tailieunhanh - Statistical Methods for Survival Data Analysis 3rd phần 4

Hình Lognormal xác suất âm mưu của thời gian tồn tại của 234 bệnh nhân nam mắc bệnh bạch cầu lymphocytic mãn tính. (Từ Feinleib và MacMahon, 1960 sao chép lại bởi sự cho phép của nhà xuất bản.) | LOGNORMAL DISTRIBUTION 147 Months after diagnosis Figure Lognormal probability plot of the survival time of 234 male patients with chronic lymphocytic leukemia. From Feinleib and MacMahon 1960. Reproduced by permission of the publisher. Example In a study of chronic lymphocytic and myelocytic leukemia Feinleib and MacMahon 1960 applied the lognormal distribution to analyze survival data of 649 white residents of Brooklyn diagnosed from 1943 to 1952. The analysis of several subgroups of patients follows. The survival time of each patient is computed from the date of diagnosis in months. Analytical method is used to fit the lognormal distribution to the data. The method is discussed in Chapters 7 and 8. Figure gives the probability plot of the survival time of 234 male patients with chronic lymphocytic leukemia in which the horizontal axis for the survival time is in logarithmic scale and the vertical axis is in normal probability scale. When plotting 1 S t on this graph paper a straight line is obtained when the data follow a two-parameter lognormal distribution. An inspection of the graph shows that the distribution is concave. Gaddum 1945a b has pointed out that such a deviation can be corrected by subtracting an appropriate constant from the survival times. In other words the three-parameter lognormal distribution can be used. Figure gives a similar plot in which the survival time of every patient plus 4 is plotted. The configuration is linear and hence empirically it seems valid to assume that the lognormal distribution is appropriate. Similar graphs for male patients with chronic myelocytic leukemia and for female patients with chronic lymphocytic or myelocytic leukemia are given in Figures and . Parameters of the lognormal distribution are estimated. Feinleib and MacMahon report that the agreement between the observed and calculated distributions is striking for each group except for women with chronic lymphocytic leukemia. The .