Regression analysis to estimate brain ion concentration

[John B]

Hi,
We want to calculate the brain interstitial sodium (Na_brain) by using a probe inserted in the brain that recovers ions every hour and can be measured at the bedside. The setup is quite simple: 1) a micropump that injects a fluid that contains a known and fixed amount of Na, 2) a probe that is implanted in the brain and 3) a microvial were a volume of brain fluid is recovered every hour. An osmotic interchange occurs between the probe and the brain so the recovered volume contains a concentration of Na that reflects the true brain Na but with an unkown error. In order to calculate the "brain Na" from the microvial readings we went to an in vitro experiment changing the brain by a container (matrix) with different concentrations of Na. We get a quite robust regression and a linear relationship between the Na concentration in the microvial (Na_out) and the matrix concentration of Na. 

This is the equation 1: Na_m= 8.6 + 0.89*Na_out (R2=0.95, P <0.001); 95% CI for the 0.89 slope (0.83 - 0.96).
Where Na_m is the concentration of Na in the problem solution (matrix) and Na_out the measured output of Na .  
Our conclusions are the following:
1.According to the in vitro data (n=40), Na in the matrix and the brain can be calculated quite accurately by applying equation 1. So if we have a measured Na_out of 162 mmol/L we can estimate that Brain_Na will be 154.4 mmol/L. 
2.If the variability among the measurements in 5 probes was neglegible, equation 1 can be used to estimate Brain Na in the clinical setting.
3.For some unkown reason measured Na overestimates on average by 10% de real concentrations of Brain_Na/matrix_Na. 

I would appreciate your feedback regarding these conclusions, any evident flaw you may detect in them and whether we need to modify the analysis to convince any potential referee about these conclusions. We are clinical doctors, not  statisticians….

Many thanks in advance

[ציפי שוחט‎]

Dear Dr.

You stated that  the brain was changed by a container. Is it possible that brain and container are dissimilar, and this may be causing the overestimation?

Tzippy Shochat

2012/5/23 John B <bangali...@gmail.com>

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[John B]

On Wednesday, May 23, 2012 8:53:11 AM UTC+2, Tzippy Shochat wrote:

Dear Dr.

You stated that  the brain was changed by a container. Is it possible that brain and container are dissimilar, and this may be causing the overestimation?

Hi,

Thanks for your question. We cannot disregard this factor. The container reproduces quite accurately the conditions of pressure, temperature, etc that are expected in the brain. However for any substance we want to measure by this technique (called microdialysis), the only way to know the in vivo performance is to test the in vitro performance first with the same conditions of infusion speed.

[John B]

[Giulio Flore]

Hi,

 

When regression analysis generates biased estimates this is usually due to not including in the regression one or more explanatory variables (omitted variable bias). As implicitly noted by the other contributor, you might need to consider which factor that is present in your in-vitro experiment that need to be included in the regression analysis to simulate adequately the in-vivo conditions.

 

To check whether this is indeed the case, you should repeat the regression and then check with your statistical package the key diagnostic statistics for omitted variable bias (If you use Stata this is quite straightforward). if the output flags omission of a variable(s), you need to go back to the drawing board and figure out what need to be added to the regression model to make it more reflective of the in-vivo situation.

 

Good luck

 

Giulio

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