U.S. patent application number 12/546234 was filed with the patent office on 2009-12-17 for fulfilling demand for particular blood group types.
Invention is credited to Michael Seul, Yi Zhang.
Application Number | 20090313042 12/546234 |
Document ID | / |
Family ID | 39325218 |
Filed Date | 2009-12-17 |
United States Patent
Application |
20090313042 |
Kind Code |
A1 |
Zhang; Yi ; et al. |
December 17, 2009 |
Fulfilling Demand for Particular Blood Group Types
Abstract
Disclosed is a registry for candidate transfusion donors, which
invokes an inventory management policy to create and actively
manage lists of candidate donors in order to minimize imbalances
between demand and supply across multiple regions and across
multiple categories of donors and recipients. Together with a
genotyping laboratory, the registry does targeted recruitment of
prospective donors who are typed for a set of genetic markers
relating to clinically relevant antigens including mutations of
Human Erythrocyte Antigens (HEA), genetic variants of Rh, and
possibly additional antigens such as HLA and HPA. The registry
monitors incoming demand for transfusion antigen genotypes,
preferably stratify the demand into a set of categories
representing stable subpopulations, and will apply strategies,
disclosed herein, to tune the composition of candidate donor lists
to match the demand, thereby avoiding excess, and unnecessary,
typing of candidate donors.
Inventors: |
Zhang; Yi; (Hillsboro,
NJ) ; Seul; Michael; (Fanwood, NJ) |
Correspondence
Address: |
ERIC P. MIRABEL
35 TECHNOLOGY DRIVE, SUITE 100
WARREN
NJ
07059
US
|
Family ID: |
39325218 |
Appl. No.: |
12/546234 |
Filed: |
August 24, 2009 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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11412667 |
Apr 27, 2006 |
7613573 |
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12546234 |
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11092420 |
Mar 29, 2005 |
7363170 |
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11412667 |
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60621196 |
Oct 22, 2004 |
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60586931 |
Jul 9, 2004 |
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Current U.S.
Class: |
705/2 ;
705/7.31 |
Current CPC
Class: |
G06Q 30/02 20130101;
G16H 40/20 20180101; G16H 40/67 20180101; G06Q 30/0202
20130101 |
Class at
Publication: |
705/2 ;
705/10 |
International
Class: |
G06Q 50/00 20060101
G06Q050/00; G06Q 10/00 20060101 G06Q010/00 |
Claims
1-18. (canceled)
19. A method of maximizing the likelihood fulfilling a certain
number of requests for specific antigen bloodtypes for distribution
to a recipient population having known frequencies of occurrence of
pre-selected genetic determinants of bloodtypes, comprising:
selecting candidate donors from two or more populations, each said
population having known frequencies of occurrence of said genetic
determinants of blood type, wherein the number of candidate donors
selected from each such population as a fraction of the total
number of candidate donors recruited reflects said relative
frequency of occurrence of said pre-selected genetic determinants
among the populations, and wherein the selecting is performed by a
processor and the candidate donors selected are output in a user
readable format.
20. The method of claim 19 wherein the frequency of occurrence of
at least one pre-selected genetic determinant in the recipient
population differs from that of the same genetic determinant in the
candidate donor populations.
21. The method of claim 19 wherein the recipient population is
predominantly in one geographic location and the candidate donor
populations are predominantly in another.
22. A method of determining, for a donor registry which collects
the bloodgroup antigen type of candidate donors and provides the
identity and bloodgroup antigen type of candidate donors to
customers, where different populations of candidate donors
represent populations with a higher proportion of a particular
bloodgroup antigen type, what proportion of donors from each
population to type, comprising: anticipating the demand for blood
products of particular bloodgroup antigen types based on analysis
of historical data using a processor; determining, using a
processor and based on the anticipated demand, the number of
members of the populations having a higher proportion of said
particular bloodgroup antigen types to type, and outputting the
number in a user readable format; and typing said number of said
members.
23. A method of determining, for a donor registry which collects
the bloodgroup antigen type of candidate donors and provides the
identity and bloodgroup antigen type of candidate donors to
customers, where different populations of candidate donors
represent populations with a higher proportion of a particular
bloodgroup antigen type, what proportion of donors from each
population to type, comprising: generating, using a processor, a
coefficient governing the proportion to type from different
populations to type, based on anticipated demand and which, when
applied, minimizes screening of candidate donors beyond those
needed to satisfy the demand; outputting the proportion of
different populations to type as indicated by the coefficient, in a
user readable format; and typing the proportion of different
populations as indicated by the coefficient.
24. A method of determining, for a donor registry which collects
the bloodgroup antigen type of candidate donors and provides the
identity and bloodgroup antigen type of candidate donors to
customers, where different populations of candidate donors
represent populations with a higher proportion of a particular
bloodgroup antigen type, what proportion of donors from each
population to type, comprising: generating, using a processor, a
coefficient governing the proportion to type from different
populations to type, based on anticipated demand and which, when
applied, minimizes screening of candidate donors beyond those
needed to satisfy the demand; outputting the proportion of
different populations to type as indicated by the coefficient, in a
user readable format; typing the proportion of different
populations as indicated by the coefficient; and adjusting, using a
processor, the coefficient to reflect fluctuations in demand for
particular bloodgroup antigen types and outputting the coefficient,
as adjusted, in a user readable format.
25. A method of determining the ratio of candidate transfusion
donors in different subpopulations, where different subpopulations
have different frequency of occurrence of particular blood group
antigen types, to type, in order to fill anticipated demand, where
orders for transfusion units include blood group antigen type
demanded but do not identify the subpopulation of the recipient,
comprising: dividing, using a processor, the donor subpopulations
on the basis of the frequency of occurrence of combinations of
heterozygous alleles; and determining, using a processor, the ratio
of candidate donors from different subpopulations to type for said
combinations of heterozygous alleles, where there is a known
frequency of occurrence of certain of said combinations of
heterozygous alleles and/or blood group antigen types in the
different subpopulations, in order to fill the anticipated demand
for transfusion units of particular blood group antigen types and
outputting the ratio in a user readable format.
26. The method of claim 25 wherein the subpopulations are based on
ethnicity.
