·
Definitions
of rates, hazards, ratios, and proportions

·
Crude rates, specific rates, and standardized/adjusted
rates.

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**Key Words and Terms:**

·
Denominator

·
Numerator

·
Parameter

·
Proportion

·
Rate, adjusted
rate

·
Rate, crude
rate

·
Rate, incidence rate

·
Rate, specific
rate

·
Rate, standardized
rate

·
Statistic

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*Unit Outline*

RATES

A. Definition

B. Crude Rates

C. Specific Rates

D. Adjusted /Standardized Rates

E. Standardization

PROPORTIONS

A. Definition of a Proportion

B. Examples of Proportions

UNIT SYNOPSIS

DEFINITIONS

Data can be summarized using parameters, computed from populations, or statistics, computed
from samples. Discrete data is categorized in groups and can be qualitative or quantitative. It can be categorized before
summarization. The main types of statistics used are measures of location such as rates, hazards, ratios, and proportions
and measures of spread. Measures of location indicate accuracy or validity. Measures of spread or variation, such as variance
and range, indicate precision.

RATES

A rate is the number of events in a given population over a defined time period and has
3 components: a numerator, a denominator, and time. The numerator is included in the denominator. The incidence rate of disease
is defined as a / {(a+b) t} where a = number of new cases, b = number free of disease at start of time interval, and t = duration
of the time of observation.

A crude rate for a population assumes homogeneity and ignores subgroups differences. It
is therefore un-weighted, misleading, and unrepresentative. Inference and population comparisons based on crude rates are
not valid.

Rates can be specific for age, gender, race, and cause. Specific rates are more informative
than crude rates but are cognitively difficult to internalize, digest, and understand so many rates or be able to reach some
conclusions.

An Adjusted or standardized rate is a representative summary that is a weighted average
of specific rates free of the deficiencies of both the crude and specific rates.

Standardization eliminates the ‘confusing’ or ‘confounding’ effects
due to subgroups. Standardization can be by direct standardization, indirect standardization, and life expectancy or regression
techniques.

Both direct and indirect standardization involve the same principles but use different
weights. Direct standardization is used when age-specific rates are available and indirect standardization is used when age-specific
rates are not available. Both direct and indirect standardization use a ‘standard population’ which can be a combination
of the two or more populations being compared, use of just one of the comparison populations as a standard for the others,
using the national population, and using the world population.

Life expectancy is a form of age-standardized standardized mortality rate. Regression
techniques provide a means of simultaneous adjustment of the impact of various factors on the rate.

PROPORTIONS

A proportion is the number of events expressed as a fraction of the total population at risk without a time dimension.
The formula of a proportion is a/ (a+b) and the numerator is part of the denominator. Examples of proportions are: prevalence
proportion, neonatal mortality proportion, and the perinatal mortality proportion. The term prevalence rate is a common misnomer
since prevalence is a proportion and not a rate. Prevalence describes a still/stationary picture of disease. Like rates, proportions
can be crude, specific, and standard.