145
Mixture Analysis of Erythrocyte
Lithium-Sodium Countertransport
and Blood Pressure
Alan B. Weder and Nicholas J. Schork
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This study employs multivariate normal mixture analysis, a technique for identifying discrete
subgroups within populations, to examine the relation of erythrocyte lithium-sodium (RBC
Li+-Na+) countertransport and blood pressure in a group of 474 healthy adults. After adjusting
for effects of age, gender, race, height, and weight, univariate mixture analysis of the
distribution of mean arterial blood pressure (MAP) revealed the presence of only one group,
whereas the distribution of RBC Li+-Na+ countertransport values was composed of a mixture
of two groups (/?<0.00©05). When bivariate mixture analysis was applied to the combined
distribution of MAP and RBC Li+-Na+ countertransport, two commingled subgroups were
identified (p<0.00005). The smaller group (19%) had significantly higher values for both MAP
(108.7±16.7 mm Hg, mean±SD) and RBC Li+-Na+ countertransport (0.455±0.147 mmol Li+/1
cells • hr) than the larger (81%) group (MAP 93.3±12.2 mm Hg, RBC Li+-Na+ countertransport 0.247±0.080 mmol Li+/1 cells • hr,p<0.0001 for both differences). The relation of MAP to
RBC Li+-Na+ countertransport was distinctly different in these two subgroups. In the larger
group, we found a weak positive (r=0.21, p<0.0001) correlation for unadjusted values, which
was not significant after adjustment. The smaller group, with higher levels of MAP and RBC
Li+-Na+ countertransport, showed significant negative correlations for both unadjusted (r= -0.28,
p<0.008) and adjusted ( r = - 0 . 4 1 , p<0.0001) values. (Hypertension 1989;13:14S-150)
E
ssential hypertension is clearly heritable, but
its specific biochemical lesions are obscure
and their genetic determinants unknown.
Studies in twins and in relatives of hypertensive
individuals have proven that several physiological
processes relating to blood pressure control, which
include sympathetic nervous system function,1 plasma
renin activity,2 excretion of a sodium load,3 and the
degree of sodium sensitivity of blood pressure,4 are
heritable, but these phenomena are too complex to
have yet yielded to a more detailed mechanistic
analysis at cellular or molecular levels. Other relatively simple heritable biochemical markers associated with hypertension (MN blood group haplotypes5)
or sodium sensitivity (haptoglobin phenotypes6) have
no obvious physiological relation to blood pressure
control. Of greater promise is elevated red blood cell
lithium-sodium (RBC Li+-Na+) countertransport,7 a
From the Division of Hypertension, Department of Internal
Medicine, University of Michigan Hospitals, Ann Arbor, Michigan.
Supported by National Heart, Lung, and Blood Institute Grant
R01 HL-34464.
Address for reprints: Alan B. Weder, MD, University of
Michigan Hospitals, Department of Internal Medicine, Division
of Hypertension, Kresge Medical Research Building, R6681,
Ann Arbor, MI 48109-0500.
Received April 11, 1988; accepted September 23, 1988.
recently proposed marker for essential hypertension
that has been shown to be associated with high blood
pressure in many studies8-16 and also to be related to
organ-scale abnormalities of potential pathogenetic
importance to hypertension.17-19 Recently, Turner et
al20 demonstrated that the distribution of values of
RBC Li+-Na+ countertransport in a normotensive
group of blood bank donors could be resolved into
two normal subdistributions. It was suggested that
individuals in the higher Li+-Na+ countertransport
subdistribution could be at increased genetic risk for
future hypertension, although an association between
elevated countertransport and high blood pressure
could not be proven because individuals with established hypertension were excluded. We examined
the relation of RBC Li+-Na+ countertransport and
blood pressure in a combined population of normotensive and hypertensive subjects by using a novel
bivariate analytic technique to test the hypothesis
that high blood pressure cosegregates with elevated
RBC Li+-Na+ countertransport.
