Inverse transform samplingInverse transform sampling (also known as inversion sampling, the inverse probability integral transform, the inverse transformation method, Smirnov transform, or the golden rule) is a basic method for pseudo-random number sampling, i.e., for generating sample numbers at random from any probability distribution given its cumulative distribution function. Inverse transformation sampling takes uniform samples of a number between 0 and 1, interpreted as a probability, and then returns the smallest number such that for the cumulative distribution function of a random variable.
Proportional hazards modelProportional hazards models are a class of survival models in statistics. Survival models relate the time that passes, before some event occurs, to one or more covariates that may be associated with that quantity of time. In a proportional hazards model, the unique effect of a unit increase in a covariate is multiplicative with respect to the hazard rate. For example, taking a drug may halve one's hazard rate for a stroke occurring, or, changing the material from which a manufactured component is constructed may double its hazard rate for failure.
Breast cancer screeningBreast cancer screening is the medical screening of asymptomatic, apparently healthy women for breast cancer in an attempt to achieve an earlier diagnosis. The assumption is that early detection will improve outcomes. A number of screening tests have been employed, including clinical and self breast exams, mammography, genetic screening, ultrasound, and magnetic resonance imaging. A clinical or self breast exam involves feeling the breast for lumps or other abnormalities.
Bias of an estimatorIn statistics, the bias of an estimator (or bias function) is the difference between this estimator's expected value and the true value of the parameter being estimated. An estimator or decision rule with zero bias is called unbiased. In statistics, "bias" is an property of an estimator. Bias is a distinct concept from consistency: consistent estimators converge in probability to the true value of the parameter, but may be biased or unbiased; see bias versus consistency for more.
Metastatic breast cancerMetastatic breast cancer, also referred to as metastases, advanced breast cancer, secondary tumors, secondaries or stage IV breast cancer, is a stage of breast cancer where the breast cancer cells have spread to distant sites beyond the axillary lymph nodes. There is no cure for metastatic breast cancer; there is no stage after IV. Metastases can occur several years after the primary breast cancer, although it is sometimes diagnosed at the same time as the primary breast cancer or, rarely, before the primary breast cancer has been diagnosed.
Gene expressionGene expression is the process by which information from a gene is used in the synthesis of a functional gene product that enables it to produce end products, proteins or non-coding RNA, and ultimately affect a phenotype. These products are often proteins, but in non-protein-coding genes such as transfer RNA (tRNA) and small nuclear RNA (snRNA), the product is a functional non-coding RNA.
Hazard ratioIn survival analysis, the hazard ratio (HR) is the ratio of the hazard rates corresponding to the conditions characterised by two distinct levels of a treatment variable of interest. For example, in a clinical study of a drug, the treated population may die at twice the rate per unit time of the control population. The hazard ratio would be 2, indicating higher hazard of death from the treatment. A scientific paper might utilise a Hazard Ratio (HR) to state something as follows.
Lung cancerLung cancer, also known as lung carcinoma, is a malignant tumor that begins in the lung. Lung cancer is caused by genetic damage to the DNA of cells in the airways, often caused by cigarette smoking or inhaling damaging chemicals. Damaged airway cells gain the ability to multiply unchecked, causing the growth of a tumor. Without treatment, tumors spread throughout the lung, damaging lung function. Eventually lung tumors metastasize, spreading to other parts of the body.
Multivariate normal distributionIn probability theory and statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional (univariate) normal distribution to higher dimensions. One definition is that a random vector is said to be k-variate normally distributed if every linear combination of its k components has a univariate normal distribution. Its importance derives mainly from the multivariate central limit theorem.
Stomach cancerStomach cancer, also known as gastric cancer, is a cancer that develops from the lining of the stomach. Most cases of stomach cancers are gastric carcinomas, which can be divided into a number of subtypes, including gastric adenocarcinomas. Lymphomas and mesenchymal tumors may also develop in the stomach. Early symptoms may include heartburn, upper abdominal pain, nausea, and loss of appetite. Later signs and symptoms may include weight loss, yellowing of the skin and whites of the eyes, vomiting, difficulty swallowing, and blood in the stool, among others.
