Potassium Data

Overview

Here is a dataset containing measurements of both plasma and WBC Potassium. While not the same as RBC K, I think the same basic membrane voltage concepts apply. This gives an idea of what might be done with the Gubbio Study RBC and serum K dataset.

It contains 33 subjects in three groups:

Cardiac - Cardiac patients taking diuretics
NonCardiac - Other patients taking diuretics
Untreated - Untreated cardiac patients

We will look at how the plasma and WBC K measurements vary between the three groups.

The data source is Leucocyte electrolytes in cardiac and non-cardiac patients receiving diuretics.
Paper PDF

Some additional information on RBC and WBC K measurements:
A method for simultaneously estimating plasma, erythrocyte, and leukocyte sodium, potassium, and magnesium: reference values and considerations from biological variation data

Analysis

First load the data from an Excel spreadsheet saved as CSV.

Kdata <- read.csv("Lancet1974.csv")
kable(Kdata, row.names=FALSE)

Group	Patient_number	K_p	K_wbc	K_ratio	E_k	Notes
Cardiac	1	4.6	116.0	25.2	-87.1	Leucocyte electrolytes in cardiac and non-cardiac patients receiving diuretics
Cardiac	2	4.0	142.0	35.5	-96.4	http://www.thelancet.com/journals/lancet/article/PIIS0140673674930013/abstract
Cardiac	3	5.1	103.0	20.2	-81.1
Cardiac	4	4.6	122.0	26.5	-88.5
Cardiac	5	4.7	123.0	26.2	-88.1
Cardiac	6	4.5	95.6	21.2	-82.5
Cardiac	7	5.1	100.0	19.6	-80.4
Cardiac	8	4.5	114.0	25.3	-87.3
Cardiac	9	3.9	111.0	28.5	-90.4
Cardiac	10	4.6	90.0	19.6	-80.3
Cardiac	11	4.7	126.0	26.8	-88.8
Cardiac	12	5.2	126.0	24.2	-86.1
Cardiac	13	4.3	140.0	32.6	-94.0
Cardiac	14	5.0	116.0	23.2	-84.9
Cardiac	15	3.9	115.0	29.5	-91.4
Cardiac	16	4.7	79.4	16.9	-76.3	Two sickest
Cardiac	17	3.5	65.8	18.8	-79.2	Two sickest
Cardiac	18	4.3	154.0	35.8	-96.6
NonCardiac	19	3.5	137.0	39.1	-99.0
NonCardiac	20	3.9	128.0	32.8	-94.3
NonCardiac	21	3.0	129.0	43.0	-101.6
NonCardiac	22	4.3	132.0	30.7	-92.5
NonCardiac	23	4.0	131.0	32.8	-94.2
NonCardiac	24	3.0	190.0	63.3	-112.0
NonCardiac	25	2.8	110.0	39.3	-99.1
NonCardiac	26	3.6	135.0	37.5	-97.9
NonCardiac	27	2.8	149.0	53.2	-107.3
NonCardiac	28	3.8	143.0	37.6	-98.0
Untreated	29	4.9	120.0	24.5	-86.4
Untreated	30	4.7	123.0	26.2	-88.1
Untreated	31	4.4	130.0	29.5	-91.4
Untreated	32	3.2	108.0	33.8	-95.0
Untreated	33	3.8	97.9	25.8	-87.7

Display the three groups of subjects in a scatterplot.

invisible( # suppress id output
scatterplot(K_p ~ K_wbc | Group, data=Kdata, smooth=FALSE, reg.line=FALSE,
            id.n=nrow(Kdata), xlab="WBC K (mEq/L)", ylab="Plasma K (mEq/L)")
)

This plot is interesting because the groups separate the most cleanly using a diagonal line from lower left to upper right (i.e. roughly equivalent to a constant membrane voltage).

The diuretic treated and untreated cardiac patients look like they belong in one group (though the treated subjects appear “worse”, here more dysaerobic) with the non-cardiac diuretic subjects in a separate group to the lower right (more anaerobic).
Although this is not a complete separation (i.e. there is overlap) I find the plot suggestive.
This can also be seen to some extent in the membrane voltage boxplot below, but I think this scatterplot shows things more clearly.

Here is another variant of the scatterplot showing membrane voltage contour lines.

K_p <- seq(2.7, 5.4, 0.1)
K_wbc <- seq(60, 195, 5)
grd <- expand.grid(K_wbc, K_p)
colnames(grd) <- c("K_wbc", "K_p")
grd$E_k <- -27 * log(grd$K_wbc / grd$K_p) # mV

contourplot(E_k ~ K_wbc * K_p, grd, cuts=10,
            main="Resting Membrane Potential Due to Potassium (mV)",
            xlab="WBC K (mEq/L)", ylab="Plasma K (mEq/L)",
            xlim=c(64,195), ylim=c(2.7,5.3),
            panel = function(...) {
              panel.contourplot(...)
              panel.abline(h=4.2,lty=2)
              panel.abline(v=128,lty=2)
            }, 
            colorkey = FALSE, region = TRUE)
trellis.focus("panel", 1, 1, highlight=FALSE)
invisible(lpoints(Kdata$K_wbc, Kdata$K_p, pch=19, col=Kdata$Group))
ltext(Kdata$K_wbc, Kdata$K_p, labels=Kdata$Patient_number, adj=c(0,0))
trellis.unfocus()

Notice how a membrane voltage of between -92 and -97 mV comes close to separating the groups as described above.
Also notice how the two subjects described in the paper as the sickest (16 and 17) have the most depolarized membrane voltages!

Here is another way of showing the separation of the groups with Boxplots of E_k. Notice there is minimal overlap between the cardiac (both treated and untreated) and non-cardiac groups with no overlap for the 2Q-3Q portions shown by the boxes.

Dashed horizontal lines have been drawn at -92mV and -97mV to illustrate the range of best separation proposed above.

boxplot(E_k ~ Group, data=Kdata, ylab="Membrane Voltage (E_k, mV)")
abline(h=-92, lty=2)
abline(h=-97, lty=2)

Appendix

Display Boxplots of other variables by group. The main thing to notice here is that K_p and K_wbc do not separate the cardiac and non-cardiac groups as well as E_k did. K_ratio is simply a transformation of E_k so it has a similar separation.

boxplot(K_p ~ Group, data=Kdata, ylab="Plasma K (mEq/L)")

boxplot(K_wbc ~ Group, data=Kdata, ylab="WBC K (mEq/L)")

boxplot(K_ratio ~ Group, data=Kdata, ylab="WBC/Plasma K Ratio")

File originally created: Wednesday, April 22, 2015
File knitted: Fri Jun 19 14:33:47 2015

Potassium Data

Richard Seiter

Friday, June 19, 2015

Overview

Analysis

Appendix