Genetics of Classic von Willebrand s Disease. II. Optimal Assignment of the Heterozygous Genotype (Diagnosis) by Discriminant Analysis

Transcription

1 Genetics of Classic von Willebrand s Disease. II. Optimal Assignment of the Heterozygous Genotype (Diagnosis) by Discriminant Analysis By Connie H. Miller, John B. Graham, Lynn R. Goldin, and Robert C. Elston In classic von Willebrand s disease (vwd). assignment of the heterozygous genotype for genetic studies and diagnosis for clinical purposes (which are not exactly the same) are formidable problems. We have pointed out in the first report in this series that almost 50% of the members of two large kindred who transmitted this disease. and were therefore heterozygous. were scored as normal by the usual tests of hemostasis. This report describes how this large proportion can be significantly reduced by application of discriminant analysis. Using linear discriminants in three variables-coagulation factor VIII (VIll:C), factor-vill-related antigen (VIIIR:Ag). and the ristocetin cofactor related to factor VIII (VIIIR:WF)-we were able to classify as heterozygous more than 80% of the transmitters in the two large kindred. It was of particular interest that the four parents of two related vwd homozygotes could be scored as heterozygous by discriminant analysis even though all their laboratory tests were within the normal ranges. T HE FIRST REPORT in this series documented the wide phenotypic variation among the members of two large families transmitting classic von Willebrand s disease (vwd) when bleeding time (BT), factor VIII coagulant activity (VI I I:C), factor-vi I I-related antigen (VI I IR:Ag), and ristocetin-related platelet aggregation or Willebrand factor (VIIIR:WF) were tested. Specifically, 1 1 of the 16 phenotypes possible when the results of the four tests are considered simultaneously as binary variables were observed in the two families. It was also pointed out that only 58% of a group of 6 transmitters, presumably heterozygous, could be so identified by these tests. Assigning the heterozygous vwd genotype to a particular individual in genetic studies or for clinical purposes is difficult. This report will evaluate most of the methods currently used for this purpose, including each of the factor-vill-related activities and certain ratios between these activities. We have also applied linear discriminant analysis using three variables (VIII:C, VIIIR:Ag, and VIIIR:WF) and have found it to be superior to all other procedures examined. From the Division of Thrombosis and Hemostasis, Department of Pathology. School of Medicine. the Curriculum in Genetics, and the Department of Biostatistics, School of Public Health, University ofnorth Carolina. Chapel Hill. NC. Submitted July ; accepted March 1 9, /979. Supported by U.S. Public Health Service Research Grants HL from the National Heart, Lung. and Blood Institute and GM from the National Institute of General Medical Sciences. Training Grant GM-0709 from the National Institute of General Medical Sciences, and Research Scientist Award MH Address reprint requests to John B. Graham. M.D.. Department of Pathology. School of Medicine. University ofnorth Carolina. Chapel Hill. NC by Grune & Stratton, Inc /79/540-OO15$O1.OO/O Blood, Vol. 54, No. 1 (July),

