1. DEMONSTRATION OF USING SPSS Logistic Regression Models for Prediction 2016/11/71

2. PPDAC Problem To indentify the women undergoing curative surgery for squamous cell carcinomas (SCC) at cervix who were potentially at high risk of recurrence using tumor characteristics and age. Plan Design: A prospective study. Year: Between August 1991 and August 1993. Setting: A gyneoncologic clinic at a tertiary center. Data The number of recurrent cases was 38 and the number of non recurrent cases was 61. Tumor markers SCC and CEA, tumor size, histological grade and age were collected. 2016/11/72

3. DATA ANALYSIS Descriptive statistics  Numbers such as five number summary.  Tables such as frequency tables.  Graphs such as histograms and boxplots. Inferential statistics  Bivariate analysis.  Multivariable analysis. 2016/11/73

4. CAN THE SERUM SCC DISTINGUISH BETWEEN RECURRENT AND NON RECURRENT CERVICAL CANCERS? Is SCC a ‘good’ predictor for recurrence?  A good predictor is one that can increase prediction accuracy such as sensitivity and specificity.  A good predictor should possess sufficient discriminatory power calculated as, for example, the area under the receiver operating characteristic (ROC) curve. 2016/11/74

5. SCC BY RECURRENCE STATUS 2016/11/75

6. PREDICTION USING BOTH TUMOR SIZE AND SCC Can the addition of tumor size for prediction increase the prediction accuracy significantly as compared to the prediction using SCC alone? 2016/11/76

7. A SCATTERPLOT OF TUMOR SIZE VERSUS LOG TRANSFORMED SCC 2016/11/77 r: recurrent case

8. DISCRIMINANT FUNCTION 2016/11/78 Reproduced from online Cross Validated: http://stats.stackexchange.com/questions/111421/reproduce-linear-discriminant-analysis- projection-plot

9. LOGISTIC REGRESSION Outcome variable/ dependent variable (DV)  Recurrence or non recurrence. Predictor variables / independent variables (IV)  Age, tumor markers SCC and CEA, tumor size, histopathological grade. Logit models  Predicted log odds of a DV is so called Logit (P) where P is the probability of occurrence. The logistic regression assumes that Logit (P) =  0+  1  (IV1)+  2  (IV2)+…+  k  (IVk). 2016/11/79

10. SCORE FUNCTION Score=  0+  1  (IV1)+  2  (IV2)+…+  k  (IVk)  It is a hyperplane on the k-dimensional space (IV1, IV2, …, IVk).  On a 2D space, it is a line.  On a 3D space, it is a plane. Under the logit model, the risk of an event, P, is related to the score by  P=exp(score)/(1+exp(score)).  http://www.meta-calculator.com/online/http://www.meta-calculator.com/online/ 2016/11/710

11. A SCATTERPLOT OF TUMOR SIZE VERSUS LOG TRANSFORMED SCC 2016/11/711 r: recurrent case

12. PARSIMONIOUS PREDICTION MODELS  Selection of predictor variables  Forward selection, backward elimination, stepwise select, best subset selection.  Adjusted R square, Mallow’s Cp, Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC).  Assessment of the performance of prediction models  Calibration.  Discrimination.  Cross validation. 2016/11/712

13. LOGIT MODELS FOR PREDICTION OF RECURRENCE OF CERVICAL CANCERS Logit (P)=  0+  1  SCC Logit (P)=  0+  1  SCC+  2  COLPO Logit (P)=  0+  1  SCC+  2  COLPO+  3  AGE … Logit (P) =  0+  1  age+  2  stage+  3  SCC+  4  CEA+  5  COLPO. All possible models are 2 5. The goal is to select parsimonious prediction models and compare their performance. 2016/11/713

14. THANK YOU FOR YOUR ATTENTION 2016/11/714