Equivalent doses for anticancer agents used in pediatric oncology: A literature review and evaluation of a novel approach for conversion factors

Abstract Background Epidemiological research on late effects of therapy shows the necessity to aggregate chemotherapy agents to substance classes. This requires using conversion factors by substance classes. Aims The aim of this study was to identify previously used conversion factors from the literature, to present a novel approach for additional factors, and to compare these approaches. Methods and Results A literature review was performed, which identified two main principles of deriving conversion factors: effect‐equivalence and equimolar. Thirty‐five articles presenting effect equivalence‐based factors in the widest sense were found in the literature. Ten articles presented the equimolar approach which can be applied to almost all chemotherapy substances. Based on a comprehensive list of treatment protocols used in German pediatric oncology, we derived alternative conversion factors from typical doses. We compared the conversion factors using Pearson correlation coefficients and linear regression. At least two types of conversion factor were available for each of the 49 substances included. The equivalent effect‐based and the typical dose‐based factors were highly correlated with a regression coefficient close to 1. The equimolar factors are independent. Conclusions For substances for which no conversion factor based on some type of effect equivalence has been published so far, a factor based on a typical doses‐approach may be used in epidemiological late effects research. Doses aggregated based on the equimolar approach may not be compatible with doses aggregated based on equivalent effects.


| INTRODUCTION
Our working group is working on a case-control study on second neoplasms after childhood cancer (second tumors after tumor therapy (STATT)) using data from the German Childhood Cancer Registry (GCCR) and German clinical therapy trials in pediatric oncology, soon to be published). For this we obtained retrospective cumulative chemotherapy dose data for the former patients. It became clear that the number of different substances is too large for joint statistical analysis and some substances are applied rarely and therefore allow no statistical analysis. Other groups working on late effects of chemotherapy had been using the solution of grouping substances by pharmacologic principles, 1,2 usually using a conversion factor before aggregating cumulative doses in a substance group (e.g., . Clinical replacement rules require conversion factors, too. 9,10 Given the sometimes very different dose range of substances in a substance group, aggregating them without conversion is not indicated.
However, a comprehensive list of substances used in pediatric oncology and conversion factors for them turned out not to be available in the pertinent literature. Therefore, we initiated a very broad literature search aiming to collect factors having been used before in this field of late effects research, with a special focus on childhood cancer survivors. We are presenting the results of this search here.
In addition, we developed an algorithm to fill in conversion factors for which conversion factors cannot be found in our literature search.
This approach is based on typical doses determined from a comprehensive list of treatment protocols of the German Society for Pediatric Oncology and Hematology (GPOH) from the years 1970 to 2018. 11,12 We are presenting these factors here, too. The final question was whether it is justified using conversion factors based on different principles in the same analyses; for this we compared the factors statistically.

| Inclusion and grouping of substances
We included all substances with reported conversion factors in the pertinent literature and which have been used in treatment protocols for pediatric oncology in Germany since the 1970s. 11,12 They were included if they are considered as antineoplastic agents (Group L01) according to the Anatomical Therapeutic Chemical (ATC) code, 2 excluding immunotherapy and supportive substances. We also examined glucocorticoids which are used as antineoplastic agents in pediatric oncology although they are not listed as such according to the ATC (Group H02AB). 13 Doses were given in or converted to the unit mg/m 2 (except for asparaginase (L01XX), where International Units (IU)/m 2 are generally used). The substances were classified into 12 substance groups according to the ATC. 2 For each class, a reference substance was chosen. Based on the ATC, procarbazine and estramustine belong to the group 'other antineoplastic agents' (L01X).
However, due to their mode of action, they are usually grouped with alkylating agents (L01A) in oncology literature. 3

| Literature review
The literature review was performed as a scoping review according to the PRISMA-ScR (Preferred Reporting Items for Systematic reviews and Meta-Analyses extension for Scoping Reviews) checklist. 14 The literature search was performed in Medline via PubMed on December 13th, 2022 and in Web of Science Core Collection on November 29th, 2022.
The search strategy with criteria for inclusion and exclusion was defined a priori (see Table 1). Given that we were mainly interested in applying this to research on secondary carcinogenicity in treated children, we used the following search terms: 'childhood second cancer AND chemotherapy AND dose' (Search 1). In order to include articles examining glucocorticoids as well, we performed an additional specific search using 'cortisone AND equivalence dose'. The resulting queries are provided in detail in Supplementary Table 1. Articles were included if they had been published since 1985 because of incomplete availability of older publications. Inclusion of adults in the respective studies was no exclusion criterion, as we were generally not interested in the respective study results, but in the method sections. The first author screened the titles and abstracts and evaluated the full texts of the remaining articles.
As we had started with generally researching the topic of carcinogenic effects of chemotherapy in children when preparing the STATT T A B L E 1 Inclusion and exclusion criteria for the literature review Step Inclusion criteria Exclusion criteria Wherever we found more than one conversion factor based on the same underlying principle for the same substance, we needed to select a factor for our purpose. We applied the following criteria (defined a priori) in this order: (1) most recent publication year and (2) articles which developed their own conversion factor based on their own literature review of equivalence. We present all factors found, indicating the one we selected (see section 3).

