ROC Analysis / Odds Ratios

[KEVIN MANNING]

Dear all,

   I want to compute the Odds Ratio for a specific cut-off score derived from ROC analysis to indicate the presence / absence of disease.

   Not sure how to do this.  I was thinking to create a dichotomous variable based on performance above (theoretically indicating the absence of disease) and below this score and then run a cross-tabs with disease (absent / present).  Does this sound like a reasonable thing to do?

   Thanks!
Kevin

[Hector Maletta]

        Yours seems a good idea, Kevin, if you are only interested in
computing the ODDS of disease (not the odds RATIO). The odds of disease
equal the probability of disease divided by the probability of non-disease,
i.e. p/(1-p), where p is the proportion of cases at or above the cutoff
point. An odds RATIO is the ratio of two odds, e.g. the odds for vaccinated
subjects divided the odds for not vaccinated ones. A more common indicator
is the logarithm of the odds ratio, indicating how many times more likely is
the outcome in one group relative to the other.
        You can use your dichotomous variable, based on the cutoff point
derived from ROC, to apply some predictive analysis e.g. logistic regression
with disease as dependent variable and the same cutoff point, using whatever
predictors of disease you may have, such as vaccine, gender, age group and
so on. The odds ratios would emerge as a by product of log regression as
well.

        Hector

        -----Mensaje original-----
De: SPSSX(r) Discussion [mailto:[hidden email]] En nombre de KEVIN
MANNING
Enviado el: 25 January 2007 13:50
Para: [hidden email]
Asunto: ROC Analysis / Odds Ratios

        Dear all,

           I want to compute the Odds Ratio for a specific cut-off score
derived from ROC analysis to indicate the presence / absence of disease.

           Not sure how to do this.  I was thinking to create a dichotomous
variable based on performance above (theoretically indicating the absence of
disease) and below this score and then run a cross-tabs with disease (absent
/ present).  Does this sound like a reasonable thing to do?

           Thanks!
        Kevin

[Marta García-Granero]

Hi Hector

You wrote:
HM>         Yours seems a good idea, Kevin, if you are only interested in
HM> computing the ODDS of disease (not the odds RATIO). The odds of disease
HM> equal the probability of disease divided by the probability of non-disease,
HM> i.e. p/(1-p), where p is the proportion of cases at or above the cutoff
HM> point. An odds RATIO is the ratio of two odds, e.g. the odds for vaccinated
HM> subjects divided the odds for not vaccinated ones. A more common indicator
HM> is the logarithm of the odds ratio, indicating how many times more likely is
HM> the outcome in one group relative to the other.
HM>         You can use your dichotomous variable, based on the cutoff point
HM> derived from ROC, to apply some predictive analysis e.g. logistic regression
HM> with disease as dependent variable and the same cutoff point, using whatever
HM> predictors of disease you may have, such as vaccine, gender, age group and
HM> so on. The odds ratios would emerge as a by product of log regression as
HM> well.

Not necessarily. Kevin can also obtain OR with CROSSTABS (by adding
"RISK" to /STATISTIC subcommand):

data list list/exposed outcome counts (3 F8).
begin data
1       1       165
1       2       135
2       1       75
2       2       125
end data.
val lab exposed 1'Yes' 2'No'/outcome 1'Case' 2'Control'.
var lev exposed outcome (nominal).
weight by counts.

CROSSTABS
  /TABLES=exposed BY outcome
  /FORMAT= AVALUE TABLES
  /STATISTIC=CHISQ RISK.

Kevin wrote:
HM>            I want to compute the Odds Ratio for a specific cut-off score
HM> derived from ROC analysis to indicate the presence / absence of disease.

HM>            Not sure how to do this.  I was thinking to create a dichotomous
HM> variable based on performance above (theoretically indicating the absence of
HM> disease) and below this score and then run a cross-tabs with disease (absent
HM> / present).  Does this sound like a reasonable thing to do?





--
Regards,
Dr. Marta García-Granero,PhD           mailto:[hidden email]
Statistician

---
"It is unwise to use a statistical procedure whose use one does
not understand. SPSS syntax guide cannot supply this knowledge, and it
is certainly no substitute for the basic understanding of statistics
and statistical thinking that is essential for the wise choice of
methods and the correct interpretation of their results".