27-36. (canceled)
Description
RELATED APPLICATIONS
[0001] This application claims priority to U.S. application Ser.
No. 11/092,420, filed Mar. 29, 2005.
BACKGROUND
[0002] The matching of an extended set of significant antigens
(ExtendedMatch.TM.) will minimize adverse transfusion reactions
(see Hillyer et al., Blood Banking and Transfusion Medicine;
published by Churchill Livingston, Philadelphia Pa.) and other
potential complications arising from allo-immunization. This is so
particularly for patients receiving multiple transfusions who, as
in the case of hemoglobinopathies, may otherwise become refractory
to transfusion. However, the virtually exclusive current practice
of invoking serological methods to determine antigen phenotypes,
one at a time, creates considerable logistical and economic
challenges for the effective implementation of this standard. Thus,
the use of serological typing methods to identify large numbers of
prospective donors with a desirable repertoire of major and minor
transfusion antigens so as to support diverse inventories of blood
products will require a substantial investment of both time and
resources, especially given the increasing expense for increasingly
rare serological reagents. Further, in part reflecting this
investment, the cost of acquiring such units, typically priced to
include a surcharge per desirable antigenic marker matched per
unit, can be prohibitive. The procurement of matched blood for
recipients, who either display an uncommon antigen or lack a common
antigen, is particularly problematic. While collections of
transfusion donors with rare minor blood group phenotypes have been
initiated (see the Redcross website), they remain limited, for
example with currently only 30,000 donors registered in the
American Rare Donor program.
[0003] Recent technological innovation (Hashmi et al., Transfusion,
45, 680-688 (2005)) has the potential to enable the replacement of
serological methods of transfusion antigen determination by methods
of genetic analysis. These methods would not only obviate the need
for rare and expensive serological reagents but also would permit
the concurrent ("multiplex") analysis of an entire set of genetic
determinants of transfusion antigen phenotypes. Large-scale
multiplexed transfusion antigen genotyping, particularly when
combined with non-invasive collection of samples such as "finger
sticks" or buccal swabs, would provide a basis for rapidly
surveying donors for an extended set of clinically significant
antigens and to construct a diversified inventory prior to
collecting, processing and storing blood products.
[0004] The concept of a candidate donor inventory previously has
been implemented in the form of bone marrow donor registries which
have been organized around the world to provide a diverse pool of
candidate donors who can be genetically matched to patients by
comparing the relevant genetic loci within the Human Leukocyte
Antigen (HLA) complex. However, in view of the highly variable
nature of the HLA gene complex, these registries, in order to
ensure a finite probability that a request for a specific HLA type
can be filled, must acquire and maintain a large inventory by
"taking all comers" Yet, by the same token of genetic diversity
within the HLA complex, the likelihood of any donor being called
upon is small, repeat donation exceedingly rare, and inventory
turnover low. In view of the substantial expense of recruiting and
typing prospective bone marrow donors, the operation of such
repositories in an economically viable manner is difficult at best,
and in fact, generally requires public expenditure (as in the case
of the National Marrow Donor Program, see their website) or private
philanthropy (as in the case of private registries maintained by
foundations around the world).
[0005] In contrast to bone marrow and organ donation, blood
donation is relatively painless, and is performed in high volume,
at an annual rate of approximately 50 million donations worldwide,
routinely including repeat donation, creating high turnover in
existing supplies of blood products. The introduction of
large-scale genetic typing into transfusion diagnostics would
permit a systematic increase in the diversity of the inventory to
support an ExtendedMatch strategy in a practical and cost-effective
manner. A diversified inventory in turn would permit the rapid
selection of a donor for a recipient with known transfusion antigen
genotype (TAG) by genetic cross matching (see U.S. application Ser.
No. 11/298,763, incorporated by reference).
[0006] The selection of compatible candidate blood donors in
response to requests posted to a registry of such donors would
facilitate the timely procurement of compatible blood products.
This would be desirable in order to improve the public health and
to minimize the cost accruing in the health care system in the form
of unnecessarily prolonged hospital stays and adverse clinical
effects arising from the administration of incorrectly or
incompletely matched units of blood products such as red cell or
platelets.
[0007] The operation of a transfusion donor registry of diverse
composition and "critical mass" in a commercially viable manner
calls for an effective organizational architecture and for
strategies of optimal inventory management that represent a
departure from the passive repository concept.
SUMMARY
[0008] The invention discloses strategies for the creation and
commercially viable operation of a diverse registry of candidate
transfusion donors, preferably within a transfusion registry and
exchange network (TRXN). As described herein, the registry invokes
an inventory management policy to create and actively manage lists
of candidate donors in order to minimize imbalances between demand
and supply across multiple regions and across multiple categories
of donors and recipients. The registry monitors demand and manages
supply, preferably by forming a commercial alliance with (or by
operating its own) genotyping laboratory, by targeted recruitment
of prospective donors who are typed for a set of genetic markers
relating to clinically relevant antigens including mutations of
Human Erythrocyte Antigens (HEA), genetic variants of Rh, and
possibly additional antigens such as HLA and HPA.
[0009] To permit the determination of actual strategies (or
"policies"), of managing the registry's inventory under various
conditions, the registry described herein operates as an actively
managed buffer between the fluctuating demand and the procurement
of supply by directed recruitment of candidate donors to be placed
into the list(s). The registry will monitor incoming demand for
transfusion antigen genotypes, preferably stratify the demand into
a set of categories representing stable subpopulations, and will
apply strategies, disclosed herein, to tune the composition of
candidate donor lists to match the demand. Methods of stratifying
demand into a set of known, stable subpopulations also are
described, as are strategies for directed recruiting of prospective
donors, preferably by way of non-invasive sample collection
[0010] The demand, in the form of requests posted by member
institutions for units needed instantly as well as in the form of
units reserved for later use, generally will display regional
imbalances and, at any one location, generally will fluctuate in
time. The invention discloses strategies of operating the registry
so as to maximize the probability of fulfilling the set of requests
received at any one time--that is, to minimize the probability of
failing to procure a set of donors who are genetically compatible
with the set of requests--under the constraint of a preset
budget.
