種子發芽試驗資料的統計分析模型

Abstract

在種子發芽試驗裡，種子發芽時間長短常常受到溫度及光照等環境因素的影響，甚至導致部分種子進入休眠狀態，所以假設種子在未來時間裡全部一定都會發芽是不合理的，另一方面，由於記錄種子發芽的時間點都是間斷的和有限的，因此常見的數據型態為右設限資料和區間設限資料，綜合以上兩點因素，可以使用存活分析 (survival analysis) 裡的治癒模型 (cure model) 來分析這類事件發生所需時間 (time-to-event) 的資料。 在醫學研究中，醫師通常對於某特定或有興趣的疾病想要去研究它，會在一段時間內去觀察被實驗的對象有沒有發生事件(即被實驗的對象有沒有發生有興趣研究的疾病)，但實際狀況裡，被實驗的對象又可包含了對疾病免疫的人，即使觀察時間拉的很長，對於這些免疫的人，還是不會發病，而存活分析裡的混合的治癒模式 (mixture cure model)，建構的特色就是對於疾病免疫者在模式裡假設有一部分治癒的比例，再針對非免疫者的發病時間假設服從一個合理的機率分配,所形成的混合模式。 本篇文章主要在治癒模式的架構之下，進一步考慮溫度對於種子休眠比例和發芽時間的影響，並以不同的統計方法，包括最大概似估計法 (MLE) 和馬可夫鏈-蒙地卡羅 (MCMC) 估計法來估計模式裡的未知參數。我們透過模擬研究來比較不同種子發芽模式下參數估計的結果，並以不偏性、標準誤、均方差及區間估計覆蓋率來比較不同的估計方法的好壞。最後，我們使用R裡〝drc〞這個套件裡的小麥、綠豆、水稻實際種子發芽資料來進行最大概似估計法和馬可夫鏈-蒙地卡羅估計法的比較。

In the seed germination and emergence assays, one fundamental question is how to measure the effect of experimental factors on the process of germination and emergence. Germinating time is often affected by environmental factors such as temperature and light, even lead seeds to dormant. It is unrealistic to assume that all seeds will germinate in the future. Since inspection times are finite and intermittent, the data type are considered as right-censored data and interval-censored data. Therefore, we can use the cure model in the survival analysis to analyze this kind of time-to-event data. In medical research, physicians usually want to study a particular or interesting disease and observe experimental units for a period of time. In reality, some patients may be immunized against the disease. Even if the monitoring time is long enough, the immune person is still not sick. The major characteristic of mixed cure model in survival analysis is that there is a cured fraction in the model and the time of onset of non-immunized people is assumed to be a reasonable probability distribution. This is the mixed cure model. In this paper, the effects of temperature on the dormancy ratio and germinating time were mainly considered under the framework of the cure model. The maximum likelihood estimation (MLE) and Markov Chain Monte Carlo (MCMC) are used to estimate the unknown parameters in the model. We compare the results of parameter estimation with different models through simulation studies, and compare the performances of different estimation methods in terms of bias, standard error, mean square error and coverage probability. In addition, we use the data of wheat, mung bean, and rice in the 'drc' package of R to compare the maximum likelihood estimation and the Markov Chain Monte Carlo estimation.