Subjects and Methods
The population studied consisted of 474 healthy
adults who had participated in a variety of studies at
the University of Michigan Hypertension Division
146
Hypertension
Vol 13, No 2, February 1989
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from 1983-1987. These subjects were not randomly
selected, but included all individuals for whom
standardized blood pressure and RBC Li+-Na+ countertransport measures were available. Generally,
participants had been recruited by blood pressure
level, and most studies compared untreated, borderline (at least one casual blood pressure measurement > 140/90 mm Hg and at least one < 140/90 mm
Hg within the preceding year) or mild (average
casual blood pressure > 140/90 mm Hg) hypertensive subjects with normotensive control subjects
(blood pressure < 140/90 mm Hg). No subjects with
recognized coronary or cerebrovascular disease,
renal insufficiency, or endocrine or liver disease
participated in any study, and all had abstained
from antihypertensive drugs and estrogen-containing
preparations for at least 4 weeks. For all subjects,
blood pressure measurement was performed in the
seated position after at least 10 minutes quiet rest.
Blood pressure was determined three times with a
mercury sphygmomanometer and a cuff of appropriate size for the individual's arm; the average was
used to calculate mean arterial blood pressure (MAP)
as diastolic blood pressure plus one third of the
pulse pressure. In addition to MAP, the height,
weight, gender, age, and race (self-determined) were
recorded. Blood for RBC Li+-Na+ countertransport, obtained on the same day as blood pressure
was measured, was assayed by the method of
Canessa et al,7 as previously reported for our
laboratory.16 No preselection based on RBC Li+Na + countertransport activity was exercised.
Statistical Methods
Values are reported as mean±SD. The significance of group differences was assessed with Student's / test and by x1 when appropriate. Significance was accepted at p^0.05. The technique of
mixture analysis has been described rigorously,2122
and the present application is similar to previously
worked examples (A.B. Weder, N.J. Schork, and
M.A. Schork, unpublished observations). Briefly,
data were first adjusted to eliminate the effects of
measured concomitant variation. Race and gender,
along with the first-, second-, and third-order (i.e.,
power) effects of weight, height, and age, and all
combinations of these variables (to allow for possible interaction effects) were entered into a stepwise
regression algorithm as independent variables with
blood pressure and RBC Li+-Na+ countertransport
as separate dependent variables. Those variables
that contributed significantly (p^0.05 by F test) to
overall variability in blood pressure and countertransport activity were retained in a final multiple
regression model, which was performed with forward
selection, that is, the variable explaining the most
variability was entered first, that explaining the most
residual variability next, and so on until all significant
variables were entered. The residual values from
these empiric models, which represented variability
not explained by demographic or body size factors,
TABLE 1. Characteristics of the Study Population
Variables
Age (yr)
Gender (M:F)
Race(W:B)
Weight (kg)
Height (cm)
Seated blood pressure (mm Hg)
Systolic
Diastolic
Mean
RBC Li+-Na+ countertransport
(mmol Li+/1 cells • hr)
Mean±SD
34.0±8.0
338:136
425:49
80.1±17.1
174.4±9.2
(47.0-174.6)
(147.5-196.0)
126.4±18.3
81.1±14.0
96.2±14.5
0.286±0.126
(86-197)
(42-132)
(63-154)
(0.003-0.948)
Range
(18-74)
Subjects in study population, n=474. M, male; F, female; W,
white; B, black; RBC Li+-Na+, red blood cell lithium-sodium.
were generated for subsequent mixture analyses after
adding back the mean values of the unadjusted variables to aid in interpretation. Next, the individual
distributions of these derived values for MAP and
RBC Li+-Na+ countertransport were examined for
the presence of mixtures with simultaneous adjustment for skewness. Adjustment for skewness is a
critical component of mixture analysis because skewness alone can result in the appearance of a mixture.22
The optimal number of mixed distributions within
each population was determined by x2 testing. Finally,
bivariate analysis was applied to the combined distribution of MAP and RBC Li+-Na+ countertransport,
again with simultaneous adjustment for skewness and
likelihood ratio testing.
Standard deviations of the proportions classified
into each group and the group parameter means and
standard deviations were derived from an analysis of
200 bootstrap samples.23 These bootstrap errors generally represent the "stability" of the mixture (i.e.,
that the mixture is not due to outliers or statistical
"noise") with small errors indicating stability.24
Results
The characteristics of the study population are
shown in Table 1. The data adjustments undertaken
to account for the possible confounding effects of
measured demographic and body size factors
explained a total of 39.6% of the initial variability in
MAP and 15.1% of the variability in RBC Li+-Na+
countertransport rates. The contributions that were
significant for individual variables, power effects of
individual variables, and interactions between variables are shown in Table 2.