2 138 MILLER ET AL. MATERIALS AND METHODS The families transmitting vwd were selected, examined, and tested as described previously. The data collected on 75 members of family I and 106 members of family included BT, VlII:C, VIIIR:Ag, VIIIR:WF, and a detailed history concerning excessive bleeding. The details of the tests and the method of assessing the symptoms are described at length in the first report in the series. The general method for determining the values of the various procedures was the following. Three reference groups were assembled from within the kindred: unrelated normals, affected persons, and transmitters. The normals were 30 unrelated persons who had married members of the kindred, and this group was used to establish the normal limits for the various tests. The actual data are contained in Table 3 of the preceding report. Estimated 95% limits (mean ± I.96 SD) for each of the F-VIII-nelated activities in the unrelated normals were calculated and used diagnostically in a one-tailed test. This implies, of course, that.5% of normal people lie outside the limits in the direction expected in vwd. In determining these limits, values for VIII:C, VIIIR:Ag, and VIIIR:WF were transformed to logarithms to produce nonskewed normal distributions for the calculations, whereas BTs were used in original units. Then every person in the main line of descent of each family was scored as affected or unaffected using the normal limits, an affected person being one who had one on more test value outside the 95% limits in the direction expected in vwd. There were 4 such affected persons in family I and 34 in family. For calculating a discniminant function, those who were scored as affected on the basis of this criterion and on whom complete data were available were used as the reference group of affected persons, and the group used for establishing the normal limits was used as the reference group of normals; however, individual IV-l in family was excluded from the normal group because of hen extremely high VIIIR:WF value. The value of each diagnostic method was assessed on the basis of its ability to detect heterozygosity for vwd in a third reference group, a group of 6 persons designated as transmitters. The 6 transmitters were persons in the main line of descent of either kindred who had produced one on more affected descendants (affected as defined previously); thus, the selection of the transmitters was based directly on genetic evidence and only indirectly on phenotypic evidence. It is important, therefore, that the assumption that transmitters are heterozygotes be soundly based. Two types of information that are pertinent are shown in Table I : the number of abnormal descendants from each transmitter and the number of phenotypic abnormalities of each transmitter. It is assumed that multiple affected descendants or multiple phenotypic defects are strong evidence of heterozygosity. Fifteen of the 6 transmitters had multiple affected descendants. Four of the remaining 1 1 transmitters had multiple phenotypic defects. Three of the remaining 7 transmitters each had a single affected descendant with multiple phenotypic defects. This means that only 4 transmitters each of whom had a single affected descendant had descendants with marginal defects. These were IV-63, V-l7, and V-l8 of family I and V-l of family. Thus there is good evidence supporting the heterozygosity of of the 6 transmitters. Standard statistical calculations were performed using subroutines available in the Statistical Analysis System on SAS. Descriptive statistics including mean, SD, and skewness were calculated in original units and after square-root and logarithmic transformations of each variable. The significance ofskewness in each distribution was determined by reference to standard tables,3 and the transformation eventually used in each instance was the one that brought about a more nearly normal distribution. A few outlying values that contributed significantly to skewness after transformation were eliminated from the sample. Except as noted below, the discniminant functions were calculated using the method described by Elston et al.,4 generalized for three variables. The effect of age on the various tests in the various vwd subgroups was a problem, as it sometimes has been in the detection of hemophilia A carriers.4 However, it has tended to be more difficult in vwd kindred because both males and females of all ages must be assessed and hormonal differences may be at play that are affected by both age and sex. Data on both sexes were pooled whenever possible. Assuming normally distributed discniminant scores in each group, distributions were determined for affected persons and normals by the sample means and variances, and the proportions in these two linkage 5Family I is HGAR3 and family is HGAR4 in Dr. Elston s registry of large kindred assembled for studies.

3 GENETICS OF VON WILLEBRAND S DISEASE: 139 Table 1. F-VIII-Related Activities of the Test Group of Transmitters Number of Age BT VIll:C VlllR:Ag VIIIR:WF Affected Subject (w) Sex (mm) (U/cl) (U/dI) (U/cS) Symptomsf Descendants Family IV-i 67 F lv F lv-8 58 F IV M lv F lv-95 6 F IV F V-6 41 F V-i3 48 F V-i7 39 F V-i8 46 M i >i ii #{149} MIld 69 Mild 16 Moderate 1 Moderate 85 Mild 93 Moderate 81 Mild 3 Moderate 39#{149} Mild 66 None 5O None 3 3 Family IV-7 81 F lv-8 79 M IV-9 76 F IV-0 74 M IV F IV M V F V-1 58 M V-5 56 F V-9 4 F V-3 49 F V F V F M VI F #{149} #{149} 34#{149} > Moderate 70 MIld 76 Moderate 149 None 7 Moderate 70 Mild 4 Mild 100 None 153 None 36 Moderate 53 None 19 None 38 None 48 Moderate 38 None Values outside 95% limits of normal controls in the vwd direction. tme 4-point scale for grading symptoms is described elsewhere. groups were used to calculate the area of overlap between them.5 This area of overlap is the theoretical minimum misclassification rate of the sample using the particular discniminant function, and it provides one means of assessing the discniminant. The overlap may also be regarded as the total error of the method. (The total error is the sum of two types of error, false positives and false negatives, false positives being the normal individuals classified as affected, and false negatives being the affected persons classified as normal.) A second and more nearly independent method ofassessing a discniminant was to determine its usefulness in identifying the members of the reference group of transmitters believed to be the heterozygous for genetic reasons. The discriminant among the several tested that correctly identified the maximum number of transmitters as heterozygous was regarded as the superior function, provided it did not misclassify an excessive number of normal persons. To do this, each transmitter was classified as affected or normal according to whether, on the basis of the discriminant and the same prior probabilities as used to calculate the area of overlap, the probability of being affected was greater than or less than the probability of being normal. Although mathematically equivalent, this was computationally simpler than calculating a cutoff point, since for one of the discniminant functions the cutoff was the root of a quadratic function of age. The usefulness of ratios between the F-VlII-related activities was also examined. Ratios of VIII:C to VIIIR:Ag and VIII:C to VIIIR:WF among the normal controls were calculated using the age-corrected values in original units. The distributions of the ratios were not significantly skewed after one outlier had been removed. Mean, SD, and 95% limits (mean ± I.96 SD) were determined for each ratio, and a ratio outside the 95% limits in the direction expected in vwd was regarded as indicative of heterozygosity.