(Adapted from WinPepi manual - I'm sure Joe Abrahmson will not mind)

[Hector Maletta]

        Marta,
        Of course our colleague can use CROSSTABS/STAT RISK to obtain odds
ratios if he has another variable to cross with the presence or absence of
disease (such as having been vaccinated or not against that disease). I
abstained from recommending it because he only mentioned ONE variable,
namely a continuous score indicating the disease, with a cutoff point found
through a ROC, and asked how to compute the odds ratio of THAT. Under those
conditions, no odds ratio can be computed.
        Hector

        -----Mensaje original-----
De: SPSSX(r) Discussion [mailto:[hidden email]] En nombre de Marta
García-Granero
Enviado el: 26 January 2007 05:58
Para: [hidden email]
Asunto: Re: ROC Analysis / Odds Ratios

        Hi Hector

        You wrote:
        HM>         Yours seems a good idea, Kevin, if you are only
interested in
        HM> computing the ODDS of disease (not the odds RATIO). The odds of
disease
        HM> equal the probability of disease divided by the probability of
non-disease,
        HM> i.e. p/(1-p), where p is the proportion of cases at or above the
cutoff
        HM> point. An odds RATIO is the ratio of two odds, e.g. the odds for
vaccinated
        HM> subjects divided the odds for not vaccinated ones. A more common
indicator
        HM> is the logarithm of the odds ratio, indicating how many times
more likely is
        HM> the outcome in one group relative to the other.
        HM>         You can use your dichotomous variable, based on the
cutoff point
        HM> derived from ROC, to apply some predictive analysis e.g.
logistic regression
        HM> with disease as dependent variable and the same cutoff point,
using whatever
        HM> predictors of disease you may have, such as vaccine, gender, age
group and
        HM> so on. The odds ratios would emerge as a by product of log
regression as
        HM> well.

        Not necessarily. Kevin can also obtain OR with CROSSTABS (by adding
        "RISK" to /STATISTIC subcommand):

        data list list/exposed outcome counts (3 F8).
        begin data
        1       1       165
        1       2       135
        2       1       75
        2       2       125
        end data.
        val lab exposed 1'Yes' 2'No'/outcome 1'Case' 2'Control'.
        var lev exposed outcome (nominal).
        weight by counts.

        CROSSTABS
          /TABLES=exposed BY outcome
          /FORMAT= AVALUE TABLES
          /STATISTIC=CHISQ RISK.

        Kevin wrote:
        HM>            I want to compute the Odds Ratio for a specific
cut-off score
        HM> derived from ROC analysis to indicate the presence / absence of
disease.

        HM>            Not sure how to do this.  I was thinking to create a
dichotomous
        HM> variable based on performance above (theoretically indicating
the absence of
        HM> disease) and below this score and then run a cross-tabs with
disease (absent
        HM> / present).  Does this sound like a reasonable thing to do?





        --
        Regards,
        Dr. Marta García-Granero,PhD           mailto:[hidden email]
        Statistician

        ---
        "It is unwise to use a statistical procedure whose use one does
        not understand. SPSS syntax guide cannot supply this knowledge, and
it
        is certainly no substitute for the basic understanding of statistics
        and statistical thinking that is essential for the wise choice of
        methods and the correct interpretation of their results".

        (Adapted from WinPepi manual - I'm sure Joe Abrahmson will not mind)

[Marta García-Granero]

Hi

I supposed the 2nd variable involved was presence/absence of the
disease, to be crossed with above/below the cut-point

HM>         Of course our colleague can use CROSSTABS/STAT RISK to obtain odds
HM> ratios if he has another variable to cross with the presence or absence of
HM> disease (such as having been vaccinated or not against that disease). I
HM> abstained from recommending it because he only mentioned ONE variable,
HM> namely a continuous score indicating the disease, with a cutoff point found
HM> through a ROC, and asked how to compute the odds ratio of THAT. Under those
HM> conditions, no odds ratio can be computed.

Happy weekend for everybody

Marta

[KEVIN MANNING]

Thank you both for your help.  Indeed, the 2nd variable was the presence/absence of disease to be crossed with above/below cut-point.
   Kevin


Research Study Coordinator
Division of Medical Psychology
The Johns Hopkins Hospital
600 N. Wolfe Street / Meyer 218
Baltimore, MD 21287-7218
phone: [phone]
fax: [phone]
e-mail: [hidden email]

----- Original Message -----
From: Marta García-Granero <[hidden email]>
Date: Friday, January 26, 2007 12:34 pm
Subject: Re: ROC Analysis / Odds Ratios
To: [hidden email]

> Hi
>
> I supposed the 2nd variable involved was presence/absence of the
> disease, to be crossed with above/below the cut-point
>
> HM>         Of course our colleague can use CROSSTABS/STAT RISK to
> obtain odds
> HM> ratios if he has another variable to cross with the presence or
> absence of
> HM> disease (such as having been vaccinated or not against that
> disease). I
> HM> abstained from recommending it because he only mentioned ONE variable,
> HM> namely a continuous score indicating the disease, with a cutoff
> point found
> HM> through a ROC, and asked how to compute the odds ratio of THAT.
> Under those
> HM> conditions, no odds ratio can be computed.
>
> Happy weekend for everybody
>
> Marta