Lecture 16- Reference Range Flashcards
What is a reference range?
A reference range, sometimes called a reference interval, is an estimate of the range of values of some measured variable that would be considered to be ‘usual’ for that variable in the population under observation.
What is a common application of the idea of a reference range?
Laboratory test results, doctors need to know what a normal range is in order to know what is abnormal
What is a common number we use as a reference range?
A 95% reference range is the range which contains the central 95% of all the values of the measured variable in a healthy population.
What does it mean if there is a value outside the 95% reference range?
It doesn’t necessarily mean that there is something wrong with the person but we have to call it somewhere. It simply provides a good portion for doctors to follow up (not so much that it is impossible, not so little that you would miss important cases).
What function in r do we use to find areas under curves and thus could be used to find the lower and upper limit of the reference range?
qnorm
use 0.025 to find lower limit
and 0.975 (1-0.025) to find upper limit
To save time in finding the upper and lower limits for a reference range what can be done?
Convert the normal curve to a standard normal using Z
This means that the lower limit is always at -1.96 and the upper at 1.96
You can then convert the limits back to the original scale using the rearranged Z formula (x=mean +sd times z
Suppose we wish to construct a 95% reference range for cholesterol
levels. If we know that cholesterol levels in the adult NZ population
are normally distributed with a mean of 5.7 mmol/L and a standard
deviation of 1.2 mmol/L.
Find the 95% reference range…
LLN = µX − 1.96(σX ) = 5.7 − 1.96(1.2) = 3.35 ULN = µX + 1.96(σX ) = 5.7 + 1.96(1.2) = 8.05
in terms of standard deviations what does a Z value of 1.96 mean for the 95% reference range?
For any normal distribution, 95% of the population have values within 1.96 standard deviations of the mean.
What do you do if your distribution does not fit a normal distribution and you want to find the reference range?
-Log of random variable always follows a normal distribution
-So take log of data then calculate mean and sd and then do the normal way i.e. mean(log(rawdata)) ± 1.96 × sd(log(rawdata))
-We can back-transform these to the original scale using the
exponential function e (exp in R)
What’s important to note when taking the log and calculating means?
Have to take log then calculate the mean of this, can’t take the given mean from the original scale and log it.
