Kidney Exchange

• p. 43 Section 9.4, description of Tables 4–6

  third column is the percentage of patients upgraded to the top of the waitlist

• p. 61 Table 4 header

  Waitlist Upgrade %

• p. 42 Section 9.4, description of Tables 4–6

  The first column in these tables reports the total live donor transplants as percentage of the population size, which is the sum of next two columns

• p. 43 Section 9.4

  The third column is the percentage of patients upgraded to the top of the waitlist

Judge's note: Checked the p42–43 text against the Table 4–6 headers (p61–63): Total, Own Donor Trans., Trade%, Waitlist Upgrade%, Rel. Risk, HLA Mis. The numbering is off by one unless Own and Trade are treated as sub-columns, which the wording 'next two columns' does not support.

Second check: another model agreed

• p. 3 Introduction, paragraph 1

  another 900 became too ill to be eligible for transplantation. See Table 1.

• p. 3 Introduction, para 1

  about 3,400 patients died while on the waiting list, and another 900 became too ill to be eligible for transplantation. See Table 1.

• p. 4 Table 1 rows

  Total Waitlist Patients

• p. 4 Table 1

  Total Waitlist

Judge's note: Table 1 on page 4 has only six rows: cadaveric donors, cadaveric transplants, live donors, live donor transplants, total waitlist patients and new waitlist registrations. The pointer supports the transplant and waitlist counts, not the death and too-ill figures it directly follows.

Second check: another model agreed

• p. 4 Table 1, 2002 column

  6,233

• p. 4 Table 1, 2002 column, Live Donor Transplants

  6,236

• p. 4 Table 1, 2002 column

  6,233 ... 6,236

Only the authors can say what is right here.

Judge's note: Checked on the page 4 image: in 1992–2001 donors are always greater than or equal to transplants (for example 2001: 5,974 vs 5,969). In 2002 transplants exceed donors by 3. The 2002 column comes from a different source (the national database rather than the annual report), which may count differently, but the paper does not say so. Only the authors can say which value is right.

Second check: another model agreed

• p. 40 Section 9.2

  Since the median waiting time in the waitlist exceeds 3 years (it was 1134 days for a female and 1023 days for a male in 1998)

• p. 40 Section 9.2

  it was 1134 days for a female and 1023 days for a male in 1998

• p. 8 Section 3

  The median waiting time for a cadaveric kidney exceeds three years

• p. 40

  Since the median waiting time in the waitlist exceeds 3 years

Only the authors can say what is right here.

Judge's note: On the p40 image, 3 years ≈ 1095 days: the female figure exceeds this but the male figure does not, so the evidence in the parenthesis only partly supports the claim. The p8 statement has no year attached and may refer to a pooled or later figure. Only the authors know which median the claim refers to.

Second check: another model agreed

• p. 27 Example 2, Rounds 3–4

  Upon removing the w-chain W2, a new cycle C3 = (k4, t4, k8, t8) forms.

• p. 27 Example 2, Round 3 and Round 4

  Assign w to t9, k9 to t1, and k1 to t10 but do not remove them.

• p. 27 Example 2, Round 4

  Upon removing the w-chain W2, a new cycle C3

Judge's note: Pages 25 and 27: in Round 5, (k12,t12) joins W2, so W2 has not been removed. In this paper 'removed' is a technical term (p.23 Step 3(b)i), so 'removing' should read 'fixing' or similar. The final matching is not affected.

Second check: another model agreed

• p. 31 Example 3

  Upon removal of this w-chain, there are two cycles (k4, t4), (k5, t5)

Judge's note: After t1–t3 and k1–k3 are removed (under the removal rule the tail kidney k3 goes to the waitlist, per Step 3 on p23–24), t4's remaining top choice is k4 and t5's top choice k4 is still available. So the only cycle is (k4,t4). (k5,t5) forms only in the next pass of Step 2b, after (k4,t4) is removed. The final matching μ is unchanged; only the wording of the step is imprecise.

Second check: another model agreed

• p. 39 Section 9.2, MRS bullet

  5.10 years of younger donor age per each additional HLA mismatch for patients older than 59

• p. 43 Section 9.4, parameter values

  1.05 for older patients

• p. 39 Section 9.2, bullet list

  5.10 years of younger donor age per each additional HLA mismatch for patients

Only the authors can say what is right here.

Judge's note: The parameters are stated on p43 (a=1.06/1.05, b=1.12/1.10) and the MRS formula on p39. The younger-patient value reproduces exactly (5.14) from the rounded parameters, but the older-patient value comes out at 5.12, not 5.10. Unrounded Mandal et al. estimates could explain the gap, but they are not given in the files. The authors should say which values were used. (Separately, the printed formula '−10 ln(a)/ln(b)' would be negative; it is not part of this cluster.)

Second check: another model agreed

• p. 45 Section 9.4, result 3

  5.7-6.5 pairs

• p. 69 Table 12, W-chain Length Max., Cautious TTCC f, Waitlist 10%

  5.58

Judge's note: The Table 12 Max. w-chain values are 6.01, 6.01, 5.69, 5.58, 6.32, 6.27, 6.07, 6.01, 6.47, 6.46, 5.99, 5.96. Only 5.58 falls outside 5.7-6.5, and it rounds to 5.6. Unlike C033, leaving out the 40% rows does not explain this. The discrepancy is small.

