The Research Of T Cell Receptor Diversity Estimation

Since the diversity of human T Cell Receptor（TCR）is closely related to immune system,many statisticians have been committed to evaluate the diversity of human TCR,but measuring the diversity of human TCR is very complicated.Firstly,there are different evaluation standards for ’diversity’,such as Richness,Shannon entropy,Simpson index,etc.Secondly,when sampling the entire TCR repertoire,it is always difficult to find some rare clonetypes in a sample,i.e.the diversity of a sample（e.g.,a 5 ml clinical blood sample）may differ significantly from the diversity of the whole repertoire from which it originated（e.g.,5 liters of blood in the body）.Finally,there are always experimental errors in the process of measuring TCR diversity,which mainly come from inaccurate cell count,sequence errors caused by amplification and sequencing,and labeling errors in data processing.In this thesis,firstly,we compare the effects of non-parametric estimators Chao1,ACE and Jackknife under the Richness measurement criteria,and find that the larger the sample size is,the better the effect is.The best estimators are different under different species abundance models and different sample sizes.Secondly,in order to solve the problem that TCR sequencing would produce sequence errors,which would lead to a sharp increase in singlets of TCR,the TCR sequencing data were revised.Based on the revised data,the diversity of TCR clonetypes was measured under the three criteria of Richness,Shannon entropy and Simpson index.It was found that the Richness and Shan-non entropy of TCR clonetypes decreased with the increase of age,but Simpson index of TCR clonetypes did not decrease significantly.Finally,in order to solve the problem of insufficient sampling,this paper proposes a Bayesian change-point model based on tail stationary to theoretically obtain the saturated sample size needed to measure TCR clonetypes’ Richness.