# Questions tagged [somers-d]

Somers' $d$ is a measure of ordinal association between ordinal or continuous variables (converted to ranks)

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### Relating population-level AUC (Somers's $D_{xy}$) to a mean shift

Say we have group $0$ distributed as $N(\mu, \sigma^2)$ and group $1$ distributed as $N(\mu+\delta, \sigma^2)$. We then use the Gaussian-distributed variables to predict group membership. It seems ...
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1 vote
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### Somers' D for continous variables

I have read up Somers' D and everywhere it states that the statistic is a measure of association between ordinal variables. Can someone explain to me why I cannot use this metric for assessing the ...
676 views

### Why does the formula of Somers' D remove number of Y ties in this formula?

I am researching how to calculate Somers' D in python for a discrete dependent variable and continuous independent variable, I found this answer on stack overflow: https://stackoverflow.com/questions/...
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### Somers' D. Is there an assumption about sample size

Is it possible to run Somers' D (and its accompanying significance tests) on a very small sample? In my case, I have a 2x3 (one variable is ordinal, the other 0/1 coded) table but only 36 cases. If ...
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### Somers' D for model validation

Somers' D as defined for example in "The predictive accuracy of credit ratings: Measurement and statistical inference" by Walter Orth is defined for the case when Y is predicted by X as  D_{XY} = \...
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### What is a reliable way to obtain an optimism-correct AUC with confidence limits?

I have seen that Frank Harrell's rms package does not offer a CI for Somers Dxy (and subsequently the c-statistic/AUROC). I am trying to look at a method with ...
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### Chi-square test and Somers' d

I have two ordinal variables. I would like to know if there is a dependency between these two variables and also how strong this dependency is. So, I performed a chi-square test (34.53, df=8) where ...
1 vote
344 views

### How to interpret asymptotic standard error of Somers' D

I see SAS provide asymptotic standard error of Somers' D. My question is how to interpret it and when should I used it for the statistical testing for Somers' D? Now I only have one out of time ...
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1 vote
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### Interpreting the Somers' D statistics

I'm running a logistic regression model by using SAS PROC LOGISTIC. In the Association Statistics table that SAS provides as analysis output there is the Somers' D stat. Could you provide an ...
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1 vote
981 views

### What is the significance level for Somers'd?

For tests such as chi square, the significance level is usually 0.05, but I've seen some people interpret p-values for Somers'd such as .000 as significant, displaying the results similar to this: (d= ...
1 vote
1k views

### Computing AUC (or Somers' D) for ordinal logistic regression out-of-sample (cross-validation)

I have fit a proportional odds model with an ordinal response using Harrell's rms package. Now I want to measure the quality of prediction by computing Somers' D (...
285 views

### How to choose rank correlation coefficient?

I want to quantify correlation between rankings. Rankings in this case have got ties. Also rankings don't rank all the same entries, the rankings might be of different sizes and rank different sets, ...
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### bootstrap estimation of optimism vs. internal validation using bootstrapping

I used bootstrap (N = 1000 samples) to quantificate optimism and subsequently corrected c-index and Somers´ D statistics to select a final model with best predictive accuracy among three "candidate" ...
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1 vote
962 views

### Computing c-index for an external validation of a Cox PH model with Stata

I have developed a Cox prognostic model based and internally validated it using bootstrapping. I also evaluated its calibration using Harrell’s $c$ statistic and Somers' $D$. I have also checked ...
1k views

### Measure of Association between two Ordinal Variables

I have two ordinal variables. One is independent and the other one is dependent variable. I would like to test if there is monotonic relationship between these two or not. I am using Somers' d measure ...
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### How to compare predictive power of survival models?

Frank Harrell describes the concordance (or Somer's D) as not being sensitive enough to compare multiple survival models for their diagnostic ability, and I've observed this in my own work with ...
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### What does a negative Somers' D say about model discriminative power?

I developed a Cox proportional hazard regression model in R. Then I tried using validate in Professor Harrell's rms package to ...
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### Bootstrapping Hmisc::rcorrp.cens for paired concordance?

As Frank Harrell says here and other places, it's better to compare two predictive models (Cox proportional hazards in this case) wrt discrimination (C-index) using the paired U-statistic (Hmisc::...
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### Am I using Goodman-Kruskal gamma or Somers D or Kendall tau correctly and what do they mean?

I am seemingly blindly following this publication that has done work very similar to what I need to accomplish (page 18-21). My analysis is a multinomial logistic regression where I have 3 possible ...
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1 vote