ABSTRACT
The purpose of this article was to introduce the χ2 distribution and related contents， including χ2 distribution and non-central χ2 distribution. It focused on showing the definition of two χ2 distributions， the graph and the main properties of the probability density function. Among them， the two most important properties were： first， the limiting distribution of the χ2 distribution was the normal distribution； second， n-1s2σ2followed the χ2 distribution with n-1 degrees of freedom.In addition， it also explained the relationship between the χ2 distribution and the normal distribution， the relationship between χ2 test statistic and Z test statistic. Finally， it illustrated the computational approaches of the χ2 distribution based on the two SAS functions in SAS software.
ABSTRACT
The purpose of this article was to introduce the goodness of fit test and its SAS implementation. The main contents included the following four aspects： ① Pearson΄s goodness of fit test； ② deviance or likelihood ratio goodness of fit test； ③ Hosmer-Lemeshow goodness of fit test； ④ goodness of fit test for the sparse data. In the aforementioned “fourth aspect”， there were six specific test approaches， namely “information matrix test” “information matrix diagonal test” “Osius-Rojek test” “unweighted residual sum of squares test” “Spiegelhalter test” and “Stukel test”. The paper implemented the four types of the goodness of fit tests mentioned above with the help of the SAS software through an example， explained the output results， and made statistical and professional conclusions.
ABSTRACT
Background: Helicobacter pylori (Hp) infection is an important public health problem, and the transmission mode of Hp is not yet fully understood, however, human-to-human transmission route has been widely recognized, thus familial aggregation may occur for Hp infection. Aims: To explore the Hp infection in family members of Hp-positive patients and to analyze the familial aggregation of Hp infection. Methods: A total of 976 patients who underwent 14C-urea breath test (14C-UBT) from January 2018 to January 2019 were enrolled. According to Hp infection, the subjects were divided into Hp-positive group (case group) and Hp-negative group (control group), and all family members of all the subjects were encouraged to detect Hp infection. The Hp infection of family members in the two groups, the consistence of Hp infection between husband and wife, and the relationship between Hp-positive parents and Hp infection of children in case group were analyzed, and the goodness-of-fit test for binomial distribution was used to explore familial aggregation of Hp infection. Results: Among the 493 complete families who completed the survey, Hp-positivity rate in parents, spouses, children in case group were 70.6%, 62.1%, 65.9%, respectively, and were significantly higher than those in parents, spouses, children in control group (63.2%, 54.4%, 56.7%, respectively) (P0.05). Among 548 children in case group, 361 children were Hp positive, and the infection rate was increased with the increase of parental infection (P<0.05). The goodness-of-fit test showed that there were statistically significant differences in the actual households distribution and theoretical households distribution of Hp infection (P<0.05). Conclusions: There is a certain familial aggregation of Hp infection. When a member of the family is infected, the risk of Hp infection of parents, spouses and children may increase.
ABSTRACT
As a follow-up to a previous article, this review provides several in-depth concepts regarding a survival analysis. Also, several codes for specific survival analysis are listed to enhance the understanding of such an analysis and to provide an applicable survival analysis method. A proportional hazard assumption is an important concept in survival analysis. Validation of this assumption is crucial for survival analysis. For this purpose, a graphical analysis method and a goodness-of-fit test are introduced along with detailed codes and examples. In the case of a violated proportional hazard assumption, the extended models of a Cox regression are required. Simplified concepts of a stratified Cox proportional hazard model and time-dependent Cox regression are also described. The source code for an actual analysis using an available statistical package with a detailed interpretation of the results can enable the realization of survival analysis with personal data. To enhance the statistical power of survival analysis, an evaluation of the basic assumptions and the interaction between variables and time is important. In doing so, survival analysis can provide reliable scientific results with a high level of confidence.