[0011] Genotyping of prospective donors represents a principal
contribution to the cost of operations. The identification,
characterization and recruitment of donors with special and thus
generally less common phenotypes (and corresponding genotypic
attributes) requires special effort and corresponding expense, and
fully characterized blood products from such donors generally
command premium prices. It will be a specific objective of the
registry to maintain a list of such special donors. To that end,
certain strategies are disclosed for improving upon random sampling
in identifying donors with special phenotypes by stratification of
the donor population into stable sub-populations. The optimal
desirable composition of the list(s) matching the anticipated
demand across a set of categories dictates the fractional
allocation of funds available for genotyping stratified
subpopulations.
[0012] The registry disclosed herein generates revenue by issuing
to its member institutions including hospital transfusion services
and traditional donor centers, the "permission to call" specific
donors. That is, a member institution can acquire the right to call
upon a specific donor, for one or more blood donations over a
specified period, and perhaps for specific application of derived
blood products. Several arrangements and corresponding pricing
options including the analog of license and royalty payments are
disclosed. There is a "flat" pricing model for units selected under
ExtendedMatch criteria in order to facilitate placement of such
units to generally greater clinical benefit to the recipient.
Further, there are methods of providing incentives to encourage
repeat donations from donors with desirable TAG attributes,
including equity participation and/or profit sharing by individuals
or community organizations.
[0013] In addition, the registry gains revenue by charging fees for
membership as well as for services such as searches applying
cross-matching rules (U.S. application Ser. No. 11/298,763,
incorporated by reference) and for providing a forum for member
institutions to trade the "permission-to-call" licenses among one
another. Preferably, the registry also can provide access to linked
inventories of linked inventories of typed units of donor blood
("actual" units) maintained by its member institutions, thereby
creating a larger potential market for providers, and a larger
product selection to users. In addition, the registry can offer
ancillary services such as transaction management (see U.S.
application Ser. No. 11/092,420, incorporated by reference)
including on-line "genetic cross-matching, to identify available
("callable") compatible donors on its list. Rules relating to the
selection of compatible donors under conditions of varying
stringency are disclosed in U.S. application Ser. No.
11/298,763.
[0014] Revenue generation is determined by the probability of being
able to match requests submitted to the registry reflecting the
inventory policies of member institutions--which in turn reflect
requirements from within a population of recipients of known
genotype distribution and certain actuarial risk profile relating
to the occurrence of accidents and need for surgical procedures.
This probability in turn depends on the size and composition of the
registry. Within the framework of dynamic programming, the
evolution in time of candidate donor list(s) within this buffer is
managed to reflect the events that affect the list composition,
including: acquisition of new candidate donors, selected from the
set of such genotyped donors accepted into the list; re-acquisition
of donors released from "permission to call" agreements by member
institutions; and placement of compatible or desirable (potentially
compatible) donors into permission-to-call agreements with member
institutions attempting to manage their own respective inventories;
as well as the gradual loss of callable donors who become
unavailable.
Preferably, the registry forms part of a transfusion registry
network (TRN), in the form described, which would ensure effective
communication, and would create an effective forum for exchange of
products and services between providers ("sellers") and users
("buyers"), both members of the network. To maximize the clinical
benefit of a transfusion registry network, particularly under a
ExtendedMatch paradigm, the network must offer access to a diverse
population of donors reflecting the wide range of genetic
characteristics of a diverse population of recipients.
Glossary:
[0015] "List".ident.a list of active callable donors;
"Registry".ident.a list of active donors plus "dormant" but
callable donor. "Availability" means the exclusive right of use is
available; in the other words, list is also the real-time inventory
maintained at TRN IT department. "Callable donor".ident.a
collection of information of a donor including identity, address,
callability, genotype, blood type, and other relevant information.
"Callability".ident.an indicator of a donor measuring his/her
willingness to donor one unit of blood next time,
0<callability.ltoreq.1. "Not callable".ident.a situation when a
donor is not active for donation and removed from the "list", i.e.,
callability=0. "Blood type".ident.a combination of the presence of
antigens or the absence of antigens (antigen negatives) in donor's
blood. "Category".ident.a collection of people with stable
fractions of sub-populations (ethnicities). Category can be
demographic, such as local community, or birthplace, or genotype
such as HLA types, etc.
Parameters and Variables
[0016] Part 1: cost parameters I. K=fixed cost to start a typing
program (such as planning and setup fees). v=frequency of a blood
type. c.sup.t=typing cost per perspective donor (fixed).
c.sup.d=typing cost rate per callable donor (varies depending on
active management). c.sup.r=cost rate for initial acquisition
costs. h.sup.r=additional holding cost rate for callable donor
inventory at donor centers. p.sup.r=penalty cost rate for
backorders at donor centers. Part 2: logistic parameters
.alpha.=discount rate (one period) of cash,
0.ltoreq..alpha..ltoreq.1. L=lead time of a typing program. Part 3:
state variables. u=one-period demand for callable donors, a
nonnegative random variable. u.sup.b=one-period demand for blood
units, a nonnegative random variable. w.sup.d=inventory level of
callable donors in the List. x.sup.r=pooled inventory level of
callable donors at donor centers. .mu.=u<.infin..
.mu..sup.b=u.sup.b<.infin.. y.sup.i=outstanding typing program
initiated i periods ago, i=1, . . . , L. {tilde over (y)}=(y.sup.1,
. . . , y.sup.L). Part 4: decision variables. z=pooled order size
from donor centers to TRN-registry. y=internal request size from
TRN-registry-IT to TRN-registry-Lab. Part 5: auxiliary state
variable. v.sup.d=echelon inventory held in the system, i.e., donor
center pool and the TRN-registry. From this definition, the echelon
inventory equals
v.sup.d=x.sup.r+w.sup.d.
Part 6: index. n=the number of periods remaining until the end of
the planning horizon. Part 7: some constraints
y.gtoreq.0, z.gtoreq.0, x.sup.r+z.ltoreq.v.sup.d+y.sup.L.
Part 8: cost parameters II. .beta.=natural decay rate of one
callable donor unit over one period, 0.ltoreq..beta..ltoreq.1.
