We thank T Sobue1 for his Letter to the Editor and for debating our approximate 'exposed person-time observed', which we determined from data published by the Fukushima Health Management Survey (FHMS)2. T Sobue's Letter to the Editor gives us the opportunity to explain our method in a focused exemplary way, and, above all, to compare our person-time with the person-time ascertained by the Fukushima Medical University (FMU) for the FHMS. This comparison lets us conclude that our approximate person-time on average underestimates the person-time announced by FMU/FHMS by only 3.5 percent. In other words, our independently determined person-time and the person-time by the FMU/FHMS corroborate each other.
T Sobue's assumption: 'Authors defined 'exposed person-time' as the time from March 11, 2011 to the time of screening thyroid ultrasonography and used this as a denominator of detection rate' is incomplete and not entirely correct. The accusation that we confused 'time for exposure' and 'time for outcome' has no basis in the context of our article. We clearly stated that the exposed person-time is determined by the two time-intervals (1) from the nuclear accidents to the start of the screenings in the municipalities and (2) from the start of the screenings to when the numbers of diagnoses and their according municipalities were summarized. This information was announced consecutively at 16 dates for the 1st round and at 11 dates for the 2nd round. See section '2.3 Person-time observed' in our article2 for precise definitions. At which point in time within the observed periods the dynamic biological/medical 'outcome' thyroid cancer occurred is of course not known. And when exactly 'thyroid cancer (TC)' or 'no TC' was diagnosed individually has not yet been published by the FHMS. Therefore, the term 'outcome' that we did not employ makes no technical sense in our investigation.
We now demonstrate that our approximate person-year determination leads to very similar person-year statistics as submitted by the FMU to the 'Thyroid Function Evaluation Subcommittee' of the FHMS on November 30, 2017; see https://www.pref.fukushima.lg.jp/uploaded/attachment/244313.pdf (downloaded January 20, 2020). To this end, we collapsed the Table 1 and Table 2 in our paper2 to 4 groups of municipalities (average dose-rate): Aizu less exposed (0.19 µSv/h), Hamadori moderately exposed (0.40 µSv/h), Nakadori moderately exposed (0.69 µSv/h), and Hamadori highly exposed including the evacuated regions (3.73 µSv/h); see Table 1 and Table 2 below. Table 3 extracts and compiles pertinent information necessary for the comparisons of the FMU/FHMS document '244313.pdf ' with our data. These comparisons are presented in Table 4. Since the FMU/FHMS person-years are counted from the end of the 1st screening to the examination in the 2nd screening, the person-years of FMU/FHMS should be similar if not even nearly identical to the difference of our person-years of the 2nd screening minus the person-years of the 1st screening. Indeed, our total person-years difference between the screenings of 505,083 is only 3.5% less than the person-years reported by the FMU/FHMS of 523,442; see Table 4. The correlation between the two variants of the person-years over the 4 groups of municipalities in the tables below is r=0.9991, p-value 0.0009. This can be considered an excellent agreement between our necessarily approximative method and the presumably exact method by the FMU/FHMS of computing the person-years in the 1st and 2nd screening rounds. From this point of view, in our approach there are no 'flaws in methodology' claimed by T Sobue.
We emphasize that although the difference of our person-time of the 2nd minus the 1st round agrees apart from a 3.5% underestimation with the FMU/FHMS person-time, we nevertheless think that the person-time by the FMU/FHMS is not suited for an epidemiologically meaningful detection rate. The person-time should rather count from the biologically important onset of the exposure in 3/2011 and not from the incidental end of the 1st round. However, for the determination of a dose-specific detection rate ratio (DRR) this distinction is less important. Table 5 compiles the DRRs according to the various possible scenarios based on the 4 differentially exposed groups of municipalities in Tables 1 to 4. Table 5 essentially shows that an increase in the dose-rate by 1 order of magnitude approximately doubles the thyroid cancer incidence.
We further disagree with the T Sobue's opinion: 'This finding should be interpreted as areas with earlier screening have higher detection rate, because of shorter 'exposed person-time' used as denominator, and incidentally areas with higher radiation dose conducted screening earlier.' This can be rejected by noting that in the document '244313.pdf ' not only the detection rate is significantly related to the dose-rate but also the thyroid cancer proportions in the children and adolescents who participated in the 2nd round. The odds ratio according to logistic regression per unit increase in the decadic logarithm of the dose-rate is 2.65 with 95%‑CI (1.45, 4.85), p-value 0.0016; see Figure 1 below. Importantly, radiation exposure is known to be carcinogenic whereas there is no reason in assuming that the timing of the screenings as such influenced the prevalence and the incidence of TC. The insinuation that timing and dose-rate correlate by chance is wrong as the highly contaminated regions were screened deliberately before the less radiologically impacted areas.