Second check: another model agreed

• p. 56 Proof of Claim 1, induction step

  is assigned his top choice in K \ ∪s−1u=1Ku under φ(P)

• p. 56 Appendix, proof of Claim 1 (Theorem 3), inductive step

  top choice in K \ ∪s−1 u=1Ku under ϕ(P)

Only the authors can say what is right here.

Judge's note: On the page image (PDF p.56) the step reads 'under φ(P)'. At this point in the proof nothing is known about φ(P); that φ(P) = µ is what Claim 2 proves afterwards, using Claim 1. Reworking the step, the needed fact is that under the TTC outcome µ each patient leaving at Round s gets his top choice among the remaining kidneys. That holds by the definition of TTC and is how the base case is worded ('by matching µ'). With µ in place of φ(P) the step is valid and Claim 1 and Theorem 3 stand. As printed it relies on the conclusion of Claim 2. This looks like a slip of the symbol.

Second check: another model agreed

• p. 67 Table 10, Rational TTC row

  14.65

• p. 69 Table 12, Rational TTC row

  79.54

Only the authors can say what is right here.

Judge's note: Checked Table 10 (p067) and Table 12 (p069). For No-Exchange and Paired, Cycle No × Mean matches the transplanted pairs: 18.50×1.11 ≈ 20.5 against 68.50% of 30 = 20.55 in Table 4. For Rational TTC at n=30, 14.65×2.95 = 43.2. That exceeds both n=30 and the 24.7 pairs transplanted (82.47% of 30). The table SDs bound the covariance at 2.22×0.43 ≈ 0.95, which cannot close the gap. The other definitions I tried also fail to reproduce 2.95: (a) excluding compatible self-cycles gives (24.74-6.91)/(14.65-6.91) ≈ 2.30; (b) a mean per cycle limited to the transplanted pairs is at most 24.74/14.65 ≈ 1.69. The caption says only that 1-pair cycles with incompatible pairs are not counted, and the text (p.42) says 'average length'. Neither explains this. Only the authors can say how Mean was computed.

Second check: another model agreed

• p. 44 Footnotes 27 and 28

  Wilcoxen signed rank test

• p. 45 Footnote 29

  Wilcoxen signed rank test

• p. 44 Footnotes 27 and 28

  (paired-sample) Wilcoxen signed rank test

• p. 3 Footnote 2

  Nelson et al. (1993)

Judge's note: The page images of PDF pp.44-45 show 'Wilcoxen' in all three footnotes. One reviewer also noted that footnote 2 cites 'Nelson et al. (1993)' with parentheses where the rest of the paper uses square brackets (reference [12] gives [1993]). That is a minor style inconsistency within the same copy-edit cluster.

Second check: none (judge only)

• p. 4 Introduction

  However Ross and Woodle note that his may have a negative impact

• p. 4 para after Table 1

  Ross and Woodle note that his may have a negative

• p. 37 Table 2 caption

  ditributions

• p. 39 Footnote 24

  nemely

Judge's note: All four typos are visible on the page images. A fifth item in this cluster, 'carry our' (p.23), is covered separately as C012.

Second check: none (judge only)

• p. 5 Introduction

  (Roth and Postlewaite [1977], and that the

• p. 5 Introduction, para 2

  (Roth and Postlewaite [1977], and that

Judge's note: The page 5 image confirms the parenthesis is never closed before ', and that'.

Second check: none (judge only)

• p. 5 Introduction

  what it’s welfare implications might be

• p. 5 Introduction, para 1

  what it’s welfare implications

Judge's note: The page 5 image confirms the text.

Second check: none (judge only)

• p. 11 Section 4, item 3

  reduce the adverse affect to O blood-type patients

• p. 48 Section 10, item 4

  The adverse affect of the present indirect exchange programs

• p. 49 Footnote 34

  reduce the adverse affect of indirect exchange programs

• p. 11 Section 4, list item 3

  eliminate or at least reduce the adverse affect to O blood-type patients

Judge's note: All three occurrences appear on the crop images.

Second check: none (judge only)

• p. 12 Footnote 10

  either of two allocations methods

Judge's note: The crop image confirms the text.

Second check: none (judge only)

• p. 20 Section 7.1, definition of head/tail

  We refer the last pair

Judge's note: The crop image of page 20 confirms the text.

Second check: none (judge only)

• p. 23 TTCC mechanism, Step 3(a)

  carry our the basic indirect exchanges

• p. 23

  In this case carry our the basic indirect exchanges

Judge's note: The crop image of page 23 confirms the text.

Second check: none (judge only)

• p. 27 Round 3

  each kidney-patient pair starts an w-chain

• p. 49 item 4(d)

  is an w-chain where kidney k1

Judge's note: Seen on p27 (Round 3) and p49 item 4(d). The text layer also has 'an w-chain' at other places (lines 2723, 2851), but 'a w-chain' is the usual form across the paper. This is a cosmetic inconsistency in the article.

