BioStatsSHpt2 Flashcards
Statistical Analysis
We have a null hypothesis : No difference or association. when a researcher suspects something and wants to come up with a study. They come up with a null hypothesis. Null means zero. No association between 2 things. No correlation. It could be correct or incorrect, it doesn’t matter. If you do find a an association, it is purely due to chance. It’s the job of the researcher, to DISPROVE this null hypothesis, so they come up with an alternative hypothesis
Alternative Hypothesis : there is an association according to the study
Two types of error you can make. Type1 error: when there is no association but you thought there was. You saw an association that does not exist in reality. A false rejection of null hypothesis. Null hypothesis is rejected when it is true. A false rejection.
Eg) if i say I’m trying to figure relationship between statins and asthma. Null hypothesis : no association , statins do not cause asthma attacks. Alternative hypothesis : statins do causes asthma attacks. this is a type 1 error. We use letter alpha to represent type 1 error. You want alpha to be less than 0.5. That corresponds to p value of < 0.5. P value is probability of type 1 error.
Type 2 error
There is an association but you missed it.
Eg) statins and cholesterol level relationship. Null: statins do not do anything to cholesterol levels. You do the study and say i agree with null. You missed the association that exists. TYPE2 error. The letter designated is beta. The value the scientific community uses is 0.20. You don’t want the chance of the type 2 to be more than 0.20.
A false acceptance of null hypothesis
P value
Probability of type 1 error. We want it to be less than < 0.05 and when it is it’s statistically significant. A p value less than .05 ( 5% ). Chance of making a type one error is less than 5%. You saw an association that does not exist, -error ( you want this less than 5% )
Clinical significance
What you have found, does it make sense for the patient or not. Eg) new DM med and it brings A1C by .1 unit. 8.5 to 8.4. P value of 0.05 so statistically significant true. But is it clinically significant. 8.5 to 8.4 is not a big deal. So not clinically significant
Power
Power = 1 - Beta
1-.20 = power is a minimum of 0.80 or 80%. You wanna be able to find an association or a difference 80% of the time if it correctly exits. That’s the minimum power for a study to be considered important.
Power is the likelihood of not making a type 2 error.
Power increases as sample size increases, and 2nd ) when the association between the two things you’re measuring, when theres a strong association between the 2 is very noticeable or noticeable difference between the two, that increases the power
Confidence interval
When you collect your data and you get the mean of your data. That mean is based on only sample of the population and you got the mean. What if you do the study a second time with a second sample and get mean. It will probably be close to the first mean you got, but it will likely not be exactly the same. Close to it but slightly different. What if you do it a third time, and you notice it’s close to the first two but not exactly like the first two. If you do this 100 times you’ll end up an interval that should include your mean 95 /100 times. Why do we use confidence interval? Bc every time you do this your mean might be a little bit different. So it will be more accurate if you report your result with a confidence interval rather than a point value. That’s why we use a confidence interval.
Definition of a 95% confidence interval: the interval or the range that will include the true mean of your population 95% our of 100 times.
When you report the results or your study, you can report as a point value but it will be more accurate if you report as an interval.
RR with 95% confidence interval ( CI )
Relative risk = EER / CER
ASA case. RR reduction was 33 % in that case. That’s a point value estimate.
Second sample your value might a little different. Might be 35%. If you do this 100 times. 95 out of 100 times you’ll end up with an interval and you’d like this value to end up within this range. If you figure confidence interval was 21% to 45 % that means the RR reduction you found was 33 % however it could be as low as 21% percent or high as 45%. The interval is a more accurate that just saying I’m sure this one value is correct.
When you use CI interval range, there are times that it could help you with statistical significance. Cases that make your results to be statistically significant. 95% CI another way of determining statistical significance. Not just p value
Different parameters we use to report the results of a study.
