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From |
Tinna <statalist@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Can Y be a predicted variable? |

Date |
Fri, 9 Sep 2005 15:45:40 -0400 |

So will I get fried if I do it my proposed way, or will the results just be difficult to read for non-statisticians. Tina On 9/9/05, Roger Newson <roger.newson@kcl.ac.uk> wrote: > At 18:31 09/09/2005, Tina wrote: > >Dear statalisters, > > > >I have a dependent variable in 5 levels (Self-Assessed Health Status > >from very good to very poor). I am currently assuming a latent > >continuous variable, but that is problematic for some of my analysis. > >I have some other measures of health in my data and was wondering if > >it was appropriate to create a new one that would be continuous. My > >suggestion would be: > > > >1. regress SAHS on other health variables. > >2. Predict SAHS (lets call it SAHShat) based on the previous regression. > >3. The new measure would be calculated as an average of SAHS and SAHShat > > > >This looks like a good idea to me, but I wonder why I don't see anyone > >else doing this if it is OK. Those of you that fell of your office > >chairs in laughter could maybe get back on and explain why not, > >because it seems fine idea to me right now. > > In general, categorical ordinal outcomes like SAHS are a problem, > especially if you want to have a parameter estimate that can be understood > by non-statisticians. > > A possible solution is to use Somers' D, which can be estimated (with > confidence limits) using the -somersd- package (downloadable from SSC using > the -ssc- command). Somers' D is defined in terms of Kendall's tau-a, which > is defined as > > tau(X,Y) = E[sign(X1-X2)sign(Y1-Y2)] > > where (X1,Y1) and (X2,Y2) are sampled independently from the same > population. Somers' D is defined as > > D(Y|X) = tau(X,Y)/tau(X,X) > > Therefore, Kendall's tau-a is the difference between 2 probabilities, > namely the probability that the larger of 2 randomly-sampled X-values is > associated with the larger of the 2 corresponding Y-values and the > probability that the larger of the 2 X-values is associated with the > smaller of the 2 Y-values. Somers' D is the difference between the 2 > corresponding conditional probabilities, given that the 2 X-values are not > equal. Somers' D and Kendall's tau-a are discussed in the manual > -somersd.pdf-, distributed on SSC with the -somersd- package, and also in > Newson (2002). > > Tina does not mention the proposed predictor variables in the proposed > regression model. However, in a multivariate regression model, there is > usually one predictor X that is really interesting and other predictors > that are confounders. For instance, we might want to know how daily > cigarette consumption predicts SAHS, adjusting for confounders such as > income, access to a car. and other indicators of general standard of > living. To estimate a Somers' D of SAHS with respect to cigarettes adjusted > for the confounders, the first step is to define a propensity score for > cigarette consumption by regressing cigarette consumption with respect to > confounders and using the predicted level of cigarette consumption > (calculated using -predict-) as the cigarette propensity score. We can then > use -xtile- to define a number of cigarette propensity groups from the > propensity score, and use -somersd- with the -wstrata()- option to estimate > a Somers' D of SAHS with respect to cigarette consumption stratified by > cigarette propensity group. This Somers' D measures association between > SAHS and cigarette consumption in pairs of patients in the same cigarette > propensity group. If it is high, then we can say that higher cigarette > consumers have poorer health than lower cigarette smokers with similar > "cigarette propensity" based on the confounders. In other words, if the > stratified Somers' D is high, then the poorer health of cigarette smokers > is not caused by the fact that cigarette smokers are cigarette-prone > because of their low general standard of living. Some references about > propensity scores are given on the manual -somersd.pdf-. > > I hope this helps. > > Roger > > > References > > Newson R. Parameters behind "nonparametric" statistics: Kendall's tau, > Somers' D and median differences. The Stata Journal 2002; 2 (1): 45-64. > Also downloadable from my website at > http://phs.kcl.ac.uk/rogernewson/papers.htm > > > > -- > Roger Newson > Lecturer in Medical Statistics > Department of Public Health Sciences > Division of Asthma, Allergy and Lung Biology > King's College London > > 5th Floor, Capital House > 42 Weston Street > London SE1 3QD > United Kingdom > > Tel: 020 7848 6648 International +44 20 7848 6648 > Fax: 020 7848 6620 International +44 20 7848 6620 > or 020 7848 6605 International +44 20 7848 6605 > Email: roger.newson@kcl.ac.uk > Website: http://phs.kcl.ac.uk/rogernewson/ > > Opinions expressed are those of the author, not the institution. > > * > * For searches and help try: > * http://www.stata.com/support/faqs/res/findit.html > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ > * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: Can Y be a predicted variable?***From:*Constantine Daskalakis <C_Daskalakis@mail.jci.tju.edu>

**References**:**st: Can Y be a predicted variable?***From:*TinnaLaufey Asgeirsdottir <statalist@gmail.com>

**Re: st: Can Y be a predicted variable?***From:*Roger Newson <roger.newson@kcl.ac.uk>

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