Second check: none (judge only)

• p. 32 Section 7.4, before Theorem 2

  What happens when indirect changes are allowed?

Judge's note: p32 image, first line. The paragraph before it (p31) says 'in the absence of indirect exchanges', so 'changes' is evidently meant to be 'exchanges'.

Second check: none (judge only)

• p. 32 Example 4

  profiting form his preference misrepresentation

Judge's note: Seen in Example 4 on the p32 image.

Second check: none (judge only)

• p. 37 Table 2 caption

  age ditributions for new patients

• p. 37 Table 2 caption

  ditributions for new patients

• p. 37 Table 2 caption

  ditributions

• p. 37

  ABO Blood-type, gender, and age ditributions for new patients

Judge's note: Seen in the Table 2 caption on the p37 image.

Second check: none (judge only)

• p. 37 Section 9.1

  About 25.3% all living-donor transplants

• p. 37 Section 9.1

  About 25.3% all living-donor transplants were in this category

Judge's note: Seen in Section 9.1 on the p37 image.

Second check: none (judge only)

• p. 39 Footnote 24

  nemely the Caucasian ESRD patients

Judge's note: Seen in footnote 24 on the p39 image.

Second check: none (judge only)

• p. 44 Section 9.4, result 1

  this rate increases to 73.5% under the paired-kidney-exchange

• p. 62 Table 5, Paired row, Total Trans. %

  73.59

• p. 44 Section 9.4, result 1

  this rate increases to 73.5% under

Judge's note: Table 5 (p62) Paired row: Total 73.59 = 54.79 + 18.80. The text figure is truncated rather than rounded; the difference is cosmetic.

Second check: none (judge only)

• p. 47 Footnote 32

  “first to forth, forth to third, third to second, and second to first.”

Judge's note: The page image (PDF p.47) shows 'forth' twice in footnote 32. The quoted Lucan et al. passage in the body also has 'forth' (and 'for pairs'), which may reproduce the source, but the footnote is the authors' own wording.

Second check: none (judge only)

• p. 54 Proof of Theorem 3, strategy-proofness

  We want show that his assignment

Judge's note: The crop shows 'We want show that his'. Two lines earlier the same proof correctly has 'We want to show'.

Second check: none (judge only)

• p. 55 Proof of Claim 1, base case

  either φ(P′) = µ(ti) or φ(P′) = ki1

• p. 55 Appendix, proof of Claim 1, base case

  either ϕ(P 0) = µ(ti) or ϕ(P 0) = ki1

Judge's note: The page image (PDF p.55) shows φ(P′) with no subscript i in both places. The next sentences and the inductive step use φi(P′). With the subscript restored the argument is unaffected.

Second check: none (judge only)

• p. 55 Proof of Claim 1

  let Ku denote the the set of kidneys

• p. 55

  or any Round u, let Ku denote the the set of kidneys each

Judge's note: Confirmed on the page image (PDF p.55), at the last lines of the page.

Second check: code check

• p. 56 Appendix, proof of Claim 2, |T|=1 display

  ϕi(P 0)R0 iϕ(P 0 −i, Pi)

Judge's note: The page image (PDF p.56) shows no subscript i on the right-hand φ, while the companion inequality on the same line uses φi. R′i compares assignments of ti, so the subscript is needed. The conclusion is unaffected.

Second check: none (judge only)

• p. 56 Figure 9 caption

  Figure 9: ϕ(P 0 −i, Pi) = µ(ti) by strategy-proofness.

Judge's note: The page image (PDF p.56) shows the figure labels as φi(P′−i, Pi), but the caption omits the subscript.

Second check: none (judge only)

• p. 58 Reference [10]

  Does cadavaric donor renal transplantation ever provide better outcomes

Judge's note: The crop of PDF p.58 shows 'cadavaric'. The text layer contains no other instance; the paper spells it 'cadaveric' elsewhere.

Second check: none (judge only)

• p. 61 Table 4, Waitlist 40%, Rational TTCC e, standard errors

  (8.49

• p. 61 Table 4, Waitlist 40%, Rational TTCC e

  (8.49 9.60)

• p. 61 Table 4, Waitlist 40%, Rational TTCC e row, Total Trans. and Own Donor columns

  (8.49 / 9.60)

Judge's note: Confirmed on the page image of Table 4 (PDF p.61). Every other standard-error cell has the form (x.xx).

Second check: none (judge only)

• p. 61 Table 4, No Exchange row, Rel. Risk column

  1 (0.04)

Judge's note: The page image of Table 4 (PDF p.61) shows '1 (0.04)'. The other rows of Table 4 and the No-Exchange row of Table 5 (PDF p.62) print '1.00'. This is cosmetic only.

Second check: none (judge only)

• p. 61 Table 4 row label

  No Exchange

• p. 62 Table 5 row label

  No-Exchange

Judge's note: Page images p061 and p062 show Table 4's row label "No Exchange" and Table 5's "No-Exchange". The text layer shows "No-Exchange" in every later table (5–12). This is a cosmetic label inconsistency only.

Second check: none (judge only)