4 140 MILLER ET AL. RESULTS The various conventional methods of assessing vwd are evaluated in Table. The rates of identification of the transmitters as heterozygotes are shown in the first column, and the rates of misclassification of the normal controls by the same methods are shown in the second column. Symptoms (line I ) proved to be very common among the transmitters, 65% of them scoring positively. However, symptoms were poor discriminators, since they misclassified 3% of the normal controls. No single laboratory test (lines -5) detected more than 4% of the transmitters, the level of VIII:C being the least effective detector and the level of VIIIR:WF being the most effective detector. When an abnormality in any one of the four tests (the definition of an affected person, as developed in the preceding report ) was used as the detector (line 6), 58% of those transmitting the disease were classified as heterozygous, and the positive diagnostic error was 7%. A ratio of VIII:C to VIIIR:Ag greater than unity has been used by other investigators6 to detect asymptomatic transmitters in the families of homozygous vwd patients. We calculated ratios of VIII:C to VIIIR:Ag and VIII:C to VIIIR:WF in our normals using age-adjusted values, the normal upper 95% limit of the ratio of VIII:C to VIIIR:Ag being 1.90 and that of VIII:C to VIIIR:WF being I.99. Only 3% of the transmitters had either ratio outside the normal limits. Regression analysis has also been used in studying vwd kindred,7 8 but because of the serious theoretical objections raised to its use in detecting carriers of hemophilia A,9 #{176} which also apply to vwd, we did not examine regression. The value of discriminant analysis in assigning the heterozygous genotype to potential carriers of hemophilia A has been well documented.4 We followed a similar procedure using VIII:C, VIIIR:Ag, and VIIIR:WF simultaneously as variables. Age ranges were wide in all our reference groups, e.g., yr among the affected persons and yr among the transmitters, and it was necessary to adjust for age because of significant effects on different F-VIII-related activities in some of the subgroups. Age effects, although not consistent between normals and affected persons, or even for all activities within a single group, were sometimes quite pronounced, e.g., a 1% per year increase for VIII:C and VIIIR:Ag in normals without a comparable effect on VIIIR:WF. Furthermore, it became necessary in some cases to use separate adjustments for the two sexes within the same reference group. A family-specific discriminant was developed separately for each family Table. Identification of Transmitters and Misclassification of Normals as Heterozygous Using Conventional Methods Classification Method of Assessment Identification Transmitters (n - 6) of M isclassification of Normals (n - 30) 1. Symptoms alone 1 7 (65%) 7 (3%). Bleeding time alone 7 (7%) 1 (3%) 3. Vlll:C levels alone 4 ( 1 5%) 1 (3%) 4. VIIIR:Aglevelsalone 7(7%) 0 5. VIIIR:WF levels alone 1 1 (4%) 0 6. At least one abnormal test 1 5 (58%) (7%) 7. Abnormal ratio of either Vlll:C/VIIIR:Ag or VIlI:C/VIIIR:WF 6 (3%) 3 (10%)

