Risk ratios and Odds ratios Flashcards
Any finding that we observe in our study can be wither of three things:
- A true finding
- A spurious (false) finding due to random error
- A spurious /false) finding due to a “systematic”, non-random error: bias or conducting
Random error:
Any difference between sample mean and population mean that is attributable to the sampling.
Random error is a ….., Standard Error is its …..
Phenomenon and measure
Standard error:
The standard error (SE) is the basic measure of random error for any quantity that we measure or calculate in a sample.
What is the standard error inversely proportional to?
The square root of the sample
Null hypothesis (H0):
Both population means are the same, μ1 = μ2, and any difference in sample means is due to random error.
Alternative hypothesis (H1):
Population means are actually different μ1 ≠ μ2, and that is the cause of the difference in sample means.
The two-sample t-test:
Are used to compare just two samples. They test the probability that the samples come from a population with the same mean value.
If the probability is very low (by convention: p<0.05) then we have to
Reject the null hypothesis H0 and choose the alternative hypothesis (H1)
Definition of p-value:
The p-value is the probability of getting this or a more extreme result if the null hypothesis is true.
If the p-value is higher than 0.05 we have failed to reject the null hypothesis H0 and to show that there`s an underlying difference:
- There might be an underlying difference in population means that we have failed to demonstrate (e.g., because our sample size was too small) or there might not be.
- We describe the difference as “statistically non-significant”.
- We never ever accept the null hypothesis; we only fail to reject it.
If p<0.05 then:
The 95% CI will not include zero (the “null” value).
If p>0.05 then:
The 95% CI will include zero.
If p=0.05:
One of the 95% CI limits will be equal to zero
We can create a contingency table showing:
The frequency distribution of the two variables (cross-tabulation)
The chi-square test:
It is a measure of the difference between actual and expected frequencies.
What is the expected frequency:
Is the frequency we would see if the null hypothesis were true
What happens if the observed and the expected frequencies are the same?
The x^2 value would be zero
Fisher´s exact test (X^2 non-paramedic brother):
Is sometimes used to analyze contingency tables. It is the best choice as it always give the exact p-value, particularly where the number are small.
What is risk?
Risk is he probability that an event will happen.
How is risk calculated?
It is calculated by dividing the number of event by the number of people at risk.
Odds ratio is used?
By epidemiologists in studies looking for factors which do harm, it is a way of comparing patient who already have a certain condition (cases) with patient who do not (controls) - a case-control study
Relative risk (RR):
(Risk of the outcome among the exposed )/(Risk of the outcome among the unexposed) = (d/(c+d))/(b/(a+b))
Odds ratio (OR):
(Odds of exposure among those with the outcome )/(Odds of exposure among those without the outcome ) = (d/b)/(c/a)
Risk =
Probability
The odds ratio is:
Symmetric
The RR and OR have their own Standard Errors:
SE(logRR) = √(1/d=1/(c+d)=1/b=1/(a+b))
SE(logOR) = √(1/a=1/b=1/c=1/d)
The RR and OR have their own Standard Errors, which means:
That means we can calculate a 95% Confidence Interval, by going ±1.96 Standard Errors from log RR and log OR (and then exponentiating, to return to the original scale)
(In practice, these calculations are done by computer with R * Extremely easy once you’ve got your data loaded)
