Calculation of disease and death rate

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Calculation of Disease and Death Rates

Epidemiological rates are the foundation of public health. They quantify how often disease occurs or how often people die within a defined population over a specified time period. All rates share the same general structure:

Rate = (Numerator / Denominator) × Multiplier (10^n)

PART 1 - MEASURES OF DISEASE (MORBIDITY RATES)

1. Prevalence

Prevalence measures the total existing burden of a disease at a point in time (or over a period).

Type	Formula
Point Prevalence	(All current cases at a point in time / Total population at that time) × 100
Period Prevalence	(All cases during a period / Average population during that period) × 100

Useful for chronic diseases (e.g., psoriasis, diabetes, hypertension)
Example: Psoriasis prevalence in US adults = 2 to 4 per 100 (2-4%)

Key relationship:

Prevalence ≈ Incidence × Average Duration of Disease

2. Incidence

Incidence measures new cases arising in a population at risk over a defined period. Only people who are "at risk" (i.e., do not already have the disease) are counted in the denominator.

a) Cumulative Incidence (Incidence Proportion)

(Number of new cases during a period / Population at risk at the start) × 100 (or 1,000)

Assumes the entire sample is followed for the full period
Example: 15 smokers develop head and neck cancer among 1,000 followed for 5 years → Cumulative Incidence = 15/1000 = 1.5%
Good for closed cohorts with complete follow-up

b) Incidence Rate (Incidence Density)

(Number of new cases / Total person-time at risk) × 1,000

Also called force of morbidity, hazard rate, or incidence density. Used when subjects enter the study at different times or are lost to follow-up.

Example: 15 cancers in 5,000 person-years → Incidence Rate = 15/5,000 = 3 cases per 1,000 person-years
The formula: Cumulative Incidence ≈ Incidence Rate × Average Follow-Up Time (when disease is rare)

- Scott-Brown's Otorhinolaryngology Head & Neck Surgery Vol 1, p. 519; Fitzpatrick's Dermatology Vol 1-2

3. Attack Rate (Outbreak-Specific)

Used in outbreak investigations for a defined exposure event (e.g., a foodborne outbreak):

(Number ill during outbreak period / Number ill + well at risk) × 100

Expressed as a percentage
Secondary Attack Rate: New cases among contacts of primary cases / Total susceptible contacts × 100

PART 2 - MEASURES OF DEATH (MORTALITY RATES)

1. Crude Death Rate (CDR)

The most basic mortality measure - covers all deaths in the whole population.

(Total deaths during a year / Mid-year population) × 100,000

"Crude" because it does not account for age, sex, or other differences
Example: 50,000 deaths in a population of 10 million → CDR = 500 per 100,000

2. Cause-Specific Death Rate

(Deaths due to a specific cause in a year / Mid-year total population) × 100,000

Allows comparison of the burden of individual diseases (e.g., cardiovascular mortality, cancer mortality)

3. Age-Specific Death Rate

(Deaths in a specific age group during a year / Mid-year population in that age group) × 100,000

Accounts for the fact that death rates vary dramatically by age
Used to construct life tables and standardized rates

4. Case-Fatality Rate (CFR)

Measures the severity / lethality of a disease - the proportion of people diagnosed with a disease who die from it.

(Deaths due to disease X during a time interval / New cases of disease X during the same interval) × 100

Example: 50 deaths among 200 new cases of a disease → CFR = 50/200 = 25%
High CFR = high lethality (e.g., rabies ~100%, Ebola ~50-70%)
CFR is not the same as mortality rate (different denominator)

5. Proportional Mortality Ratio (PMR)

(Deaths from a specific cause / Total deaths from all causes) × 100

Shows what proportion of all deaths are due to a given cause
Does not require total population size

6. Infant Mortality Rate (IMR)

(Deaths in children under 1 year / Live births during same year) × 1,000

Sensitive indicator of a nation's overall healthcare quality and socioeconomic status

7. Neonatal Mortality Rate

(Deaths in first 28 days of life / Live births) × 1,000

Reflects quality of newborn and intrapartum care.

8. Maternal Mortality Rate

(Deaths due to complications of pregnancy/childbirth / Live births) × 100,000

Denominator is live births (ideal would be all pregnancies, but live births are more reliably registered)

9. Under-5 Mortality Rate

(Deaths in children aged 0-4 years / Live births) × 1,000

PART 3 - MEASURES OF ASSOCIATION (How disease/death relates to risk factors)

Risk Ratio (Relative Risk, RR)

Incidence in exposed / Incidence in unexposed

RR = 1: no association
RR > 1: increased risk (e.g., psoriasis patients have RR of death = 1.5, meaning 50% increased risk)
RR < 1: protective effect

Attributable Risk (Risk Difference)

Incidence in exposed - Incidence in unexposed

The absolute excess risk due to the exposure
Example: 21.3 - 12.0 = 6 per 1,000 person-years attributable to psoriasis

Odds Ratio (OR)

(Odds of exposure in cases) / (Odds of exposure in controls)

Used in case-control studies and logistic regression
Approximates RR when disease is rare (< 10% prevalence)

- Fitzpatrick's Dermatology Vol 1-2, p. 2088-2091

PART 4 - Distinguishing Rates, Proportions, and Odds

Measure	Has Time Component?	Numerator subset of Denominator?	Type
Rate	Yes	Yes	Rate
Proportion	No	Yes	Proportion
Odds	No	No	Ratio

PART 5 - Standardization

When comparing crude rates between populations with different age structures, standardization is used:

Direct standardization: Apply the age-specific rates of each population to a single standard population
Indirect standardization: Apply a standard set of age-specific rates to each population; yields the Standardized Mortality Ratio (SMR)

SMR = (Observed deaths / Expected deaths) × 100

SMR > 100: Higher than expected mortality

SMR < 100: Lower than expected mortality

Summary Table

Measure	Numerator	Denominator	Multiplier
Prevalence	All existing cases	Total population	100 or 1,000
Cumulative Incidence	New cases	Population at risk (start)	100 or 1,000
Incidence Rate	New cases	Person-time at risk	1,000 per year
Attack Rate	Ill during outbreak	Ill + well exposed	100
Crude Death Rate	All deaths	Mid-year population	100,000
Cause-Specific Death Rate	Deaths from one cause	Mid-year population	100,000
Age-Specific Death Rate	Deaths in age group	Population in that age group	100,000
Case-Fatality Rate	Deaths from disease X	New cases of disease X	100
Infant Mortality Rate	Deaths < 1 year	Live births	1,000
Maternal Mortality Rate	Maternal deaths	Live births	100,000
SMR	Observed deaths	Expected deaths	100

Sources: Fitzpatrick's Dermatology (Vol 1-2), Scott-Brown's Otorhinolaryngology Head & Neck Surgery (Vol 1); NCBI StatPearls - Epidemiology Morbidity and Mortality; OpenStax Population Health - Epidemiologic Measures

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