Epidemiology Research International
Volume 2015 (2015), Article ID 182721, 9 pages
http://dx.doi.org/10.1155/2015/182721

Research Article

The Time of the Insult/Triggering Event in Primary Osteosarcoma and Ewing’s Sarcoma of Bone as Determined by Incubation Period Modeling and Age Distribution of Such Malignancies

Randall T. Loder and Meagan Sabatino

Department of Orthopaedic Surgery, Indiana School of Medicine, Indiana University and the James Whitcomb Riley Children’s Hospital, Indianapolis, IN 46202, USA

Received 9 July 2014; Accepted 20 February 2015

Academic Editor: Huibert Burger

Copyright © 2015 Randall T. Loder and Meagan Sabatino. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

The time for the triggering event in neoplasms can be estimated using incubation period modeling techniques. We applied these techniques to primary osteosarcoma and Ewing’s sarcoma of bone using the Surveillance Epidemiology and End Results database for all cases of osteosarcoma or Ewing’s sarcoma of bone from 1993 through 2010. Secondary neoplasms were excluded. The age at diagnosis, gender, ethnicity, and anatomic location were collected. The time () of the insult/triggering event was calculated using the best fit frequency distribution of age at diagnosis. There were 4,356 patients with osteosarcoma and 1,832 patients with Ewing’s sarcoma. The Pearson IV distribution was the best fit for both osteosarcoma () and Ewing’s sarcoma (). For these distributions is −0.7 years of age (4 weeks after conception) for Ewing’s sarcoma, 0.45 years for long bone osteosarcoma, and 10.4 years for parosteal osteosarcoma. This confirms the genetic etiology of Ewing’s sarcoma since an is 4 weeks after conception. Long bone osteosarcoma is not entirely genetic, as was 0.4 years for conventional osteosarcoma and 10.4 years for parosteal osteosarcoma. The etiologies for those two different types of osteosarcoma are thus different.

1. Introduction

Osteosarcoma and Ewing’s sarcoma are the most common primary osseous malignancies, especially in children and young adults [1–4]. The etiology of osteosarcoma and Ewing’s sarcoma is becoming more defined. Nearly all cases of Ewing’s sarcoma (>90%) are associated with a t(11;22)(q24;q12) translocation that encodes the EWS/FLI oncoprotein [4–11]. The genetic etiology of osteosarcoma is less apparent, although it has been associated with various genetic abnormalities [12–18]. The genetic abnormalities postulated are loss of chromosome 13 (with the long arm (13q) containing the RB1 tumor-suppressor gene) [12], amplification of the MDM2 gene, and aberrant expression or loss of the tumor suppressor genes Rb and p53 [4, 15] and potential other associations [16–18] with certain populations being at risk [18] although definitive oncogenes or tumor suppressor genes are still unknown [16].

The time of the triggering event which starts the development of these neoplasms is unknown. An estimation of such time can be determined using incubation period modeling techniques. This modeling has been applied to malignancies [19–22] but not those involving long bones. It was the purpose of this study to apply incubation period modeling to osteosarcoma and Ewing’s sarcoma of bone and determine the age of “exposure” to the triggering event.

2. Methods

2.1. Data

The Surveillance Epidemiology and End Results (SEER) Program of the National Cancer Institute database was queried for all patients with osteosarcoma or Ewing’s sarcoma diagnosed from 1993 through 2010 [38]. SEER collects and publishes cancer incidence data from population-based cancer registries covering approximately 28% of the US population [39]. We collected the age at diagnosis, gender, ethnicity, tumor type (e.g., conventional osteosarcoma, parosteal sarcoma, Ewing’s, sarcoma of bone, or soft tissue), state of origin, anatomic location of sarcoma (e.g., long bone, jaw, vertebra), and the data about the malignancy whether it is primary or secondary. Ethnicity was classified according to Eveleth and Tanner [40] as White, Black, Amerindian (Hispanic and Native American), Indo-Malay (Asian origins), Indo-Mediterranean, and Native Australian/Polynesian. The USA state of origin was classified into four different groups using the 2000 Healthcare Cost and Utilization Project Kids’ Inpatient Database (KID) [41] criteria (Northeast, South, Midwest, and West). Those with a secondary tumor were excluded (e.g., pagetic, previous malignancy). This study was determined to be exempt by the local Institutional Review Board. Further details regarding the acquisition of the SEER data can be found at http://www.seer.cancer.gov/.

