乳癌是台灣婦女常見的疾病，而其高發生率及高死亡率，在防治工作推展上深受各界重視。其發生率與死亡率在最近十年來有逐年上升的趨勢。乳癌發生率從民國83年的每十萬人18.42例上升到民國90年的每十萬人41.91例。在台灣地區乳癌已經成為僅次於子宮頸癌的第二大女性癌症，並且在女性癌症的死亡率排名第四位，因此，乳癌的防治在台灣已經愈來愈重要。與歐美比較中，歐美婦女乳癌的發生傾向於更年期之後，死亡率也正在逐漸下降；反觀我國婦女乳癌的資料顯示有年輕化的跡象，在國、內外醫學研究中指出，婦女愈晚生第一胎罹患乳癌的風險愈高，停經年齡愈晚得乳癌機率愈大，而初經年齡愈晚得乳癌機率愈小，更年期後肥胖者罹患乳癌的機率比非肥胖者高。
由於乳癌篩選之臨床資料並不易獲得，本研究將以模擬的方法對謝欣如等人(2002)所提之截段指數分配(piecewise exponential distribution)與韋伯分配（Weibull distribution）做一比較討論。同時在本文中我們建議用Gompertz分配取代韋伯分配之估算，也就是說在狀況為正常（Normal）到臨床症前可偵測期（preclinical screen-detectable phase，PCDP）時，本文採用Gompertz分配，即在非同質性三狀態下的馬可夫鏈程序中，第0期到第1期採用Gompertz分配，同時對狀態0（Normal）到狀態1（PCDP），其影響
之因素有婦女第一次懷孕年齡（AP）、身體肥胖指數（BMI）。而模擬推估證實採用Gompertz分配所推估的轉換率與Hsieh等人(2002)，所提之韋伯分配估算之結果是相似的，由此可證明Gompertz分配也適合運用在乳癌疾病的研究進展上。 Breast Cancer has been an important issue for women in Taiwan; both high incidence and high mortality of the disease have also become the reason to promote the prevention and control. In the past decade, the incidence and mortality of breast cancer have been rising e.g., the incidence is rising 18.42 per 10 thousand people to 41.91 per 10 thousand people. The Breast Cancer has become the second leading disease for women in Taiwan only next to the cervix cancer . And it ranks the fourth cause of death in woman’s cancer diseases, thus the prevention and medication has been weighted more importance in Taiwan.
Compared with Europe and America, it’s the most different from Taiwan that the emergence of breast cancer occurs after menopause, and the mortality is alleviated gradually too. The materials of breast cancer show an incline to younger woman in Taiwan. All the researches conclude that the later women give their first birth, the higher risk they’d suffer from the breast cancer. Women who get their first menses later, and the women not overweight after the menopause are under less hazards.
Due to the difficulties on acquiring breast cancer data, this research establishes a simulation model in order make a discussion on the compare Piecewise exponential (Hsieh, et al.,2002) and Weibull distribution.
Furthermore we replace the Weibull distribution with Gompertz distribution estimation. In other word, for the period from Normal to Preclinical screen-detectable phase(PCDP),we adopt Gompertz Distribution. And under the non-homogeneous three states of Markov chain model, period 0~1: Gompertz distribution, the variables to 0(Normal) and 1(PCDP) are AP, BMI .And it can be verified that the estimated ratio of conversion by Gompertz is similar to the Hsieh’s Weibull distribution, therefore we conclude that Gompertz shall be a suitable tool applied to the breast cancer research,too.