In conclusion, the person-years computed according to our method2 for all 59 municipalities are in excellent agreement with the person-years by the FMU/FHMS when collapsed to the 4 areas Aizu (less exposed), Hamadori (moderately exposed), Nakadori (moderately exposed), and Hamadori (highly exposed), see Tables 1 to 5. Moreover, not only the detection rate but even the prevalence according to the 2nd round FMU/FHMS data discloses a significant dose-response association with the log10 of the dose-rate, see Figure 1. Therefore, we can reject all of T Sobue's concerns and criticisms.
Hidehiko Yamamoto, Medical Doctor (MD), Osaka Red Cross Hospital attached facility of physically handicapped children, 5-30 Fudegasaki-cho, Tennouji-ku Osaka-Shi 543-8555 Osaka, Japan
Keiji Hayashi, Medical Doctor (MD), Hayashi Children’s Clinic, 4-6-11-1F Nagata, Joto-ku Osaka-Shi 536-0022 Osaka, Japan
Hagen Scherb, Dr. rer. nat. Dipl.-Math., https://orcid.org/0000-0002-2730-5619; Helmholtz Zentrum München, German Research Center for Environmental Health, Institute of Computational Biology; D-82223 Eichenau, Germany, E-Mail firstname.lastname@example.org
 Sobue T. Letter to the Editor: Association between the detection rate of thyroid cancer and the external radiation dose-rate after the nuclear power plant accidents in Fukushima, Japan. Medicine (Baltimore) Correpondence Blog. https://journals.lww.com/md-journal/Blog/MedicineCorrespondenceBlog/pages/post.aspx?PostID=112. Accessed January 22, 2020.
 Yamamoto H, Hayashi K, Scherb H. Association between the detection rate of thyroid cancer and the external radiation dose-rate after the nuclear power plant accidents in Fukushima, Japan. Medicine (Baltimore). 2019;98(37):e17165.
 UNSCEAR. Report 2013, Volume I, United Nations Scientific Committee on the Effects of Atomic Radiation, REPORT TO THE GENERAL ASSEMBLY, SCIENTIFIC ANNEX A: Levels and effects of radiation exposure due to the nuclear accident after the 2011 great east-Japan earthquake and tsunami, http://www.unscear.org/docs/reports/2013/13-85418_Report_2013_Annex_A.pdf. Accessed November 5, 2019.
Table 1. Target population, participants, and numbers of thyroid cancer cases for the 1st and the 2nd rounds of the TC screening in 4 regions of the Fukushima prefecture; for the index codes of the municipalities see Table 1 in our paper2.
Table 2. Person-time observed and thyroid cancer detection rate (100,000) for the 1st and the 2nd rounds of the TC screening and for both rounds combined in 4 regions of the Fukushima prefecture; average dose-rates [µSv/h] in the municipalities based on UNSCEAR3; for the index codes of the municipalities see Table 1 in our paper2.
Table 3. Information contained in or deduced from the document "244313.pdf" by FMU/FHMS: https://www.pref.fukushima.lg.jp/uploaded/attachment/244313.pdf; for the index codes of the municipalities see Table 1 in our paper2.
Table 4. Comparison of the FMU/FHMS data for the 2nd round with the data (YHS data) of our article2; data selected and compiled from Tables 1 to 3 and https://www.pref.fukushima.lg.jp/uploaded/attachment/244313.pdf; py: person-years.
Table 5. Poisson regression of the thyroid cancers detected in the person-years and according detection rate ratios (DRR) per log10 of the dose-rate [µSv/h] across the 4 groups of municipalities according to our article2 and the document* https://www.pref.fukushima.lg.jp/uploaded/attachment/244313.pdf, see Tables 1 to 4.
Figure 1. Frequency of thyroid cancer (TC) in children and adolescents who participated in the 2nd round (n=270,516) and 95%-CLs by the decadic logarithm of the dose rate; linear logistic regression line: odds ratio per log10(dose-rate [µSv/h]) 2.65 with 95%‑CI (1.45, 4.85), p-value 0.0016; for the data see rows 4 and 13 in the Table of the document https://www.pref.fukushima.lg.jp/uploaded/attachment/244313.pdf.