Figures 1 and 2 show the frequency distributions
for unadjusted and adjusted values for MAP and
RBC Li+-Na+ countertransport. Mixture analysis of
the adjusted MAP distribution demonstrated the
presence of a single population (Table 3). In agreement with the report of Turner et al,20 the distribution of adjusted Li+-Na+ countertransport values
showed a mixture of two subgroups (Table 3). The
presence of two groups did not result from skew-
RBC Li + -Na + Counter-transport and M A P
Weder and Schork
147
TABLE 2. Stepwise Multiple Regression Model Showing Contribution of Independent Variables to Variability in Mean
Arterial Blood Pressure and Erythrocyte Lithium-Sodium Countertransport
Li + -Na 4 Countertransport
MAP
Independent
variable
Weight
Age
Gender
Height
Height x Age
GenderxAge
Height x Weight x Age
Weight x Age 3
Height x Age 2
Cumulative
r2
Independent
variable
P
<0.00001
<0.00001
0.0002
0.0005
0.225
0.320
0.339
0.355
0.369
0.375
0.380
0.387
0.396
0.0018
0.0301
0.0436
Cumulative
r2
Gender
0.077
Race
Weight
Weight3
0.102
0.118
0.132
0.144
0.151
Race x Weight
Height
P
<0.00001
0.0003
0.0036
0.0048
0.0016
0.0441
0.0279
0.0084
Independent variables are measured demographic and body size factors. Mean arterial pressure (MAP) and
lithium-sodium (Li + -Na + ) countertransport are dependent variables.
Downloaded from http://hyper.ahajournals.org/ by guest on June 14, 2017
ness in the original distribution, as two subpopulations were still present when skewness was controlled during the mixture analysis.
Bivariate mixture analysis of MAP and RBC
Li+-Na+ countertransport demonstrated a highly
significant (p<0.00005) probability that two subpopulations were commingled in our sample (Table 3).
The smaller subpopulation (19±13%) had higher
levels of MAP and RBC Li+-Na+ countertransport
than the larger (81 ±13%). Table 4 shows the characteristics of the two groups as defined by this
bivariate commingling analysis.
We have previously reported1619 a positive correlation between unadjusted, seated MAP and RBC
Li+-Na+ countertransport, and a similar relation
was present in the entire population for both the
unadjusted (/•=().27, p<0.0001) and the adjusted
(r=0.16, p<0.0003) values of those variables. However, when the two subgroups identified by mixture
analysis were examined separately, qualitatively
different relations were found. In the larger group,
characterized by lower MAP and countertransport
values, a significant positive relation was found for
unadjusted values (r=0.21, p<0.0001) but was
reduced to nonsignificance (r=0.06, p=0.19) by
adjustment for measured concomitants. However,
in the smaller group with higher MAP and countertransport levels, a significant inverse relation was
60-
found for both unadjusted (r=-0.28, p<0.008) and,
as shown in Figure 3, adjusted (r= -0.41, p=0.0001)
values. We hypothesize that the positive correlation
found in the original, entire population may be a
manifestation of the "polarization" of the two groups
into distinct corners of the MAP/RBC Li+-Na+
countertransport space.
Discussion
The present study demonstrates a cosegregation
of high values of RBC Li+-Na+ countertransport
and blood pressure in our study group. Although we
studied a population of individuals who were initially selected for blood pressure levels, univariate
examination of blood pressure values in the entire
sample revealed the presence of a single group. It is
therefore highly unlikely that the subsequent finding
of a mixture in the bivariate analysis results from
subject preselection. Univariate analysis of RBC
Li+-Na+ countertransport did reveal two groups, in
agreement with an earlier report that examined a
randomly selected group of normotensive blood
bank donors.20 In that study, a trend toward an
association of high Li+-Na+ countertransport activity and high blood pressure was noted, and our
observations confirm that high RBC Li+-Na+ countertransport is a marker for hypertension.
