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Bootstrapping in logistic regression - c statistic

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Georgios Chalikias
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Bootstrapping in logistic regression - c statistic

Georgios Chalikias
Dear All,

At the moment I am building a prediction model (logistic regression).

I need to validate my model, therefore I decided to "shrink" the
optimism of the model by bootstrapping method.

However, when the bootstrapping command is ON in PASW-SPSS 18 I cannot
save the predicted probabilities in order to calculate the c-statistic
(via AUC of the pre1) of all the bootsrapping derived models.

Can anyone help me ?

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Marta Garcia-Granero
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Re: Bootstrapping in logistic regression - c statistic

Marta Garcia-Granero
Georgios Chalikias wrote:

> At the moment I am building a prediction model (logistic regression).
>
> I need to validate my model, therefore I decided to "shrink" the
> optimism of the model by bootstrapping method.
>
> However, when the bootstrapping command is ON in PASW-SPSS 18 I cannot
> save the predicted probabilities in order to calculate the c-statistic
> (via AUC of the pre1) of all the bootsrapping derived models.
>
>
Kalimera Georgios!

When I beta tested PASW 18 I criticized the fact that the bootstrap
module ignored some statistics (like r-square in linear and logistic
regression). I finally wrote my own bootstrap program to get them. I'm
attaching a sample dataset (Shapiro.txt, I can't attach it as a SAV
file) to show you how to use it:

* First, import data from text (variable names are at 1st row) & label
variables *.
VAR LABEL ocu 'Oral contraceptive use' /case 'Myocardial infarction'.
VALUE LABEL  Agegrp
 1 '25-29 years'
 2 '30-34 years'
 3 '35-39 years'
 4 '40-44 years'
 5 '45-49 years'.
VALUE LABEL Smoke
 1 'Non smoker'
 2  '1-24 cig/day'
 3  ' >=25 cig/day'.
VALUE LABEL ocu 0 'No' 1 'Yes'.
VALUE LABEL case 0'Control' 1 'Case'.
* Replace Agegrp by MeanAge for regression model *.
COMPUTE MeanAge=27+(Agegrp-1)*5.
FORMAT MeanAge (F8).
VAR LABEL MeanAge 'Mean group age (years)'.

DATASET NAME OriginalData.

* Creating 100 (k) Boot Samples *.
* These steps are fully automatic, the only modifiable step is k (number
of samples) *.

DATASET DECLARE BootData.
PRESERVE.
* Use Mersenne Twister as random number generator *.
SET RNG=MT MTINDEX=RANDOM.
SET MXLOOPS=100. /* Should not be smaller than k *.

* Matrix program. WARNING: all variables must be numeric (it won't work
with String variables, AUTORECODE them first)  *.
MATRIX.
GET DATA /VAR=ALL /NAMES=VNames.
COMPUTE n=NROW(data).
COMPUTE p=NCOL(data).
* Put original data in first block of bootstrapped samples *.
COMPUTE BootData={MAKE(n,1,0),Data}.
* Number of bootstrap samples, can be increased, but then MXLOOPS must
be increased too *.
COMPUTE k=100.
COMPUTE BootSamp=MAKE(n,p,0).
LOOP i= 1 TO k.
. COMPUTE flipcoin=1+TRUNC(n*UNIFORM(n,1)).
. COMPUTE BootSamp=Data(flipcoin,:).
. COMPUTE BootData={BootData;MAKE(n,1,i),BootSamp}.
END LOOP.
* Export Bootsamples to new dataset *.
COMPUTE VNames={'BootNr',Vnames}.
SAVE BootData/OUTFILE=BootData /NAMES=VNames.
END MATRIX.
RESTORE.

* Formatting variables in BootData *.
DATASET ACTIVATE BootData.
APPLY DICTIONARY
  /FROM OriginalData
  /SOURCE VARIABLES = ALL
  /FILEINFO
  /VARINFO ALIGNMENT FORMATS LEVEL MISSING VALLABELS = REPLACE ATTRIBUTES =
  REPLACE VARLABEL WIDTH .
FORMAT BootNr (F8).
VALUE LABEL BootNr 0'Original Dataset'.