.gamma.=decay rate of one callable donor unit per usage, or per
blood unit acquired, 0.ltoreq..beta..ltoreq.1. .epsilon.=fraction
of revenue payable from donor centers to registry per blood unit
sold per callable donor unit held at donor centers. .eta.=fraction
per excess callable donor unit the donor centers considered selling
back to the registry. x.sub.c=critical callable donor inventory
level, above which donor centers will consider selling a fraction
of excess callable donors back to registry. .rho.=revenue from
sells per unit blood at donor centers. .rho..sup.b=buy-back revenue
per callable donor unit at donor centers.
DESCRIPTION OF THE FIGURES
[0017] FIG. 1 depicts cross-matching probability of finding at
least one and two phenotype-matched donors in two homogenous
populations. FIG. 2 depicts a scheme for organization of a
transfusion registry network(s) (TRN), with hospitals, donor
centers, patients and candidate donors, where the cross-matching of
donors and recipients is carried out with genetic cross-matching
(gXM) of genotypes.
DETAILED DESCRIPTION
Section 0: Managed Donor List and Management Policy--The Case of
Identical Donor and Recipient Populations
[0018] A problem in a registry as described herein is to determine
the optimal size of a candidate donor pool (to maximize the
probability of having a match with recipients, yet reduce the costs
associated with typing candidate donors) within a single homogenous
or at least stable ("fully stratified") population identical to
that of the recipient(s). The solution, given a distribution of
phenotypes--and that of the underlying transfusion antigen
genotypes, the matching probability (under a specified
compatibility criterion--either an exact match or a match under the
relaxed matching criterion, where the donor does not express any
antigens not expressed by the recipient; see gXM application)--a
cross-match probability is readily calculated--this provides the
basis for determining the optimal number of donors from the same
population that best fulfills transfusion demand without costly
excess screening.
[0019] Probability of finding at least n donors of a certain blood
type (indexed by l or the l-th type) in a randomly sampled donor
set from the said population
Pr ( x .gtoreq. n | N , f l ) = 1 - j = 0 n - 1 ( N j ) f l j ( 1 -
f l ) N - j ##EQU00001##
where parameter N is the size of a donor sample and f.sub.l is the
frequency the blood type. The summation is from 0 to n-1.
Example I
Effect of Donor Set Size and Recipient Blood Type on the
Probability of Finding at Least n Donors
[0020] It is clear that screening donors adds cost, but also that
under-screening can result in donors not being available to fill
demand, which results in revenue loss. Thus, it is beneficial to
balance and arrive at a minimum number screened, so as to reduce
cost, but maintain adequate inventory.
Example I
Illustration of Donor Sample Size Effect on Cross-Matching
Probability in a Homogenous Population
[0021] FIG. 1 illustrates the cross-matching probability of finding
at least one and two phenotype-matched donors in two homogenous
populations, Chinese and Israeli. One particular
phenotype--Do(a+b-)--is considered in this example. Occurrence
frequencies of this phenotype in Chinese and Israeli populations
are respectively 1.26% and 16.56%. Those frequencies were
determined by genotyping a number of donors. Obviously the more
abundant the phenotype in a population, the higher the chance of
finding matches; and, the larger the sample size, the higher the
chance.
[0022] Probability of fulfilling a set of requests from recipients
randomly selected from a given homogeneous (or "stable")
population, as a function of the size of a donor pool randomly
selected from the same population
Pr ( F F l ) = Pr ( x r .ltoreq. x d | N r , N d , f l ) = 1 - i
> j ( N r i ) ( N d j ) f l i + j ( 1 - f l ) N r + N d - i - j
##EQU00002##
where N.sub.r and N.sub.r are recipient sample size and donor
sample size, respectively, and f.sub.l is the frequency of the l-th
blood type.
[0023] Active inventory management is the practice of matching
inventory to average anticipated demand (as opposed to blindly
maximizing inventory, thereby ensuring that requests will be met
with high probability, but reducing turn-over, thereby incurring a
low return on the initial investment of gTyping an excess number of
candidate donors), which leads to the optimal solution. Maintaining
inventory at a certain preset multiple of anticipated average
demand is most desirable.
[0024] Demand for particular bloodtypes will vary based on factors
including the genetic distribution of the relevant blood group
antigens in each local recipient population. Where increased demand
for certain bloodtypes is anticipated, stratification of donor
populations such that those representing a larger proportion of
such bloodtypes are identified, can be used to maintain
demand/supply balance.
Section I: Right-to-Call Pricing and the Value of Repeat Donors
[0025] Candidate donors with desirable transfusion antigen
attributes--generally implying premium pricing of blood
products--are particularly valuable as repeat donors since no
additional genotyping is required--this concept is not part of
current blood bank pricing policies. Thus, simply selling an assay
permitting genotyping may under-represent the potential future
value of information derived by application of the assay. On the
other hand, excess cost will be incurred.
[0026] The solution is a "right-to-call" pricing model, connecting
price and cost of operations, most notably the cost of genotyping,
which is further connected to transfusion antigen genotype (TAG)
frequencies in the population and other factors. This pricing model
is distinct from current methods where pricing is based on
irrelevant parameter--e.g., the number of antigen negatives, that
discourages efficient registry management and utilization of
resources.
[0027] The "right-to-call" pricing structure would typically
include an upfront payment ("access fee"), a periodic payment for
the continued (de facto exclusive) right to call, and a fee based
on the fraction of recurring revenue from sales of blood products
derived from a specific donor. In return for undertaking a
screening program at its own expense, hence at its own risk, a
registry can identify candidate donors with special attributes. In
return for having made an investment and having accepted the risk,
the registry, when conferring upon a producer or distributor of
blood products the right to call upon such a donor, can charge an
upfront ("access") fee, a fraction of all revenue derived by the
producer or distributor from such a donor ("royalty") and a
periodic payment while the producer or distributor--in accordance
with its own inventory policy--holds the right to call upon said
donor, said periodic payment reflecting the registry's inability to
generate revenue from conferring to a third party the right to call
upon said donor. The size of the periodic payment can be based on
the loss of revenue otherwise generated in the form of an access
fee and royalty payments charged to a third party (periodic payment
must be sufficiently high to deter producer from simply "shelving"
the callable donor).
