Biostats- Summarizing data & Quantifying disease

Why do smaller/rural countries have highest and lowest kidney cancer rates ?

Due to natural variability

• population characteristics, access to healthcare, and environmental factors

How can level of variability/uncertainty in results be accounted for ?

Probability, sampling distributions, confidence intervals, hypothesis testing

What are the two main categories for summarizing data with graphics ?

Categorical & quantitative

What are the two types of categorical graphics ?

Bar charts & pie charts

What are the five types of quantitative graphics ?

Histograms, box plots, scatter plots, bar charts, stem/leaf plots

What are the 3 types of categorical data ?

Nominal, ordinal, and binary

Categorical nominal data

Order of categories is irrelevant/unordered such as colors, brands, or species.

Categorical ordinal data

Order of categories is relevant/ordered/ranked such as socioeconomic status, education level, or satisfaction ratings.

Categorical binary data

Only 2 possible values (dichotomous) such as yes/no or female/male

Quantitative discrete data

Values equal to integers or whole numbers that can be counted such as the number of students in a class or number of cars in a parking lot.

Quantitative continuous data 

Values that can take any number within a range and are measurable, such as height or weight.

How can we summarize categorical data with numbers ?

1. proportions (percent) of observations in each category

2. using counts/# in each category (frequency)

*IMPORTANT: provide totals such as denominators of percentages

Categorical data: Pie chart

Variable pictorial that displays percentage of whole

• requires proportional reasoning so not best form to estimate/summarize data (common in media/non expert reports)

• most appropriate when aims to convey relative size of parts of whole (usually around 3-7 categories )

Categorical AND quantitative data: Bar chart

Represents summary measure for each category

• X axis indicates category and y is percentage of observations

• Alphabetize for easier understanding 

What are factors observed in quantitative data ?

• most common/average center of data

• variability/how spread out is data

• outliers/values far from bulk of data

Quantitative data: Histogram

Graphical representation of the distribution of numerical data

• X axis corresponds to values of quantitative variable in contiguous series of subintervals

• Bars indicate frequency/percentage of observations within interval

• Displays variation, shape of distribution, outliers, and approximate freq/percentage in given range

*# of bins = square root of # of observations (to avoid unequal widths)

Quantitative data: Stem & leaf plot

Stem = first digits & Leaf = remaining digits

• shows variation, shape of distribution, outliers, actual measurements, and typical values

What is central tendency ?

Way to decribe middle of data in quantitative data

Key differences in mean vs median

• Mean is sensitive to extreme values while median is resistant to outliers

• sym data means mean = median

1. for right skew: mean > median

2. for left skew: mean < median

Standard deviation

A measure of the amount of variation or dispersion in a set of values (indicates how many individual data points differ from the mean) and is calculated as the square root of the variance.

Computing standard deviation

Interquartile range

Upper quartile range - lower quartile range

A measure of statistical dispersion that represents the middle 50% of data.

*IQR less sensitive to outliers

Which two statistical variables are sensitive to outliers ?

Range and SD

• Range increases w sample size

How should mean and median be reported ?

Mean = SD

Median = IQR

Quantitative data: Box plots

Displays median, quartiles, and range of data

Outer whiskers found by multiply IQR * 3

*anything outside from whiskers = outliers

Quantitative data: Scatter plot 

Illustrates relationship between two quantitative variables, where each point represents an observation. It helps identify trends, correlations, and potential outliers in the data.

What is correlation in statistics ?

Numerical description of strength of linear asssociation btwn 2 variables in correlation

-denoted by “r” and ranges btwn -1 to 1

r>0 indicates higher values of one variable correspond to higher of the other 

r<0 indicates higher values of one variable corresponds to lower of the other

r +- 1 indicates perfect linear relationship

r=0 indicates no linear association

What is cumulative incidence (CI) ?

Proportion of a population that develops a condition over a specified time period

CI = # of new cases/ # of of pop at risk

What are contingency tables used for ?

For organizing/summarizing categorical data to examine the relationship between two or more variables. They display the frequency distribution of variables, allowing for analysis of associations and testing of independence.

