Epidemiologic Measurements: A review Counts, ratios, proportions, and rates

NBC Nightly News, Saturday September 5, 2015 Salmonella Linked to Cucumbers from Mexico Since July 3, 2015: 27 states involved One person has died (California) – 51 cases in this state No cases reported thus far in Florida 285 persons have become ill; 53 hospitalized 54% of the ill persons are children younger than18; 57% are female Organism: Salmonella Poona Found worldwide in both cold-blooded and warm-blooded animals, and in the environment. Source: Imported cucumbers from Mexico distributed by Andrew & Williamson Fresh Produce Eleven illness clusters have been identified in seven states. An illness cluster is defined as two or more people who do not live in the same household who report eating at the same restaurant location, attending a common event, or shopping at the same location (grocery store) in the week before becoming ill. 4-2

The facts: Food may be contaminated during food processing or food handling. Food may become contaminated by the unwashed hands of an infected food handler. Beef, poultry, milk, and eggs are most often infected with salmonella but vegetables may also be contaminated. Contaminated foods usually look and smell normal. Symptoms include: diarrhea, fever, and abdominal cramps. Symptoms develop 12 to 72 hours after infection Illness usually lasts 4 to 7 days. Most people recover without treatment; diarrhea and dehydration may be so severe that hospitalization is necessary. Older adults, infants, and those who have impaired immune systems are at highest risk. 4-3

Epidemiologic measurements: The Basics Four types of data DescriptionExamples NominalCategorical – unordered categories Two levels – dichotomous More than two levels – multichotomous Sex, disease (yes, no), race, marital status, educational status OrdinalCategorical – ordering informative Preference rating (e.g., agree, neutral, disagree) DiscreteQuantitative – IntegersNumber of cases ContinuousQuantitative – Values on a continuum Dose of ionizing radiation, temperature, tire pressure

Types of data Categorical: Nominal or ordinal No numerical scale, just groups. Male/Female, Yes/No, Married/Single/Divorced Quantitative: Takes on numerical values. Discrete data: integers or counts that differ by fixed amounts, no intermediate values are possible. Examples are number of children, number of times married, number of sick days you have accrued Continuous data take on many values on a finely- grained scale. Examples are temperature, weight, age

Categorical data Nominal Ordinal 4-6 Level A Level C Level B

Quantitative data: Discrete and Continuous 4-7

Another Epidemic: Reported late 2012 The American Association of Poison Control Centers reported 2,950 cases of exposure to detergent packets like Tide Pods The patients were typically 10 to 20 months old and suffered serious consequences after biting or ingesting the contents of a laundry detergent pod. Symptoms included intense vomiting, somnolence, absence of response, seizure-like symptoms, and respiratory distress. Only one patient required intubation with a prolonged hospital admission Others were released following 48 hours of intubation.

Reported poisonings Product introduced February 2012 In early May, Texas poison control centers report receiving 57 emergency calls in a 20-day period May-June 2012, CDC undertakes investigation Surveillance of calls to Poison Control Centers involving suspected ingestion of the content of detergent pods Charlotte, NC reported 2 cases Philadelphia, PA reported 2 cases No deaths (PA cases required subsequent speech therapy) Nationwide from May 17-June 17, 2012: 1008 laundry detergent exposures 485 cases involved pods 4-9

Counts: Provide only limited interpretation Cases of Reporting Location Disease Period Population Charlotte Philadelphia Annual Rate of Occurrence = Count ÷ Population Charlotte20 / 100 = 1 / 5 Philadelphia 100 / 1000 = 1 / 10

* Simplest, most frequently performed measure in epidemiology Refers to the number of cases of a disease or other health phenomenon being studied Useful for allocation of health resources Limited usefulness for epidemiologic purposes without knowing size of the source population Counts

Epidemiological Outcomes Ratio: Relationship between two numbers Example: males/females In a ratio the values of x and y are independent such that the values of x are not contained in y Proportion: A ratio where the numerator is included in the denominator Example: males/total births Example: deaths from pod ingestion/deaths from all household cleaning agents Rate: A proportion with the specification of time Example: the annual rate of occurrence in the pod poisoning scenario

