When it comes to statistical testing, more so in life-critical fields like medicine balancing Type I and Type II errors could quite literally be the difference between life and death. Using a practical scenario, I will attempt to explain where and why there is a trade off between the two errors as well as the implications to healthcare, patients and stakeholders.
Imagine a diagnostic test for a serious yet treatable ailment, say early stage pancreatic cancer. It's a rare disease but early detection can greatly increase survival rates. Suppose a doctor is evaluating a new screening test for this strain of cancer. The test is not perfect and could return both false positives or false negatives. The big question would be, would you prefer to throw caution to the wind and detect more cases even though some could end up being false alarms or err on the side of certainty and only diagnose when you are very sure even if, in so doing, you might end up missing some real cases?
Hypothesis Parameters
In this case, our Null Hypothesis(H₀) would be The patient does not have pancreatic cancer and the Alternative Hypothesis(H₁) would be The patient has pancreatic cancer. Our predefined significance level here would be (α = 0.05)
❗ Type I Error (False Positive)
Here we would reject the null hypothesis when in actual case it is true. Basically the test results would show the patient having pancreatic cancer when in reality they do not. Possible consequences to this scenario would be:
The patient would undergo unnecessary stress and psychological trauma on receiving the diagnosis.
There would be costly follow up procedures like biopsies and CT scans in an attempt to determine the severity of the ailment.
The patient could develop side effects from the unnecessary treatments as cancer treatment takes a toll on the body.
The patient would also realize that he would actually suffer no physical harm if he were to ignore or miss treatment sessions.
Type II Error (False Negative)
Here we would fail to reject the null hypothesis when the alternative is true. Basically, the test results show the patient does not have pancreatic cancer but they do. Possible consequences to this scenario would be:
This will lead to a delayed diagnosis because the cancer will progress to a later stage.
Due to the fact that the diagnosis will come later when the patient's health has deteriorated, survival chances would be reduced and the treatment cost would also be higher.
There is a real possibility of irreversible harm and ultimately death if the cancer is detected in the later stages.
⚖️ The Trade-Off: What's Worse?
Finding a balance can be tricky since a low Type I error rate (fewer false positives) would come at the cost of a higher Type II error rate and vice versa. Thus a Type II error is far more dangerous than a Type I error. Therefore, the test must have a decision threshold set to maximum sensitivity so it accepts a higher false positive rate (Type I) in order to catch as many true cases as possible.
In conclusion, in high stakes medical applications it is ethically justifiable to accept a higher Type I error rate in order to minimize the risk of a Type II error. The cost of missing a real diagnosis can be catastrophic while false positives can be managed through additional testing and monitoring.
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