2.2. Statistical Analysis

Discrete data are reported as frequencies and percentages and continuous data as the mean standard deviation. Due to the asymmetric distribution of the age data, analyses between groups of continuous data were performed using nonparametric statistics (Mann-Whitney test: 2 groups; Kruskal-Wallis test: ≥3 groups). Differences between groups of discrete data were analyzed by the Pearson test. Statistical analyses for standard demographic data were performed with Systat 10 software (2000, SPSS Inc., Chicago, IL).

Incubation period modeling was used to determine the time of the insult/triggering event [19–21, 42–48]. The ideal best fit distribution should have an . In addition to the values, plots of the model and the data were subjectively examined to see if there was a peculiarity of the model’s fit that visually makes it a less suitable model. Only asymmetric distributions were evaluated which includes the log normal distribution. Statistical analyses for incubation period modeling and were performed using TableCurve 2D software v5.0 (2002, Systat Software, Richmond, CA). The details and theory behind incubation period modeling are given in the appendix.

3. Results and Discussion

3.1. Osteosarcoma

Subgroups were created since it is well known that there are differences in the epidemiology/demographics between conventional osteosarcoma (osteosarcoma not otherwise specified; chondroblastic, fibroblastic, telangiectatic osteosarcoma) separated by long and short bones; central and small cell medullary osteosarcoma; parosteal osteosarcoma; and osteosarcoma involving the mandible, skull, pelvis, and rib/sternum/clavicle [49].

There were 4,356 patients with osteosarcoma; 3,998 (91.8%) were conventional and 225 parosteal (5.2%). The remaining types accounted for 3%. There was a slight male predominance (55.6% male, 44.4% female). Statistically significant differences between the conventional and parosteal types by age, gender, race, and anatomic location were noted (Table 1). Within the conventional group there were statistically significant differences in anatomic location for age, race, and gender (Table 2).

Table 1: Demographics for conventional and parosteal osteosarcoma.

Variable
Total
Conventional
%
Parosteal
%
value

Average age (yrs)
28.0 ± 20.3
28.1 ± 20.8
—
28.4 ± 13.0
—
<0.0001

Median age (yrs)
19
19

26

Geographic location in the USA

    Midwest
727
679
17.0
48
21.3
0.39

    Northeast
553
526
13.2
27
12.0

    South
589
561
14.1
28
12.4

    West
2344
2222
55.7
122
54.2

Sex

    Male
2338
2235
56.0
103
45.8
0.003

    Female
1875
1753
44.0
122
54.2

Race

    White
3217
3051
77.3
166
75.1
0.28

    Black
607
568
14.4
39
17.6

    Indo-Malay
247
238
6.0
9
4.1

    Amerindian
37
34
0.9
3
1.4

    Indo-Mediterranean
25
22
0.6
3
1.4

    Polynesian
37
36
0.9
1
0.5

Primary site

    Long bone
3142
2942
75.2
200
88.9
<0.0001

    Short bone
98
90
2.3
8
3.6

    Mandible
179
175
4.5
4
1.8

    Pelvis
316
316
8.1
0
0.0

    RSTCl
89
83
2.1
6
2.7

    Skull
215
209
5.3
6
2.7

    Vertebral
98
98
2.5
1
0.4

RSTCl: rib, sternum, clavicle.

Table 2: Demographics of conventional osteosarcoma by anatomic location.

Total
Long bone
Mandible
Pelvis
RSTCl
Short bone
Skull
Vertebral
value

3988
2942
175
316
83
90
209
98

Age (yrs)

23.1 ± 17.4
40.6 ± 20.0
43.1 ± 23.3
37.5 ± 22.7
33.2 ± 22.5
39.2 ± 20.5
44.0 ± 23.2
<0.0001

Median age (yrs)
19
17
38
41
33
29
39
42

Gender

    Male
2190
1679
71
175
50
53
109
53
0.0021

    Female
1263
104
141
33
37
100
45

Geographic Location in the USA

    Midwest
663
506
23
57
13
18
35
11
0.078

    Northeast
512
364
24
51
10
19
25
19

    South
552
403
36
47
8
11
33
14

    West
2186
1669
92
161
52
42
116
54

Race

    White
2989
2217
116
272
75
69
163
77
0.0001

    Black
562
436
39
29
2
12
33
11
(<0.0001)∧

    Indo-Malay
235
192
10
10
4
4
7
8

    Amerindian
33
30
1
0
1
1
0
0

    Indo-Mediterranean
22
15
3
1
0
3
0
0

    Polynesian
35
27
1
4
0
0
2
1

RSTCl: rib, sternum, clavicle.

