The two-parameter lognormal distribution is a variant of the normal distribution and the three-parameter lognormal distribution is an extension of the two-parameter lognormal distribution by introducing a location par...The two-parameter lognormal distribution is a variant of the normal distribution and the three-parameter lognormal distribution is an extension of the two-parameter lognormal distribution by introducing a location parameter. The Q-Q plot of the three-parameter lognormal distribution is widely used. To obtain the Q-Q plot one needs to iteratively try different values of the shape parameter and subjectively judge the linearity of the Q-Q plot. In this paper,a mathematical method was proposed to determine the value of the shape parameter so as to simplify the generation of the Q-Q plot. Then a new probability plot was proposed,which was more easily obtained and provided more accurate parameter estimates than the Q-Q plot. These are illustrated by three realworld examples.展开更多
Multiple myeloma (MM) is a type of cancer that remains incurable. In the last decade, most research into MM has focused on investigating the improvement in the therapeutic strategy. Our study assesses the survival pro...Multiple myeloma (MM) is a type of cancer that remains incurable. In the last decade, most research into MM has focused on investigating the improvement in the therapeutic strategy. Our study assesses the survival probability of 48 patients diagnosed with MM based on parametric and non-parametric techniques. We performed parametric survival analysis and found a well-def- ined probability distribution of the survival time to follow three-parameter lognormal. We then estimated the survival probability and compared it with the commonly used non-parametric Kaplan-Meier survival analysis of the survival times. The comparison of the survival probability estimates of the two methods revealed a better survival probability estimate by the parametric method than the Kaplan-Meier. The parametric survival analysis is more robust and efficient because it is based on a well-defined parametric probabilistic distribution, hence preferred over the non-parametric Kaplan-Meier. This study offers therapeutic significance for further enhancement in the treatment strategy of multiple myeloma cancer.展开更多
基金National Natural Science Foundation of China(No.71371035)
文摘The two-parameter lognormal distribution is a variant of the normal distribution and the three-parameter lognormal distribution is an extension of the two-parameter lognormal distribution by introducing a location parameter. The Q-Q plot of the three-parameter lognormal distribution is widely used. To obtain the Q-Q plot one needs to iteratively try different values of the shape parameter and subjectively judge the linearity of the Q-Q plot. In this paper,a mathematical method was proposed to determine the value of the shape parameter so as to simplify the generation of the Q-Q plot. Then a new probability plot was proposed,which was more easily obtained and provided more accurate parameter estimates than the Q-Q plot. These are illustrated by three realworld examples.
文摘Multiple myeloma (MM) is a type of cancer that remains incurable. In the last decade, most research into MM has focused on investigating the improvement in the therapeutic strategy. Our study assesses the survival probability of 48 patients diagnosed with MM based on parametric and non-parametric techniques. We performed parametric survival analysis and found a well-def- ined probability distribution of the survival time to follow three-parameter lognormal. We then estimated the survival probability and compared it with the commonly used non-parametric Kaplan-Meier survival analysis of the survival times. The comparison of the survival probability estimates of the two methods revealed a better survival probability estimate by the parametric method than the Kaplan-Meier. The parametric survival analysis is more robust and efficient because it is based on a well-defined parametric probabilistic distribution, hence preferred over the non-parametric Kaplan-Meier. This study offers therapeutic significance for further enhancement in the treatment strategy of multiple myeloma cancer.