5 GENETICS OF VON WILLEBRAND S DISEASE: II 141 Table 3. Value of Linear Di scriminant Analy sic in vwd Method Overlap Between Distributions of Normal and Affected Reference Groups Misclassification of Normals (ri - 30) Identification of Transmitters Family 1 Family Combined (n - 1 1) In - 1 5) (n - 6) Family-specific discriminant: DF and DM 15% (7%) 9 (8%) 1 (80%) 1 (8 1%) D, 13% (7%) 8 (73%) 1 1 (73%) 19 (73%) Pooled discriminant: D and D,.,,, 1% 3 (10%) 8 (73%) 1 1 (73%) 19 (73%) using data from the normal reference group and the affected members of that family. The results are shown in Table 3. We start with the results for family, since it did not have certain complications that occurred in family I. It was found best to use logarithms of the three variables, and the normal and affected groups could be pooled to determine a common age effect. It was sufficient to adjust the logarithms of the variables for age by linear regression, as follows: ln VIII:C separately by sex, ln VIIIR:Ag sexes pooled, and ln VIIIR:WF females only. After age adjustment, there were no significant sex differences in means or variances and no significant group differences in variances. A single linear discriminant was therefore obtained by pooling the age-adjusted values for the two sexes. In terms of the unadjusted values, this procedure yielded the following best discriminant functions for males (DM) and females (DF). DM ln VIII:C ln VIIIR:Ag DF ln VIII:C ln VIIIR:Ag ln VIIIR:WF age ln VIIIR:WF age These two discriminants are evaluated in the first line of Table 3. There is 15% overlap between the reference group of normals and the affected members of family, and the positive diagnostic error is low, only 7%. When applied to the transmitters, the discriminant performed very well, identifying 8% of the transmitters in family 1 and 80% of those in family (8 I % overall). In family 1 we were unable to find a discriminant function by this procedure that was approximately normally distributed in the two groups. However, we were able to find such a function by the following method. A constant was added to the ages of those in the normal group to make the mean age the same in both groups. Linear regression on age was then used, separately for each sex, to adjust the ln VIII:C and ln VIIIR:Ag values of all individuals in the normal group to that appropriate for their new ages (In VIIIR:WF showed no significant regression on age). Finally, after pooling the two sexes, the best linear discriminant between the two groups was found using these three adjusted variables, together with the natural logarithm (adjusted) of age as a fourth variable (taking the logarithm of age more nearly equalized the variance of age in the two groups). The resulting discriminant function was D, = ln VIII:C +.58 ln VIIIR:Ag ln VIIIR:WF ln age

6 14 MILLER ET AL. This discriminant was found to be significantly dependent on age in the normals but not in the affected persons; it was not significantly different between the two sexes. The evaluation of this discriminant is shown in the second line of Table 3. The overlap between the density distributions of normal and affected reference groups was 1 3%, slightly less than in family. The positive diagnostic error was 7%. The discriminant identified 73% of the transmitters in the family from which it had been derived and 73% in the other family also. Since, as discussed in the preceding report, both families appeared to have classic vwd, an attempt was made to find a common discriminant by pooling all of the data. Sex-specific pooled discriminants (DPM for males, DpF for females) were developed for the pooled families in the same way as for family, but they were based on square-root transformations of the variables as best approximating normality and on the use of common age regressions obtained from affected persons and normals pooled. These functions were DPM O.8/VIIEC + O.45 fviiir:ag + l.13/viiir:wf age DPF 0.8[VIII:C IVIIIR:Ag + h.3jv1tir:wf age It was verified that these discriminants were approximately normally distributed in the two groups. The values of the pooled discriminants are evaluated in the bottom line of Table 3. There was slightly less overlap between normal and affected reference groups ( I %) and slightly more misclassification of normals ( h 0%) than with the familyspecific discriminants. In terms of identifying the transmitters, the pooled discriminants were slightly less useful than those derived from family. The various methods of classification were further evaluated by applying them individually to the four parents of the two homozygotes in family, and a surprising result was obtained. This family, shown in Fig. 1, was first described many years ago and has been followed regularly by our group for 15 yr. Each parent is the second cousin of the other three, and the severely affected homozygotes are third cousins. The laboratory tests on the parents (subject IV-8, IV-9, IV-37, and IV-38 of family ) are shown in the lower portion of Table I, where it will be noted that all values on all tests are within the 95% limits of the normal controls. The ratios of VIII:C to VIIIR:Ag and VIII:C to VIIIR:WF were also within normal limits. Fig. 1. Abridgment of the pedigree of family. which is shown in more detail in Fig. of the preceding report. The homozygous probands are V-37 and V-i 38. They and their parents (IV-8. IV-9. IV-37. and lv-38) are descended from I-i and l-. who were English settlers in the Blue Ridge Mountains of North Carolina in the early nineteenth century.

