Biostats Midterm

Statistics

Drawing conclusions from data while accounting for uncertainty

Biostatistics

Statistics applied to biological and health data

When done correctly, statistics reduces ____

Bias in human reasoning

Probability

Number from 0 to 1 for how likely an event is

Probability of 0

Event is impossible

Probability of 0.5

Equally likely to happen or not

Probability of 1

Event is certain

Statistical model

Simplified mathematical approximation of reality

All statistical models rely on ____

Assumptions

If a model's assumptions are wrong ____

Results can be very inaccurate

Birthday problem: people needed for ~50% chance of a shared birthday

23

Birthday problem: chance of a shared birthday with 70 people

99.9%

Birthday problem takeaway

We underestimate how common coincidences are

Problem with "3 patients on drug A gained weight"

Tiny sample, no denominator, no comparison group

Overconfidence effect

People are more certain than they should be

People 100% sure of their answers were wrong about ____ of the time

20%

Gambler's fallacy

Believing past random outcomes affect future ones

Probability of red in roulette

18/38 = 0.474

Better chance of red: 1 in 10 or 7 in 100?

1 in 10 (small bowl)

Multiple testing problem

More tests → more false positives by chance

P-hacking

Running analyses until something is "significant"

Expected false positives from 2,676 tests at α = 0.05

~134

6 areas where statistics corrects bad intuition

Small data, overconfidence, randomness, coincidence, probability, multiple testing

4-step big picture of research

Define population → sample → calculate statistics → infer to population

Population

Complete set of individuals you want to study

Sample

Subset of the population you actually study

Key assumption when using a sample

The sample is representative

2 reasons to study a sample instead of everyone

Cost/feasibility and enough accuracy

Statistics are calculated on the ____

Sample

Sample statistics estimate ____

Population values (parameters)

Descriptive statistics

Describe the sample only (no CIs or p-values)

Inferential statistics

Generalize to the population (with CIs or p-values)

Why most science is inferential

Results should apply beyond one sample

5 steps of research

Design, data collection, visualization, analysis, dissemination

Decisions made in study design

Question, population, sampling, study type, outcome, analysis plan

Literature review

Reviewing existing research before designing a study

Validity

Measures what it's supposed to measure (accuracy)

Reliability

Gives similar results when repeated (reproducibility)

Example of a data entry/storage system

REDCap

3 purposes of data visualization

Find errors, see patterns, check model assumptions

Table 1

Summary of the sample's demographics

Table 1 tells readers ____

What population the results generalize to

Biggest caution when disseminating results

Don't overgeneralize

Variable

Feature that varies between members of a population

2 broad types of variables

Categorical and numeric

Categorical variable

Which category a subject falls into

Other name for a categorical variable

Factor

Nominal variable

Categories with no natural order

Ordinal variable

Categories with a natural order

Binary variable

Nominal variable with only 2 categories

Variable type: blood type

Nominal

Variable type: Likert scale

Ordinal

Variable type: BMI categories

Ordinal

Variable type: smoker = 1, non-smoker = 0

Binary

Continuous variable

Numeric; any value including decimals

Other names for continuous variables

Quantitative, interval, scale

Discrete (count) variable

Numeric; whole numbers only

Variable type: number of children

Discrete (count)

Variable type: blood pressure

Continuous

Why researchers categorize numeric variables

Easier interpretation

Dichotomizing

Splitting a numeric variable into 2 groups

Why dichotomizing is not recommended

Loses information and power; arbitrary cut-point

Survival (time-to-event) variable

Time from enrollment until an event

Why survival data need special methods

Censoring

Why variable type matters

It decides the right summaries, plots, and tests

Summary for categorical variables

Count and % in each category

Plots for categorical variables

Bar chart, pie chart

Summaries for continuous variables

Mean, median, SD, IQR

Plots for continuous variables

Histogram, boxplot, scatterplot

Summaries for count variables

Counts and rates

Summaries for survival variables

Median survival, 5-year survival

Plot for survival variables

Kaplan-Meier curve

Tests for a categorical outcome

Chi-square/Fisher's exact, logistic regression

Tests for a continuous outcome

t-tests, ANOVA, correlation, linear regression

Tests for a count outcome

Poisson or negative binomial regression

Tests for a survival outcome

Kaplan-Meier, log-rank test, Cox regression

Outcome variable

The result you're measuring

Other names for the outcome variable

Response, dependent variable, y

Exposure variable

What may affect the outcome

Other names for the exposure variable

Predictor, explanatory, independent variable, x

Intermittent fasting and weight loss: outcome

Weight loss (continuous)

Intermittent fasting and weight loss: exposure

Fasting yes/no (binary)

Cavities in kids who do vs don't brush: outcome type

Count

COVID 30-day mortality by sex: outcome type

Binary

Number of cars and air quality: outcome

Air quality

Rows in a dataset

Subjects

Columns in a dataset

Variables

Vaccine survey: variable type of race

Nominal

Vaccine survey: variable type of agree/disagree items

Ordinal

Statewide vaccine survey: study population

All adults in the state

Variable type: brain hemorrhage (yes/no)

Binary

Variable type: gestational age

Continuous

Variable type: time until death

Survival (time-to-event)

Variable type: U.S. state

Nominal

Variable type: salary category (<20k, 20–50k, 50–100k)

Ordinal

Variable type: exact yearly salary

Continuous

Variable type: disease status (present/absent)

Binary

x̄ estimates ____

μ (population mean)

p̂ estimates ____

π (population proportion)

s estimates ____

σ (population SD)