Biostatistical Challenges in Molecular Data Analysis

Epidemiology is the study of the distribution and size of disease problems in human populations, in particular to identify etiological factors in the pathogenesis of diseases and to provide the data essential for the management, evaluation and planning of services for the prevention, control and treatment of disease (Everitt, 1998). Molecular epidemiology uses molecular biology to identify the etiological factors, and is a growing and important area of biomedical research. Molecular epidemiology presents new challenges to data analysts. Modern molecular biology can measure tens of thousands of molecular variables rapidly and cheaply (e.g., gene chips measure the activity of tens of thousands of genes, genotyping is routinely done at hundreds or thousands of markers, and proteomics has the potential of characterizing the entire protein content of tissues). The limiting step in molecular epidemiology is the small number of human subjects these measurements are made on relative to the large number of variables (the large P, small N problem). In this paper I address three statistical problems faced when analyzing molecular epidemiology data. The first problem is the proper identification of patient subgroups within which statistical tests of genotype-phenotype association should be applied. The second problem is the testing of clinical covariates against a large number of molecular variables. The third problem is the selection of important molecular factors related to disease. While these problems can be defined in the language of classical statistics (i.e., population stratification, over-determined systems, and variable selection, respectively), I believe their solution will require combining statistics with discrete mathematics and computer science. 1. Epidemiology Epidemiology has been defined as the “study of the distribution and size of disease problems in human populations, in particular to identify etiological factors in the pathogenesis of diseases and to provide the data essential for the management, evaluation and planning of services for the prevention, control and treatment of disease” (Everitt, 1998). By quantifying disease occurrence and location, and using this information to identify etiological causes of the diseases by observing differences in exposures among areas with different distributions and size of the disease problem, modern epidemiologists have successfully identified serious risk factors associated with many diseases. For example, heart disease, skin cancer, and lung cancer have very clear etiological risk factors – obesity, sun, smoking – contributing to their occurrence. These were all identified through modern epidemiological studies. The quantitative statistical tools of modern epidemiology have been well worked out both theoretically and for applied data analysis. Consider the simple case of trying to decide whether a particular exposure increases the odds of having a disease. Under a suitable controlled (and defined) experiment a set of cases (those with the disease) and controls (those without the disease but in all other senses similar to the cases) are obtained and the frequency of the exposure in the two groups is compared. This is easily displayed in the adjacent Figure where NYY is the number of people with the disease and with the exposure, NYN is the number of people with the disease and without the exposure, etc. From this we calculate the odds ratio (OR) which is a statistical measure of the association of exposure with disease by the simple formula: Exposure