| Conversion factors based on typical doses
This simple approach assumes that the ratio of typical doses of two substances in a group probably comes close to a conversion factor based on therapeutical equipotency. We provide regression coefficients with confidence limits for the individual (CLI) values and the mean predicted values (CLM). The statistical analyses were performed with SAS 9.4 (proc corr and proc reg).

| RESULTS
3.1 | Literature review Figure 1 gives an overview of the article selection process using the above mentioned search strategy and inclusion and exclusion criteria.
In total, we identified 479 articles after removing duplicates. In 10 out of the 151 articles screened which met all inclusion criteria, the authors suggested converting mg/m 2 of chemotherapeutics to moles/m 2 to quantify the total dose of a drug in each drug class (equimolar approach). [18][19][20][21][22][23][24][25][26][27] As molecular weights are easily available for almost all chemotherapeutic substances, we were able to calculate additional factors using this approach ourselves. The factors were calculated using the molecular weights, independently from any article. The higher the molecular weight, the fewer active molecules are included per weight of a substance. Under this assumption, we calculated factors derived from the molecular weights for each substance as described above for the other factors.
Twenty-two further studies not (only) using the equimolar approach met all inclusion criteria. Additionally, we identified seven more articles of this type, which had been cited by the articles identified in the original search, 16,17,[28][29][30][31][32] and added another six articles which had been known from our former general research 5,9,10,15,33,34 on late effects of childhood cancer. Hence, 35 articles with conversion factor suggestions other than those based on the equimolar approach were included in the literature review. Tables 2 and 3 list all 24 studies examining chemotherapeutics other than glucocorticoids ( Table 2) and 11 articles examining glucocorticoids (Table 3) separately.
Two 30,34 out of these 35 articles set out to challenge the idea that factors based originally on hematologic toxicity can be used for studying cardiologic late effects, citing a large number of such factors previously used. We extracted these factors stated in the methods section of the articles according to our criteria in Table 1.
As the same literature was cited in both articles, we only included the factors derived from the literature and used in the study in the later article. 34 3.2 | Principles for effect equivalencechemotherapeutics other than glucocorticoids The basis of assessment of the different principles for effect equivalence other than the equimolar approach was usually not entirely clearly stated and rather diverse. For chemotherapeutics except Number of records idenƟfied through database searching: • MEDLINE via PubMed with keywords "childhood second cancer AND chemotherapy AND dose" (n = 211) • MEDLINE via PubMed with keywords "corƟsone AND equivalence dose" (n = 21) • Web of Science Core CollecƟon with keywords "childhood second cancer AND chemotherapy AND dose" (n = 361) • Web of Science Core CollecƟon with keywords "corƟsone AND equivalence dose" (n = 1) Total: ( F I G U R E 1 Flow chart of inclusion and exclusion of identified articles. *One study is mentioned twice because it referred to molecular weights and in a second analysis assumed equality between substances  (3) of which a full-text in English or German was available (see Table 1). b In studies on childhood cancer survivors, the inclusion in the study might have taken place as adults. The age groups were defined as follows:  (3) of which a full-text in English or German was available (see Table 1). b In studies on childhood cancer survivors, the inclusion in the study might have taken place as adults. The age groups were defined as follows: children: below the age of 18; adults: above the age of 18; adolescents: age 16-25 (only mentioned if there were mixed groups of either adolescents and adults or children and adolescents).
glucocorticoids (24 articles), the conversion factors in the literature were mostly (15 out of 24) based on a principle which can be summarized by the term isotoxic. Toxicity referred to cardiotoxicity (n = 6), hematotoxicity (n = 8), or hematological toxicity, non-hematological toxicity and cardiotoxicity (n = 1). An isotoxicity factor of, for example, four for a substance means that one unit of the substance was considered four times more toxic than one unit of the reference substance.
Three articles (3 out of 24) referred to the intended effects of the chemotherapeutics, using the terms antitumor efficacy (n = 2) or potency (n = 1), respectively. These can be summarized by the term equipotency. One additional article justified a factor with both cardiotoxicity (isotoxicity) and potency (equipotency).
Five articles out of 24 did not explicitly state a basis for their conversion factors; we conclude an underlying assumption of isotoxocity or equipotency from the context and usage of the factors in the respective studies.
For 17 substances, more than one factor was found in the literature. For all substances except Thiotepa, these factors were generally rather similar; however, the basis stated could still differ. As an example: Epirubicin was presented with a factor of 0.67 based on hematological toxicity 4,5,7 as well as on cardiotoxicity. 10,33 Another article mentioned similar factors for epirubicin based on hematological toxicity, cardiotoxicity or non-hematological toxicity, respectively. 16 One article justified the factors for anthracyclines with both cardiotoxicity (isotoxicity) and potency (equipotency). 32

