# Statistics 2

## Types of Study

#### Case control study

• observational and retrospective
• compares a group with a disease to a group without
• Looks for prior exposure or risk factor
• Measures Odds Ratio (think of odd case)

#### Cohort Study

• Observational and prospective
• Compares two groups, one with exposure, one without exposure
• Looks to see if exposure increases likelyhood of disease
• Measures Relative Risk  (Think of Arnold in court – relative co(h)ort)

#### Cross Sectional Study

• Observational
• Collects data from a group of people to asses frequency of disease and related risk factors at a particular point in time
• Can show risk factor association – but not causality

#### Twin Concordance Study

• Compares the frequency with which both monozygotic twins and dizygotic twins or both sets develop a disease
• Compares sibling raised by biolgic vs adoptive
• Measures heritability

• Compares siblings raised with biologic vs adoptive
• Measures heritability and influence of environment

## Evaluation of Diagnostic Tests

Uses a 2 x 2 table to compare test results with the actual presence of the disease

TP = True Positive, FP = False Positive, TN = True Negative, FN = False Negative. with this be aware that the disease and test may be flipped around which will inver the table

###### Sensitivity
• Sensitivity = all the people with the disease who test positive
• Sensitivity  = TP/(TP+FN)
• It’s the ability of the test to detect the disease when it is present
• Value approaching 1 is desirable – indicates a low false negative
• If it’s a very sensitive test (when negative) will rule OUT the disease – SeNsitive = OUT –> SNOUT
###### Specificity
• Specificity = proportion of those without the disease who test negative
• Specificity = TN / (FP + TN)
• The ability of the test to indicate NON disease when disease is truely not present
• A value of approaching 1 is good – indicates a low false-positive rate
• A very specific test rules IN a disease with a high degree of certainty – SPecificity = In –> SPIN

#### Positive Predictive Value

• The portion of positive test results which are true positives
• Given a positive test result this is the probability the person actually has the disease
• NB: If the prevalance of a disease in a population is low even a test with a high sensitivity and specificity will have a low postitive predictive value
• PPV = TP / (TP + FP)

#### Negative Predictive Value

• The probablity of a person actually not having the disease given a negative test result
• NPV = TN / (TN + FN)

#### Likelyhood Ratio for positive test result

• How much the odds of a disease increase when the test result is positive
• sensitivity / (1 – specificity)

#### Likelyhood ratio for negative test result

• How much the odds of the disease decrease when the test result is negative
• (1 – sensitivity)  / specificity

Neumonic: Remember the PIG is always ontop – (SNOUT = sensitivity is always in the numerator)

## Prevalence Vs Incidence

Point Prevalence =    Total cases in a population at a given time  /                               .                                                total population at a give time

Incidence = new cases in population over a given time period /                                         .                         total population at risk in that time period

Prevalence = incidence x disease duration

For chronic diseases prevalence is more than incidence

For acute diseases prevalence is same as incidence

Note: when doing calculations – those with the disease or who have previously had it are not considered at risk for that disease

# Odds Ratio Vs Relative Risk • EE = Experimental group where the event happened
• EN = Experimental group where the event didn’t happen (negative)
• CE = Control group where the event happened
• CN = Control group where the event didn’t happen (never happened / negative)
• ES = Total Number of Subjects in the Experimental group
• CS = Total number of subjects in the Control Group
• EER = Experiment Event Rate
• CER = Control Event Rate

#### Odds Ratio OR

• This is used for Case control studies
• Mneumonic – Think of this ODD suitCASE
• • Odds ratios are used for Case Control studies

Odds ratio = Odds of having the disease in the exposed group divided by the odds of having the disease in the unexposed group

Exposed group up top – imagine a flasher at the top of the railway bridge

Odds ratio = (EE / EN) / (CE / CN)

Or Odds ratio = (EE x CN) / (CE x EN)

#### Relative Risk (RR)

• Used for cohort studies
• Nmeumonic: Think of Arnold in Court – Relative in Court = Relative Cohort
• Relative Risk Uses TOTALS (ES & CS)  – Arnold in court – a TOTAL FUCKUP (Odds ratio – doesn’t use totals)
• Relative probability of getting a disease in the exposed group compared to the unexposed group
• Calculated as the percentage with the disease in the exposed group divided by percentage with disease in the unexposed group
• (AGAIN the exposed group is upto – flasher ontop of railway bridge)
• RR = (EE / ES) / (CE / CS)
• RR = EER/CER  So same thing written a different way would be to say that Relative risk – used for cohort studies is EER / CER

(relative risk = experimental event rate / control event rate)

#### Relative Risk Reduction

RRR = ARR / CER

(Lion = Pirate / cerebellum)

