Error Using More Than A Single Value

Now that we have looked at how there is error in a single value, what happens when we work with a multiple numbers, when working on the same patient. To add, subtract, multiple, or divide two sets of numbers hypothetically increases your overall error. So the questions is, how much do these values affect each other? Let's take a look at an example on how this could occur YOUR nuclear medicine department.

1. Propagation of statistical error increases when adding numbers. The formula to determine %SD is noted below:



2. What happens when numbers are subtracted? Statistical error increases when the formula is applied:



3. In the third example propagation of error increases if numbers are multiplied or divided. The formula is noted:



4. From what we have learned before, you can now apply counting values that are summed, subtracted, multiplied, and/or divided. Let us look at a specif situation that routinely comes up in nuclear medicine, propagation of error in a thyroid uptake exam.

Problem: The thyroid uptake has the following values (Background as already applied):

• 0 hr net counts = 1258454
• 24 hrs net counts = 105076
• df = 0.284
• Determine %SD

Issue: From the above calculations the patient has a 29.4% uptake. Assuming that a 30% uptake is classified as hyperthyroid, how confident are you that the patient doesn't have a hyperthyroid?

Answer: Using the multiplication and division %SD, at a 68% level of confidence the percent SD value is 0.4% with the 29.4% (uptake value). How does this effect your final results? What happens to this %uptake at 2 and 3 standard deviations?

As you can see the high normal uptake value could be actually be abnormal, once 2 or 3 SDs are applied

Given this scenario, what should the physician do? Should the patient be given a ¹³¹I therapy treatment. In a situation I am grateful that I do not have to make that decision.

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