Transcript x ̅ 1 - ARUP Laboratories

Partitioning Reference Intervals Using
Genetic Information
Brian H.
1Department
Methods:
We evaluated Clinical Laboratory and Standards Institute
guidelines for partitioning reference intervals to develop a
method appropriate to the specific situation of partitioning
reference intervals using genetic variants with dominant
effects.
Results:
The partitioning decision point for a dominant genetic
polymorphism is 4% of total variance attributable to the
polymorphism. Similarly, partitioning decision curves are
presented based on difference in mean between two
subgroups, sample standard deviation, and subgroup or allele
frequency. We evaluate the example of Gilbert syndrome, for
which developing laboratory specific partitioned reference
intervals would be statistically reasonable for Caucasian and
African-American populations, but not for Asian populations.
Conclusions:
• We present a simple method consistent with commonly
used guidelines and sample sizes for evaluating whether
partitioning based on dominant genetic effects is statistically
justified.
• There are significant limitations to accepted practice in
developing and using reference intervals that may prevent
future integration of genetic and clinical information.
• Additional research on developing approaches to evaluate
patient normality while incorporating additive genetic effects,
multigenic, and other multifactorial effects is needed to realize
societal goals of rational personalized medicine.
Introduction
The most common statistical tool used by clinicians to evaluate
between patient variation is the population based reference
value. Ideally, reference values are determined by individual
laboratories measuring the analyte levels in a group of
reference individuals who are representative healthy
individuals from the community in which the reference interval
will be used(1). Partitioning can reduce variance and improve
the predictive utility of the reference intervals.
Integrating genetic and laboratory information, where
appropriate, would increase the accuracy of the reference
intervals by eliminating genetic outliers and increasing the
percentage of outliers with underlying pathology.
Unfortunately, if the difference between groups is small the
benefit of subdividing may be offset by the increased
uncertainty around reference range estimates caused by the
decrease in sample size. Before going to the effort of collecting
extra data for partitioning based on genetic information,
laboratory directors will wish to know if including additional
variables would improve the performance characteristics of
reference intervals.
A major goal of this research is to provide a method that allows
an estimate of the utility of partitioning to be made before
beginning sample recruitment for reference studies.
Brian R.
1,2
Jackson
of Pathology, University of Utah School of Medicine, 2ARUP Institute for Clinical and Experimental
Pathology, Salt Lake City, Utah
Statistical Background on the Decision to Partition
Accepted methods for determining reference intervals are outlined in Clinical
Laboratory and Standards Institute (CLSI) documents(1), which are based on the
work of Harris and Boyd(2). Briefly, under CLSI guidelines, if sub-sample standard
deviations are similar, a z- statistic is calculated for the difference between
distribution means,
Figure 1: Partitioning cutoff expressed in terms of sample
Limitations
proportion and ratio of difference in mean between subgroups
to total sample standard deviation
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[1]
There may be relatively few situations where our cutoffs can be utilized
directly because:
• Polymorphisms that have additive effects and subdivide the
population into three subgroups.
• In many situations multiple genes and environmental factors each
contribute small amounts to the total variance.
• Where there is large deviation from Gaussian distribution other
method for partitioning may be more appropriate(4).
1.2
where x ̅1 and x ̅2 are the subpopulation means, n ̅1 and n ̅2 are the number of
subjects in each subgroup, and σ12 and σ22 are the sub-population variances(3). The
suggested cutoff for z-statistics formulated by Harris and Boyd(2) and reiterated in
more general form by CLSI guidelines(1) is:
[2]
This z-statistic cutoff was set such that partitioning will be recommended when
the proportions of individuals above or below the expected lower and upper (2.5%
or 97.5%) cutoffs for subpopulations will be substantially different than those
expected by clinicians (e.g. > 4% rather than 2.5%). Although developed to
partition reference ranges where the subgroups are approximately equal in size
and follow a Gaussian distribution others have suggested that this method is
reasonable for samples of unequal size as long as the standard deviations are
similar, and the z-statistic may also be appropriate for non-Gaussian populations
when there are at least 60 individuals in each subgroup(1, 3-4). Where there are
extreme deviations from normality or large differences in subgroup size other
methods, such as those proposed by Lahti and colleagues may be more
appropriate, but may require larger samples(4).