[0028] As an alternative, donor centers may choose to sell excess
inventory of callable donors back to the registry, allowing sharing
of donor information, or may elect to list excess inventory for
sale to other participating donor centers by way of transactions
hosted by the registry.
Pricing and the Standard of Clinical Care
[0029] The Relationship Between Pricing Strategies and Standards of
Medical Care. It is clear that mismatches in some blood group
antigens are more clinically significant than others (see U.S.
application Ser. No. 11/298,763). The more clinically significant
antigens cannot be as readily mismatched. The price for obtaining
blood which can match such antigens is related to the amount of
effort required to obtain the product, which has to do with
occurrence frequency of that product in the population.
[0030] The intrinsic value of one callable donor unit is related to
the amount of effort invested for searching. If a blood type is
rare, the price is usually higher. The price .rho..sub.l of one
unit of blood of type l is approximately
.rho..sub.l.apprxeq..rho..sub.0+.rho..sub.1v.sub.l.sup.-q, where q
is a constant and 0.ltoreq.q.ltoreq.1. Before T periods later, when
one callable donor unit is fully depreciated, the total potential
value per such unit is:
.pi..sub.l.apprxeq.c.sup.r+.epsilon..rho..sub.lT.
[0031] The cost per callable donor unit can be represented by:
c l d = c l d ( y , .theta. , C max ) = C * l y l v l - q l v l - q
, ##EQU00003##
with nonnegative constant q specified above, and the price per unit
callability is related to the cost per unit by some scaling factor
plus a price offset which can be either markup or markdown in order
to match a demand curve:
p.sub.l.about.kc.sub.l.sup.d+offset
[0032] Where bloodgroup determinants are typed in a "multiplexed"
assay, which types a variety of bloodgroup determinants including
those resulting in antigens having greater clinical significance,
this avoids creating a disincentive to typing of antigens having
greater clinical significance, as would occur in serotyping--where
additional antigen typing can dramatically increase typing
cost.
Section II: Active Management of a Donor Registry by "Optimal
Mixing"
[0033] Problem: as demand for blood fluctuates over time (that is,
from period to period), imbalances may develop between demand and
supply--random sampling becomes ineffective, because random donor
sample may not reflect the actual blood type distribution in the
demand and thus cause overtyping of donors and waste of resources.
In addition, geographical imbalances between demand and supply will
exist that remain stable over time.
[0034] Having introduced the concepts of a guided selection of
candidate donors, and conferring a right to call upon available
("qualified") candidate donors and right-to-use fees, for the
special case of a fully stratified population, it is now helpful to
generalize to a situation, encountered in practice, characterized
by an imbalance between the number of requests received per period
from within a specific category ("fluctuating demand"), and the
number of callable donors from within that category available to
match those requests. The optimal strategy for active management of
a registry in handling imbalances in "same-category" demand and
supply calls for "optimal mixing" of candidate donor s selected
from multiple available categories (e.g., African-Americans,
Asians), each such category characterized by a set of antigens (and
corresponding underlying transfusion antigen genotype) frequencies,
and possibly other factors such as the readiness to donate.
[0035] Consider the function of the registry to maintain an
actively managed list of candidate donors which is "not too small"
and "not too large." In that list, each entry consists of the
identity, genotype, and (corresponding) blood type of a donor, the
blood type preferably in the form of a binary string representing
the presence or absence of specific expressed transfusion antigens.
(see gXM application). In addition, each entry also is assigned a
"category" ("slot") which relates to the distribution of
transfusion antigen genotype ("TAG") frequencies and related
factors, such as actuarial factors, affecting the availability of
candidate donors in that category. The numbers of callable (or
active) donors in the slots represent the "inventory levels" at the
TRN. Donors maintained in the list can also be inactive. Inactive
donors can be those who are not available or reachable--these
entries, after some time and in accordance with certain
criteria--are removed from the active donor list or the
inventory.
[0036] At any particular time, the number of requests from within a
specific category may exceed the inventory of callable donors from
within the same category. Maintaining an optimal inventory in such
a situation calls for an optimal "mix" of candidate donors across
multiple categories. A category, for example, can be a specific
homogeneous population within the proximity of a specific blood
bank client of the registry, or can be a demographic segment within
a certain "stable" population (of known TAG frequencies). As
discussed below, registry searches can be organized to return
candidate donors per category, for example, availability at the
nearest collection site.
[0037] The optimization problem relating to the general case is
formulated in Section III by mapping it to the determination of the
optimal inventory management policy for a 2-echelon model; it is
shown that an optimal solution exists.
Section III: Operation of an Actively Managed Donor Registry
[0038] Often times, consulting the TRN may be more appealing for
the immediate access to a greater selection of callable donors. For
example, one donor center may "deposit" the availability of
callable donors and an "order" requesting donor info of the same
blood type can be "filled" via the network. Information sharing
benefits both patients and service providers. Data centralization
and "exchange" functionality of the TRN allows expansion of the
network, and economies of scale will be readily assessable. The
real-time aggregate demand and supply also provides the direct
affiliates within the network a unique opportunity to forecast and
better administer their donor recruiting programs.
III.1 Functional Organization
[0039] The TRN would actively managed the list ("buffer") between
fluctuating aggregate demand in the form of pooled recipient
requests and supply in the form of candidate donors recruited and
TAG-typed at a laboratory, and would respond to specific requests
from the list manager specifying optimal mixing ratios across
specific donor categories. Receiving and Processing Requests within
a Network--A request for a particular blood product typically is
initiated by a hospital on a patient's behalf. The patient's
genotype and so-derived blood type are sent to the donor center. If
a matching unit is found in the donor center's own inventory of
blood products, it is delivered. If no matching unit is found, the
donor center subscribing to the services of a TRN (such as that
disclosed in co-pending application Ser. No. 11/092,420) may take
one of two actions--it may look up a local list of callable donors
and make arrangement for blood donation, or it may post a request
for a unit of particular blood type on a listing hosted at the
TRN.
[0040] All interested parties, including peer donor centers within
the TRN, are able to view the listing and compete to fulfill the
request, for example, by bidding (in accordance with an auction or
other mechanism, see below) the winning donor center owns the right
to deliver the unit. The mechanism of listing and bidding,
preferably hosted at TRN's network site, such as a
password-protected world-wide-web (WWW) site, facilitates
competition and enables an efficient way of utilizing blood
resources.
