Unsure what test to use...

#1
I'm hoping someone can help. As an example lets say a patient comes to clinic every 3 months and has their resting heart rate measured. If I wanted to see whether the latest resting heart rate measurement for a specific patient differed significantly from their own previous resting heart rate measurements, how would I go about this? To be clear, I'm not looking to compare the current measurement to each of the previous measurements; I'm looking to compare the current measurement to the group of previous measurements to determine whether any change in the measurement on this occasion is significant relative to the general variability that has been seen up to now. My first thought was to obtain a mean for the previous resting heart rates and then compare that to the current resting heart rate using a Paired Samples T-Test. However am I right in saying a Paired Samples T-Test should really compare two means (in this cause I'm comparing a mean to a single observation value)?

Secondly, let's say the patient's resting heart rate was initially 60 BPM, then 70, 80 and 90 at each subsequent time point three months apart. If their latest measure is back down to 70 BPM, it is unlikely (I would guess) to be significant considering the mean of the previous four measures is 75. However, since these are across time, I'm thinking the more recent measurements of 80 and 90 should probably carry more weight than the earlier measurements of 60 and 70? In saying that, I still think the earlier measurements should be factored in for context of variability. Is there any way to "load" the previous measurements such that the more recent ones are given more weight?
 

Miner

TS Contributor
#2
I recommend looking into the Individuals control chart (aka, I-MR chart, process behavior chart, etc.). It is a tool used in industrial statistics to separate the signal (shift in process output) from the noise (measurement variation, normal process variation. There is also an Exponentially Weighted Moving Average (EWMA) chart that places more weight on the more recent measurements.
 
#3
I recommend looking into the Individuals control chart (aka, I-MR chart, process behavior chart, etc.). It is a tool used in industrial statistics to separate the signal (shift in process output) from the noise (measurement variation, normal process variation. There is also an Exponentially Weighted Moving Average (EWMA) chart that places more weight on the more recent measurements.
This sounds perfect - will read up on it. Thanks.

As an aside, it was also suggested to me from someone with a medicine background that I simply look to see whether the most recent measurement sits outside two standard deviations of the mean of previous measurements. I've never really come across this approach before (my own background in stats relates to psychology and pharmacology). I understand that given a normal distribution, two standard deviations covers 95.45% of all values, so a value outside of two standard deviations is almost certainly statistically significant. However it's not exactly like running a statistical test that that explicitly tests for significance. Any input on this approach?
 

Miner

TS Contributor
#4
The concept of a control chart is very similar to the method that you described. The biggest drawback with that method is in how the standard deviation was calculated. See the following article by Dr. Wheeler on Individuals Charts Done Right and Wrong. This covers the correct and incorrect ways to calculate the standard deviation and the impact that it has on the control limits. Another drawback, from an industrial statistics perspective, was too many false alarms (type 1 error) when using two standard deviations. Three standard deviations were chosen as an economical balance between type 1 and type 2 errors.