These limitations highlight the need for additional research on
statistical and potential diagnostic implications of multivariate
stratification to enable more personalized medicine.
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Example: Partitioning bilirubin using proportion of
variance due to UGT1A1 polymorphisms, Gilbert
Syndrome
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Population subgroup frequency
Partitioning by a genetic variant with recessive effects
Partitioning cutoffs relationship to proportion of
variance
For two subgroups with equal variance the total population variance is a function
of the subgroup variance, means of the subgroups, and the relative frequencies of
the populations:
[3]
where σt2 is the total variance, σg2 is variance of the subgroups, x̅1 and x ̅2 are
subgroup means, and a1 and a2 are the relative proportions of the total group
made up by each subgroup. If the variance attributable to the factor that
distinguishes a1 and a2 is represented by θ then σt2 = σg2 + θ and the proportion
of the total variance attributable to a polymorphism is θ/σt2. In this situation the
numerator of the z-statistic (equation 1) can be expressed in terms of θ:
[4]
If the minor allele frequency is represented as q and major allele is represented as
p, a genetic variant with dominant effects divides the population into two
subpopulations with proportions p2, and 2pq+q2 , which can be substituted into
equation 7:
[8]
Figure 2: Partitioning cutoff expressed in terms of minor allele
frequency and ratio of difference in mean between subsamples
to total sample standard deviation with example of Gilbert
syndrome plotted
1.6
Setting z set equal to Harris and Boyd’s recommended cutoff for z* (equation 2):
Gilbert syndrome is characterized by elevated serum unconjugated
bilirubin caused by changes in the UDP-glucuronosyltransferase gene
(UGT1A1), which is responsible for glucuronidation of bilirubin. Elevated
serum bilirubin is most often considered a recessive trait, although other
modes inheritance have been noted(5-7). In populations of western
European descent the TA7 variant has a MAF of approximately 0.4(8-10).
The difference between in means between TA7/TA7 individuals and the
rest of the population is 0.2 mg/dl, and the standard deviation is
0.23mg/dl(8). It would make sense to partition as (x ̅1-x ̅2)/σt is 0.85
(see Figure 2). This is consistent with studies reporting the variability in
bilirubin attributable to the TA repeat to be 27%, which is much greater
than the 4% cutoff(9).
The TA7 allele frequency is between 0.35 and 0.45 in African-Americans
and approximately 0.16 in Asians(9-10). If the effect of the promoter
variant is similar in these populations, generating laboratory specific
partitioned laboratory values would make sense in a lab that serves
mostly African-Americans, but may not in a laboratory that serves
mostly Asians (see Figure 2).
The equation for dominant effects is reverses p and q in this equation (Figure 2).
1.4
Conclusion
•We present a simple method consistent with commonly used
guidelines and sample sizes for evaluating whether partitioning
based on dominant genetic effects is statistically justified.
• This method uses information that would be available to a
laboratory director before recruiting reference samples,
allowing for a preliminary decision on partitioning to be made
prior to recruiting reference individuals.
[5]
1.2
Which simplifies to:
[6]
Thus, a proportion of the total variance of 4% or greater would justify
partitioning into two groups if subsamples have equal standard deviations. This
partitioning cutoff does not change for large or small relative sample proportions
because the calculation of variance already accounts for the influence of sample
proportion.
Similarly, as sample proportion and ratio of difference in mean between
subsamples to total sample standard deviation, changes, so does the proportion
of total variance attributable to the partitioning factor:
(x ̅1-x 2̅ )/ σt
Background:
Integrating genetic and laboratory information could increase
the accuracy of reference intervals by reducing outliers with
non-disease associated genetic variation and increasing the
detection of outliers with underlying pathology. However,
under currently advocated statistical methods the benefit of
subdividing reference groups may be offset by the increased
uncertainty around reference range cutoffs caused by the
decrease in sample size.
Andrew R.
2
Wilson ,
(x 1̅ -x 2̅ )/ σt
Abstract
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Shirts ,
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References
Caucasian
Asian
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African-American
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Minor Allele Frequency
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