1. Practical Solutions Additional Regression techniques

2. 2 1.To produce the basic Cox regression output requires syntax such as: Practical Solutions: Instructions * Producing the basic Cox model. COXREG time /STATUS=status(1) /CONTRAST (ln_yesno)=Indicator(1) /METHOD=ENTER ln_yesno /PRINT=CI(95) /CRITERIA=PIN(.05) POUT(.10) ITERATE(20).

3. 3 Practical Solutions: Output There is a highly significant difference between the survival, dependent on whether the cancer is within the lymph nodes or not (p<0.001). Survival is better when the cancer is not in the lymph nodes. The hazard ratio for when it is present, relative to when it isn’t, is 2.52 (95% CI: 1.58 to 4.02).

4. 4 Practical Solutions: Instructions * The full Cox model, saving the residuals. COXREG time /STATUS=status(1) /PATTERN BY ln_yesno /CONTRAST (ln_yesno)=Indicator(1) /METHOD=ENTER pathsize age ln_yesno /SAVE=PRESID /PLOT SURVIVAL /PRINT=CI(95) /CRITERIA=PIN(.05) POUT(.10) ITERATE(20). * The stratified model to produce the LML plot. COXREG time /STATUS=status(1) /STRATA=ln_yesno /METHOD=ENTER pathsize age /PLOT LML /CRITERIA=PIN(.05) POUT(.10) ITERATE(20). 2.To produce the full set of output for the controlled Cox model requires the following:

5. 5 Practical Solutions: Output

6. 6 Within Cox regression (using the PLOT button) it is possible to produce a plot of the survival function split by one of the categorical variables and plotted at the mean of the other continuous outcome variables. This is in effect an adjusted Kaplan-Meier curve, but it is not that commonly seen.

7. 7 Practical Solutions: Output

8. 8 * Calculating the ranks. RANK VARIABLES=time (A) /RANK /PRINT=YES /TIES=MEAN. * Plotting the residuals. GRAPH /SCATTERPLOT(BIVAR)=Rtime WITH PR1_1 /MISSING=LISTWISE /TITLE= 'Plot of partial residuals against rank time'.

9. 9 Practical Solutions: Output * Plotting the residuals. GRAPH /SCATTERPLOT(BIVAR)=Rtime WITH PR2_1 /MISSING=LISTWISE /TITLE= 'Plot of partial residuals against rank time'.

10. 10 Practical Solutions: Output * Plotting the residuals. GRAPH /SCATTERPLOT(BIVAR)=Rtime WITH PR3_1 /MISSING=LISTWISE /TITLE= 'Plot of partial residuals against rank time'.

11. 11 Practical Solutions: Comments The log-log plot indicates no significant evidence against the PH assumption. The partial residual plots are also pretty good, although there are a seemingly small number of points. The key factor here is that we have a small number of actual events (72) despite the 1207 cases and partial residuals cannot be calculated for censored cases.

12. 12 Practical Solutions: Comments Age has no significant effect on survival but its inclusion means that the other variables are age adjusted. The size of the tumour is highly significant in regards to survival, with each cm increase in size increasing the hazard by 71%: hazard ratio of 1.71 (95% CI: 1.43 to 2.05). There is a highly significant difference between the survival, dependent on whether the cancer is within the lymph nodes or not (p=0.024). Survival is still better when the cancer is not in the lymph nodes but the effect is now not as large as it was without including the other variables. The hazard ratio for when it is present, relative to when it isn’t, is 1.79 (95% CI: 1.08 to 2.98).

13. 13 Practical Solutions 3) Putting CAT2 in as the dependent variable, GROUP in as the only covariate and setting GROUP up as a categorical variable with the last level (Placebo group) as the reference leads to the above final model result.

14. 14 Practical Solutions There is no significant difference in odds of CAT2>=7 between the groups (p=0.150). As the highest level of CAT2 is >=7 then this is what is being modelled. Therefore the odds ratio listed for GROUP(1) is the odds ratio for Active A compared to placebo. As it is less than 1 (0.506) it means that Active A is 0.506 times more likely (i.e. less likely) to have a CAT2 value >=7 than the placebo group, although this result does not quite reach statistical significance at the 5% level (p=0.053). Notice the CI for the odds ratios cross 1 and are hence non-significant.

15. 15 Practical Solutions 4) With the addition of the extra variables there are now differences in odds between the groups. Again, as the highest level of CAT2 is >=7 then this is what is being modelled. Therefore the odds ratio listed for GROUP(1) is the odds ratio for Active A compared to placebo. As it is less than 1 (0.240) it means that Active A is 0.240 times more likely (i.e. less likely) to have a CAT2 value >=7 than the placebo group, having adjusted for baseline level and gender and this is statistically significant (p=0.013).

16. 16 Practical Solutions If we want to express the results as the odds of a CAT2 score <7 then we could rearrange the levels of CAT2 (making <7 the highest category) and refit the model or we can take the reciprocal of the odds ratio (1 / odds ratio i.e. 1 / 0.240 = 4.17 here). Therefore the odds of the Active A group of having a CAT2 score <7 are 4.17 times greater than for the placebo group once we adjust for baseline level and gender. Odds ratios >1 are generally easier to interpret and understand.

17. Survival Analysis: An Introductory Course Session Questions and Answers

18. 18 Session Questions & Answers For the Breast cancer dataset: 1.What was the unadjusted hazard ratio for lymph node involvement? What did this hazard ratio change to having adjusted for age and size of tumour and would it alter your conclusions? A)2.52 (95%CI: 1.58 to 4.02) 1.79 (95% CI: 1.08 to 2.98) 2.How would you interpret this adjusted hazard ratio? A)A patient with lymph node involvement (of a given age and tumour size) who has not yet died by a certain time, is 79% more likely to die by the next point in time than a similar patient with no lymph node involvement.