∧The 3 most common races, White, Black, and Indo-Malay.

Incubation period modeling was performed separately for each subgroup of osteosarcoma. The Pearson IV and log normal distributions were excellent fits for long bone osteosarcoma (Table 3) ( of 0.987 and 0.97, resp.) (Figure 1). These result in an at the 99 and 99.9% levels of 2.2 and 0.45 years for the Pearson IV and 2.95 and 0.3 years for the log normal distribution. Thus the triggering event for conventional long bone osteosarcoma is under 3 years of age but not prenatal since was not ≤0. Parosteal long bone osteosarcoma demonstrated a moderate fit , with an of 8.6 and 7.65 years at the 99 and 99.9% points, respectively. When reviewing the data (Figures 2(a) and 2(b)), there were 200 cases separated by 1-year increments, creating significant scatter. The age data was collapsed into groups of 3 years (1 to 3, 4 to 6, etc.); subsequent analysis demonstrated equally excellent fits with both the Pearson IV and log normal ( of 0.96 for both), or of 10.5 and 10.4 years for the 99 and 99.9% points, respectively (Figures 2(c) and 2(d)). There were no significant fits for any of the other osteosarcoma types, even when collapsing the age into groups of 3 years.

Table 3: Incubation period modeling results for osteosarcoma and Ewing’s sarcoma of bone.

Type of malignancy

Average age (yrs)
Pearson IV distribution
Log normal distribution

99%
99.9%

99%
99.9%

Conventional osteosarcoma

    Long bone
3142
23.1 ± 17.4
0.977
2.2
0.45
0.971
2.95
0.3

    Short bone
98
33.2 ± 22.5
0.41

0.32

    Mandible
179
40.6 ± 20.0
—

0.39

    Pelvis
316
43.1 ± 23.3
—

0.39

    RSTCl
89
37.5 ± 22.7
—

0.32

    Skull
215
39.2 ± 20.5
0.38

0.36

    Vertebral
98
44.0 ± 23.2
—

—

Parosteal long bone osteosarcoma
200
27.7 ± 12.5
0.77
8.6
7.65
0.77
8.6
7.65

Ewing’s sarcoma of bone
1832
18.4 ± 11.4
0.985
0.4
−0.7
0.946
ND
ND

RSTCl: rib, sternum, clavicle.

(time of insult or causative triggering] event) is when all are >99 and 99.9%, respectively, for the distribution function, or when is only 1 or 0.1%, respectively.

ND: function not definable, since < 0 is required.

(a)

(b)

Figure 1: Asymmetric single peak distribution function fits for long bone conventional osteosarcoma with the Pearson IV (a) and log normal distribution (b). The log normal distribution is a slightly better fit at the young ages but does not capture the peak age of 15 years as well as the Pearson IV distribution.

(a)

(b)

(c)

(d)

Figure 2: Single asymmetric peak distribution function fits for parosteal long bone sarcoma with the Pearson IV (a) and log normal (b) distributions. Although the of 0.77 is relatively high, visual observation of the fits demonstrates significant variability. After collapsing the age groups into 3-year spans, the fit is much better, with an of 0.96 for both the Pearson IV (c) and log normal (d) distributions.

3.2. Ewing’s Sarcoma

There were 1,832 patients with primary osseous Ewing’s sarcoma; the average age at diagnosis was years. There were 1,158 males (63.2%) and 674 females (36.8%); ethnicity was 1,683 White, 49 Black, 43 Indo-Malay, 17 Amerindian, 14 Indo-Mediterranean, and 18 Polynesian. Incubation period modeling again demonstrated that the Pearson IV and log normal distributions were excellent fits ( of 0.99 and 0.95, resp.) (Figure 3). This results in an at the 99 and 99.9% points of 0.4 and −0.7 years for the Pearson IV distribution. The log normal distribution is not definable at the values of and so must be excluded. Thus the triggering event for Ewing’s sarcoma of bone is prenatal at −0.7 years (36 weeks before birth or 4 weeks after conception).

(a)

(b)

Figure 3: Single asymmetric peak distribution function fits of Ewing’s sarcoma of bone with the Pearson IV distribution (a) and the log normal distribution (b). Note that the log normal distribution poorly fits the younger ages, making it difficult to determine .