[0041] Donor centers, in order to replace blood units delivered in
response to requests, may consult the registry to identify local
callable donors and may elect to call upon such donors for
donations.
[0042] Demand Monitoring by the List Manager--While fluctuations in
demand at individual donor center may be large and random, the
aggregate demand may display a smaller stochastic component. The
reason is that, a hospital may choose to send request for a
specific blood unit to any one of the available donor centers. If
those centers are linked to a common registry network, demand
fluctuations are distributed across the entire set of member
institutions.
Problem: predictability of demand fluctuation.
[0043] The solution is to pool demand by monitoring demand pattern
in a centralized blood unit exchange. "Noise cancellation" would
improve demand distribution prediction and facilitate development
of optimal policy in inventory control. Callability is generally
reserved for donors who have been genotyped but have not actually
donated blood.
Replenishing the List: Donor Callability Status--This circle
related to the handling and usage of blood product reduces
"callability" of donors on the lists at donor centers. Again, the
"callability" is an indicator measuring a donor's willingness to
donate one unit of blood upon request. The value of callability is
between 0 and 1. A value of zero means the donor is not callable
and thus is removed from the list. If one adds up capability values
of all donors in each category, the sum represents a measure of the
level of a local inventory of qualified donors. If this level drops
below some threshold, the center will attempt to replace the
"spent" capabilities, by either identifying and typing qualified
donors by itself or purchasing information units from a TRN of
which it is a member.
[0044] A TRN, organized in accordance with the present invention,
hosts an information-technology (IT) division which maintains a
list of callable donors, provides cross-matching (xM) and bidding
services to the donor centers, and generates requests for qualified
donors. The TRN also has a relationship with a diagnostic
laboratory, which directs selection of candidate donors and manages
g-typing programs. The laboratory can be part of the TRN, for
example, as a division, or it can be a TRN affiliate, funded by the
TRN and/or other public expenditure.
[0045] Genotyping as a method of erythrocyte antigen typing and
blood type determination makes it possible to separate--in time and
in space--the processes of targeted recruiting of candidate donors;
making the bloodtype determination (for example in an affiliated
laboratory); and collecting and processing the actual blood;
[0046] The submission preferably takes place via an interface such
as a website. Upon receiving a request, the user interface sends a
request to the database management software at IT division of the
TRN. The software looks up the active donor list, locates suitable
donor(s) of the requested blood type(s), and then returns the
information for downloading.
III.2 Transactions-Flowchart
III.2A Typical 2-Party Transaction:
TABLE-US-00001 [0047] Requesting Entity (location A):
TheRegistry
III.2B 3-Party Transaction without Delay:
TABLE-US-00002 Requesting Entity (location A): TheRegistry
(location B): Field Collection Unit (location A) Requesting Entity
(location A): Receive or anticipate request for specific blood
type(s) place request to REGISTRY for specific bloodtype
TheRegistry (location B): receive and process request (via gXM
Engine); IF MATCH in Actively Managed Donor List (AMDL) { notify
donor; schedule collection (local Processing Entity, or Field
Collection Unit); manage shipment of unit to Requesting Entity; }
ELSE ("out of balance supply") { notify closest Field Collection
Unit; trans-ship sample to selected genotyping partner; notify
donor; schedule collection (local Processing Entity, or Field
Collection Unit); manage shipment of unit to Requesting Entity;
}
III.2B 3-Party Transaction with Delay ("Scheduled Delivery"):
TABLE-US-00003 Requesting Entity (location A): TheRegistry
(location B): Processing Entity (location A)
III.3 Operating an Actively Managed Donor List: Optimal Inventory
Policy
[0048] An active donor list at TRN can be viewed as a separate
"virtual" inventory operating in tandem with an inventory of all
local lists combined.
[0049] The optimal inventory policy at the registry is designed to
absorb fluctuations in demand, in the form of the aggregate of
requests generated by donors centers within the network. The active
donor list at the registry is maintained in accordance with the
optimal inventory policy by the registry's IT division which
forwards requests for typing of new candidate donors to the
diagnostic laboratory affiliate which organizes typing programs in
order to fill the requests.
[0050] To develop an optimal inventory policy for an actively
managed registry handling the general case of demand-supply
imbalance within the context of a network of interacting parties
participating in the procurement of transfusion products, consider
a registry as an element of a transfusion network. Such a
transfusion network can be organized as illustrated in FIG. 2,
comprising major entities including transfusion registry network(s)
(TRN), donor centers, hospitals, patients and candidate donors.
Optimal Inventory Policy
[0051] A TRN preferably co-hosts listing and bidding services for
blood unit exchange among the donor centers. Since the requests for
callable donors reflects the requests for blood units after some
time delay, a transfusion network may explore this correlation and
improve its capability of predicting near-term overall demand for
callable donors.
Actively Managed Buffer:
[0052] Inventory control coordinates demand (hospitals), retail
inventory (donor centers), and warehouse inventory (registry)
revenue. Best policy of recruiting and typing qualified donors
depends on demand distribution, gXm, inventory levels, and cost per
unit qualified donor unit quoted from affiliated lab.
[0053] Formulation of the optimization problem--minimize
.delta..sub.PxM at a given cost, and write down appropriate
evolution equations to map onto dynamic programming and 2-echelon
inventory models. (Buffers: blood center, registry).
[0054] Some Assumptions--To simplify an callable donor inventory at
a donor center, we assume donor centers can always manage to
replenish blood inventory level shortly after units are delivered
before they further request donor contacts from a donor registry.
Dynamics of inventory level at donor centers should also take into
account the decrease in excess inventory due to the buy-back
program at the registry.