Like a proportion, ratio is a fraction, BUT without a specified relationship between the numerator and denominator Example: Occurrence of Major Depression Female cases = = ----2:1 female to male Male cases = Ratios

Proportion In a proportion, x is contained in y A proportion is typically expressed as a percentage, such that the rate base is 100 © 2010 Jones and Bartlett Publishers, LLC

In epidemiology, proportions tell us the fraction of the population that is affected. Persons included in the numerator are always included in the denominator: A Proportion: A + B Indicates the magnitude of a part, related to the total. Proportions

Proportions – Example: Injuries involving children ABTotal (A + B) # child pod poisoning cases # child bouncy castle injuries Total study population 1,4009,65011,050 P = A / (A + B) = (1,400 / 11,050) = For ease of usage, multiply a proportion by 100 to get a percentage: p = = 12.7%

Rate A rate may be thought of as a proportion with the addition that it represents the number of health- related states or events in a population over a specified time period © 2010 Jones and Bartlett Publishers, LLC

A proportion in which TIME forms part of the denominator Epidemiologic rates contain the following elements: * a defined time interval (day, week, month year, decade, century, etc) * number (or count) of events occurring in that time interval * estimate (or count) of the population at risk in the time interval * a multiplier or constant (x 10; x 100; x 1000; etc) Rates

Calculate crude annual death rate in the US: Annual death count Crude death rate = x 1,000 Reference population (during midpoint of year) Death count in U.S. during 1990: 2,148,463 U.S. population on June 30, 1990: 248,709,873 2,148,463 Crude death rate = x 1,000 = 8.64 per 1, ,709,873 Rates – Example

In epidemiology, the occurrence of a disease or condition can be measured using rates and proportions. We use these measures to express the extent of these outcomes in a community or other population. Rates tell us how fast the disease is occurring in a population. Proportions tell us what fraction of the population is affected. (Gordis, 2000)

Morbidity Measures Incidence is always calculated for a given period of time An attack rate is an incidence rate calculated for a specific disease for a limited period of time during an epidemic Population at risk X 1,000 Number of new events during a time period Incidence Rate =

Morbidity Measures Point prevalence measures the frequency of all current events (old and new) at a given instant in time Period prevalence measures the frequency of all current events (old and new) for a prescribed period of time Population at risk X 1,000 Number of existing events, old and new Prevalence =

What might be the reason for: A disease or health-related event having a high prevalence rate? A disease or health-related event having a low prevalence rate? 4-23

High prevalence may reflect: High risk Prolonged survival without cure Low prevalence may reflect: Low risk Rapid fatal disease progression Rapid cure Examples: Rhinovirus (common cold vs Ebola virus)

Relationship Between Incidence and Prevalence (cont.) Cancer of the pancreas Incidence low Duration short Prevalence low Adult onset diabetes Incidence: Increasing Duration long Prevalence high Roseola infantum Incidence high Duration short Prevalence low Essential hypertension Incidence high Duration long Prevalence high

Calculation Practice You want to investigate the cases of skin cancer recorded on Knightro Beach: 1. Point prevalence on 3/11/ Period prevalence for year Incidence rate for year 2012 What information will you need?

Morbidity Measures Prevalence is not a rate Point prevalence measures the frequency of all current events (old and new) at a given instant in time Period prevalence measures the frequency of all current events (old and new) for a prescribed period of time Population at risk X 1,000 Number of existing events, old and new Prevalence =

                                                        Diagnosed cases of Skin Cancer On Knightro Beach Point Prevalence (3/11/2013) = (10/450)*1000 = 22 per 1000 # of existing cases = 10 Total population at risk = 450 

                                                              Diagnosed cases of Skin Cancer on Knightro Beach, 2012 Average population at risk = 500 Incidence rate (year 2012) = (5/500)*1000 = 10 per 1000 Period prevalence (year 2012) = (15/500)*1000 = 30 per 1000 # of new cases = 5 # Existing cases (10) + New cases (5)