| Principles for effect equivalenceglucocorticoids
For glucocorticoids (11 articles), all factors in the literature were based on the concept of equipotency (n = 8). In these articles, the following principles were used: potency (either general or inflammatory) (n = 4), conventional glucocorticoid replacement therapy (n = 1), hydrocortisone-equivalent dose (n = 2) or prednisone equivalent (n = 1). In three articles, the basis of the conversion factor was not stated explicitly. We conclude an underlying assumption of equipotency from the context and usage of the factors in the respective study.
The usage of and stated bases for conversion factors in the literature seem to suggest that at least some authors assume the concepts of isotoxicity, isotoxicity for a specific outcome, and equipotency are sufficiently similar for general usage in late effects research. We concur for now and will refer to both concepts (isotoxicity and equipotency) as effect equivalence below. These factors are listed in Table 4 column 3.

| Equimolar principle
The rationale behind the equimolar principle is that 'a molecule of a given drug generally has one active site, whatever its weight. Even if a particular drug may have more than one active site per molecule, the error introduced by this hypothesis is probably lower than that introduced when summing the weights'. 27 The molecular weights (g/mol) of substances with an ATC code are readily available for all substances from the Website PubChem, 66 not only for the substances included in the papers found in the literature search. [18][19][20][21][22][23][24][25][26][27] This permitted directly calculating equimolar conversion factors for all substances (save one, see below), presented in column 9 in Table 4.
For asparaginase (ATC-code L01XX02) and pegylated asparaginase (L01XX24), we could not present factors derived from molecular weights because this chemical approach is not applicable to enzymes.  Table 4, column 7.    Comparing these three types of conversion factors, we found the effect equivalence-based and the typical dose-based factors to be highly correlated (r = 0.83) and on average close to being identical.

| Comparing factors based on different principles
The correlation of the factors derived from molecular weights with the other factors was moderate or close to zero. Based on two criteria (defined a priori), which were applied in the following order: (1) most recent publication year, (2) articles which developed their own conversion factor based on their own literature review. b According to the ATC index, Procarbazine is a Methylhydrazine (L01XB) and belongs to the group "other antineoplastic agents" (L01X). However, due to its mode of action, it is usually grouped with the alkylating agents (L01A) in oncology literature. 3,8 c According to the ATC index, Estramustine belongs to the group "other antineoplastic agents" (L01X). However, due to its mode of action, it is usually grouped with the alkylating agents (L01A) in oncology literature. 3 The typical doses-approach was feasible and had a very broad information basis, as pediatric oncology in Germany has been using nationwide, centralized treatment protocols since the 1970s, 68 and we had access to a complete overview over all these protocols until 2018. 11,12 We needed a criterion to select a factor when more than one was available in the literature. Using the latest information and one which stated its basis clearly seemed sensible, but they are still somewhat arbitrary and readers may make a different selection from Table 4 The method used by the authors of two articles 30,34 to derive factors from their own data was based on substance specific regression coefficients after applying a factor from the literature to then compare the effect sizes per dose. The authors suggest to use these ratios for obtaining a different conversion factor for a joint estimate; they do not apply this factor to obtain a joint dose-response estimate for their outcome, however. This is an interesting approach. One must be aware, however, that small studies and substances with small numbers of exposed patients are likely to randomly produce outlying regression coefficients, which could provide these substances randomly with an outlying weight (although the bootstrap approach chosen would render such estimates less likely). Moreover, it is questionable whether This study gives an overview over dose conversion factors of anticancer agents to a reference substance within their class by mode of action with an emphasis on usage in childhood cancer late effects research. We were able to present factors for 49 substances.
As a first step we present results from a literature review. The factors based on effect-equivalence seem to be more widely used and well justified for late effects research. For substances for which no such conversion factors could be found in the literature, we proposed factors from a rather simple approach, relating typical doses. Our original question had been whether we could justify filling in these factors for the 11 substances where we could not find an effect-equivalence factor in the literature. Based on our comparison results we consider this justified. The data base for the typical dose approach was specific for pediatric oncology in Germany; therefore, our factors may not be directly applicable to adults or in other countries.
A smaller number of articles suggested factors derived from molecular weights (equimolar). Obtaining such factors is straightforward using publicly available mole weights. These factors were basically independent from the other approaches. Results in terms of dose effects in late effects research using these factors may not be comparable to results based on data using effect equivalence-based factors.
These conversion factors in general and their underlying principles potentially have great value for research with aggregated data, such as epidemiological late effects research.

DATA AVAILABILITY STATEMENT
Data available on request from the authors.

ETHICS STATEMENT
The authors declare that this work has been done in accordance to Wiley "Best Practice Guidelines on Research Integrity and Publishing Ethics" and that is has been performed in an ethical and responsible way, with no research misconduct, which includes, but is not limited to data fabrication and falsification, plagiarism, image manipulation, unethical research, biased reporting, authorship abuse, redundant or duplicate publication, and undeclared conflicts of interest ORCID Meike Ressing https://orcid.org/0000-0001-6326-9005 Peter Kaatsch https://orcid.org/0000-0002-8565-0832