B
6040-
I]/
S020-
I
B0-
to ra totottononottOMoao
Moan Bkxxl Prmsu* (mm Hg]
llftflL .
n ** m 96 t7 M w
Ad]u«t*d Mean Blood Pressure
IvUtnry irtttj
FIGURE 1. Bar graphs showing the distribution of unadjusted (panel A) and
adjusted (panel B) mean arterial blood
pressure in the study group. As indicated
by the overlay, a single normal distribution provides the best fit for the data.
148
Hypertension
Vol 13, No 2, February 1989
2. Bar graphs showing distribution of unadjusted (panel A) and adjusted
(panel B) red blood cell lithium-sodium
{RBC Li+-Na+) countertransport. Superimposed on the histogram of adjusted
values are the two normal distributions
defined by mixture analysis.
FIGURE
frh 0.10204040604070400
Na - Li Countartrantport
(mmote/l eels x hr)
-2J -13 -01 07 17 27 3 7 4 7
Atfusted N i - U Ca*itertran*port
(arbitrary units)
Downloaded from http://hyper.ahajournals.org/ by guest on June 14, 2017
The importance of this finding is twofold. First,
normal mixture analysis allows us to define, by
means of a single biochemical marker, a distinct
subgroup of hypertensive individuals in whom
hypotheses of possible biochemical or physiological
mechanisms underlying hypertension can be tested.
Second, although the presence of a mixture alone
can never prove that a genetic process is operative,
in light of the strong genetic determination of RBC
Li+-Na+ countertransport variability,23 the presence of a mixture in the distribution of this trait
does suggest the possibility that a single gene or
group of genes controls the phenotypic expression
of countertransport activity. The finding that one
subgroup has both high Li+-Na+ countertransport
and hypertension strongly supports the potential
use of countertransport as a genetic marker of
hypertension. Although the molecule effecting transmembrane Li+-Na+ countertransport in RBCs has
not been isolated, it seems likely to be a single
intrinsic membrane protein coded by a single gene.
The clear association of this gene product with
hypertension, if confirmed by pedigree studies,
should provide a reliable genetic marker for studies
of the heritable basis of human hypertension,
whether it is expressed in cardiovascular effector
tissues where it could directly cause hypertension,
or not.
TABLE 3.
Although mixture analysis unequivocally demonstrates that there are two commingled subgroups in
the population studied, it should be pointed out that
the proportions classified into, and the particular
demographic and body size characteristics attributed to, each group may vary with subject selection. To clearly define the prevalence of individuals
in each subpopulation, a large, population-based
survey of RBC Li+-Na+ countertransport and blood
pressure will be required. However, the mean RBC
Li+-Na+ countertransport values in the two groups
we identified (0.247 and 0.455 mmol Li+/1 cells • hr)
are very similar to the values reported by Turner et
al20 (0.24 and 0.42 mmol Li+/1 cells • hr) for subgroups detected in a population of normotensive
blood bank donors. The agreement in the two studies, and the further agreement of both sets of values
with the average countertransport values reported in
many case-control comparisons of normotensive and
hypertensive subjects (see Reference 20) suggests
that elevated Li+-Na+ countertransport is a phenotype with limited interpopulation variability and
reliable association with hypertension.
It has been noted that the use of an efflux medium
in which Mg2+ is substituted for Na+ can result in
partial suppression of Li+ efflux.26 The consequent
overestimation of Li+-Na+ countertransport, which
is calculated as the difference in Li+ efflux in Na+ and
Univariate and Bivariate Mixtnre Analyses for Mean Arterial Blood Pressure and Erythrocyte LtthJum-
Sodium Countertransport
Analytic approach,
variables (adjusted
values)
Univariate
MAP
RBC Li + -Na +
countertransport
Bivariate
MAP
RBC Li + -Na +
countertransport
Group 1
%of
total
100
Group 2
Mean
SD
%of
total
Mean
SD
96.1
0.9
...
...
...
27± 10
1.070±0.510
1.176±0.227
<0.00005
1.0+0.2
<0.00005
73±16
0.009±0.137
0.603±0.097
81±13
95.9±0.1
0.6±0.1
81±13
0.004±0.122
0.584±0.097
19±13 96.7+0.2
19±13
1.50+0.38
P*
NS
1.11+0.41
Standard deviation of the proportions and group means and standard deviations were derived from 200 bootstrap
samples.23-24 MAP, mean arterial blood pressure; NS, not significant; RBC Li + -Na + , erythrocyte lithium-sodium.
