1. CMS Assess, York, Nov. 2002 ADJUSTED SURVIVAL GRAPHS in SPSS ? by Gilbert MacKenzie & Yasin Al-tawarah Centre for Medical Statistics

2. CMS Assess, York, Nov. 2002 Introduction There is a growing awareness generally of the importance of Evaluation in the Health and Education communities. A key factor in Evaluation has been the introduction, by Government, of: League Tables for example, for schools and hospitals. Formally, such data are observational and classically their statistical evaluation is by covariate adjustment.

3. CMS Assess, York, Nov. 2002 Time to Event League Table Data One key class of data to arise in this context is: Survival Data Time to Event Data leading to: Survival Graphs Adjusted Survival Graphs for crude and adjusted for case-mix comparisons, respectively.

4. CMS Assess, York, Nov. 2002 Models, Graphs & Software The most common survival model is: COXs PH model (1972) and so we should look at: PH Adjusted Survival Graph and of course PH Adjusted Survival Graph in SPSS *Does SPSS do a good job here ?

5. CMS Assess, York, Nov. 2002 Graphical Sense* Represent the Process Authentically Makes Statistical and Mathematical Sense Reasonable Scales, etc Visual and Scientific Truth *Recall Alan Reeses impromptu lecture last conference

6. CMS Assess, York, Nov. 2002 Statistical Sense Kaplan Meier Adjusted Nelson-Aalen (Breslow variant) where d i is the number of deaths and n i is the number at risk at time t i, for i =1,…, n subjects.

7. CMS Assess, York, Nov. 2002 Adjusted Survival Coxs is invariant to x-location change (but not scale) COXREG stores and not as one expects Need to be clear about basics ! S 0 (t), S(t|x) require the xs used with in the model

8. CMS Assess, York, Nov. 2002 Adjusted Survival - Categorical Suppose x = (x 1, x 2 ): x 1 is categorical & x 2 is cont. Suppose x 1 has 3 categories: 0, 1 and 2. Then we need to see 3 adjusted survival curves Where the adjustment is made at the mean of x 2 ie What are the differences in x 1 when ?

9. CMS Assess, York, Nov. 2002 Adjusted Survival - Categorical Fit a model with x 11 and x 12, using x 10 as the reference and include x 2. Regression Model: Adjusted Survival

10. CMS Assess, York, Nov. 2002 Example 1 – Dialysis Survival study of Dialysis Patients n= 306 Fit 2 covariates: x 1 = Referral Time, x 2 = Age. Categories of x 1 : x 10 = <3mths (reference), x 11 = 3mths-1yr, x 12 = 1+yrs Analysis is time to death or censoring

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14. CMS Assess, York, Nov. 2002 What, if anything, is Wrong? 1. Note the first Graph is KM (unadjusted) which shows the jumps of the process in each category 2. The second graph is Cox Adjusted, but it estimates a common 0 (t) and so is evaluated at every t, but the graphical procedure does not respect the jumps in the process in the separate categories – so you are led to think that the process jumps at the same time in every category! This is misleading. Also the follow-up time is wrong. The 3 rd graph produced by a macro corrects these mistakes and shows the jumps in each category separately. This is more authentic and the follow-up time is again correct.

15. CMS Assess, York, Nov. 2002 Example 2 – Elderly Facility Survival study of Elderly Patients 204 patients admitted to one Facility Between 1996 and 2001 Study conducted in 2002 Survival: Year of Admission adjusted for Age This is an example of suspicious mortality

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19. CMS Assess, York, Nov. 2002 The Same things are wrong again! 1.The first graph is OK 2.The second graph has the same process jumps at each time point in all years of entry to the study – now there is suspicious mortality – clockwork death!! - and propagates the wrong duration (4 years) in each year of entry. 3.The last graph produced by a specially written macro fixes all of these problems.

20. CMS Assess, York, Nov. 2002 Conclusions The SPSS adjusted survival graph procedure does not correctly reproduce the jumps in the underlying process in the categories or pattern. The SPSS procedure does not even faithfully represent the time-scale on which the process is measured The Adjusted Survival Graphs produced by SPSS are therefore not authentic and are potentially highly misleading especially in the type of comparisons considered in the last example.

21. CMS Assess, York, Nov. 2002 What is required ? The realisation by SPSS that 1. what they produce in Coxreg by way of graphical output is not what the user wants and is not helpful 2. their standard adjusted graph with a common 0 (t) is not properly produced with respect to time scale or to the jumps in the process in the categories of the pattern variable 3. the user always needs to see the Cox model compared with the data ie the KM curve. The final question is how long will it take to see these obvious corrections made ?