Lecture 28: Confidence Intervals Flashcards
Single value most likely to represent the true difference between experimental & control treatments
point estimate
the actual measurement you get (the single
value)
– The calculated RR
– If you were to redo the study over and over, your point estimate would
likely be different every time, due to random error
If you were to redo the study over and over, your point
estimate would likely be different every time, due to random error
• Provides the range of values within which one can be confident (to 95%) that the point estimate will fall into in repeated experiments
confidence interval
Confidence Intervals vs p-Value
- CIs indicate the strength of the evidence about quantities of direct interest and this is why the CI approach is preferred
- p value is a measure of the strength of the evidence against the null hypothesis of “no effect”
• p value contains no information about the size of the
difference or the direction, only whether this difference is statistically “significant”
plain lang interpretation
read
• People wearing compression socks were 90% less likely to develop symptomless DVT than
those wearing regular socks (point estimate)
• The data is consistent with a benefit as large as a _____reduction, or a small as a
____reduction. (95% CI)
• This difference is large, statistically significant, and precise.
Interpreting the 95% CI
Remember RR of 1 means no difference between groups
– So if the CI cross 1, some of the time there will be no difference between groups and therefore the groups are NOT statistically significantly different
– However, statements like “duct tape is effective for treatment of warts” or “duct tape is not effective for treatment of warts” based on the dichotomous interpretation of 95% CI can sometimes be misleading…
check to see if the conf interval contains 1
what determines width of conf interval?
the larger the abs number of events, the ________ the confidence intervals and the more _________ the results
the larger the abs number of events, the smaller the confidence intervals and the more precise the results
Generally, as you increase sample size, you will end up with more events
Sometimes you get very rare events where you need to study thousands or 10s of thousands people in order to get those events to occur
Increase sample size and you will end up with imprecise estimate on effect
Confidence intervals can be reported on
– Categorical data
– Continuous data
• If the investigators do not report CI, look at the p-value
what 2 factors lead to imprecision?
• Small sample size
– Small number of events
• Wide confidence intervals
– Uncertainty about magnitude of treatment effect
Not precise if it crosses the line of no effect - NOT TRUE
Even tho it may cross that line, conf interval can still be very narrow and precise and shows no treatment effect
how do you decide what is too wide?
Decision threshold: pt oriented research suggest we need to prevent 10 strokes in 1000 pts (ARR of 1%) to be worth the increased bleeding risk), suggested by pt
Bottom line: if Cl crosses decision threshold, results are not sufficiently precise
If Cl does not cross decision threshold, results ar e sufficiently precise
When there is no treatment effect (i.e. ARR = 0) what is the
NNT?
infinity
If it crosses infinity, there is not statistically signifcant difference
how can you calculate NNT from ARR
• The 95% CI for the NNT is obtained by taking the reciprocal of the values for the ARR
– E.g. ARR 10% (95% CI: 5% to 15%)
– NNT = 10 (95%CI: 6.7 to 20)
What happens when the confidence interval is wider? – E.g. ARR 10% (95% CI: -5% to 25%) – NNT = 10 (95%CI: -20 to 4) • NNT of -20 means \_\_\_\_\_\_\_\_\_ • NNT of 4 means\_\_\_\_\_\_\_\_ • NNT of ARR= 0 is \_\_\_\_\_\_\_\_\_\_
treatment is harmful
treatment is helpful
infinity
conf int is centered around infinity
