Measurement Scales, Rates And Ratios

Question 1

Difference between probability and statistics

Answer 1

Purpose of statistics is to generalise / infer about the populations

So probability is the idea that if you know exactly what’s in the bag, predict what’s going to be in your hand when you take a ball out

Statistics is given the colour of the ball in your hand infer what colour ratio is in the bag

We often want to make inferences about the entire population - so we take a sample (cant do entire pop of the uk

Question 2

Sample populations and potential errors limitations with these samples

Answer 2

We want our sample population to be:
Representative
Unbiased
Precise

2 types of error that can occur in a sturdy that could influence the results -
Chance (random error) - due to sampling variation, but this can be reduced by increasing the sample size (as you reduce uncertainty and increase precision)

Bias (systemic error) - bias is quantified by the difference between the true value and the expected value (this does not reduce if you increase the sample size)

Sources of bias include:

• Selection biases - of study sample (external validity) study sample is not representative of entire population
  - Group selection within a study (internal validity) groups within a study may not be comparable
  - Healthy worker effect - workers usually exhibit lower overall mortality than the general population (e.g. severely ill people usually excluded from employment)
• Information bias - of recall error, difference in recollection from study participants regarding events from the past
  - observer/interviewer error, interviewer may have preconceived expectations that may influence result
  - measurement error, differences in the measurement of participants
  - misclassification, participants are put into the wrong group (e.g. put into diseased when not diseased) , usually comes form observational or measurement error

Question 3

Measurements - Prevalence vs Incidence

Answer 3

Prevalence - the proportion of people who have a disease at a given point in time
Counts the number of people with existing disease (both OLD and NEW cases)
Takes a “snapshot” at a given point in time
Describes the ‘burden of disease’
Useful to determine resource/service allocation
Often reported as a proportion (it is not a rate!):
Prevalence = the number of people with the disease / total population

Incidence - The number of new cases of a disease within a given
timeframe.
Focuses on NEW cases only
Useful when monitoring epidemics
E.g. number of new cases of zika virus in the Americas
Often reported as a rate (e.g. 50 per 100,000 person years):

Incidence rate = number of new cases/ patient time at risk

Question 4

Incidence rate ratio

Answer 4

The incidence rate ratio compares the incidence rate in one group to another

The IRR is a relative measures between 2 groups

We often use reactive measures to compare 3 groups for factors such as mortality rate ratios

Question 5

relative risk and odds

Answer 5

Odds - if the probability of an event is p then the odds of that event are P/1-P e.g. for a coin toss, probability of tails is p=0.5 so 0.5/1-0.5 = 0.5/0.5 = 1
We can use odds in a medical setting - we can use ratio of odds to compare two exposure groups

Odds is a ratio -
odds for disease in group A = diseased(A)/ non diseased (B)
Odds for disease in group B = diseased (C)/ non diseased (D)
Odds ratio is a ratio of ratio -
Odds ratio between these 2 groups is odds of group A/ odds of group B

Relative risk is the underlying quantity we wish to approximate
In a cohort study where we have consistent follow up for all patients we can calculate odds ratios or relative risk estimates directly
Risk is a proportion
Absolute risk for group A is diseased/ diseased - non diseased
Absolute risk for group B is diseased/disease - non diseased
Relative risk is a ratio of proportions
Relative risk = absolute risk for group A/absolute risk for group B

Question 6

How to interpret Odds ratio and Relative risk ??

Answer 6

OR<1 if group represented in the numerator has a lower odds of the event.
RR<1 if group represented in the numerator has a lower risk of the event.
This is desired if the event is a bad outcome e.g. death

OR>1 if group represented in numerator has a greater odds of the event.
RR>1 if the group represented in the numerator has a greater risk of the event.
This is desired if the event is a good outcome e.g. smoking cessation

Question 7

When comparing groups need to be aware of..

And how to combat it?

Answer 7

Confounding factors - when comparing groups the association or effect between an exposure and outcome is distorted by the presence of another variable

E.g. Have a result that suggest males are more likely to get cancer of the mouth and pharynx
But a confounder is alcohol
Males are more likely to consume larger amounts of alcohol and alcohol is a risk factor for cancer of the mouth and pharynx

Therefore inferring that being male is more likely to give you mouth cancer is not the truth

In statistics, we can adjust for differences in (known)
confounding factors
A common type of adjustment is standardisation
This form of analysis uses weighted averages to allow us to
compare “like-for-like”
E.g. we may want to standardise (choose weights as a basis for
comparison, i.e. calculate a standard) by age and sex
However, a lot of confounding factors are unknown,
This is more difficult to address