RR / RRR/ Odds ratio
RR: relative risk was experimental event rate / Controlled event rate = EER / CER - a ratio. Rate of events in experimental group divided by rate of event of controlled group. If ratio is 1 then event on top ad bottom is the same. The med didnt do anything. No effect. Experimental and control the same.
What if relative risk of < 1.0 eg) RR = 0.67 that means the the rate of event in the experimental group was .67 times the rate of event in the control group
RR < 1 then you have reduced the event rate compared to the control group. When RR < 1 - experimental event rate on top is less than control event rate. That exp event rate was less.
If RR > 1 then numerator EER high that CER that has increased the event rate
RR applied with CI So instead of a point value we report as interval . Look at figure a on left. Blue circle is relative risk point value. You can see range of CI next to it. Whole interval is left of 1.0. Means it’s smaller than 1. When you have that, you can say the treatment reduced the event rate for sure. At least with 95% with CI for sure you can say that.
Figure B: blue circle is relative risk. Whole interval, The range is above 1.0. It means it has increased the event rate.
Figure C: interval part of is it less than 1.0 and part is more than 1.0: it means it might have reduced the rate, it might have stayed at zero, it might have increased the rate. You cannot draw a conclusion from that. If your CI crosses that 1.0 line, that means study is not statistically significant. You cant draw a conclusion from this.
RRR with 95% CI. Instead of RR we are talking about RRR and using the CI to talk about that.
Formula for RRR = 1 - RR.
What if reduction amount was zero. That means i did not reduce the RR by anything. Medication did not have an effect.
If RRR was a positive value, that means i did reduce the risk. What if RRR was a negative value ( then i have not reduced the risk i have actually increased the risk ).
With RR point of reference was 1.0. RR was a ratio. W/ RRR, 1.0 is no longer a point of reference. RRR = 1- RR, so point of reference here is zero. Figure D - RRR CI ( interval ) is bigger than zero. That means we reduced the risk. Figure E the whole interval is less than 0 so we increased the risk here. And figure F it crosses the zero so either reduced the risk or might have increased the risk or might have done nothing ( therefore this is not statistically significant. Figure D and F are statistically significant and figure F is not statistically significant.
Odds ratio with confidence interval
ODDs ratio formula = [ EER/ ENR ] / [ CER / CNR ]
If ratio is 1.0 top and bottom is same. No change in likelihood.
If ratio < 1.0 then likelihood has gone down.
If ratio > 1.0 then likelihood has gone up.
Let’s apply Confidence interval to it.
1.0 is reference. Look at figure CI range from 1.2 to 1.4. It has not crossed the line of 1.0. So this is statistically significant. Interval not crossing 1.0
In this figure odds ratio CI < 1.0 ( it’s 0.7 = blue circle range is .7 to .8). Whole ratio less than 1.0 and it’s reduced the likelihood.
Example 3) the odds ratio is 1.3, interval is 0.9 to 1.7 ( smaller than 1.0 to 1.7). So 0.9 means you’ve reduced the likelihood of outcome and 1.7 means you’ve increased the likelihood. No conclusion can be drawn so this is not a significant study.
Think of odds ratio CI such as this:
when you say range is 0.9 to 1.7, that means i might have reduced likelihood by 10 percent ( 100 % - 90% = 10 % ) or i might have increased the likelihood by 70 % ( 170% -100% = 70% ).
Anyhow that range has crossed the 1.0 reference line.
So remember for relative risk and odds ratio the reference is 1.0. Numerator on top and denominator on bottom. If ratio is 1.0 then means no difference. No change. No association.
RR is an amount of reduction so zero is the reference point.
Sensitivity
Specificity
4 cell table. Top left : True positive : means person has it and the test also says they have it.
False negative : has it but test missed it. : a type 2 error. There was correlation but we missed it. Designated with Beta
False positive: thought it was but wrong: type 1 error. Alpha
True negative: the test says doesn’t have it and person doesn’t actually it.
They way to calculate sensitivity : TP / ( TP + FN )
Specificity : TN / ( TN + FP )