* Split file by BootNr and get all the 101 regression models *.
SPLIT FILE LAYERED BY BootNr .

* End of automatic steps *.

* Run logistic regression model (modify it for your model) and save
predicted probabilities *.

PRESERVE.
SET PRINTBACK=NONE/ ERRORS=NONE /RESULTS=NONE. /* Shut down output *.
LOGISTIC REGRESSION VARIABLES  case
  /METHOD = ENTER MeanAge Smoke ocu
  /CONTRAST (Smoke)=Indicator(1)
  /CONTRAST (ocu)=Indicator(1)
  /SAVE = PRED.
RESTORE.

* Run ROC analysis with Pre_1 and get de 101 AUC *.
PRESERVE.
SET OLANG=ENGLISH.
DATASET DECLARE BootAUC.
OMS
 /SELECT TABLES
 /IF COMMANDS = ["ROC Curve"]
     SUBTYPES = ["Area Under the Curve"]
 /DESTINATION FORMAT = SAV
  OUTFILE = BootAUC.
OMS
 /SELECT TABLES
 /IF COMMANDS = ["ROC Curve"]
     SUBTYPES = ["Case Processing Summary"]
 /DESTINATION   VIEWER = NO.

* ROC analysis (replace "case" by the name of the outcome variable in
your dataset) *.
ROC  PRE_1  BY case (1)
  /PLOT = NONE
  /PRINT = SE
  /CRITERIA = CUTOFF(INCLUDE) TESTPOS(LARGE) DISTRIBUTION(FREE) CI(95)
  /MISSING = EXCLUDE .

OMSEND.
RESTORE.

* 101 c-indexes ready to be examined *.
DATASET ACTIVATE BootAUC.
DELETE VARIABLES Command_ Subtype_ Label_ Var2.

SUMMARIZE
  /TABLES=ALL
  /FORMAT=LIST NOCASENUM NOTOTAL LIMIT=1
  /TITLE='Statistics from Original Dataset'
  /CELLS=NONE.

COMPUTE filter_$=($casenum GT 1.).
FILTER BY filter_$.
FREQUENCIES
  VARIABLES=Area
  /FORMAT=NOTABLE
  /PERCENTILES= 2.5 97.5
  /STATISTICS=STDDEV MEAN MEDIAN.


HTH,
Marta GG (from Spain)

--
For miscellaneous SPSS related statistical stuff, visit:
http://gjyp.nl/marta/


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Marta Garcia-Granero
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Re: Bootstrapping in logistic regression - c statistic -> MACRO

Marta Garcia-Granero
In reply to this post by Georgios Chalikias
Georgios Chalikias wrote:
> At the moment I am building a prediction model (logistic regression).
>
> I need to validate my model, therefore I decided to "shrink" the
> optimism of the model by bootstrapping method.
>
> However, when the bootstrapping command is ON in PASW-SPSS 18 I cannot
> save the predicted probabilities in order to calculate the c-statistic
> (via AUC of the pre1) of all the bootsrapping derived models.
>
Hi everybody!

Just in case anyone is interested, Georgios and I had an off list
exchange of mails, the code works OK, and, following Georgios'
suggestion, I also added some code to bootstrap the calibration.

BTW Georgios, I forgot to mention that you are performing an internal
validation, a bit optimistic. Take a look at this series of 4 papers at
BMJ (Research Methods and reporting):

Moons et al. Prognosis and prognostic research: what, why and how? BMJ
2009; 338:b375
Royston et al. Prognosis and prognostic research: developing a
prognostic model. BMJ 2009; 338:b604
Altman et al. Prognosis and prognostic research: validating a prognostic
model. BMJ 2009; 338:b605 <--- Specially this one
Moons et al. Prognosis and prognostic research: application and impact
of prognostic models in clinical practice. BMJ 2009; 308:b606

I have turned everything into an old fashioned - obsolete? - macro (I
think I can also hear Jon's big sigh). I will upload it very soon (give
me a couple of hours, I have a meeting right now) to the web page you
can find below my signature.

Best regards,
Marta GG

--
For miscellaneous SPSS related statistical stuff, visit:
http://gjyp.nl/marta/

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