7 GENETICS OF VON WILLEBRAND S DISEASE: II 143 However, their discriminant scores, with each of the discriminants, indicated that they were more probably heterozygous than normal. DISCUSSION Assigning the heterozygous genotype in an individual instance is a serious problem not only in recessive disorders, where heterozygotes are expected to have a normal phenotype, hut also in dominant disorders. Geneticists have long recognized that phenotypic variability is common in diseases that are dominantly inherited, 3 vwd being a prime example. Unless the primary gene product or something very closely related to it can be examined directly and/or qualitatively, it is usually difficult to establish that an asymptomatic individual does not carry an abnormal allele when penetrance is less than hoo%. As discussed elsewhere, #{176} detecting the vwd heterozygote is not different in principle from detecting carriers of hemophilia A or B. The purpose of our study was to evaluate in kindred with vwd the usefulness of current diagnostic methods and the efficiency of the statistical procedures that have been developed for identifying heterozygous carriers of hemophilia. The test subjects used in our evaluation were transmitters, the members of two large kindred who had transmitted the vwd allele to their descendants. The selection of this group on the basis of genetic transmission rather than phenotype largely avoids the circularity that results when data from subjects are used to develop phenotypic ranges, with the same subjects also being used to validate the ranges. We were not able to avoid this problem entirely, since I 5 of the 6 transmitters used to validate the method were also I 5 of the 54 affected persons used to establish the discriminants. However, we were forced to use them for both purposes because of the small numbers of subjects in some of our subgroups. Since the I 5 transmitters constituted only 8% (1 5 of 54) of the affected group used to calculate the discriminant, we regard their inclusion as a more conservative step than their removal, since removal might also have introduced a bias. The data in this report and those in the preceding report show that no single test is highly indicative of the heterozygous state for vwd. However, when multiple tests are done, a value in any one of the tests lying outside the 95% limits of a group of normal controls in the direction expected in vwd is strong presumptive evidence that an individual is heterozygous, particularly if a member of a family is known to be transmitting vwd. However, we found that having all test values within the normal range is not conclusive evidence against heterozygosity. In line 6 of Table it can be seen that 4% of our heterozygous transmitters had normal values on all tests, i.e., penetrance was 58%. This means that a member of one of our families having a 50% risk of being heterozygous has a 1 % chance (50% of 4%) of carrying the vwd allele even though all tests are in the normal range. An ideal test for genetic purposes is one that identifies all of the heterozygotes and does not misclassify any of the normals. The rate of positive diagnostic error, (i.e., misclassification of normals as affected) varied in our material from 3% for symptoms to zero for VIIIR:Ag or VIIIR:WF, thus eliminating symptoms as a reliable discriminator. Despite the low positive error rates for VIIIR:Ag and VIIIR:WF, they were poor positive indicators, because they correctly identified less than 50% of the transmitters. The positive error rates of ratios and discriminants were low (7%-l0%), but the low rate of identification of transmitters by ratios