#### Attributable Risk

• The difference in risk between exposed and unexposed groups
• or the proportion of disease occurrence which are attributable to exposure
• Attributable risk = (EE/ES) – (CE/CS)
• Or AR = EER – CER

#### Absolute Risk Reduction (or absolute risk increase)

• The reduction or increase in risk with a treatment when compared to a placebo
• The difference in the event rate in the intervention group compared with the event rate in the control group
• ARR = CER – EER
• If It’s CER-EER < 0 then it’s an absoulte risk reduction
• If CER – EER > 0 then it’s an absolute risk increase

Attributable risk and absolute risk are opposite – Attributable risk is EER – CER, Absoulte risk recuction is CER – EER.

Att Eer Cer

Ab Cer Er (abs cool – er)

NNT = 1/ARR

#### Number Needed To Harm

NNH = 1 / Absolute risk increase

## Worked Example EER = EE/ES = 15/150 = 0.1 = 10%

CER = CE/CS = 100/250 = 0.4 = 40%

Absolute Risk Reduction = ARR = CER – EER (abs cool er) = 0.4 – 0.1 = 0.3 = 30%

Relative Risk Reduction = ARR / CER  (lion = pirate / cerebellum) = 0.3/0.4 = 0.75 = 75%

Number needed to treat = 1/lion  = 1/ARR = 1/0.3 = 3.33

Relative Risk = EER / CER = (EE/ES) / (CE/CS) = 0.1/0.4 = 0.25 = 25%

Odds Ratio = (it’s odd it doesn’t have total) = (EE/EN)/(CE/CN) = (15/135)/(100/150) = -0.111/0.666 = 0.167

Attributable Risk = (At risk ere if youre cqueer) = At Risk = ERR – CER = 0.1 = 0.4 = -0.3

## Bias ### Type 1 error (α)

• stating that there is an effect or a difference when none exists – accepting the experimental hypothesis in error
• p = probability of making a type 1 error
• p is judged against a preset level of significance – usually p < 0.05
• AKA “false positive error”

## Type 2 error (β)

• stating that there is not an effect of difference where one does exist
• β is a “False negative error”
• accepting a nul hypothesis which isn’t actually the case

## Power

• Probability of correctly rejecting the null hypothesis or correctly accepting the experimental hypothesis
• Power = 1 – β

## Normal distribution So 68% fall within one standard deviation of the mean, 95% fall within 2 standard deviations of the mean, 99.7% fall within 3 standard deviations of the mean.

95% confidence interval = Mean +/- 1.96 x Standard Error

Standard Error = Standard deviation / √number of patients

• t-test: checks the differences between the MEANS of 2 groups (MR T is MEAN!)
• ANOVA checks the differences between the means of 3 groups (MR T AND ANOVER! – mr t is two – add another and you have the means of three groups)
• ANCOVA
• Chi Squared (X2) check the differences between percentages of proportions of categorical variable (like eye colour)  (not means) Metanalysis Displaying / interpretation of data ## Forest Plot / Blobogram

#### Blob / Square

• findings from each study are a blob or square
• If the square is to the left the new treatment is better, if to the right it’s worse
• The size of the square is proportional to the precision of the study (roughly proportional to the sample size)

#### The horizontal line on each square –

• this representst the 95% confidence interval
• represents the UNCERTAINTY of estimate of treatment effect
• The wider the line the less certainty
• If the line passes the vertical line of no effect it means the study is not statistically significant

#### The diamond

• the aggregate effect found from all studies are displayed as a diamond
• the width of the diamond shows the 95% confidence interval
• If the diamond crosses the vertical line of no effect, it means overall there is no statistically significant effect

#### The vertical line

• line of no effect
• odds ratio of 1
• Risk and benefits are equal
• any statistically significant study does not cross this line

#### Heterogenicity

• if all studies are kinda reporting different things this will be super low
• if the P value is say larger than 0.1 then we can be reassured they’re all measuring pretty similar things

# Funnel Plot

• Funnel plots are designed to highlight the existance of publication bias  in systematic reviews & metaanyalysis
• It assumes that large studies will be near the average and smaller studies will be spread on both sides of the average
• Variation from this assumption can indicate publication bias Its sometimes difficult to identify this by eye so Egger’s Test  is a statistical test to check for publication bias – it is a formal way of looking at the funnel plot and working out whether there’s kinda like studies missing.

# Cox Model

• analyses survival data
• isolates effects of treatment from effects of other variables

# Kaplan – Meire Method

• Censored survival time – you can’t know when some people in the study are gonna die cos they’re still alive
• so the Kaplan meire method – it calculates the proportion of such people surviving a given lenght of time