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

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 ( 𝑥 𝑡 ) 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 ( 𝑟 2 = 0.987 ) and Ewing’s sarcoma ( 𝑟 2 = 0.99 ). For these distributions 𝑥 𝑡 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 𝑥 𝑡 is 4 weeks after conception. Long bone osteosarcoma is not entirely genetic, as 𝑥 𝑡 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.

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][20][21][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.sarcoma diagnosed from 1993 through 2010 [38].SEER collects and publishes cancer incidence data from populationbased 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 Incubation period modeling was used to determine the time of the insult/triggering event [19][20][21][42][43][44][45][46][47][48].The ideal best fit distribution should have an  2 > 0.99.In addition to the  2 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. Satistical 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.

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).
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) ( 2 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

(d))
. There were no significant fits for any of the other osteosarcoma types, even when collapsing the age into groups of 3 years.Polynesian.Incubation period modeling again demonstrated that the Pearson IV and log normal distributions were excellent fits ( 2 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  ≤ 0 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).

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][26][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].
Ewing's sarcoma is nearly always associated with a t(11;22)(q24;q12) translocation [4][5][6][7][8][9][10][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][13][14][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][53][54][55].With ovarian carcinoma, there is fair agreement in grade [52]; with non-Hodgkin's lymphomas the diagnosis was very

2. 1 .Figure 1 :
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.

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

Table 1 :
Demographics for conventional and parosteal osteosarcoma.

Table 3 :
Incubation period modeling results for osteosarcoma and Ewing's sarcoma of bone.  (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.
bone osteosarcoma demonstrated a moderate fit ( 2 = 0.77), with an   of 8.6 and 7.65 years at the 99 and 99.9% points, respectively.When reviewing the data (Figures2(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 ( 2 of 0.96 for both), or   of 10.5 and 10.4 years for the 99 and 99.9% points, respectively (Figures2(c) and 2