3.3. Discussion

This is the largest series to date of the demographics for these two primarily pediatric osseous malignancies. Our results are similar to others (Table 4) confirming the slight male predominance for both neoplasms [2, 25, 30, 31, 33, 50] as well as the rarity of Ewing’s sarcoma in African/Black people [2, 3, 25–27, 35]. Ewing’s sarcoma was also noted to be rare in Amerindians (Hispanics/Native Americans) (22/2321, 0.94%), and Asians (Indo-Malay’s) (75/2321, 3.2%). Due to the rarity of Asian ethnic subgroups in this country, and thus the SEER database, we cannot comment on the differences previously noted between different Asian people [23, 51].

Table 4: Demographics of osteosarcoma and Ewing’s sarcoma from the literature.

Study
Year
Time span
Location

M
F
% M
W
B
Hispanic
Asian
% W
% B

Osteosarcoma

    Present study
—
1993–2010
USA
4594
2535
2059
55.2
3508
663
41
273
77.1
14.4

    Bovill Jr. et al. [23]
1975
1969–1972
Malaysia
68
40
28
58.8

    Young Jr. and Miller [24]
1975
1969–1972
USA
61
32
29
52.5
51
10

83.6
16.4

    Buckley et al. [25]
1998
1982-1983
USA/Canada
152
75
77
49.3
127
15
10
0
83.6
9.9

    Jensen and Drake [26]
1970
1940–1968
USA (AFIP)
677

595
82

87.9
12.1

    Fraumeni Jr. and Glass [27]
1970
1960–1966
USA
819
452
367
55.2
692

84.5
—

    Bassin et al. [28]
2006
1989–1992
USA
103
60
43
58.3
81
16

3
78.6
15.5

    Finkelstein [29]
1994
1950–1983
Ontario, Canada
20
15
5
75.0

    Operskalski et al. [30]
1987
1972–1982
Los Angeles, CA
64
34
30
53.1
43
13
8

67.2
20.3

    Eyre et al. [31]
2009
1981–2002
Northern England and West Midlands
206
95
111
46.1
—
—
—
—
—
—

    Stiller et al. [32]
1991
1981–1990
UK
150

130

7
86.7
0.0

    Stiller et al. [33]
2006
1978–1997
Europe
1609
889
720
55.3

0.0

    Cotterill et al. [34]
2000
1968–1995
Northern England
131
77
54
58.8
—
—
—
—
—
—

Ewing’s Sarcoma

    Present study
—
1993–2010
USA
2321
1420
90
61.2
2098
70
22
75
90.4
3.0

    Young Jr. and Miller[24]
1975
1969–1972
USA
26
15
11
57.7

—

    Buckley et al. [25]
1998
1982-1983
USA/Canada
153
89
64
58.2
139
1
10
3
90.8
0.7

    Jensen and Drake [26]
1970
1940–1968
USA (AFIP)
239

237
2

99.2
0.8

    Fraumeni Jr. and Glass [27]
1970
1960–1966
USA
482
265
217
55.0
456
—
—
—
94.6
—

    Linden and Dunn [35]
1970
—
California, USA
149

147
2

98.7
1.3

    Finkelstein [29]
1994
1950–1983
Ontario, CA
15
9
6
60.0

    Moore et al. [36]
2005
1983–1985
USA
196
120
76
61.2
184

93.9
0.0

    Holly et al. [37]
1992
1978–1986
San Francisco, CA
43
28
15
65.1

0.0
—

    Eyre et al. [31]
2009
1981–2002
Northern England and West Midlands
144
74
70
51.4

0.0
—

    Stiller et al. [32]
1991
1981–1990
UK
172

0.0
156

8
90.7
—

    Stiller [33]
2006
1978–1997
Europe
1182
647
535
54.7
—
—
—
—

—

    Cotterill et al. [34]
2000
1968–1995
Northern England
81
53
28
65.4
—
—
—
—

—

Ewing’s sarcoma is nearly always associated with a t(11;22)(q24;q12) translocation [4–11]. Such a translocation may be due to many different mechanisms (spontaneous mutation, environmental exposures to parents, etc.). Regardless of the mechanism, we hypothesized that incubation period modeling would demonstrate a time of “insult” as prenatal or birth. We found that the for Ewing’s sarcoma of bone at the 99.9% point was −0.7 years (36 weeks before birth, or ~4 weeks after conception). This demonstrates that incubation period modeling is extremely accurate and is in complete agreement with the genetic data; any other result would be in stark contrast to the well known genetic translocation. This confirms the accuracy of this modeling and can thus be used for other neoplasms.

