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Survival Analysis

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Survival Analysis is a branch of statistics focused on the study of time-to-event data, usually called survival times. This type of data appears in a wide range of applications such as failure times in mechanical systems, death times of patients in a clinical trial or duration of unemployment in a population. One of the main objectives of Survival Analysis is the estimation of the so-called survival function and the hazard function. If a random variable has density function $f$ and cumulative distribution function $F$, then its survival function $S$ is $1-F$, and its hazard $λ$ is $f/S$.

Source: Gaussian Processes for Survival Analysis

Image: Kvamme et al.

데이터셋

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GBSG2

The German Breast Cancer Study Group (GBSG2) dataset studies the effects of hormone treatment on recurrence-free survival time. The event of interest is the recurrence of cancer time. This data frame contains the observations of 686 women: * horTh: hormonal therapy, a factor at two levels (yes and no). * age: age of the patients in years. * menostat: menopausal status, a factor at two levels pre (premenopausal) and post (postmenopausal). * tsize: tumor size (in mm). * tgrade: tumor grade, a ordered factor at levels I < II < III. * pnodes: number of positive nodes. * progrec: progesterone receptor (in fmol). * estrec: estrogen receptor (in fmol). * time: recurrence free survival time (in days). * cens: censoring indicator (0- censored, 1- event). References * W. Sauerbrei and P. Royston (1999). Building multivariable prognostic and diagnostic models: transformation of the predictors by using fractional polynomials. Journal of the Royal Statistics Society Series A, Volume 162(1), 71–94 * M. Schumacher, G. Basert, H. Bojar, K. Huebner, M. Olschewski, W. Sauerbrei, C. Schmoor, C. Beyerle, R.L.A. Neumann and H.F. Rauschecker for the German Breast Cancer Study Group (1994), Randomized 2 × 2 trial evaluating hormonal treatment and the duration of chemotherapy in node- positive breast cancer patients. Journal of Clinical Oncology, 12, 2086–2093 Source: Lifelines

PBC

Primary sclerosing cholangitis is an autoimmune disease leading to destruction of the small bile ducts in the liver. Progression is slow but inexhortable, eventually leading to cirrhosis and liver decompensation. The condition has been recognised since at least 1851 and was named "primary biliary cirrhosis" in 1949. Because cirrhosis is a feature only of advanced disease, a change of its name to "primary biliary cholangitis" was proposed by patient advocacy groups in 2014. This data is from the Mayo Clinic trial in PBC conducted between 1974 and 1984. A total of 424 PBC patients, referred to Mayo Clinic during that ten-year interval, met eligibility criteria for the randomized placebo controlled trial of the drug D-penicillamine. The first 312 cases in the data set participated in the randomized trial and contain largely complete data. The additional 112 cases did not participate in the clinical trial, but consented to have basic measurements recorded and to be followed for survival. Six of those cases were lost to follow-up shortly after diagnosis, so the data here are on an additional 106 cases as well as the 312 randomized participants. * age: in years * albumin: serum albumin (g/dl) * alk.phos: alkaline phosphotase (U/liter) * ascites: presence of ascites * ast: aspartate aminotransferase, once called SGOT (U/ml) * bili: serum bilirunbin (mg/dl) * chol: serum cholesterol (mg/dl) * copper: urine copper (ug/day) * edema: 0 no edema, 0.5 untreated or successfully treated, 1 edema despite diuretic therapy * hepato: presence of hepatomegaly or enlarged liver * id: case number * platelet: platelet count * protime: standardised blood clotting time * sex: m/f * spiders: blood vessel malformations in the skin * stage: histologic stage of disease (needs biopsy) * status: status at endpoint, 0/1/2 for censored, transplant, dead * time: number of days between registration and the earlier of death, transplantion, or study analysis in July, 1986 * trt: 1/2/NA for D-penicillmain, placebo, not randomised * trig: triglycerides (mg/dl) Source: R

Survival Analysis of Heart Failure Patients

The dataset contains cardiovascular medical records taken from 299 patients. The patient cohort comprised of 105 women and 194 men between 40 and 95 years in age. All patients in the cohort were diagnosed with the systolic dysfunction of the left ventricle and had previous history of heart failures. As a result of their previous history every patient was classified into either class III or class IV of New York Heart Association (NYHA) classification for various stages of heart failure.

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