[0055] Cost in the System--Suppose a donor registry serves more
than one blood center, the pooled cost includes the fixed cost of
subscription fee (A.sup.s) and one-period expected penalty and
holding (licensing) costs. If there is negligible variable cost of
information delivery, the system-wide variable holding cost is
negligible and only cost is penalty cost, that is
p.sup.rE[u-.beta.x.sup.r-z].sup.+. Besides holding cost
(licensing), other expected costs include initial acquisition cost
and cost due to sales of blood unit drawn from the callable donors
at hand (loyalty). The total expected cost is expressed as:
E ( [ c d ( y , .theta. , C max ) + .DELTA. ] z + u b ) = [ c d ( y
, .theta. , C max ) + .DELTA. ] z + .gamma. .mu. . ##EQU00004##
On the other hand, system-wide expected costs related to setup and
typing acquisition
[0056] A Finite-Horizon Dynamic Program--A dynamic program,
.sub.n({tilde over (y)}, v.sup.d, x.sup.r), can be formulated to
address minimum total discounted expected costs with n periods
remaining, if the system begins from some initial state ({tilde
over (y)}, v.sup.d, x.sup.r), excluding all the fixed costs . .
.
[0057] Existence of Solution--Following footsteps of Clark and H.
Scarf, "Optimal Policies for a Multi-Echelon Inventory" Problrm.
Mgmt. Sci. 6, 475-490 (1960), the problem is decomposed into a pair
of sub-problems, which also makes it more relevant to the interest
of donor centers. The first of the sub-problems involves donor
center pool alone: Since R(.cndot.) is a convex function and adding
a linear function of a function does affect the its convexity, a
critical-number policy solves this problem.
[0058] From system's standpoint, neglecting the cost encountered
between donor centers and TRN, which nets to zero, an induced
penalty cost functions may be defined and a second dynamic program
can be defined. Assume the demand probability distribution peaks,
the penalty function should be a decreasing function of .xi. and
set to zero as .xi. becomes greater than a critical level
x.sub.n.sup.r*. If the cost rate c.sup.d such that it does not
affect the declining nature of the penalty cost at small y's, the
minimization problem .sub.n.sup.d({tilde over (y)}, v.sup.d)
clearly is convex and an (s, S) optimal policy exists. Basically,
shifting the initial acquisition cost appropriately to the loyalty
charges later on facilitates the transactions between donor centers
and the network and reduces the system-wide penalty of not filling
requests from transfusion recipients.
[0059] The general minimization problem is now decoupled into sum
of two sub-problems that are solvable:
.sub.n({tilde over (y)}, v.sup.d, x.sup.r)= .sub.n.sup.r(x.sup.r)+
.sub.n.sup.d({tilde over (y)}, v.sup.d),
and an optimal policy for the system consists of an optimal policy
for .sub.n.sup.d({tilde over (y)}, v.sup.d) for the typing programs
and a modified critical-number policy for .sub.n.sup.r(x.sup.r) as
the order policy from the donor centers.
[0060] The above formulation was derived for one blood type
inventory and the budget constraint C.sub.max aims at a single
blood type. In reality, many blood types coexist in the inventory.
The above formulation is still valid in this case, except C.sub.max
then stands for the budget constraint for typing programs
attempting to find qualified donors of more than one blood type.
The parameter .theta. will be introduced in the next section, which
is related to the knowledge of stratified donor population. It will
be seen the effect of the budget is reflected in the cost per
callable donor, c.sup.d, which takes part in the overall
optimization of the current inventory control.
[0061] In a more general case: fluctuating demand from complex
time-varying population.fwdarw.inventory control alone is not
sufficient because demand distribution can greatly differ from any
homogenous distribution.fwdarw.call for active management on supply
side.
Active Management of Supply: "Optimal Mixing"
[0062] Problem: how to enhance representation of callable donors in
view of fluctuating policies of heterogeneous nature resulted from
inventory control?
[0063] Solution: selecting candidate donors and tuning inventory to
minimize per callable donor cost by active mixing of at least two
populations (and typing based on a mixing ratio). The goal is to
minimize overall cost per unit callable donor, c.sup.d, an implicit
parameter in active demand management, related to the typing
policy, categories, and a budget constraint:
c.sup.d=c.sup.d(y, .theta., C.sub.max), by way of directed sampling
on the supply side.
[0064] The first step is to gain as much information as possible of
the populations at hand. This step basically is to study the
composition in the donor populations or, in the other words, to
"stratify" a stable population into finer subpopulations, such as
"pure" ethnicities or any other relevant stable categories.
[0065] Knowing the BloodType Distributions is a Prerequisite--In
donor populations, bloodtype distribution is a prerequisite and the
only way to arrive at an accurate result is by way of genotyping,
so that a registry network has thoroughly collected information
about the donor population. First of all, genotype frequencies of
the sub-populations (ethnicities) are known, which are denoted by
{f.sub.jl} with index l for different genotypes and j for different
sub-populations. The summation of {f.sub.jl} over all genotypes for
any given sub-population is thus unity, or
l f jl = 1. ##EQU00005##
We define ethnicity profile, which has been surveyed, for each
category, indexed by i, as a set of mixing coefficients {c.sub.ij},
which satisfies
i c ij = 1. ##EQU00006##
Since the frequency of occurrence of bi-allelic combination is
additive, one can calculate the genotype frequencies in any given
category by way of linear combination. We denote such frequencies
with {.theta..sub.il} and the whole set with .theta.. There is
then
.theta. il = j c ij f jl . ##EQU00007##
The frequencies of the sub-populations are time-invariant and the
frequencies of the categories may vary slowly over time but can be
monitored closely. Those observables are assumed known and not
tunable. However, if sufficient genotype distribution in donor
population is known, in principle, one can adjust the sampling
strategy on the donor population so as to type and seek in the
categories that are known to be richer in the genotypes of
interest. Consequently, the overall typing cost of the qualified
donors is lowered by directed sampling.
[0066] Formulate the Problem--We introduce {.omega..sub.i} to
denote a set of mixing coefficients of the categories, or
collectively by .omega.. Let the mixed donor population be
{v.sub.l}. There is then
v l = i .omega. i .theta. il = i , j .omega. i c ij f jl .