Attack rate (cumulative incidence rate) Describes diseases or events that affect a larger proportion of the population than the conventional incidence rate. Used when new cases rapidly occur over a short period of time in a well-defined population Ex. Cases of bacterial gastroenteritis (food poisoning) within a community following a church picnic © 2010 Jones and Bartlett Publishers, LLC

Crude vs. age-adjusted rates The crude rate of an outcome is calculated without any restrictions, such as by age or sex, on who is counted in the numerator or denominator These rates are limited if we try to compare them between subgroups of the population or over time because of potential confounding influences, such as differences in the age-distribution between groups © 2010 Jones and Bartlett Publishers, LLC

The importance of age-adjustment In 2002, the crude mortality rate in Florida was 1,096 per 100,000 compared with 579 per 100,000 in Utah The crude mortality rate ratio is 1.9, meaning the rate in Florida was 1.9 times higher than in Utah However, the age distribution differs considerably between Florida and Utah. In Florida 6.3% of the population is under five years of age and 16.7% of the population is 65 years and older. Corresponding percentages in Utah are 9.8% and 8.5%. © 2010 Jones and Bartlett Publishers, LLC

Importance of age-adjustment (continued) Using the direct method of age-adjustment based on the 2000 US standard population yielded rates of 762 in Florida and 782 in Utah per 100,000 Thus, after adjusting for differences in the age distribution, the rate in Florida is 0.97 times that in Utah © 2010 Jones and Bartlett Publishers, LLC

Objective: Be familiar with tables, graphs, and numerical methods for describing epidemiologic data Tables Line listing Frequency distribution Graphs Bar chart, pie chart Histogram Epidemic curve Box plot Two-way (or bivariate) scatter plot Spot map Area map Line graph © 2010 Jones and Bartlett Publishers, LLC

Frequencies example: Aphasia 35 Summary Table 35 Class Frequency Class percentage = class relative frequency x 100

Describing Qualitative Data – Qualitative Data Displays Bar Graph: Used for frequency distributions when qualitative in nature. Space placed between bars to show measurement is not continuous. 36

Methods for Describing Quantitative Data 37 The Data 37

Describing Quantitative Data Histogram Uses the height of a vertical bar (y axis) to show frequency of occurrence and the size of the interval is represented by the width of the bar on the horizontal bar (x axis). 38

Shapes of large distributions 39 Polygon: Places the midpoint of the intervals on the X axis, places a dot at the frequency of an interval based on the y axis, and then connects the dots by straight lines. 39 A dot is placed at the midpoint of each class interval represented on the X axis Height of the dot = the frequency of the relative class frequency.

Measures of Central Tendency 40 Mean: the sum of scores divided by the number of scores (average) Median: the score with an equal amount of scores above and below it (50 th percentile) Mode: the score that occurs the most often in a set of data

Measures of dispersion (variability) 41 Variability – the spread of the data across possible values 3 commonly used measures of Variability 1) Range 2) Variance 3) Standard Deviation 41

42 Range = Largest measurement minus the smallest measurement Loses sensitivity when data sets are large These 2 distributions have the same range. How much does the range tell you about the data variability? 42 Measures of dispersion

43 2) Variance May provide a better way of describing the variety that exists among the values in a data set The average of the squared differences of the observations from the mean

Standard Deviation 44 Normal curve calculated from diastolic blood pressures of 500 men, mean 82 mmHg, standard deviation 10 mmHg. BMJ Statistics at Square One

Correlation coefficient: Understanding the literature Denoted by “r” Measures the strength and direction of the association between two variables Values range between -1 and +1 Positive values indicate that the two variables are positively correlated (vary in the same direction) Negative values indicate that the two variables are negatively correlated, meaning the two variables vary in the contrary direction. Values close to +1 or -1 reveal the two variables are highly related. 4-45

“P” values: Understanding the literature The p-value is a probability, which is the result of a statistical test. This probability reflects the measure of evidence against the null hypothesis. Small p-values correspond to strong evidence The level of significance of 0.05 (or 5%) is often chosen. If the p-value is less than this limit, the result is significant and it is agreed that the null hypothesis should be rejected and the alternative hypothesis—that there is a difference—is accepted. 4-46