If people have diseases, tests {medical testing} have probabilities {sensitivity, test} of finding diseases. If people do not have diseases, tests have probabilities {specificity, test} of indicating no diseases. Diseases have probabilities {prevalence, disease} in populations. Prevalence is typically less than one per thousand. Probability that people have disease if tested positive is prevalence times sensitivity divided by one minus specificity: p * se / (1 - sp).
Survival-function estimates {life table estimate, actuarial method} for grouped data, for example grouped by time interval, is number surviving at end divided by number at beginning minus half number censored for each interval, multiplying interval probabilities {actuarial method, test}.
Risk in people exposed to factor, minus risk in people not exposed, measures number of factor-caused outcomes {attributable risk}.
Non-random quantities {bias, measurement} {measurement bias} can include selecting non-randomly {selection bias}, failing to account for hidden factors {confounding bias}, measuring with non-random tools, or having goals.
Statistical methods {Cox regression} {proportional hazards model} can analyze survival data as multiple regression, for quantitative data, or multiple logistics, for qualitative data. Surviving also depends on treatment weights Cn and prognostic variables Xn. Proportional hazard model is: ln(l(t)) = C0(t) + C1*X1 + C2*X2 + ... + Cn*Xn.
For same age and sex, cured-patient survival rate can be similar to healthy-people survival rate {cure}. Age-corrected survival divides actual survival in each interval by survival for healthy people of same age and sex. Curve can become horizontal {point of definitive cure} {definitive cure point}.
treatment effectiveness {efficacy, treatment effectiveness}|.
People have disease risk {exposure, risk}| when factor is present.
Studies have quantifiable independent variables {factor, study}.
Patients have probability functions {hazard function} of failing to survive for some years or past an age.
Hypotheses {hypothesis, study} typically state that two treatments are no different in outcome. Studies can be only descriptive.
Populations can have new cases over times {incidence, population}. New cases divided by population measures probability {incidence rate} that people will have disease during that time.
Third variables can affect relation between factor and outcome {modification, study}.
Probabilities {odds ratio} that people who have disease also have factor approximates relative risk, if risk is less than 1/100.
Studies have quantifiable dependent variables {outcome, study}.
number with disease or factor divided by number in population {prevalence, population}.
Factor-strength measures {relative risk} can be ratio between risk when factor is present {exposure, factor} and risk when factor is absent.
Repeated measurements can have small range, with no oscillations or trends {reliability, study}.
Disease studies {research question} can determine number of people affected, typical stages {natural history, disease stages}, outcomes {prognosis, disease}, causes {etiology, disease}, or treatment effectiveness {efficacy, treatment}. Studies often compare two treatments.
If factor is present, outcome has probability {risk, study}.
If factor is present, outcome risk {risk factor} can increase.
Regions and groups have populations {reference population} {source population}. Source-population subsets {sample frame} can be about sex, age, or other variable. Studies are about random reference-population subsets {sample, study} that have similar sample frames.
Over time, people have decreasing survival probability {survival function}| {survival analysis}. Survival-function estimates for ungrouped data, for example, individual patients, multiply probability of surviving interval by probability of surviving next interval, for all intervals {Kaplan Meier Survival Curve} {product limit}. Kaplan-Meier curve falls rapidly between 70% and 30% surviving and ends below 50% survival. Survival-function estimates for grouped data, for example, grouped by time interval, are number surviving at end divided by number at beginning minus half number censored for each interval, multiplying interval probabilities {life table estimate, survival} {actuarial method, survival}.
tests
Tests {log rank test} can have null hypothesis that there is no difference in survival between two groups. Mortality rate in one group is typically always higher than mortality rate in another group, and mortality-rate ratio can stay constant over time {proportional hazards}. If ratio is high enough, difference in groups is significant. Tests {stratified log-rank test} can compare two groups if there is another variable. Tests {generalized Wilcoxon test} can give more weight to early deaths.
Tests can correctly check if hypothesis is true or false {validity, study}. Studies can use unbiased measurements {internal validity}. Studies can use random samples {external validity}.
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Date Modified: 2022.0225