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are independent. Hence, the probability that leukemia is detected at time t in a child who experienced an initiating event prior to birth can be represented as
*f t
0
Age-Specific Incidence of Acute Lymphoblastic Leukemia in U.S. Children: In Utero Initiation Model Malcolm A. Smith, Timothy Chen, Richard Simon*
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~z!f2~t − z!dz,
where the variable of integration z represents the random time of the transforming event. For f2, we used the normal distribution with mean m and standard deviation s. We examined two alternatives for f1. Under the assumption that the risk of neoplastic transformation in an infected host is constant over time, f1 should be an exponential distribution. Alternatively, it is possible that the number of infected cells that are susceptible targets for the second event is exponentially increasing over time from clonal expansion. Assuming that the clonal expansion is taking place at birth gives the limiting case and implies that f1 should be the density of an extreme-value distribution. The hazard function h(t) for the extreme-value distribution is of the form h(t) 4 r0er1t, where r0 and r1 are parameters. The exponential distribution is a special case of the extreme-value distribution with r1 4 0. The model used contains three parameters in total when the exponential distribution is used for f1 and four parameters in total when the extremevalue distribution is used. The parameters were estimated by fitting the models to the Surveillance, Epidemiology, and End Results (SEER)1 population-based age–incidence data (Fig. 1). In estimating the parameters, we made two modifications to the SEER data. We reduced the incidence rate for the first year of life from 28.8 to nine cases per 106, because approximately two thirds of these cases have genomic rearrangements involving the MLL gene at chromosome band 11q23 and are likely to have an etiology different from that of B-precursor ALL that occurs in children beyond infancy (6–8). We also corrected for T-cell ALL cases (see Fig. 1 legend), since although T-cell ALL represents only a small proportion of cases among children 2–3 years old, it represents 15%–20% of cases in children at the upper age range (9). The criterion used to fit the models to the data was minimal contingency chi-squared. Let Oi denote
~Oi − Ei!2 . Ei i=1 10
(
Both models provided good fits to the data, as shown in Fig. 1. The threeparameter model gave an average absolute error of 10.2% and the fourparameter model gave an average absolute error of 10.4%. The estimated latency distributions were similar for both models (means of 1.6 and 1.7 years, respectively, and standard deviations of 0.7 year for both). For the exponential model, the exponential parameter is estimated as 0.30 (i.e., 30 events are expected for every 100 person-years of at-risk time). For the four-parameter model, the parameter values were r0 4 0.30 (similar to the exponential parameter) and r1 4 0.027. We also fit a model with a normally distributed latency distribution but with no second (i.e., postnatal) event required for leukemic transformation. We optimized the parameters of the latency distribution, but the model provided a very poor fit to the data with an average absolute error of 35%. The fact that the four-parameter model did not fit the data better than the three-parameter model suggests that the target cell population for mutational events is not clonally expanding. In fact, the model can be modified to account for the possibility that the target population of cells is independently extinguished by a non-leukemogenic event whose time of occurrence is exponentially distributed with parameter h. Under the assumption that the second event required for leukemia development oc-
*Affiliation of authors: Cancer Therapy Evaluation Program, Division of Cancer Treatment, Diagnosis, and Centers, National Cancer Institute, Bethesda, MD. Correspondence to: Malcolm A. Smith, M.D., Ph.D., National Institutes of Health, Executive Plaza North, Rm. 741, Bethesda, MD 20892. Email:
[email protected] See ‘‘Notes’’ following ‘‘References.’’ © Oxford University Press
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A large body of evidence supports the hypothesis that an infectious agent is involved in the etiology of acute lymphoblastic leukemia (ALL) in children, particularly those cases occurring in children between 2 and 5 years of age (1–4). Recently, a specific virus has been posited as a candidate etiologic agent for childhood ALL, with leukemia occurring as a consequence of primary infections of women during pregnancy that lead to in utero infection and to subsequent increased risk of developing ALL in early childhood (5). Since a critical component of this proposal is that in utero infection by a leukemiainducing agent is the first step in development of many cases of childhood ALL, we were interested to see if a mathematical model with clinically reasonable parameters in which the critical leukemogenic event occurred in utero could be developed to explain the observed incidence of ALL among young children in the United States. We examined models that represented the age at diagnosis of ALL as the sum of two time intervals. The first is the time from birth until the occurrence of an event that completes the neoplastic transformation in infants that was initiated in utero. The second time is the latent time from neoplastic transformation to clinical detection. Let the probability density function of the first time be denoted by f1( ) and the probability density function of the latent time to clinical detection be denoted by f2( ). We assume that these two time intervals
1
the observed proportion of cases that occurred in the ith year of life, for i 4 1, . . .10. Let Ei denote the expected value of this proportion predicted by the model. The model parameters were determined in order to minimize
curs at a constant rate r and is conditional on the existence of the target population of cells, the probability that leukemia is detected at time t in a child who experiences an initiating event prior to birth is
* re t
−rz
0
e−hz f2~t − z!dz,
which equates to r ~r + h!
