Just want to confirm a biostats tidbit

[Phloston]

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When the pre-set alpha increases, power increases.

If alpha is high, then sensitivity is increased, so the chance of making a beta-error decreases, and therefore power has to increase.

If alpha is lower, then specificity is increased, the chance of making a beta-error increases, and power decreases.

Therefore increasing the number of people in a study increases alpha, so increased NPV means increased alpha.

Is all of that correct? (I'm more just concerned about the first part)

I'd really appreciate anyone's response to this.

 

[mmmcdowe]

When the pre-set alpha increases, power increases.

If alpha is high, then sensitivity is increased, so the chance of making a beta-error decreases, and therefore power has to increase.

If alpha is lower, then specificity is increased, the chance of making a beta-error increases, and power decreases.

Therefore increasing the number of people in a study increases alpha, so increased NPV means increased alpha.

Is all of that correct? (I'm more just concerned about the first part)

I'd really appreciate anyone's response to this.

Yes, if you hold your sample size and expected difference between two samples constant (so for example you had 2 groups of 100 patients and had a 10% difference in their values) then your beta will decrease when your alpha increases. When beta decreases power increases.

When Power is high (with high alpha for your example) you are more likely to get false positives and less likely to get false negatives. Thus low specificity and high sensitivity.

Increasing the number of patients does not alter your alpha. Your alpha is a preset condition. Increasing the number of patients will allow you to to potentially to choose to lower your alpha, or lower your beta (thus increasing power), or identify a smaller difference as being statistically significance. For example, with 100 patients you might be powered to detect a 10% difference, but with more patients you could detect a 5% difference.

I think I understand what you are trying to say, but using alpha/beta isn't necessary the way to express it. You want to say type 1 and type 2 error, which can be predicted based on your preset alpha and beta. If you want to decrease your risk of type 1 error, you lower your alpha so that you are less likely to encounter the data that you see by chance. So an alpha of .05 says you have a 5% chance of incorrectly rejecting the hypothesis that there is no difference between your two samples. If you lower that to .01, you now will only be wrong 1 out of 100 times. You must choose to do so though, because p values will not be altered only your conclusion on whether or not it is valid. You are able to lower your alpha by increasing your sample size, increasing your beta (lowering power and increasing type 2 error), or by looking at a difference of a greater magnitute (20% difference instead of 10%), but only when everything else is held constant. Your negative predictive value will increase if the disease is rare and decrease if your disease is common. It is a measure of the known disease prevalence of the population, not of a sample. Increasing your sample size doesn't alter negative predictive value, only increases your chances that your sample is consistent with the true population characteristics, which is where alpha and beta come in. So basically if you hold everything else constant you will be able to use a lower alpha cut off when you increase your sample size if you are trying to test if your sample's rate of disease is different from rate of disease in the population. If you get a p value less than your alpha, you can conclude that there is evidence to support a different rate of disease, and thus a different negative predictive value or positive predictive assuming that a test has the same rate of false positives and negatives in both populations.

 

[Phloston]

Thanks so much. I really appreciate the thorough response. That's pretty much exactly what I needed to hear.