First choice would be a scatter plot, and then there are lots of measures of associations, but deciding requires more information about the problem (e.g., see https://cran.r-project.org/web/packages/matie/index.html).

Can't you simply convert one unit into the other?

Additional to Jochens answer, why not standardizing both variables in the same way?

I am struggled to convert the % of isoflurane gas into ug/ml which is detected in blood level. Many thanks for advice...

Rainer, the comparison of standardized variables can be misleading. Consider using z-scores, then you cannot assess any bias (bothe means are 0) and the information about different variances gets lost (in the Bland-Altman plot this would show as a positive slope of the regression line through the points). I am not sure how standardized variables are comparable - in some meaningful way. Or do I overlook something?

@ Jochen: Why would a z-transformation necessarily lead to a positive slope of the regression line through the point?

The Bland-Altman plot considers the differences (of data points from two different measures),  means of two data points, as well as the mean of differences as a marker. If I apply the transfomation for each dataset independently, then a uncorrelated data should remain uncorrelated and vice versa, shouldn't it? It is not about the means of the samples (which would both be 0, right), but about the means of the differences, or do I miss something?

I am not clear as to whether these are really the same items being measured. If so, unit conversion should be easy. As you point out, Bland Altman is a measure of agreement. But it sounds like you're measuring two different things: 1) percent isoflourane in administered anaesthetic gas, and 2) blood level achieved by this administration.  There is no reason they should be identical, just as the inspired O2 concentration and arterial oxygen concentration are related but distinct quantities even when both are measured in mmHg (since variations in the blood-alveolar barrier effect the relationship between the two).  In this context, the best you can do is to study the relationship between them, in terms of correlations, regression coefficients, Cohen's Kappa for respective quantile assignments, etc

@Rainer: Because if there is a high covariance but the variances in the variables are not equal, the scatterplot obviousely shows a cloud of points that is rotated w.r.t. the 45° line. The bland-Altman plor is a scaled rotation by 45° (clockwise), so the (rotated) cloud of points will still have some angle against the horizontal axis.

Here is some R-code for a demonstration by example:

# create some random data with a "suitable" covariance matrix

Sigma = matrix(c(2,2,2,8),2,2)*0.1

v = mvrnorm(n = 1000, rep(0, 2), Sigma)

x = v[,1]

y = v[,2]

# create a scatterplot of the data and a Bland-Altman plot

par(mfcol=c(1,2))

plot(x,y,asp=TRUE,main="Original data")

abline(0,1) # add a line for y=x (45°)

plot((x+y)/2,y-x,main="Bland-Altman plot")

abline(h=0) # add a line for y=x (here this is the x-axis!)

@Atul: 

Thank you for your input. The % of isoflurane administrated theoretically should be equal to its blood levels upon reaching equilibrium. But, my lab is only able to give me the units in ug/ml under mass spectrometry. Hence, I am facing problem to do the statistical test as both units are different. Do you all think I should use correlation etc instead of Bland Altman. Although Bland Altman is the still best statistical test to compare both measurements of similar variable. 

@ Jochen: many thanks for this valuable information, I'll have a look at it as soon as possible.

Greetz,

Rainer

Not sure they need to be identical , as there is a biological barrier creating variability. If that was the case, we'd never need to measure arterial oxygen concentration, as the inspired percentage would suffice, which clearly isn't the case. The alveolar-capillary barrier may be more permeable to isofluorane than oxygen, but this is also true of CO2, and end tidal (expired) CO2 is not a perfect surrogate for arterial concentrations.  But I'm not an anaesthetist, and there are others who can better judge  this assumption. 

If you're confident of your assumption, why not create a calibration curve and then use it to interchange units (to use Bland-Altman)? If they're truly identical except for units, you should also be able to standardize them by centering/scaling, since they should be comparable on the Z scale. 

Otherwise, you could use 

1) Correlations

2) Assign each measurement to a quantile and then compare quantile assignment (e.g a weighted Kappa). Personally, I dislike categorizing continuous variables, which discards information. 

I"m not trying to be a naysayer here, but I"m a clinician as well as a statistician, and I have a healthy respect for biological variability! 

————————————————

Atul Sharma MD, MSc, FRCPC, M.Stat

Senior Consultant | Biostatistics Group | Data Science Platform

George & Fay Yee Centre for Healthcare Innovation

It's still not entirely clear to me what you're measuring in the gas phase. I initially thought you were measuring inspired isoflourane. If you're trying to equate inspired and arteriolar concentrations, I have a hard time believing those are the same quantity, since there are many reasons for not equilibrating (alveolar-capillary barrier, VQ mismatch, etc). 

But the appendix in the paper you sent also measured isoflourane in the gas phase above a sealed blood sample, which is quite a different thing. Yes, these two should equilibrate. But the appendix ("Determination of Blood/Gas Partition Coefficient of Isoflurane for Each Patient’s Blood") does indicate that each individual has a distinct blood/gas partition coefficient, which they fit through an individual five point calibration curve. Whether you can substitute the "average" partition coefficient depends on how variable it is and the precision you require. 

Thank you very much, Atul. I will discuss this with my lab technician regarding the calibration curve. 

Appreciate all the inputs from you guys. 

Have a nice day. 

KT

The best method is to convert both variables into percentile ranks and run the analysis.

Even though this is the best method, this has not been discussed in the literature.

Standardize both variables and use the Bland Altman test. “Bland-Altman methods for comparing methods of measurement and response to criticisms” published in journal Global Epidemiology 3 (2021). stated that “An alternative method for analyzing data on different scales would be to standardize both to a common scale”.