Statistics Flashcards by Isuru Gamage

Numerical data types

Discrete - whole numbers only

Continuous - any value, scale - weight, height, length

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What % of population for 1SD?

68%

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What % of population for 2 SD?

95%

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What % of population for 3 SD?

99.7%

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Parametric data
- criteria?
- Advantages

Continuous numerical data
Population has normal distribution
Population and sample have same variance and SD

Parametric assessment has better power

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Features of non-parametric tests

Emphasis on rank
Doesn’t require specific distribution
Less power

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Central Limit theorem

For a skewed population, if N > 30, then can assume distribution will be normal

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2 groups
Unpaired
Parametric

What tests?

Equal variance - student t test

Not equal variance - Welch test

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2 groups
Unpaired
Non-parametric

Mann Whitney U test

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2 groups
Paired
Parametric

Paired t test

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2 groups
Paired
Non-parametric

Wilcoxon signed rank test

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3 or more groups
Unpaired
Parametric

One way ANOVA

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3 or more groups
Unpaired
Non-parametric

Kruksal Wallis test

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3 or more groups
Paired
Parametric

One way repeated measured ANOVA

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3 or more groups
Paired
Non-parametric

Friedman test

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Test association between 2 qualitative variables

N > 50

Chi Squared test

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Test association between 2 qualitative variables

N < 50

Fischer Exact Test

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Test linear relationship between 2 variables

Parametric

Pearson’s correlation

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Test linear relationship between 2 variables

Non-parametric

Spearman’s rank correlation

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Difference between test statistic and p value

Test statistic - standardised value used for hypothesis testing

p value - probability that test statistic is random = type 1 error probability

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When to use Z statistic

Known population mean + SD

Sample size > 30

Z = z score. Need population mean and sd

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When to use t statistic

Popualtion mean and SD unknown

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When to use F statistic

ANOVA

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Statistical Power
- What is it

Probability study will detect predetermined difference between 2 groups
= probability will correctly accept alternative hypothesis

1- power = chance of false negative = probability of type 2 error

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Changes that will increase power

Increase sample size Increase significance level (0.05 - 0.1) Increase detected difference Reduce SD

Deciding significance level

If consequences of type 1 errror are serious - use small significance level, reducetype 1 error If consequences of false negative are high, use higher significance level, increase power, reduce type 2 error chance

Drawback of post-hoc analysis

Type 1 error chance increases (selectively looking for positives, multiple error each time)

Drawback of trying to mitigate type 1 error risk in post-hoc analysis

Make total significance level smaller Increase requirement for power - if N not increased, then type 2 error increases

Event rate is also called?

Absolute risk

NNT formula

1/ARR i.e 1 divided by absolute risk reduction

Odds calculation

Number of events: number of non events e.g 20% event rate 1:4 odds

Formula for probability from odds

Prob = odds/(odds+1)

Hazard vs hazard ration

Hazard - conditional probability of event given patient has survived to that point in time. On time to event analysisi Hazard ratio - ratio of two groups hazards. Ratio should remain constant with time

Differences between hazard ratio and median ratio

Hazard ratio - odds of survival of one group to the other (odds on winning) Median ration - margin of victory (compares point in time where probabilty of survival i 0.5 for both arms)

Tests used to compare Kaplan Meir

Log rank test - compares two survival curves COX proportional regressional model - factors other variable to explain hazard

Study Start with group Trace backwards and determine exposure

Case Control

Study for rare disorders Study for disease with long lag time between exposure and otucome

Case control

Bias affecting case control

Recall bias Selection bias

Start with exposure Measure if disease occured

Cohort Measure newly occuring disease = prospective Look back in time at exposure, see if disease developed = retrospective

Study for rare risk factor/exposure

Cohort study

Study where only individuals who have experienced an event are included

Self controlled case series

Sampling to use in homogenous population

Simple random sample

Sample to use in heterogenous population with homogenous subgroups

Stratified random sample

Sample to use for population that has heterogenous subgroups, which are similar to each other

Cluster sampling e.g geography

Screening detects disease earlier, but disease course no different Survival appears longer when it is not

Lead time bias

Screening detectes earlier cancers wich might not develop into end disease

Length time bias

Assume subjects remain in randomised group, regardless of crossover

Intention to treat analysis

Limitation of intention to treat analysis

Underestimates treatment effect

Analyse patients who strictly adhered to protocol (exclude those who dropped out)

Per protocol analysis Likely to show exaggerated treatment effect

Way to reduce confounders

Randomisation

Inaccurate way to select patients for trial Produce sample that is not representative of population

Selection bias

Investigator knows which arm next patient will receive - can change who is allocated

Allocation bias Blind to reduce

Data for study collected so taht some members of population less likely to be included (e.g email and old people)

Ascertainment bias = sampling bias

Difference in how information is obtained/recorded

Interviewer bias

Poor recollection of previous events

Recall bias

Lack of response from some patients changing sample characteristics

Non-response bias = transfer bias

Participants leave trial/lost to follow up

Attrition bias

Differences that occur due to knowledge of intervention allocation

Performance bias

Participants report positive effect if they know they are being observed

Hawthorne effect

Nocebo

negatiev expectations, cause control to have more negative effect

Rely too heavily on initial piece of information for all subsequent decisions

Anchoring bias

Not all research makes it into analysis

Publication bias

Establish dosing, pharmacokinetics

Phase 1

Establish significant A/E

Phase 2

Establish efficacy

Phase 3

stablish long term f/u and surveillance of a/e

Phase 4

Ways to assess heterogeneity in meta-analysis

How different the results of different studies are 1) Overlap of confindence intervals 2) I2 statistic - >7% = high heterogeneity

Random effects model

Takes into account other studies that may have been ignored by meta-analysis

Propensity score - What is it - What does it reduce

Score from 0-1, looks at other variables that predict whether a patients is assigned to a particular group (e.g smoking --> age, socioeconomic) Aims to match groups Reduces selection bias and confounding

When you use propensity score? What does it reduce

No randomised studies Reduces treatment selection bias due to knowledge of treatment

When can allocation bias occur? When can allocation concealment be applied

Random allocation requires - Generate random sequence - this not done can lead to allocation bias Implementing random sequence so it is concealed - can use allocation concealment here

Example of allocation concealment

envelopes

Diferrence in allocation vs performance bias in terms of timing

Allocation bias occurs before allocation - randomisation - concealment Performance occurs after randomisation - recording of results due to knowledge of treatment

Coefficienct of variation

Standard deviation:mean

I2 is a measure of difference in what between studies?

Variance

Formula for variance

each value - mean, squared Average of above values