* ~r + h!e t
0
−~r + h!z
f2~t − z!dz.
The first factor of the integral is an exponential probability density. Since the number of children experiencing an initiating event is unobserved, the modified model is not distinguishable from the original model (with f1 an exponential distribution) using age–incidence data. However, the biologic implications of the initial and modified models differ: The initial model predicts that all subjects experiencing the leukemiainitiating in utero event will develop
leukemia, whereas the modified model does not require that the in utero event inevitably results in leukemia. The models that we present are able to fit the observed age–incidence pattern for childhood ALL in the United States with parameters that are clinically reasonable. Support for a latent period of approximately 1.5 years comes from the time course of relapse for children with B-precursor ALL, with recurrence of leukemia occurring not uncommonly at 3–5 years from diagnosis (i.e., 1–2 years from completion of therapy) (10,11). A plausible physiologic interpretation of the model is that children with an in utero infection by a leukemiainducing agent may be placed in a preleukemic state as a result of this infection. Those children in the preleukemic state at birth would then develop leukemia during childhood after a second event occurs. The second event might be mutation or loss of a critical tumor suppressor gene or activation of an onco-
Journal of the National Cancer Institute, Vol. 89, No. 20, October 15, 1997
References (1) Greaves MF. Aetiology of acute leukaemia. Lancet 1997;349:344–9. (2) Greaves MF, Alexander FE. An infectious etiology for common acute lymphoblastic leukemia in childhood? Leukemia 1993;7: 349–60. (3) Kinlen LJ. Epidemiological evidence for an infective basis in childhood leukaemia [editorial]. Br J Cancer 1995;71:1–5. (4) Kinlen L. Evidence for an infective cause of childhood leukaemia: comparison of a Scottish new town with nuclear reprocessing sites in Britain. Lancet 1988;2:1323–7. (5) Smith M. Considerations on a possible viral etiology for B-precursor acute lymphoblastic leukemia of childhood. J Immunother 1997; 20:89–100. (6) Ross JA, Potter JD, Robison LL. Infant leukemia, topoisomerase II inhibitors, and the MLL gene. J Natl Cancer Inst 1994;86: 1678–80. (7) Rubnitz JE, Link MP, Shuster JJ, Carroll AJ, Hakami N, Frankel LS, et al: Frequency and prognostic significance of HRX rearrangements in infant acute lymphoblastic leuke-
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Fig. 1. Observed and model-predicted incidence of acute lymphoblastic leukemia (ALL) among white children in the United States. The incidence rates of ALL by year of age are from the SEER registry for the period 1986 through 1994. Incidence rates are per 106 and are age adjusted to the 1970 U.S. standard population. Correction is made for case patients under 1 year of age to omit infants with ALL who have MLL gene rearrangements in their leukemia cells. Correction is also made to adjust for cases of T-cell ALL in the 2- to 9-year age group. Since immunophenotyping data are not available for the SEER population, we have extrapolated proportions of T-cell ALL for different ages from a report by Greaves et al. (9); we then applied these proportions to the SEER data. These calculated age-specific incidence rates of T-cell ALL appeared to be relatively constant in the 2- to 9-year age range (average rate, five per 106). This rate has been subtracted from the SEER incidence rates for these ages. The numbers above each bar are the incidence rates of ALL by year of age, either as observed from the SEER Program (with corrections as described above) or as predicted by the models. See text for description of the threeparameter and four-parameter models.
