for the OS General look about the survival proportion without any model fitting
  • 8. University of Toronto | 8 Cox Proportional Hazard Model Introduction Why this model? 1. Since we want to assess the effect of multiple covariates on overall Survival. And Cox-proportional hazards is the most commonly used multivariable survival method (we got 10) 2. Robustness: safe choice for many situation 3. The estimated hazard is always non-negative 4. Hazard rate and survival rate can be estimated under minimum assumptions 5. For example: Comparing with logistic model, it considers censoring info and survival time. ( we are going to use logistic model for 90 day mortality for score testing)
  • 9. University of Toronto | 9 Covariates Selection 1. Using univariate analysis: (with p-vlaue < 0.05 criteria to exclude non-significant covariates) Hb Plt Na Albumin Ld P- value 0.0527 0.011 0.0779 2.07e^-5 0.0122 Age Gender Meta.no. Terapy.no. Ecog P- value 0.766 0.746 0.00237 0.0158 4.09e^ -9 (Hb, Na, Gender and Age have been removed from the model, and fit Multivariate model with all the covariates p < 0.05)
  • 10. University of Toronto | 10 Covariates Selection 2. Applied both forward and backward selection method: (with the selection criteria smaller AIC and p-value < 0.05) We get the same result (model is stable) Covariates in Final Model Albumin 38-50 g/L (LLN) Number of Metastatic Sites ECOG For the final Model the C-index is 0.724
  • 11. University of Toronto | 11 Covariates Selection Model Diagnostics The residual plot is almost symmetric around 0, which indicates appropriate linearity assumption
  • 12. University of Toronto | 12 Covariates Selection Model Diagnostics Testing For the Proportionality of all 3 covariates: p value are all big enough implies there is no evidence for having a non-proportional hazard. So the coxph we proposed is quite right
  • 13. University of Toronto | 13 Model Validation On the 90 day mortality Using the same covariates as the coxph model on Overall Survival Same dataset Area under the curve is 0.6764,which is acceptable.
  • 14. University of Toronto | 14 Model Validation On the 90 day mortality 1. Note that the c-index for the logistic model is 0.724,which is already quite close to 0.8 (we consider 0.8 as the boundary of the model having good prediction ability . 2. In order to eliminate the effect of over optimism, we use bootstrap to find the modified c-index (0.731), clearly even better
  • 15. University of Toronto | 15 Conclusion Current work In addition to the work presented before, I also use the covariates and the estimation of parameters generated from dataset1, and validate the model in the dataset2. (Since, from my view I am doing very similar thing as what I did on dataset1) Result would be presented in the Report A glance of the dataset 2 In order to make the definition of covariates consistent We need to adjust the corresponding covariates from dataset 2