Alexander Tsodikov, Research Assistant Professor
Oncological Sciences

Current Trends of Research

1. Methodological research. Statistical analysis with incomplete data. Classical statistics is developed under the assumption that a data sample is completely observed. In practice, however, some observations may be incomplete (for example right censored data as a result of losses to follow-up in survival analysis). A design of a study may even be such that not a single observation is complete, as in animal sacrifice experiments or some cancer surveillance studies. The focus of research is on developing appropriate statistical methods to handle such data. Particular trends include:

1. A proportional hazards model taking account of long-term survivors and its extensions;
2. The empirical survival function from doubly censored data and data from cancer post-treatment surveillance (screening) studies;
3. Methods to fit semiparametric regression models in full (PH model, proportional odds model, etc.)
4. Models for categorical data analysis with bounded outcome score.
5. Survival analysis based on modeling cancer latency.

1. Estimating cure rates from data on survival of cancer patients. This problem has the most direct bearing on the efficacy of breast cancer treatment. In particular, the issue of curability of breast cancer has long been and still remains controversial. According to one widely accepted point of view there is no evidence for a statistical cure in breast cancer patients, while some other authors consider breast cancer as a curable disease. The analysis of survival data allowing for non-zero cure rates calls for special statistical methods. In our opinion, the inconsistencies in the literature have to do with methodological limitations, and this direction of biostatistical research needs fresh ideas. Using newly developed methods we have estimated probabilities of tumor cure for different categories of patients with breast cancer identified through the Utah Cancer Registry. This analysis reinforces the results by those authors who hold to the idea that a cure is a possible outcome of breast cancer treatment. What is now required is to develop pertinent methods for assessing the effects of various covariates (prognostic factors) within the framework of cure models. Collaboration: B. Asselain (Curie Institute, Paris), R. Kerber (HCI), A. Yakovlev (HCI).
2. Mathematical modeling and analysis of bone tumorigenesis induced by incorporated radionuclides. A new stochastic model of radiation carcinogenesis has been developed and applied to the analysis of data on radiation-induced osteosarcomas in beagles. This study has shown that immune responses play a significant part in radiation carcinogenesis. The results of experimental data analysis suggest that it is a malignant cell, rather than an initiated cell, that is the primary target of the immune attack. Using the model it is possible to estimate the contribution of radiation-induced cell death to the observed carcinogenic effect of internal irradiation. Also, the model makes it possible to study dose-rate effects with an arbitrary time-dependent dose rate, i.e., even with data of radiobiological experiments that are not specifically designed for this purpose. Collaboration: F.W. Bruenger and R.D. Lloyd (Dept. of Radiobiology), A.Y. Yakovlev (HCI), E. Polig (Research Center, Karlsruhe, Germany).
3. Methods for statistical inference from data on gene expression using MicroArray technology. The purpose of this research is to design methods for studying patterns of gene expression in different normal and neoplastic tissues. The ultimate goal is to classify developmental and pathological states of various tissues on the basis of individual expression profiles. Gene expression patterns have to be uncovered that are specific to a given tissue, and a decision rule for their classification has to be constructed. Collaboration: H. Albertsen (HCI), A. Yakovlev (HCI).

1. Tsodikov AD (1998) A proportional hazards model taking account of long-term survivors. Biometrics (in press)
2. Tsodikov AD, Hasenclever D, and Loeffler M (1998) Regression with bounded outcome score: Evaluation of power by bootstrap and simulation in a chronic myelogenous leukemia clinical trial. Statistics in Medicine (in press)
3. Tsodikov A, Loeffler M, Yakovlev A, Yu A (1998) A cure model with time-changing risk factor: An application to the analysis of secondary leukemia: A report from the International Database on Hodgkin?s Disease. Statistics in Medicine 17:27-40
4. Tsodikov AD, Loeffler M, and Yakovlev AY (1998) Assessing the risk of secondary leukemia in patients treated for Hodgkin?s Disease: A report from the International Database on Hodgkin?s Disease. J Biol Systems (in press)
5. Tsodikov AD, Asselain B, and Yakovlev AY (1997) A distribution of tumor size at detection: An application to breast cancer data. Biometrics 53:1495-1502
6. Hanin LG, Rachev ST, Tsodikov AD and Yakovlev AY (1997) A stochastic model of carcinogenesis and tumor size at detection. Advances in Applied Probability 29:607-628
7. Kruglikov IL, Pilipenko NI, Tsodikov AD and Yakovlev AY (1997) Assessing risk with doubly censored data: An application to the analysis of radiation-induced thyropathy. Statistics and Probability Letters 32:223-230
8. Yakovlev AY and Tsodikov AD (1996). Stochastic Models of Tumor Latency and Their Biostatistical Applications. World Scientific Publ., Singapore
9. Asselain B, Fourquet A, Hoang T, Tsodikov AD and Yakovlev AY (1996) A parametric regression model of tumor recurrence: An application to the analysis of clinical data on breast cancer. Statistics and Probability Letters 29:271-278
10. Tsodikov AD, Asselain B, Fourquet A, Hoang T, and Yakovlev AY (1995) Discrete strategies of cancer post-treatment surveillance. Estimation and optimization problems. Biometrics 51:437-447