關於尋找最小有效劑量的統計方法，一般而言，會先確定所採用的檢定統計量，再依據封閉降階的方式偵測最小有效劑量。由Tambane et al. (1996)的模擬比較發現，兩兩對比(pairwise contrast)型式配合封閉降階檢定方式適合偵測最小有效劑量為較低劑量；Helmert對比(Helmert contrast)配合封閉降階檢定方式則宜用於偵測最小有效劑量是較高劑量。因此，針對右設限資料，Chen (2000)提出用兩兩對比與改良式Helmert對比加權對數秩統計量，並配合封閉降階檢定方式來尋找最小有效劑量。
然而，加權對數秩檢定統計量只計算在每一失敗時間點上，各組失敗個數除上仍在涉險個數的差，而未考慮到兩個失敗時間相差的距離。所以本論文將推廣兩兩對比、改良式Helmert對比、與Helmert對比的加權Kaplan-Meier檢定統計量。除此之外，本論文用模擬探討這些對比型式應用於加權對數秩檢定統計量與加權Kaplan-Meier檢定統計量，並配合封閉降階檢定方式，以偵測最小有效劑量的適用時機。
當風險函數成等比例，且最小有效劑量為第一劑量時，模擬結果建議採用兩兩對比加權對數秩統計量，否則，採用Helmert對比加權對數秩統計量。而當風險函數不成等比例且存活時間服從對數常態分配時，在最小有效劑量為第一劑量下，模擬結果建議採用兩兩對比加權Kaplan-Meier統計量，否則，採用Helmert對比加權Kaplan-Meier統計量。

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Aalen, O. O. (1978). Nonparametric inference for a family of counting process. Annals of Statistics 6, 701-726.
Arnold, S. F. (1990). Mathematical statistics. Prentice-Hall.
Andrews, D. F. (1985). Data：a collection of problems from many fields for the student and research worker. Springer-Verlag.
Chen, Y. I. (1999). Nonparametric identification of the minimum effective dose. Biometrics 55, 1236-1240.
Chen Y. I. (2000). Identification of the minimum effective dose for right-censored survival data. NSC88-2118--008-007 Technical Report.
Chen Y. I. and Chi Y. C. (2000). Multiple comparisons between successive treatments for randomly right-censored survival data. Journal of Statistical Planning and Inference 83, 137-151.
Chi, Y. C. (2000). Many-to-one multiple testing procedures for right censored data. NSC89-2118-M-006-005 Technical Report.
Drezner, Z. (1992). Computation of the multivariate normal integral. Transactions on Mathematical Software 19, 470-480.
Fleming, T. R. and Harrington, D. P. (1981). A class of hypothesis tests for one and two-samples of censored data. Communication in Statistics 10, 131-139.
Fleming, T. R. and Harrington, D. P. (1991). Counting process and survival analysis. Wiley.
Gehan, E. A. (1965). A generalized Wilcoxon test for comparing arbitrarily singly censored samples. Biometrika 52, 203-223.

Harrington, D. P. and Fleming, T. R. (1982). A class of rank test procedures for censored survival data. Biometrika 69, 133-143.
Hornung, R. L., Longo, D. L., Bowersox, O. C. and Kwark, L. W. (1995). Tumor antigen -specific immunization of bone marrow transplantation donors as adoptive therapy against established tumor. Journal of National Cancer Institute 87, 1289-1296.
Kaplan, E. L. and Meier, P. (1958). Nonparametric estimator from incomplete observation. Journal of American Statistical Association 53, 457-481.
Mantel, N. (1996). Evaluation of survival data and two new rank order statistics arising in its consideration. Cancer Chemotherapy Report 50, 163-170.
Marcus, R., Peritz E., and Gabriel, K. R. (1976). On closed testing procedure with special reference for ordered analysis of variance. Biometrika 63, 655-660.
Pepe, M. S. and Fleming, T. R. (1989). Weighted Kaplan-Meier statistics: a class of distance tests for censored survival data. Biometrics 45, 497-507.
Peto, R. and Peto, J. (1972). Asymptotically efficient rank invariant test procedures (with discussion). Journal of the Royal Statistical Society A 135, 185-206.
Prentice, R. L. and Marek, P. (1978). A qualitative discrepancy between censored data rank tests. Biometrics 35, 861-867.
Tamhane, A. C., Hochberg, Y., and Dunnett, C. (1996). Multiple test procedure for dose finding. Biometrics 52, 21-37.
Tarone, R. E. and Ware, J. H. (1977). On distribution-free tests for equality for survival distributions. Biometrika 64, 156-160.