Osteosarcoma has been associated with various genetic abnormalities [12–15], as well as environmental exposures [7, 14, 15, 29]. If osteosarcoma is a pure genetic defect, similar to Ewing’s sarcoma, then incubation period modeling should find an “insult” time as prenatal or at birth. This study found that the at the 99.9% level for long bone osteosarcoma is very early in life at ~0.4 years but not prenatal. The exact insult is still unknown and will require further investigation. Other types of osteosarcoma demonstrated no good fit with incubation period modeling indicating that these subtypes are heterogeneous with no actual time of “insult.” The only exception might be with parosteal osteosarcoma, which demonstrated an of 10.4 years for the 99.9% point when collapsing into 3-year “buckets” of age. This may indicate that there are two factors in the etiology of these tumors, both genetic and environmental exposure. Unfortunately, our incubation period modeling technique can separate out a double hit hypothesis.

A weakness of this study is that the histologic specimens used to make the diagnosis were not reviewed by the same pathologist, which could introduce bias. There are no studies addressing this question for osteosarcoma, although there have been studies addressing other malignancies [52–55]. With ovarian carcinoma, there is fair agreement in grade [52]; with non-Hodgkin’s lymphomas the diagnosis was very accurate but reliability for the subtype was poor (59%, ) [53]; with Hodgkin lymphoma subtype agreement was overall good , and with lung cancer the histologic type was reasonably reliable but independent review was necessary for precise histologic typing. Thus the overall diagnosis appears to be reliable although the subtype classification is likely less reliable. Since this question has not been addressed for osteosarcoma, the potential impact on our results is unknown.

4. Conclusion

Incubation period modeling markedly confirms the genetic etiology of Ewing’s sarcoma. Long bone osteosarcoma is not completely genetic in etiology, as was 0.4 years for conventional long bone osteosarcoma and 10.4 years for parosteal osteosarcoma. Thus the etiologies for those two different types of osteosarcoma are likely different due to the different . It has been recognized that osteosarcoma of the mandible is a “different animal” [56], and the marked differences in age at diagnosis and variability with incubation period modeling amongst the different subtypes of osteosarcoma indicate that although pathologically they are similar, etiologically they are different. Further research will be needed to elucidate the etiologies of these various osteosarcoma types.

Appendix

Incubation period modeling originated with infectious diseases [45, 46]. The theory behind this modeling is that a pathogen infects an organism and the organism develops clinical symptoms and is subsequently diagnosed with the disease. The incubation period is the time from exposure to clinical manifestation of the disease. Different members of a population afflicted with the same disease demonstrate different incubation periods. The natural variation in incubation periods can be characterized by a frequency distribution, with the -axis representing the age at diagnosis and the -axis the number/proportion of organisms infected at that particular age/time. This modeling has been expanded to other chronic diseases [44, 57] including malignancies [19–22], such as malignancies arising from radiation exposure.

The mechanics of such modeling is to first find a frequency distribution possessing an excellent fit of the data for the entire population afflicted with the disease in question. When (frequency distribution is zero), no cases of the disease have yet occurred. The which corresponds to represents the moment in time when the host was exposed to the infectious/triggering/causative agent(s) (defined as ). Many frequency distributions are mathematically undefined when due to a particular mathematical expression (e.g., division by zero or logarithm of 0). In such instances the corresponding to an when only 0.1–1% of the population has been diagnosed with the disease is used as . This is determined by the area (integral) under the frequency distribution from to the maximum age and denotes that proportion of the entire population spanning that portion of the -axis. These integral values are then determined for those when the integral areas under the curve are 99% and 99.9%. The fitting of many complex distributions can now be easily performed today with personal computer software packages, which were not available in the first incubation period modeling studies from the 1950s.

The distribution first used historically for incubation period modeling and infectious diseases was the log normal distribution [45, 46]; however it cannot be used for (e.g., prenatal or genetic events). More recent studies fit many different distributions to find most representative fit [44, 58, 59]. Many populations are better evaluated with asymmetric distributions as they are not normally distributed [46, 47] or require to be <0 (prenatal exposure or genetic transmission, occurring at conception/before birth).

The mathematical equations for these distributions are as follows.

(1) The lognormal distribution is mathematically expressed as

where is the base of the natural logarithm.

Note that, for any , the distribution is undefined, rendering this distribution unsatisfactory for any models needing an , that is, birth or younger (i.e., prenatal exposure and/or genetic disorder).

(2) The Pearson IV distribution is mathematically expressed as

where , , , and are fitted parameters unique for the data set analyzed. This distribution can be defined for any .

Conflict of Interests

The authors declare that they have no conflict of interests.

