Semi-supervised learning for pancreas cancer survival analysis

Abstract

In this thesis, the survival analysis was of interest for the high dimensional data, in which the number of observations in the study is much less than the number of parameters, usually the clinical datasets are in this type because there are few experiments and each one includes many gene expressions. Treating with high dimensional data is necessary, because the redundant and non-prognostic genes can lead the researchers to incorrect results. In this study L1/2 regularization has been used to shrink the coefficients of unimportant genes toward zero. Four methods of Single Cox, Single AFT, Semi-supervised Cox and Semi-supervised AFT have been used to implement survival analysis. The aim of the simulation study was to compare the four models in correctly detecting the prognostic genes. So, for two types of correlated and uncorrelated simulated data with 3 different sample sizes, the four models were compared. The single cox is sensitive to sample size but the semi-supervised cox model is less sensitive to sample size because we get a high value of average correctly selected parameters also in low sample size. The total number of selected parameters is lower in correlated data compared with uncorrelated data. Hence the precision is higher for correlated data using the semi-supervised cox model. The Semi-supervised Cox model implemented in this study was done by using Modified Newton Raphson method and coordinate descent to minimize the loss function. In the Semi-supervised method, the censored data were imputed by using the mean imputation method. The fraction of censoring right in our study is more. We get slightly more parameters in simulation compared with previous study. But we also found much correctly the prognostic genes in our study. The results of semi-supervised cox were seen to be better than previous study, in both simulation study and the real dataset.