Epidemiology and Data Presentation

Population

• Measurable quantity = parameter

• Complete set

• Contain all members of this group

• Reports are a true representation

Sample

• Measurable quality = statistic

• Incomplete set

• A subset of the entire population

• Reports have a margin of error and a confidence interval

All inhabitants of the state of Texas

Population

30 students from the school of public health

Sample

The TAMU undergrad student body

(Depends on context —> TAMU undergrad student body)

All cancer patients in the US

population

1500 pre-diabetic adolescents from the Houston metropolitan area

sample

Inferential statistics use sample-based data to make conclusions about the population from which a sample has been selected – a process known as ___

estimation

The sample mean is used as an

estimate of the population mean (a parameter).

Probability sampling (random sampling)

• Every member of the population has a known probability of being sampled

• Uses statistics; thus, we measure sampling error

Non-Probability sampling (non-random sampling)

• inherently biased

• cannot measure sampling error

Probability Sampling Designs: Simple Random Sampling (SRS)

• Gives every member of the population an equal chance of being included in the sample

• Simple, often unrealistic, expensive, logistical difficulties

• Poorly distributed variables = over or under-estimation

• Basis of effective sampling techniques

• Example: random number generator, random digit dialing, draw names from a hot

Random sampling is ___

unbiased

Probability Sampling Designs: Stratified Sampling

• Target population is divided into suitable, nonoverlapping homogeneous sub-populations or strata

• A random sample is selected within each stratum to represent all strata and reduce sampling error accurately

• Offers a way to have representation from all subgroups

Probability Sampling Designs: Systematic sampling

• Used when individuals or households can be ordered

• Determines a sampling interval (n), by dividing the total population by the sample size

• Choosing a random starting point on the list, select every nth person

• Useful if the population is listed by geographic area or another stratifying characteristic

• Easy and popular method

Probability Sampling Designs: Cluster sampling

• useful in saving resources in surveys of human populations when:

  • The population is geographically dispersed

  • Sampling frame for the elements of the population studied is not available

• The units first sampled are not individual elements we are examining, but clusters or aggregates of those elements, can be space-based (State, county, block), organizational (school, grades), telephone based (area code)

Non-Probability Sampling Designs: Convenience sampling

• Using a sample that is near at hand

  • People out and about, on a road, engaged in a specific activity at the time of the survey

  • Street-corner political surveys, sampling at a clinic, internet/media-based polling

• Prone to sampling bias

  • Individuals who have been selected may not be representative of the population

• Often used to explore ideas and opinions of people about a new topic that may not be ready for a quantitative investigation

Qualitative Data

• do not have numerical value or rankings

Quantitative data

• reported as a numerical quantity

Nominal data

• Unordered

  • Dichotomous/Binary

Ordinal data

• Can be ordered

Discrete data

• finite number

Continuous Data

• infinite number

Steven’s measurement scales: Nominal

• Not ordered

• Qualitative

• Determine equality

  • Number of cases

Steven’s measurement scales: Ordinal

• Ordered/ranked

• Qualitative

• Determines greater/less

  • Median percentiles

Steven’s measurement scales: Interval

• Continuous

• Equal intervals between points

• No true zero scale

• Determines equality of intervals

  • Mean, standard deviation, correlation

Steven’s measurement scales: Ratio

• Continuous

• No True zero scale

• Determination of equality of ratios

  • Coefficient of variation

Nusrat stood outside of the MSC and selected 25 students to participate in a survey is an example of,

Convenience sampling

A survey was distributed to all students who live on the 3rd floor of Clements Residence Hall

Cluster sampling

A random sample of 50 SPH (25 undergraduate and 25 graduate) are selected to participate in a study

Stratified sampling

A random number generator was used to sample 100 students in the TAMU student population to participate in a study

Simple random sampling

The entire SPH student body was ordered by their GPA and every 20th student was invited to participate in a study

Systematic sampling

For a random sample, when the sample mean differs from the population mean, this difference is most likely a reflection of”

Random error that affected the sample

Bar charts

Useful for displaying discrete variables

Histogram

Display the frequency of distributions for grouped/ordered categories of a continuous variable

Line graph

Track trends over time

• Use different lines to show difference between subgroups

Pie chart

Useful for showing the proportions of cases according to several different categories

Mode

Number that occurs most frequently

Median

when numbers are ordered, the middle (dividing the lower and upper half)

Mean

arithmetic average

Range

H - L

• Difference between highest and lowest

Half range

Arithmetic mean of (H) and (L)

Mean deviation

Average of absolute values of the deviations of each observation about the mean

Variance

Degree of variability

Standard deviation

Square root of the variance

Distribution

Distribution curves

• Graph the frequencies of the values of a variable

• The mode of a distribution curve is the most frequently occurring value (peak)

• Can have multiple modes (peaks)

• Different distributions may exhibit different degrees of spread

Distribution curves: Normal— Math aspect

Distribution curves: Normal

• Each curve has the same mean/median/mode, but they have different dispersions

Distribution curves: Skewness

Distribution curves: Multimodal distribution

• have multiple modes (peaks) in the frequency of a condition

  • Reasons a curve could be multimodal

    • Age-related changes in immune status of lifestyle of the host

    • Chronic diseases with long latency periods

Distribution curves: Epidemic curves

• Graphic plotting of the distribution of cases by time on onset

• Unimodal curve

• Helps identify the cause and peak of a disease outbreak

Bivariate association

• Examines the relationship between two variables

• An association between two variables signifies only that they are related and not that the association is causal

• CORRELATION DOESNT EQUAL CAUSATION

Bivariate associations: Pearson Correlation Coefficient (r )

• Measures the strength of an association

• Range from -1 to +1

  • If r is negative: inverse relationship

  • If r is positive: positive relationship

  • If r is closer to +1 or -1:

  • If r approaches 0: the association becomes weaker

  • If r = 0: there is no association

There is no associated between height and exam scores

• Higher age is associated with higher earnings

  • POSITIVE relationship

• Higher age is associated with less time spent on the app

  • NEGATIVE relationship

Scatter Plots and Pearson’s R

Non-linear correlations

• Linear correlation between X and Y is essentially 0 (-0.09)

• There is no linear association, but this does not imply there is no relationship between the 2 variables. It is just non-linear

Dose Response Curves

• Graphs the correlative association between an exposure and effect

• Dose = X axis

• Response = Y axis

• Beginning flat portion = subthreshold phase (low dose, no/minimal effect)

• Steep incline = Threshold reached (increasing dose —> increasing effect

• Flattens at top = maximal response reached

Contingency Tables

• A = Exposure is present, and disease is present

• B = Exposure is present, and disease is absent

• C = Exposure is absent, and disease is present

• D = Exposure is absent, and disease is absent

Parameter estimates

• Point estimate = Single value used to estimate a parameter (using sample mean to estimate the population mean)

• Interval estimate = Range of values that with a certain level of confidence contains the parameter

  • 95% confidence level (most common): one is 95% certain that the confidence interval contains the parameter

  • For a more precise/narrower estimate of the confidence interval, one should increase the sample size (n)

Example of nominal variable

Blood type

Which variable type is best suited for ranking preferences (strongly agree, agree, neutral, disagree)

Ordinal

What type of variable would “height” be classified as?

Continuous