Acknowledgments

This study was supported in part by the Garceau Professorship Endowment, Department of Orthopaedic Surgery, Indiana University School of Medicine, and the George Rapp Pediatric Orthopaedic Research Endowment, Riley Children’s Foundation, Riley Children’s Hospital, Indianapolis, Indiana.

References

X. Dai, W. Ma, X. He, and R. K. Jha, “Review of therapeutic strategies for osteosarcoma, chondrosarcoma, and Ewing's sarcoma,” Medical Science Monitor, vol. 17, no. 8, pp. RA177–RA190, 2011.

D. M. Parkin, C. A. Stiller, and J. Nectoux, “International variations in the incidence of childhood bone tumours,” International Journal of Cancer, vol. 53, no. 3, pp. 371–376, 1993.

J. G. Gurney, R. K. Severson, S. Davis, and L. L. Robison, “Incidence of cancer in children in the United States. Sex-, race-, and 1-year age-specific rates by histologic type,” Cancer, vol. 75, no. 8, pp. 2186–2195, 1995.

C. A. S. Arndt, P. S. Rose, A. L. Folpe, and N. N. Laack, “Common musculoskeletal tumors of childhood and adolescence,” Mayo Clinic Proceedings, vol. 87, no. 5, pp. 475–487, 2012.

N. J. Balamuth and R. B. Womer, “Ewing's sarcoma,” The Lancet Oncology, vol. 11, no. 2, pp. 184–192, 2010.

H. E. Grief, “The Ewing family of tumors: Ewing's sarcoma and primitive neuroectodermal tumors,” Pediatric Clinics of North America, vol. 44, no. 4, pp. 991–1004, 1997.

R. Eyre, R. G. Feltbower, E. Mubwandarikwa, T. O. B. Eden, and R. J. Q. McNally, “Epidemiology of bone tumours in children and young adults,” Pediatric Blood and Cancer, vol. 53, no. 6, pp. 941–952, 2009.

M. Paulussen, B. Fröhlich, and H. Jürgens, “Ewing tumour: incidence, prognosis and treatment options,” Pediatric Drugs, vol. 3, no. 12, pp. 899–913, 2001.

J. D. Khoury, “Ewing sarcoma family of tumors,” Advances in Anatomic Pathology, vol. 12, no. 4, pp. 212–220, 2005.

C. Mackintosh, J. Madoz-Gúrpide, J. L. Ordóñez, D. Osuna, and D. Herrero-Martín, “The molecular pathogenesis of Ewing's sarcoma,” Cancer Biology and Therapy, vol. 9, no. 9, pp. 655–667, 2010.

E. C. Toomey, J. D. Schiffman, and S. L. Lessnick, “Recent advances in the molecular pathogenesis of Ewing's sarcoma,” Oncogene, vol. 29, no. 32, pp. 4504–4516, 2010.

W. C. Mertens and V. Bramwell, “Osteosarcoma and other tumors of bone,” Current Opinion in Oncology, vol. 6, no. 4, pp. 384–390, 1994.

W. C. Mertens and V. Bramwell, “Osteosarcoma and other tumors of bone,” Current Opinion in Oncology, vol. 7, no. 4, pp. 349–354, 1995.

C. A. Stiller, “Epidemiology and genetics of childhood cancer,” Oncogene, vol. 23, no. 38, pp. 6429–6444, 2004.

R. Gorlick, “Current concepts on the molecular biology of osteosarcoma,” Cancer Treatment and Research, vol. 152, pp. 467–478, 2009.

J. W. Martin, J. A. Squire, and M. Zielenska, “The genetics of osteosarcoma,” Sarcoma, vol. 2012, Article ID 627254, 11 pages, 2012.

S. A. Savage and L. Mirabello, “Using epidemiology and genomics to understand osteosarcoma etiology,” Sarcoma, vol. 2011, Article ID 548151, 13 pages, 2011.

G. T. Calvert, R. L. Randall, K. B. Jones, L. Cannon-Albright, S. Lessnick, and J. D. Schiffman, “At-risk populations for osteosarcoma: the syndromes and beyond,” Sarcoma, vol. 2012, Article ID 152382, 9 pages, 2012.

H. K. Armenian and A. M. Lilienfeld, “The distribution of incubation periods of neoplastic diseases,” American Journal of Epidemiology, vol. 99, no. 2, pp. 92–100, 1974.

H. K. Armenian and M. J. Khoury, “Age at onset of genetic diseases. An application for Sartwell's model of the distribution of incubation periods,” American Journal of Epidemiology, vol. 113, no. 5, pp. 596–605, 1981.

