relative risk

[drfg2008]

(I’m not quite sure if this is the right platform … maybe someone knows a better platform)

The following problem is actually from the medicine. In order to make it a little easier to understand (and maybe a little more interesting), the problem is explained as a football-example.

Case:

There are two football teams, A and B.

A and B have both played against identical football teams and won it in the following cases:

A won 75% of all matches.
B won 60% of all matches.

Now A and B play against each other. Question: What is the probability that A wins?

Relative Risk calculation:

75/60 = 1,25

1. "The 'relative risk' that team A wins, is increased by a factor of 1.25."
2. "The probability that team A wins, is 55.56%." (*)

(*) x/(1-x)=1,25 ; x = 0,556

Is there any statistic model for it: Would be the “relative risk” a feasible approach here?


Thanks

[Bruce Weaver]

I suspect the original medical example would be clearer.  If you are asking how to compute relative risks in SPSS, you can get them via CROSSTABS when dealing with simple 2x2 tables--see the Help for details.  For more complex models (that include covariates,  etc), you can use GENLIN with a log link function and binomial error distribution.  In the table of coefficients, B = ln(RR), and Exp(B) = RR.  Here's a simple example for a 2x2 table, first with CROSSTABS, then GENLIN.

* Compute RR for a 2x2 table.
data list list / row col kount (3f5.0).
begin data
1 1 750
1 2 250
2 1 600
2 2 400
end data.

weight by kount.

* Via CROSSTABS.

crosstabs row by col / stat = risk.

* Now via GENLIN with log-link and binomial error.

GENLIN col (REFERENCE=LAST) BY row (ORDER=ASCENDING)
  /MODEL row INTERCEPT=YES
 DISTRIBUTION=BINOMIAL LINK=LOG
  /CRITERIA METHOD=FISHER(1) SCALE=1 COVB=MODEL MAXITERATIONS=100 MAXSTEPHALVING=5
    PCONVERGE=1E-006(ABSOLUTE) SINGULAR=1E-012 ANALYSISTYPE=3(WALD) CILEVEL=95 CITYPE=WALD
    LIKELIHOOD=FULL
  /MISSING CLASSMISSING=EXCLUDE
  /PRINT CPS MODELINFO FIT SUMMARY SOLUTION (EXPONENTIATED).

* Notice that Exp(B) and 95% CI for Row 1 match the RR and 95% CI
* for "cohort col = 1" in the CROSSTABS output.


HTH.

drfg2008 wrote

(I’m not quite sure if this is the right platform … maybe someone knows a better platform)

The following problem is actually from the medicine. In order to make it a little easier to understand (and maybe a little more interesting), the problem is explained as a football-example.

Case:

There are two football teams, A and B.

A and B have both played against identical football teams and won it in the following cases:

A won 75% of all matches.
B won 60% of all matches.

Now A and B play against each other. Question: What is the probability that A wins?

Relative Risk calculation:

75/60 = 1,25

1. "The 'relative risk' that team A wins, is increased by a factor of 1.25."
2. "The probability that team A wins, is 55.56%." (*)

(*) x/(1-x)=1,25 ; x = 0,556

Is there any statistic model for it: Would be the “relative risk” a feasible approach here?


Thanks

[Rich Ulrich]

I will offer the observations that
(a) Odds Ratio is almost always used in models; in contrast to true
Relative Risk which is only occasionally preferred, for anything, but
not models.  Sometimes OR appears while being called RR, as in
the Mantel Haenszel model for multiple tables.
(b) When they play against the same teams, there is *apt* to be
a correlation among which opponents were defeated or not. 
If there is an easy solution, it makes use of an unrealistic
assumption of correlation being zero.
(c) For sports, the effective model for predicting competition
based on win/lose probably makes use of something similar to
the numeric basis of chess rankings.  (Computerized sports
predictions also make use of "margin of victory" and maybe more.)

As Bruce says, you may get better advice if you use your actual problem.

--
Rich Ulrich

> Date: Wed, 20 Jul 2011 11:57:10 -0700

> From: [hidden email]
> Subject: relative risk
> To: [hidden email]
>
> /(I’m not quite sure if this is the right platform … maybe someone knows a
> better platform)/
>
> The following problem is actually from the medicine. In order to make it a
> little easier to understand (and maybe a little more interesting), the
> problem is explained as a football-example.
>
> Case:
>
> There are two football teams, A and B.
>
> A and B have both played against identical football teams and won it in the
> following cases:
>
> A won 75% of all matches.
> B won 60% of all matches.
>
> Now A and B play against each other. Question: What is the probability that
> A wins?
>
> Relative Risk calculation:
>
> 75/60 = 1,25
>
> 1. "The 'relative risk' that team A wins, is increased by a factor of 1.25."
> 2. "The probability that team A wins, is 55.56%." (*)
>
> (*) x/(1-x)=1,25 ; x = 0,556
>
> Is there any statistic model for it: Would be the “relative risk” a feasible
> approach here?

[drfg2008]

Thanks Bruce, thanks Rich for your very helpful replies (as always).

Two questions:

have you got a link to literature on how in chess probabilities are computed (for win/lose)?

I’m not quite sure if my approach to compute probabilities (to ‘win’) from RR is right.

x/(1-x)=1,25 ; x = 0,556

Frank

[drfg2008]

Thank you Rich for your  private message. Yes, my question was somewhat premature. Maybe I had not understood your text properly. But I am looking for the calculation of probabilities to win a specific 'game'. And my idea was to draw such a probability from RR [1]. Thank you for pointing out the article on chess. However, it relates to rankings (ELO points), not probabilities to win a specific game. That’s also true for the ELO scheme itself [2] by Arpad Elo.

The representation of the procedure GENLIN was very helpful. Thank you.

Frank

[1] x/(1-x)=1,25 ; x = 0,556
[2] http://en.wikipedia.org/wiki/Elo_rating_system#Mathematical_details

[vlad simion]

Hi Frank,

I might be off the subject, but this looks like the Bradley-Terry for paired comparison data which can be accustomed in spss with genlog. You set up the data as a cross tabulation between the teams having the number of winnings on the upper diagonal and the number of loses on the lower diagonal and the main diagonal set as 0, as one team cannot play against itself.

Look for the quasi-symmetry loglinear model in Agresti's book "Categorical Data Analysis", page 436:

http://books.google.com/books?id=hpEzw4T0sPUC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false

Hope this helps,

Vlad

On Fri, Jul 22, 2011 at 9:11 AM, drfg2008 <[hidden email]> wrote:

Thank you Rich for your  private message. Yes, my question was somewhat
premature. Maybe I had not understood your text properly. But I am looking
for the calculation of probabilities to win a specific 'game'. And my idea
was to draw such a probability from RR [1]. Thank you for pointing out the
article on chess. However, it relates to rankings (ELO points), not
probabilities to win a specific game. That’s also true for the ELO scheme
itself [2] by Arpad Elo.

The representation of the procedure GENLIN was very helpful. Thank you.

Frank

[1] x/(1-x)=1,25 ; x = 0,556
[2] http://en.wikipedia.org/wiki/Elo_rating_system#Mathematical_details

-----
Dr. Frank Gaeth
FU-Berlin

--

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[drfg2008]

Thanks Vlad,

yes, that's it: Bradley-Terry for paired comparison data.

Frank