The mixture cure model is a special type of survival models and it assumes that the studied population is a mixture of susceptible individuals who may experience the event of interest, and cure/non-susceptible individuals who will never experience the event. For such data, standard survival models are usually not appropriate because they do not account for the possibility of cure. This paper presents an R package smcure to fit the semiparametric proportional hazards mixture cure model and the accelerated failure time mixture cure model.

Breast cancer is the most common non-skin cancer in women and the second most common cause of cancer-related death in U.S. women. It is well known that the breast cancer survival varies by age at diagnosis. For most cancers, the relative survival decreases with age but breast cancer may have the unusual age pattern. In order to reveal the stage risk and age effects pattern, we propose the semiparametric accelerated failure time partial linear model and develop its estimation method based on the P-spline and the rank estimation approach. The simulation studies demonstrate that the proposed method is comparable to the parametric approach when data is not contaminated, and more stable than the parametric methods when data is contaminated. By applying the proposed model and method to the breast cancer data set of Atlantic county, New Jersey from SEER program, we successfully reveal the significant effects of stage, and show that women diagnosed around 38s have consistently higher survival rates than either younger or older women.

This study explored a semi-parametric method built upon reproducing kernels for estimating and testing the joint effect of a set of single nucleotide polymorphisms (SNPs). The kernel adopted is the identity-by-state (IBS) kernel that measures SNP similarity between subjects. In this article, through simulations we first assessed its statistical power under different situations. It was found that in addition to the effect of sample size, the testing power was impacted by the strength of association between SNPs and the outcome of interest, and by the SNP similarity among the subjects. A quadratic relationship between SNP similarity and testing power was identified, and this relationship was further affected by sample sizes. Next we applied the method to a SNP-lung function data set to estimate and test the joint effect of a set of SNPs on forced vital capacity, one type of lung function measure. The findings were then connected to the patterns observed in simulation studies and further explored via variable importance indices of each SNP inferred from a variable selection procedure.

Traditional clustering methods focus on grouping subjects or (dependent) variables assuming independence between the variables. Clusters formed through these approaches can potentially lack homogeneity. This article proposes a joint clustering method by which both variables and subjects are clustered. In each joint cluster (in general composed of a subset of variables and a subset of subjects), there exists a unique association between dependent variables and covariates of interest. To this end, a Bayesian method is designed, in which a semi-parametric model is used to evaluate any unknown relationships between possibly correlated variables and covariates of interest, and a Dirichlet process is utilized to cluster subjects. Compared to existing clustering techniques, the major novelty of the method exists in its ability to improve the homogeneity of clusters, along with the ability to take the correlations between variables into account. Via simulations, we examine the performance and efficiency of the proposed method. Applying the method to cluster allergens and subjects based on the association of wheal size in reaction to allergens with age, we found that a certain pattern of allergic sensitization to a set of allergens has a potential to reduce the occurrence of asthma.