Random risk (95% Confidence intervals)

What is random error?

Error due to chance

Usually broken into:

Random sampling error-even if recruitment is done very well - study population will never be a perfectly representative sample of whole population of interest - every ‘representative’ sample will be slightly different by chance.

NOTE=random sampling error is inherent in every study

-Random measurement/assessment error →the measurements of exposure and comparison and outcomes are subject to this. Our ability to measure biological factors in exactly the same way, each time, is often poor, esp. if the measurement instrument requires a human operator.

-randomness inherent in biological phenomenon—>measuring factors in living organisms that are always changing-biological variability

-random allocation error - exposure and comparison groups in a RCT may differ by chance alone - solution=undertake bigger study

Why does random error occur?

-Sample size

-Participants always moving

-We can never measure everyone

True or false - 95% CI is used to describe the amount of random error in study results

True

How can we reduce random error?

-for random sampling error-increase sample size (more representative of pop)

NOTE - increasing sample size does not reduce non-random errors

-for random measurement error (large study with multiple measurements)

What are the two main ways of describing the amount of random error in a calculation or measurement?

Confidence intervals and p-values

(Confidence intervals usually more infomartive)

Define CI

‘There is about a 95% chance that the true value

in the population lies within the 95% Confidence Interval”

In CI what can the true value refer to?

EGO, CGO, RR, RD

If you have an EGO of 9.0, with a 95% CI from 8.0-10.0 how would you interpret this>

There is about a 95% probability that the true value of EGO in the whole population of interest, from which the study participants were recruited, lies between 8.0-10.0/

True or false - a narrower interval suggests lower precision, a wider one suggests more certainty.

FALSE - A narrower interval suggests higher

precision; a wider one suggests more

uncertainty

True or false - when there is no overlap between the Cls or EGO and CGO, the confidence intervals for RR and RD will not cross the no-effect line

TRUE

What does it mean when the 95% CIs for EGO and CGO overlap?

The 95% CIs for the RD and RR will usually cross the ‘no-effect’ line. In other words, it is generally not possible to determine if the true RD is positive or negative, or if the RR is more than or less than 1.0. In this situation it is the convention to state that ‘the study results are NOT statistically significanT

When the 95% CI for a RR or RD crosses the no-effect line, instead of saying there is no association between exposure and disease, what do epidemiologists prefer to say?

we prefer to state that ‘there may be too much random error to determine if there a real difference between EGO and CGO.’

What is the most common reason for differences in the width of confidence intervals between different studies?

The study size - ie how many participants are recruited. Smaller studies tend to have wider CI.

True of false - Confidence intervals can be calculated for both categorical outcomes and numerical variables?

TRUE

Describe regression to the mean

If measurement is repeated, it will be closer to the mean. In large studies with multiple measurements, most results won’t be extreme.

What are meta-analyses?

“Researchers combine the results of multiple similar studies to get one overall answer”

>generates a summary estimate of the effect

>commonly undertaken to combine the results of multiple RCTs that individually ave too much random error to demonstrate whether or not the intervention has a real effect

Helps decide is there is likely to be a real treatment effect

-increases confidence, more accurate results, avoids bias