8 144 MILLER ET AL. (3%) implied that ratios were also poor indicators. We found that discriminant analysis was clearly the best diagnostic procedure overall. Our best discriminant function, D, identified 8 1 % of transmitters as heterozygotes and misclassified only 7% of normals. As with hemophilia A carriers, we believe that discriminant functions should be formulated separately in each laboratory, based on local test methods and control populations.4 9 #{176} A discriminant for vwd is applied to the laboratory data obtained from a consultand exactly as in hemophilia A. The result on an individual consultand is a likelihood ratio (LR), the ratio between the likelihood that this score belongs to a normal and the likelihood that it belongs to a heterozygote. When the LR is combined with the probability from the family history to give a consultand the exact final probability of being a heterozygote, the same procedure will have been performed as when one has counseled a potential carrier of hemophilia A or B. Our data suggest that the results in vwd will probably be of about the same order of accuracy as in hemophilia A, since the areas of overlap between the density distributions of our normal and affected populations lie between 1 % and 1 5%, roughly the same overlap we have observed previously in hemophilia A.4 The fact that a discrimimant function is able to correctly identify 8h% of the transmitters in two vwd kindred in single testing (including several of those whose test results were in the normal range) indicates that the relationships of the F-VIII-related activities to each other as well as the actual levels in an individual are important in the identification process. No single test detected more than 60% of vwd transmitters when multiple tests were done, thus suggesting that the tests of F-VIII-related activities in vwd do not measure the primary gene product of the vwd locus or, perhaps more likely, that the primary product is interacting extensively with other genetic and/or environmental factors. We are currently developing a discriminant function that takes all the test information into account. We plan to try to identify vwd heterozygotes by simultaneously using the levels ofviii:c, VIIIR:Ag, and VIIIR:WF, the BT, and a numerical index of symptoms together with the pedigree structure under a given genetic model. The basic approach is to find that linear combination of traits that best represents the vwd gene. Preliminary indications from our two families suggest that the additional information will cause a significant further shrinkage in the area of overlap between the density functions for normal and affected groups, perhaps from 1 %-h 5% to around 5%#{149}14The recent observation that total progressive antithrombin (TPA) is significantly elevated in vwd heterozygotes 5 may provide an additional variable for further improvement of the discrimination procedures. If all of the available information can be used, it may become possible to correctly classify as many as 95% of the vwd heterozygotes of a kindred by discriminant analysis, despite the enormous phenotypic variability characteristic of subjects transmitting the disease. ACKNOWLEDGMENT These studies were approved in advance by the University of North Carolina Committee on Human Rights in accordance with an assurance (G0177) filed with and approved by the U.S. Department of Health, Education, and Welfare.

9 GENETICS OF VON WILLEBRAND S DISEASE: II 145 REFERENCES I. Miller CH, Graham ib, Goldin LR, Elston RC: Genetics of classic von Willebrand s disease. I. Phenotypic variation within families. Blood 5: , Barr AJ, Goodnight ih, Sall ip, Helwig it: A User s Guide to SAS-76. Raleigh, NC, SAS Institute, Snedecor GW, Cochran WG: Statistical Methods (ed 6). Ames, Iowa State University Press, Elston RC, Graham ib, Miller CH, Reisner HM, Bouma BN: Probabilistic classification of hemophilia A carriers by discniminant analysis. Thromb Res 8:683, Namboodini KK, Elston RC, Glueck Ci, Fallat R, Buncher CR, Tsang R: Bivaniate analyses of cholesterol and triglyceride levels in families in which probands have type lib lipoprotein phenotype. Am i Hum Genet 7:454, Lian EC-Y, Deykin D: Diagnosis of von Willebrand s disease: A comparative study of diagnostic tests on nine families with von Willebrand s disease and its differential diagnosis from hemophilia and thrombocytopathy. Am J Med 60:344, Veltkamp ii, Van Tilbung NH: Detection of heterozygotes for recessive von Willebrand s disease by the assay of antihemophilic-factor-like antigen. N EngI i Med 89:88, Italian working group: Spectrum of von Willebrand s disease: A study of 100 cases. Br i Haematol 35:97, WHO Expert Committee: Methods for the detection of haemophilia carriers: A memorandum. Bull WHO 55:675, Graham ib: Genotype assignment (cannier detection) in the hemophilias, in Rizza C (ed): Congenital Coagulation Disorders. Clinics in Haematology, vol 8. London, WB Saunders, 1979, pp I I. Reisnen HM, Katz Hi, Goldin LR, Barrow ES, Graham ib: Use of a simple visual assay of Willebrand factor for diagnosis and carrier identification. Br i Heamatol 40:339, 1978 I. Barrow EM, Heindel CC, Roberts HR. Graham JB: Heterozygosity and homozygosity in von Willebrand s disease. Proc Soc Exp Biol Med 118:684, 1965 I 3. Roberts JAF: An Introduction to Medical Genetics (ed ). New York, Oxford Press, Goldin LR: Genetic analysis of von Willebrand s disease in two large pedignees: A multivariate approach. Doctoral dissertation, University of North Carolina, Barrow ES, Graham ib: Elevation of total progressive antithrombin in von Willebrand s disease.thrombres 13:61, 1978

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