gene. It should be noted that the T antigens of the polyomaviruses (e.g., simian virus 40 and JC virus) bind to p53 and induce genomic instability (12–17). Thus, the progression to the second event could be accelerated beyond normal rates by the biologic properties of the leukemia-inducing agent. Little et al. (18) fit a variety of one-, two-, and three-mutation models to age– incidence distributions for ALL in England and Wales. They assumed that all events occurred after birth and did not account for a latent period between neoplastic transformation and clinical detection. They found that one-event models did not provide adequate fits to the data. Two- and three-event models adequately fit the data, but only if they assumed that the mutation rate representing the first event decreased abruptly after some age. Had they accounted for a 1- to 2-year latent period in detection, the age at which the initial mutation rate decreases would likely have been very early, supporting our hypothesis that the initial event occurs in utero. In closing, the ability of the proposed model to explain the incidence curve of ALL in young children in the United States supports the hypothesis that a substantial number of cases of ALL among young children in developed countries such as the United States may be initiated by in utero events.
(8)
(9)
(10)
(11)
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(13)
(14)
(15)
(16)
(17)
editor. Molecular neurovirology. Totowa (NJ): Humana Press, 1992: 25–158. Haggerty S, Walker DL, Frisque RJ. JC virus–simian virus 40 genomes containing heterologous regulatory signals and chimeric early regions: identification of regions restricting transformation by JC virus. J Virol 1989;63:2180–90. Bollag B, Chuke WF, Frisque RJ. Hybrid genomes of the polyomaviruses JC virus, BK virus, and simian virus 40: identification of sequences important for efficient transformation. J Virol 1989;63:863–72. Staib C, Pesch J, Gerwig R, Gerber JK, Brehm U, Stangl A, et al. p53 inhibits JC virus DNA replication in vivo and interacts with JC virus large T-antigen. Virology 1996;219:237–46. Laffin J, Fogleman D, Lehman JM. Correlation of DNA content, p53, T antigen, and V antigen in simian virus 40-infected human diploid cells. Cytometry 1989;10:205–13. Levine DS, Sanchez CA, Rabinovitch PS, Reid BJ. Formation of the tetraploid intermediate is associated with the development of cells with more than four centrioles in the elastase–simian virus 40 tumor antigen transgenic mouse model of pancreatic cancer [published erratum appears in Proc Natl
Acad Sci U S A 1991;88:8282]. Proc Natl Acad Sci U S A 1991;88:6427–31. (18) Little MP, Muirhead CR, Stiller CA. Modelling lymphocytic leukaemia incidence in England and Wales using generalizations of the two-mutation model of carcinogenesis of Moolgavkar, Venzon and Knudson. Stat Med 1996;15:1003–22.
Notes 1 Editor’s note: SEER is a set of geographically defined, population-based central tumor registries in the United States, operated by local nonprofit organizations under contract to the National Cancer Institute (NCI). Each registry annually submits its cases to the NCI on a computer tape. These computer tapes are then edited by the NCI and made available for analysis.
We gratefully acknowledge the assistance of Lynn Ries in providing recent data for the incidence of childhood ALL from the SEER Program. More detailed incidence, mortality, and survival information will appear in a monograph dedicated to childhood cancers to be published by SEER. Manuscript received April 10, 1997; revised July 31, 1997; accepted August 5, 1997.
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mia: a Pediatric Oncology Group study. Blood 1994;84:570–3. Greaves MF. Infant leukaemia biology, aetiology and treatment. Leukemia 1996;10: 372–7. Greaves M, Pegram S, Chan L. Collaborative group study of the epidemiology of acute lymphoblastic leukemia subtypes: background and first report. In: Greaves M, Chan L, editors. Epidemiology of leukaemia and lymphoma. Oxford: Pergamon Press, 1985:55–73. Lange BJ, Blatt J, Sather HN, Meadows AT. Randomized comparison of moderate-dose methotrexate infusions to oral methotrexate in children with intermediate risk acute lymphoblastic leukemia: a Childrens Cancer Group study. Med Pediatr Oncol 1996;27: 15–20. Buhrer C, Hartmann R, Fengler R, Schober S, Arlt I, Loewke M, et al. Importance of effective central nervous system therapy in isolated bone marrow relapse of childhood acute lymphoblastic leukemia. BFM (Berlin–Frankfurt–Munster) Relapse Study Group. Blood 1994;83:3468–72. Frisque R, White F. The molecular biology of JC virus, causative agent of progressive multifocal leukoenchephalpathy. In: Roos R,
