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Online supplement for the manuscript:

Analysis of Risk Factors Associated with Renal Function

Trajectory Over Time: A Comparison of Different Statistical

Approaches

Karen Leffondré1, Julie Boucquemont1, Giovanni Tripepi3, Vianda S. Stel4, Georg Heinze2, Daniela Dunkler2 1. University of Bordeaux, ISPED, Centre INSERM U897-Epidemiology-Biostatistics, Bordeaux, France 2. Medical University of Vienna, Center for Medical Statistics, Informatics and Intelligent Systems, Vienna, Austria 3. CNR-IBIM/IFC, Clinical Epidemiology and Physiopathology of Renal Diseases and Hypertension of Reggio Calabria, Calabria,

Italy 4. Academic Medical Center, ERA-EDTA Registry, Dept. Medical Informatics, Amsterdam, Netherlands

July 2014

Table of Contents Analyses in SPSS (Version 21) ........................................................................................................................................... 2

Naive linear regression on invidiual slopes ................................................................................................................... 2

Generalized estimating equations ................................................................................................................................ 8

Linear mixed model..................................................................................................................................................... 15

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Analyses in SPSS (Version 21) The data set can be opened in SPSS:

We assume that the reader is familiar with descriptive analyses in SPSS. We directly proceed to outcome analyses of

this data set, investigating the impact of risk factors age, gender, microalbuminuria at baseline and

macroalbuminuria at baseline on the speed of progression of CKD.

Naive linear regression on invidiual slopes This approach consists of two steps:

1) estimation of patient-specific slopes of GFR, 2) regression of slopes on risk factors.

To estimate patient-specific slopes of GFR, we first ‘split‘ the data by patient ID to have any statistical analyses to

follow carried out on each patient separately. This can be achieved by calling the dialogue Data Split File

and request Organize output by groups.

Move the following three variables into the field Groups based on:

Patient identifier [patient]

Microalbuminuria at baseline [micro]

Macroalbuminuria at baseline [macro]

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as shown below:

Next, we call linear regression by Analyze Regression Linear...:

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Simply move GFR [GFR] into the field labelled Dependent: and Time in years since baseline

[time] into the field Independent(s). Next, click on Save...:

Here, check Create coefficient statistics and type in a name for the dataset that will later contain the

slopes and intercepts per patient (e.g., Slopes).

Click on Continue and in the main linear regression dialogue, click on OK.

Don’t be surprised, a lot of output – containing the individual regression analysis for each patient - is generated now.

Most importantly, a third SPSS window opens, holding the data set with the patient-individual slopes (and some

more information):

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Call Data Select Cases:

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Check the button If condition is satisfied and specify If ROWTYPE_=“EST“. Then click on OK. This

will make sure that we can directly access the slopes per patient which are contained in rows where the variable

ROWTYPE_ contains the text EST. Actually, the slopes are in the variable Time in years since baseline

[time] since they are the regression coefficients corresponding to this variable in our former regression analysis.

The last step consists in calling linear regression (Analyze Regression Linear...) with Time in

years since baseline [time] (a/k/a the slopes) and Microalbuminuria at baseline [micro]

and Macroalbuminuria at baseline [macro] as the independent variables:

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The effects of micro- or macroalbuminuria on the speed of progression will then be evaluated:

Coefficientsa

Model

Unstandardized Coefficients Standardized Coefficients

t Sig. B Std. Error Beta

1 (Constant) -1,746 ,476 -3,665 ,000

Microalbuminuria at baseline -3,138 ,722 -,319 -4,348 ,000

Macroalbuminuria at baseline

-3,836 ,736 -,383 -5,214 ,000

a. Dependent Variable: Time in years since baseline

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Generalized estimating equations Although the model is more complex, it is actually much quicker to request a generalized estimating equations

analysis.

Simply go back to the original data set, and undo the splitting per cases (Data Split File):

Check Analyze all cases, do not create groups. Click OK.

