Terms to add to the measures of occurrence chapter

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Overview

In the Fall of 2023, I was adding the content from PowerPoint to the book. There were some hidden slides with terms I wanted to add to the chapter, but hadn't gotten around to yet. I'm writing them below in hopes that I will get time to add them sometime soon.

Terms

In looking through this list, some of these are not appropriate for the measures of occurrence chapter. I need to move them to a different list at some point.

• [x] Counts
• [ ] Numerator/denominator
• [ ] Define ratio
• [ ] Define proportion
• [ ] Define probability 
• [ ] Conditional probability
• [ ] Define odds
• [ ] Relationship between continuous variables and event occurrence.
• [ ] Dummy variables
• [ ] When to group as “any “
• [ ] Prevalence (Point, period, cumulative lifetime)
• [x] Incidence
• [ ] Cumulative incidence (incidence proportion)
• [ ] Survival analysis
• [ ] Censoring
• [ ] Life table
• [ ] Kaplan-Meier method
• [ ] Person-time
• [ ] Incidence rate (incidence density)
• [ ] Hazard rate

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Ratio

The quantitative relation between two amounts showing the number of times one value contains or is contained within the other. (Google)

RATIO The value obtained by dividing one quantity by another. RATE, PROPORTION, and percentage are types of ratios. The numerator of a proportion is included in the population defined by the denominator, whereas in other types of ratios numerator and denominator are distinct quantities, neither being included in the other. The dimensionality of a ratio is obtained through algebraic cancellation, summation, etc., of the dimensionalities of its numerator and denominator terms. Both counted and measured values may be included in the numerator and in the denominator. There are no general restrictions on the dimensionalities or ranges of ratios, but there are in some types of ratios (e.g., proportion, prevalence). Ratios are sometimes expressed as percentages (e.g., standardized mortality ratio). In these cases, the value may exceed 100. (Dictionary of Epidemiology)

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Proportion

PROPORTION A type of ratio in which the numerator is included in the denominator. The ratio of a part to the whole, expressed as a “decimal fraction” (e.g., 0.2), as a “common fraction” (1/5), or as a percentage (20%). By definition, a proportion (p) must be in the range (decimal) 0.0 ≤ p ≤ 1.0. Since numerator and denominator have the same dimension, any dimensional contents cancel out, and a proportion is a dimensionless quantity. Where numerator and denominator are based on counts rather than measurements, the originals are also dimensionless, although it should be understood that proportions can be used for measured quantities (e.g., the skin area of the lower limb is x percent of the total skin area) as well as for counts (e.g., 15% of the population died). A PREVALENCE is a count-based proportion. The nondimensionality of a proportion, and its range limitations, do not necessarily apply to other kinds of ratios, of which “proportion” is a subset. See also RATE; RATIO. (Dictionary of Epidemiology)

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Numerator and denominator

NUMERATOR The upper portion of a fraction, used to calculate a rate or a ratio. See also DENOMINATOR. (Dictionary of Epidemiology)

DENOMINATOR The lower portion of a fraction, used to calculate a rate or ratio. The population (or population experience, as in person-years, passenger-miles, etc.) at risk in the calculation of a rate or ratio. Valid information on denominators is essential in clinical and epidemiological research and also in many public health activities. See also NUMERATOR. (Dictionary of Epidemiology)

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Probability

1. Frequency probability: the limit of the relative frequency of an event in a sequence of N random trials as N approaches infinity, i.e., the limit of 2. Subjective probability: a measure, ranging from 0 to 1, of the degree of belief in a hypothesis or statement. Other definitions of probability exist (e.g., logical probability) but are rarely found in epidemiology, statistics, and clinical research. All probabilities obey the laws given by the axioms that: a. All probabilities are 0 or greater: for any event or statement A, Pr(A) ≥ 0. b. The probability of anything certain to happen is 1; i.e., if A is certain, Pr(A) = 1. c. If two events or statements A and B, cannot both be true at once (they are mutually exclusive), then the probability of their conjunction (A or B) is the sum of their separate probabilities: Pr(A or B) = Pr(A) + Pr(B). (Dictionary of Epidemiology)

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Conditional probability

Move to measures of association

The probability of an event given that another event has occurred. If D and E are two events and P (…) is “the probability of (…),” the conditional probability of D given that E occurs is denoted P(DIE), where the vertical slash is read “given” and is equal to P(D and E)/P(E). The event E is the “conditioning event.” Conditional probabilities obey all the axioms of probability theory. See also BAYES’ THEOREM; PROBABILITY THEORY. (Dictionary of Epidemiology)

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Odds

The ratio of the probability of occurrence of an event to that of nonoccurrence, or the ratio of the probability that something is one way to the probability that it is another way. If 60% of smokers develop a chronic cough and 40% do not, the odds among smokers in favor of developing a cough are 60 to 40, or 1.5; this may be contrasted with the probability or risk that smokers will develop a cough, which is 60 over 100 or 0.6. See also LOGIT. (Dictionary of Epidemiology)

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Continuous variables and event occurrence

• In epidemiology, we commonly divide continuous measures at one or more levels.
• We love our categorical variables in epi.
• The place where we divide them is a called a cut point.
• If two places, then we are dichotomizing.
• Sometimes we will dichotomization categorical variables with more than two levels (e.g., “any” of the above)
• Assumes homogeneity within group. If not, we will still get an estimate, but it will be nonsense. (Show an example with numbers)