##EQU00008##
Since the sampled population has uncertainty, we need to express
the probability of completely filling (full-fill) of the requests
(y.sub.l). We denotes such probability Pr.sup.ff and there is
Pr ff ( y l | D , .omega. , .theta. ) = d l .di-elect cons. [ 0 , D
] .delta. 0 + ( d l - y l ) Pr ( .xi. = d l | D , v l ) ,
##EQU00009##
[0067] where D is the total size of donor population and function
.delta..sup.0+(.cndot.) is defined as
.delta. 0 + ( y ) = { 1 y .gtoreq. 0 0 y < 0 , ##EQU00010##
[0068] Then,
Pr ff ( y l | D , .omega. , .theta. ) = d l = y l D Pr xM ( .xi. =
d l | D , v l = i .omega. i .theta. il ) = Pr xM ( .xi. .gtoreq. y
l | D , v l ) ##EQU00011##
[0069] where Pr.sup.xM is a cross-match probability and can be
approximated by a binomial distribution. The probability of
fulfilling all y.sub.l requests of blood type l thus equals the
probability of finding at least y.sub.l qualified donors in D
individuals drawn from a mixed population, in which l-th blood type
has a combined frequency of .nu..sub.l. And the function has the
form,
Pr xM ( .xi. .gtoreq. n | N , f ) = 1 - k = 0 n - 1 ( k N ) f k ( 1
- f ) N - k .apprxeq. P ( n , Nf ) , ##EQU00012##
[0070] which can approximated by an incomplete gamma function,
P(.cndot.).
P ( a , b ) .ident. 1 .GAMMA. ( a ) .intg. 0 x - t t a - 1 t = 1
.GAMMA. ( a ) - x b a k = 0 .infin. .GAMMA. ( a ) .GAMMA. ( a + 1 +
k ) b k ##EQU00013##
[0071] The intrinsic value of one callable donor unit is related to
the amount of effort invested to search for it. If a blood type is
rare, the price is usually higher. The price .rho..sub.l of one
unit of blood of type l is approximately
.rho..sub.l.apprxeq..rho..sub.0+.rho..sub.1v.sub.l.sup.-q, where q
is a constant and 0<q<1. Before T periods later, when one
callable donor unit is fully depreciated, the total potential value
per such unit is:
.pi..sub.l.apprxeq.c.sup.r+.epsilon..rho..sub.lT.
[0072] The objective of the active management is to tune the
sampling of donor population to minimize the probability of NOT
realizing the full value of the potential callable donor units
under given budget constraint. Such probability can be expressed
as:
.delta. Pr v ( y | C , .omega. ) = .pi. l [ v l ( .omega. , ) ] y l
[ 1 - Pr ff ( y l | D = C c _ t , .omega. , ) ] l .pi. l [ v l (
.omega. , ) ] y l ##EQU00014##
[0073] where c.sup.t is the averaged cost over categories, if
typing program adopts different configurations of the typing tools
among the different targeted categories, then
c _ t = i .omega. i c i t . ##EQU00015##
We denote optimal probability above {circumflex over
(.delta.)}.sub.Pr.sup..nu. and define the following optimization
problem:
.delta. ^ Pr v ( y , .theta. , C m , .delta. th ) = min .omega. { [
.delta. Pr v ( y | C , .omega. ) - .delta. th ] + : C .gtoreq. 0 ,
.omega. .gtoreq. 0 , i .omega. i = 1 , C .ltoreq. C m } ,
##EQU00016##
where .delta..sub.th is a threshold in percentage, e.g., 0.1%, and
C.sub.m is the maximum typing budget. If the optimal total cost is
below this budget limit, the problem is to minimize
.delta..sub.Pr.sup..nu., or if possible to make it below the
threshold .delta..sub.th. Otherwise, the problem is minimization of
.delta..sub.Pr.sup..nu. under total cost constraint, C.sub.m. Prove
Optimal Cost is the Lowest Cost--Let .omega.* and C* be solution of
the above optimization problem, namely, .omega.* denoting the
optimal mixing coefficients of categories and C* denoting the
"optimal" cost. Intuitively, the so-calculated C* is "optimal" in
the sense that it is the minimal cost of arriving at any given
.delta..sub.Pr.sup..nu.. The proof is by contradiction. Suppose the
optimal cost is not minimal cost for a given
.delta..sub.Pr.sup..nu., there should exist a total cost C**
(<C*) that achieve the same .delta..sub.Pr.sup..nu.. Then,
instead of saving on the total cost by the net amount of C*-C**, we
put it in use and type some extra prospective donors but
concentrating on one existing category. The result: with the same
C*, we achieve a lower a .delta..sub.Pr.sup..nu. with an
effectively different, obviously better, .omega.**. This
contradicts our assumption that .omega.* is optimal. The cost per
callable donor unit can be then computed as:
c l d = c l d ( y , .theta. , C max ) = C * l y l v l - q l v l - q
, ##EQU00017##
with nonnegative constant q specified above. Interestingly, a
smaller value of p shifts the cost from extremely rare blood types
to less rare ones. By using appropriate pricing strategy, the
system-wide utility efficiency can be lifted. The averaged cost per
callable donor is:
c _ d = c _ d ( y , .theta. , C max ) = C * l y l ##EQU00018##
Global Optimization--an inventory model was formulated that handles
demand fluctuation and non-zero delay in delivery of the typing
results. We showed that optimal solutions exist to solve the
inventory problem. However, the cost structure has to be decided
together with the typing programs. We then formulated the
optimization problem that finds the optimal mixing coefficients
that best fulfills the request under budget constraints. This
problem handles the uncertainty on the supply side, namely the
donor population, by way of stratification and tuning. The best
cost structure is then a negotiation parameter between the demand
solution and supply solution. By solving two solutions iteratively,
one can achieve global solutions.
[0074] In a case of an initial random mixed (patient) population,
the optimization problem is likely end up with a set of mixing
coefficients simply reflects the proportions in the mixing
coefficients of ethnicities in the sample. As the registry
operation continues, it is likely bloodtype distribution in the
patient population follows a pathway so that real-time composition
deviates unpredictably from the original one. In such case, a
general global optimization routine should be run in order to reach
an optimized mixture of donors and a system-wide low cost. An
interesting case is unusually high occurrence of rare bloodtypes
may be easily cross-matched by looking into a different ethnicity
or in a different region, in which such types are more frequently
represented--an action that is likely automatically taken by the
optimization process.
[0075] It should be understood that the terms, expressions and
examples herein are exemplary only and not limiting and that the
scope of the invention is limited only by the claims which follow,
and includes all the equivalents of the claimed subject matter.
* * * * *