S. Cobb, M. Miller, and N. Wald, “On the estimation of the incubation period in malignant disease: the brief exposure case, leukemia,” Journal of Chronic Diseases, vol. 9, no. 4, pp. 385–393, 1959.

S. A. Beach and G. W. Dolphin, “A study of the relationship between X-ray dose delivered to the thyroids of children and the subsequent development of malignant tumours,” Physics in Medicine and Biology, vol. 6, no. 4, pp. 583–598, 1962.

E. G. Bovill Jr., J. F. Silva, and N. Subramanian, “An epidemiologic study of osteogenic sarcoma in Malaysia. Incidence in urban as compared with rural environments and in each of three separate racial groups, 1969–1972,” Clinical Orthopaedics and Related Research, vol. 113, pp. 119–127, 1975.

J. L. Young Jr. and R. W. Miller, “Incidence of malignant tumors in U.S. children,” The Journal of Pediatrics, vol. 86, no. 2, pp. 254–258, 1975.

J. D. Buckley, T. W. Pendergrass, C. M. Buckley et al., “Epidemiology of osteosarcoma and Ewing's sarcoma in childhood. A study of 305 cases by the Children's Cancer Group,” Cancer, vol. 83, no. 7, pp. 1440–1448, 1998.

R. D. Jensen and R. M. Drake, “Rarity of Ewing's sarcoma in Negroes,” The Lancet, vol. 1, no. 7650, p. 777, 1970.

J. F. Fraumeni Jr. and A. G. Glass, “Rarity of Ewing's sarcoma among U.S. Negro children,” The Lancet, vol. 1, no. 7642, pp. 366–367, 1970.

E. B. Bassin, D. Wypij, R. B. Davis, and M. A. Mittleman, “Age-specific fluoride exposure in drinking water and osteosarcoma (United States),” Cancer Causes and Control, vol. 17, no. 4, pp. 421–428, 2006.

M. M. Finkelstein, “Radium in drinking water and the risk of death from bone cancer among Ontario youths,” Canadian Medical Association Journal, vol. 151, no. 5, pp. 565–571, 1994.

E. A. Operskalski, S. Preston-Martin, B. E. Henderson, and B. R. Visscher, “A case-control study of osteosarcoma in young persons,” The American Journal of Epidemiology, vol. 126, no. 1, pp. 118–126, 1987.

R. Eyre, R. G. Feltbower, E. Mubwandarikwa et al., “Incidence and survival of childhood bone cancer in northern England and the West Midlands, 1981–2002,” British Journal of Cancer, vol. 100, no. 1, pp. 188–193, 2009.

C. A. Stiller, P. A. McKinney, K. J. Bunch, C. C. Bailey, and I. J. Lewis, “Childhood cancer and ethnic group in Britain: a United Kingdom children's cancer study group (UKCCSG) study,” British Journal of Cancer, vol. 64, no. 3, pp. 543–548, 1991.

C. A. Stiller, S. S. Bielack, G. Jundt, and E. Steliarova-Foucher, “Bone tumours in European children and adolescents, 1978–1997. Report from the Automated Childhood Cancer Information System project,” European Journal of Cancer, vol. 42, no. 13, pp. 2124–2135, 2006.

S. J. Cotterill, L. Parker, A. J. Malcolm, M. Reid, L. More, and A. W. Craft, “Incidence and survival for cancer in children and young adults in the North of England, 1968–1995: a report from the Northern Region Young Persons' Malignant Disease Registry,” British Journal of Cancer, vol. 83, no. 3, pp. 397–403, 2000.

G. Linden and J. E. Dunn, “Ewing's sarcoma in Negroes,” The Lancet, vol. 1, no. 7657, p. 1171, 1970.

L. E. Moore, L. Gold, P. A. Stewart, G. Gridley, J. R. Prince, and S. H. Zahm, “Parental occupational exposures and Ewing's sarcoma,” International Journal of Cancer, vol. 114, no. 3, pp. 472–478, 2005.

E. A. Holly, D. A. Aston, D. K. Ahn, and J. J. Kristiansen, “Ewing's bone sarcoma, paternal occupational exposure, and other factors,” The American Journal of Epidemiology, vol. 135, no. 2, pp. 122–129, 1992.

National Cancer Institute and US Department of Health and Human Services, SEER As a Research Resource, National Institute of Health, 2010.

