cms assess, york, nov. 2002 adjusted survival graphs in spss ? by gilbert mackenzie & yasin...

CMS Assess, York, Nov. 2002

ADJUSTED SURVIVAL GRAPHS in SPSS ?

by

Gilbert MacKenzie & Yasin Al-tawarah

Centre for Medical Statistics


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.


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.


Models, Graphs & Software The most common survival model is:

COX’s 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 ?


Graphical Sense*

Represent the Process Authentically

Makes Statistical and Mathematical Sense

Reasonable Scales, etc

“Visual and Scientific Truth”

*Recall Alan Reese’s impromptu lecture last conference


tt|i

iii

)}n/d(exp{)t(S

i )t(

i)]}ˆxexp(/d[exp{)t(S

i0

}xexp{)t(S)x|t(S 0

Statistical Sense

Kaplan Meier

Adjusted Nelson-Aalen (Breslow variant)

where di is the number of deaths and ni is the number at risk at

time ti, for i =1,…, n subjects.


Adjusted Survival

Cox’s is invariant to x-location change (but not scale)

COXREG stores and not as one expects

Need to be clear about basics !

)xx( x

)ˆ)xxexp[()t(S)xx|t(S 0

S0(t), S(t|x) require the x’s used with in the model


Adjusted Survival - Categorical

Suppose x = (x1, x2): x1 is categorical & x2 is cont. Suppose x1 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 x2

ie What are the differences in x1 when ? 22 xx


}xxxexp{)t(S)x|t(S 2212121111

0

}xxexp{)t(S)x,,x|t(S 221111

0201 }xxexp{)t(S)x,,x|t(S 221212

0210

Adjusted Survival - Categorical

Fit a model with x11 and x12, using x10 as the reference and include x2.

Regression Model:

2212121111 xx.x

Adjusted Survival


Example 1 – Dialysis Survival study of Dialysis Patients n= 306

Fit 2 covariates: x1 = Referral Time, x2= Age.

Categories of x1 : x10 = <3mths (reference), x11 = 3mths-1yr, x12 = 1+yrs Analysis is “time to death or censoring”


Unadjusted Survival

Survival Time (years)

6543210

Cu

mu

lative

Pro

po

rtio

n S

urv

ivin

g 1.0

.8

.6

.4

.2

0.0

Referral

1+yrs

3 mnths 1 yr

lt 3 mnths


Adusted Survival - Coxreg

Time in Years

6543210

Cu

mu

lative

Pro

po

rtio

n S

urv

ivin

g1.0

.8

.6

.4

.2

0.0

Referral

1+yrs

3 mnths-1 yr

< 3 mnths


Adjusted Survival - not Coxreg

Time in Years

76543210

Cu

mu

lative

Pro

po

rtio

n S

urv

ivin

g1.0

.8

.6

.4

.2

0.0

Referral

1+yrs

3 mnths-1 yr

lt 3 mnths


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 3rd 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.


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


(KM – SPSS)Unadjusted Survival

Time in Years

6543210

Pro

po

rtio

n S

urv

ivin

g1.0

.8

.6

.4

.2

0.0

YEAR

2001

2000

1999

1998

1997

1996


Adjusted Survival by Year

Time in Years

543210

Pro

po

rtio

n S

urv

ivin

g

1.0

.8

.6

.4

.2

0.0

Year

2001

2000

1999

1998

1997

1996


Adjusted Survival - not Coxreg

Time in Years

6543210

Cu

mu

lative

Pro

po

rtio

n

Su

rviv

ing

1.0

.8

.6

.4

.2

0.0

YEAR

2001

2000

1999

1998

1997

1996


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.


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.


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 ?

cms assess, york, nov. 2002 adjusted survival graphs in spss ? by gilbert mackenzie & yasin...

Documents

adjusted survival slide

categorical x

categories of x

adjusted survival graphs

mean of x

adjusted survival coxs

adjusted survival curves

model slide