Environmental radioactive contamination caused by the Fukushima Dai-ichi Nuclear Power Plant accident has aroused great concern regarding a possible increase in the incidence of childhood thyroid cancer. The ultrasound examinations were conducted immediately after the accident as part of the Fukushima Health Management Survey (FHMS), which is divided into the preliminary baseline survey (PBLS) and the full-scale survey (FSS). Some of their outcomes are reported regularly and made available to the public. We have detailed measurements of the air-dose rates and radioactive elements in soil in many places all over the Fukushima prefecture. To study the dose-response relationship, we begin with the assumption that the external and internal doses are correlated with the air-dose rate and the amount of I in soil, respectively. We then investigate the relationship between these estimated doses and the PBLS and FSS thyroid cancer cases. Our analysis shows that the dose-response curve with the FSS data clearly differs from that with the PBLS data. Finally, we consider the potential mitigating effects of evacuation from highly contaminated areas in both external and internal exposure scenarios.