National Cancer Institute, “Surveillance Epidemiology and End Results,” Overview of the SEER Program, http://seer.cancer.gov/about/overview.html

P. B. Eveleth and J. M. Tanner, Worldwide Variation in Human Growth, Cambridge University Press, Cambridge, UK, 2nd edition, 1990.

Healthcare Cost and Utilization Project, Kids' Inpatient Database (KID) 2000, Agency for Healthcare Research and Quality, Rockville, Md, USA, 2000.

H. K. Armenian, “Incubation periods of cancer: old and new,” Journal of Chronic Diseases, vol. 40, supplement 2, pp. 9S–15S, 1987.

A. J. Hall and D. J. P. Barker, “The age distribution of Legg-Perthes disease. an analysis using Sartwell's incubation period model,” The American Journal of Epidemiology, vol. 120, no. 4, pp. 531–536, 1984.

R. D. Horner and G. Samsa, “Criteria for the use of Sartwell's incubation period model to study chronic diseases with uncertain etiology,” Journal of Clinical Epidemiology, vol. 45, no. 10, pp. 1071–1080, 1992.

P. E. Sartwell, “The incubation period of poliomyelitis,” American Journal of Public Health, vol. 42, no. 11, pp. 1403–1408, 1952.

P. E. Sartwell, “The incubation period and the dynamics of infectious disease,” The American Journal of Epidemiology, vol. 83, no. 2, pp. 204–216, 1966.

E. Limpert, W. A. Stahel, and M. Abbt, “Log-normal distributions across the sciences: keys and clues,” BioScience, vol. 51, no. 5, pp. 341–352, 2001.

R. T. Loder, R. H. Browne, A. Millis et al., “The time of the insult/triggering event in Legg-Calvé-Perthes' disease determined by incubation period modeling and the age distribution of children with Perthes',” The Iowa orthopaedic journal, vol. 32, pp. 69–75, 2012.

M. Campanacci, F. Bertoni, P. Bacchini, W. F. Enneking, and S. Notini, Bone and Soft Tissue Tumors, Springer, New York, NY, USA, 1990.

S. E. Larsson and R. Lorentzon, “The geographic variation of the incidence of malignant primary bone tumors in Sweden,” The Journal of Bone & Joint Surgery—American Volume, vol. 56, no. 3, pp. 592–600, 1974.

F. P. Li, J. T. Tu, F. S. Liu, and E. L. Shiang, “Rarity of Ewing's sarcoma in China,” The Lancet, vol. 1, no. 8180, p. 1255, 1980.

R. K. Matsuno, M. E. Sherman, K. Visvanathan et al., “Agreement for tumor grade of ovarian carcinoma: analysis of archival tissues from the surveillance, epidemiology, and end results residual tissue repository,” Cancer Causes and Control, vol. 24, no. 4, pp. 749–757, 2013.

C. A. Clarke, S. L. Glaser, R. F. Dorfman, P. M. Bracci, E. Eberle, and E. A. Holly, “Expert review of non-hodgkins lymphomas in a population-based cancer registry: reliability of diagnosis and subtype classifications,” Cancer Epidemiology Biomarkers and Prevention, vol. 13, no. 1, pp. 138–143, 2004.

R. W. Field, B. J. Smith, C. E. Platz et al., “Lung cancer histologic type in the surveillance, epidemiology, and end results registry versus independent review,” Journal of the National Cancer Institute, vol. 96, no. 14, pp. 1105–1107, 2004.

S. L. Glaser, R. F. Dorfman, and C. A. Clarke, “Expert review of the diagnosis and histologic classification of Hodgkin disease in a population-based cancer registry. Interobserver reliability and impact on oncidence and survival rates,” Cancer, vol. 92, no. 2, pp. 218–224, 2001.

J. Thariat, M. Julieron, A. Brouchet et al., “Osteosarcomas of the mandible: are they different from other tumor sites?” Critical Reviews in Oncology/Hematology, vol. 82, no. 3, pp. 280–295, 2012.

R. D. Horner, “Age at onse of Alzheimer's disease: clue to the relative importance of etiologic factors?” American Journal of Epidemiology, vol. 126, no. 3, pp. 409–414, 1987.

B. J. Cowling, M. P. Muller, I. O. L. Wong et al., “Alternative methods of estimating an incubation distribution. Examples from severe acute respiratory syndrome,” Epidemiology, vol. 18, no. 2, pp. 253–259, 2007.

H. Nishiura, “Early efforts in modeling the incubation period of infectious diseases with an acute course of illness,” Emerging Themes in Epidemiology, vol. 4, article 2, 2007.