Go to Analyze Generalized linear models Generalized estimating equations.

Follow the instructions below:

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10

11

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Here, click on Options to specify the reference categories for the categorical covariates (called ‘Factors‘ by SPSS):

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Check Descending and click Continue.

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There is nothing to specify at the remaining tabs. Click OK.

The parameter estimates of the GEE model will be shown in the output window:

Parameter Estimates

Parameter B Std. Error

95% Wald Confidence Interval Hypothesis Test

Lower Upper Wald Chi-

Square df Sig.

(Intercept) 81,382 3,8083 73,918 88,847 456,668 1 ,000 [gender=1] -2,987 1,9546 -6,818 ,844 2,335 1 ,126 [gender=0] 0

a . . . . . .

[micro=1] -20,235 1,7927 -23,749 -16,721 127,402 1 ,000 [micro=0] 0

a . . . . . .

[macro=1] -28,716 2,1087 -32,849 -24,583 185,446 1 ,000 [macro=0] 0

a . . . . . .

time -1,630 ,3727 -2,361 -,900 19,137 1 ,000 age -,256 ,0583 -,370 -,142 19,308 1 ,000 [micro=1] * time -1,557 ,5209 -2,578 -,536 8,934 1 ,003 [micro=0] * time 0

a . . . . . .

[macro=1] * time -1,053 ,6986 -2,423 ,316 2,274 1 ,132 [macro=0] * time 0

a . . . . . .

(Scale) 251,425 Dependent Variable: GFR Model: (Intercept), gender, micro, macro, time, age, micro * time, macro * time a. Set to zero because this parameter is redundant.

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Linear mixed model The mixed model can also be obtained using a single menu call. Call Analyze Mixed Models

Linear...:

Move Patient identifier [patient] into the field Subjects:

Click on Continue.

Next, specify the dependent an indpendent variables (Factors and Covariates) as below:

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Click on Fixed... to define the way the independent variables are assumed to affect the dependent variable:

Move all independent variables, as well as the interaction of micro and macro with time into the Model field. Click

Continue.

Next, click Random... to define the random effects.

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Move time into the Model field and check Include intercept. Select as covariance type Compound

Symmetry: Heterogenous. (Some other heterogenous covariance types with nonzero off-diagonals will also

lead to same result here.) Move Patient identifier [patient] into Combinations.

Click Continue.

Click on Estimation and select Maximum likelihood (ML).

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Click on Statistics and select Parameter estimates, and Covariances of random effects.

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Finally click on OK.

In the results table (below), you will notice that SPSS will use the first level of each factor as the reference category,

without offering any options to change this. This does not change the interpretation of the main results.

Estimates of Fixed Effectsa

Parameter Estimate Std. Error df t Sig.

95% Confidence Interval

Lower Bound Upper Bound

Intercept 35,813413 4,176224 198,483 8,576 ,000 27,577949 44,048877 [gender=0] 2,618476 1,677175 197,213 1,561 ,120 -,689024 5,925976 [gender=1] 0

b 0 . . . . .

[micro=0] 18,399486 1,871395 194,979 9,832 ,000 14,708711 22,090261 [micro=1] 0

b 0 . . . . .

[macro=0] 26,564716 1,892764 198,486 14,035 ,000 22,832208 30,297225 [macro=1] 0

b 0 . . . . .

time -7,752907 ,825541 187,832 -9,391 ,000 -9,381431 -6,124383 age -,287394 ,051415 197,213 -5,590 ,000 -,388787 -,186001 [micro=0] * time 2,920882 ,636944 177,043 4,586 ,000 1,663902 4,177861 [micro=1] * time 0

b 0 . . . . .

[macro=0] * time 3,091009 ,668498 189,621 4,624 ,000 1,772362 4,409656 [macro=1] * time 0

b 0 . . . . .

a. Dependent Variable: GFR. b. This parameter is set to zero because it is redundant.