What is placebo ?

A substance with no therapeutic effect used as a control in testing new drugs to compare effects against an active treatment.

What is risk factor ? What can it tell us ?

Variabel that may increase/decrease change of risk for outcome

Guides preventative measures

Does risk (of treated) = risk (of untreated)

Risk (of treated) = CI (of treated) = # of colds/ # of treated

What is relative risk ?

Risk (treated)/ risk (untreated)

0<RR<infinity

• if RR < 1, treatment associated w lower risk of outcome

• if RR > 1, treatment associated w higher risk of outcome

• if RR = 1, no association of treatment w outcome

Examples

• RR = 1.1, treatment associated with a 10% higher risk

• RR = 2.5, treatment associated with a 2.5-fold (or 150%) higher risk

• RR = 0.6, treatment associated with a 40% lower in the risk

Can relative risk be associated with causal interpretations on certain study designs ?

• if RR < 1, treatment lowers (or decreases) risk. I.e. treatment is beneficial

• if RR > 1, treatment increases risk

• if RR = 1, no effect of treatment on outcome

What is risk difference ?

RD = Risk (treated) - Risk (untreated)

• -1 < RD < 1

• If RD < 0, treatment is associated with lower risk of outcome

• if RD > 0, treatment is associated with higher risk of outcome

• if RD = 0, no association of treatment with outcome

Can relative difference be associated with causal interpretations on certain study designs ?

• RD = 0.10 treatment is associated with a 10% point higher risk. E.g., an increase of 10 cases for every 100 people, if the RD can be interpreted causally.

• RD = -0.20 treatment is associated with a 20 % point lower risk

Relative risk vs Relative difference ?

• Both are measures of association btwn risk factors & outcome

RR = 0.9: treatment means a 10% decrease in risk

RD = -0.1: treatment means 10 percentage point decrease in risk

Relative risk vs Relative difference EX

1. Relative Risk = (17/139) / (31/140) = 0.12 / 0.22 = 0.55

• In this study, risk of a cold for a child taking Vitamin C daily was 55% of the

risk of a cold for a child not taking Vitamin C daily

2. Risk Difference = (17/139) - (31/140) = 0.12 - 0.22 = -0.10

• In this study Vitamin C was associated with a 10 percentage point lower risk of a cold

What is incidence rate ?

# of new events / total person follow-up time

Unit are often per person-years

• Right censored if person being followed dropped out

Incidence rate EX 

Total person follow-up time = 18+6+12+18+18+9+12 months = 93 person-months or 7.75 person-years (since 93/12 = 7.75

Number of new events = 2 events

IR = 2 events/7.75 person-years = 0.26 events/person-year or 26 events/100 person-years

Biggest difference between CI and IR ?

CI can’t be calculated when there are drop outs, unlike IR

What is incidence rate ratio ?

A measure comparing the incidence rates of two groups, calculated as the ratio of the incidence rate in the exposed group to that in the unexposed group.

• If IRR < 1, treatment is associated with lower risk of outcome

• If IRR > 1, treatment is associated with higher risk of outcome

• If IRR = 1, no association between treatment and outcome

What is incidence rate difference ?

IR (of treated) - IR (untreated)

• If IRD < 0, treatment is associated with lower risk of outcome

• If IRD > 0, treatment is associated with higher risk of outcome

• If IRD = 0, no association between treatment and outcome

What is prevalence ?

The proportion of a population found to have a condition at a specific time, encompassing both new and existing cases.

• does not reflect when condition began/how long its existed

• only measures risk of having disease

Prevalence ratio

PR = Prevalence (exposed) / Prevalence (unexposed)

PR < 1: exposure is associated with lower prevalence

PR > 1: exposure is associated with higher prevalence

PR = 1: no association between exposure & outcome

Prevalence differences

PD = Prevalence (exposed) - Prevalence (unexposed)

PD < 0: exposure is associated with lower prevalence

PD > 0: exposure is associated with higher prevalence

PD = 0: no association between exposure & outcome