'Significance of likelihood O 2 with 4 degrees of freedom) of two (vs. one) groups, with adjustment for skewness.
Weder and Schork
RBC Li+-Na+ Countertransport and MAP
149
TABLE 4. Characteristics of Two Groups Defined by Blvarlate Mixture Analysis
Variable (unadjusted values)
n
Age (yr)
Gender (M:F)
Race(W:B)
Weight (kg)
Height (cm)
Seated blood pressure (mm Hg)
Systolic
Diastolic
Mean
RBC Li+-Na+ countertransport
(mmol Li+/1 cells • h)
Group 1
Group 2
384
33.7±7.6
263:121
343:82
78.8+16.7
173.9±9.3
90
35.2±9.6
75M5
41:8
85.5±17.9
176.3±8.6
123.0±15.8
78.4±12.0
93.3±12.2
0.247±0.O8O
140.9±20.7
92.6±15.8
108.7+16.7
0.455±0.147
P*
NS
0.005t
NSt
0.001
0.03
<0.0001
<0.0001
<0.0001
<0.0001
n, number of subjects; M, male; F, female; W, white; B, black; RBC Li+-Na+, red blood cell lithium-sodium.
'Significant by Student's / test, except as noted.
tSignificant by x2Downloaded from http://hyper.ahajournals.org/ by guest on June 14, 2017
Mg2+ media, could contribute to skewing of the
Li+-Na+ distribution toward higher values, particularly if the suppressive effect of Mg2+ is most prominent in subjects with the highest countertransport
values. However, as we controlled for skewness in
our analysis, our finding of a mixture was probably
not affected by this problem in methodology.
We 1619 and others12-20 have previously reported a
positive correlation between blood pressure and
RBC Li+-Na+ countertransport. Subgroup analysis
in the present study suggests that this correlation
results from the presence of two subgroups, one with
relatively low values for blood pressure and countertransport and the other with higher values for both
measures. When the subgroups are analyzed separately, the residual weak correlation found in the
low-MAP, low-countertransport group is abolished
by adjustment for demographic and body size measures. For the smaller group with higher MAP and
100-
£
3
99
r =-0.41
P=.0O01
9897CD • *
*•;
I 2. • 9 6 -
T3
•> *•
5
a
f
9694
-2.36
1
-0.86
1
0.66
r
2.16
1
3.66
1
6.16
Adjusted Na - Li Countertransport
(arbitrary units)
FIGURE 3. Scatter plot showing a significant inverse
relation of mean arterial blood pressure and red blood
cell lithium-sodium (RBC Li+-Na+) countertransport in
the group defined by mixture analysis as having higher
values for both measures.
countertransport, however, the relation is inverse
and is actually improved by adjustment. We can
offer no explanation for the cause of this correlation,
as the mechanisms relating high RBC Li+-Na+ countertransport and hypertension are still uncertain, but
the finding of a significant inverse relation in the
subgroup with higher MAP provides further support
for the contention that Li+-Na+ countertransport or
an analog system is intimately linked to the pathophysiological basis of hypertension in some individuals. In this regard, the recent observations reported
by Canessa et al27 that RBC Li+-Na+ countertransport may be a mode of Na+-H+ exchange and by
Livne et al28 that platelet Na + -H + exchange is
increased in essential hypertension suggest that abnormalities of the ubiquitous transmembrane Na + -H +
exchange may be a fruitful area for future research
into the cellular mechanism causing human hypertension.
In summary, we have demonstrated that high RBC
Li+-Na+ countertransport activity cosegregates with
high blood pressure independent of the effects of age,
race, gender, body weight, or height. Furthermore,
there is a highly significant inverse correlation
between countertransport and blood pressure in the
group with high values of both variables that is not
seen in the group with lower countertransport and
blood pressure levels. These findings support the
hypothesis that there is a distinct subgroup of hypertensive individuals in whom elevated RBC Li+-Na+
countertransport is a marker of a genetic predisposition to hypertension.
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Hypertension
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KEY WORDS • lithium-sodium countertransport • erythrocytes
• essential hypertension
Mixture analysis of erythrocyte lithium-sodium countertransport and blood pressure.
A B Weder and N J Schork
Hypertension. 1989;13:145-150
doi: 10.1161/01.HYP.13.2.145
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