I have two continuous variables. Variable $X$ represents the true values (basically it is atmospheric pressure measured via a barometer). Variable $Y$ represents a way to approximate the atmospheric pressure based on altitude, temperature, and some other physical parameters. I have $n=17$ values.

The question now is, how close the approximations are to the true values, i.e., how close are $X$ and $Y$. It seems to me, that the Bland-Altman-Plot (as descriptive tool) and the Concordance Correlation Coefficient are appropriate to assess the agreement of the two variables and thus the accuracy of $Y$. My only concern is, that one of the variables represents the true value (i.e. $X$) and my understanding is, that the aforementioned methods apply to situations when I'm comparing two measurements without actually knowing the true values, i.e., inter-rater reliability.

My question is whether I can use those two methods and if there are other (more) appropriate methods.

  • $\begingroup$ Why only 17 measurements? I would gather more measurements for each value of altitude, temperature etc. I would calibrate the Y's bias and precision for different ranges of the parameters. $\endgroup$ – Aksakal May 5 '14 at 15:01
  • $\begingroup$ In your situation with gold standard judgement, Bland-Altman plots are usually shown with the gold standard value on the X-axis (not the average of the two corresponding values). $\endgroup$ – Michael M May 5 '14 at 15:49
  • $\begingroup$ @Aksakal: From what I understand, measuring the true values X is actually quite expensive, since it is being done in extreme environmental Situations at remote locations. At the time only 17 measurements were done and it is not that simple to make more measurements. $\endgroup$ – Francis May 6 '14 at 7:27
  • $\begingroup$ @Francis, an ordinary test for the difference between two mean values ie true measurements and approximate measurement should help you ascertain whether these are close to each other or differ significantly say at 1 percent alpha. $\endgroup$ – Subhash C. Davar May 6 '14 at 16:21

It depends, are the measurements taken on the same time, at the same temperature and altitude etc.?

If the measurements indeed are paired I would use Bland and Altman statistics (Tukey difference-mean plots) to calculate the mean difference (mean bias) and 95% limits-of-agreement. As someone mentioned you need to plot the true value (gold standard) measurements on the x-axis of the Tukey plot.

You can also define acceptable thresholds (perhaps they already exist in your field of work?) and examine rate of misclassification and extreme-to-extreme misclassification.

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