MEDSTATS 3: Standard errors and confidence intervals..
how do we use the normal distribution to work out whats normal?
-Observe a value e.g. BP and then work out on the graph how many standard deviations above or below the mean the observed value is -If the measurement is within two standard deviations of the mean we say the measurement is in normal range if not then the result is atypical
how doe we interpret CI for a risk difference?
-Remember that Risk difference=Risk in treatment group-risk in control group -A risk difference of 0 is therefore interpreted as the null value-ie there is no difference in risk between treatment and control groups -If a 95% confidence interval for a risk difference is below 0 then we are 95% certain that the risk in the treatment group is less than the risk in the treatment group.
what is the Z score?
Instead of looking at the normal distribution curve graph to work out how many standard deviations away from the mean a value is, we can use the Z value Z value gives us the number of standard deviations away from the mean that a value is-values with z score between -2 and +2 are fairly typical (95% of values will lie within these ranges) Z value=(value-mean)/SD
how do we interpret the CI for a relative risk?
Remember that relative risk is the ratio of risk in treatment group/risk in control group A RR of 1 is therefore interpreted as there being no difference in risk between the treatment and control groups. For relative risk one is therefore known as the NULL VALUE (the value representing no difference between two comparison groups) If a 95% confidence interval for a Relative risk is below 1 then we are 95% certain that the risk in the treatment group is less than the risk in the control group.
what is the normal distribution?
-a type of frequency distribution which is symmetrical and unimodal it is a theoretical distribution which has a specified shape -a few medical measurements have distributions close to the normal distribution -Normal distributions are symmetric about the mean and their spread/width is determined by the standard deviation. -68% of observations lie within 1 standard deviations of the mean -95% of observations lie within 1.96 standard deviations of the mean -99% of observations lie within 2.58 standard deviations of the mean. -Helps us determine what is NORMAL
how do you work out the confidence interval using standard error
-using an example of Vioxx, 3.7 per 1000 patients treated with Vioxx had an MI (standard error 0.6) 95% confidence interval for this group would be rate of occurrence+/-1.96*Standard error so....3.7+/-1.96*0.6=(2.5,4.9) We are thus 95% certain that the true rate of MI in those treated with Vioxx is between 2.5 and 4.9 per 1000. 1 per 1000 patients not treated with vioxx had an MI (standard error 0.3) 1+/-1.96*0.3=(0.4,1.6) We are thus 95% certain that the true rate of MI in those in the control group is between 0.4 and 1.6.
what if the Confidence Interval includes the null value (1 for relative measure 0 for a difference)
-we cannot automatically conclude that there is no difference in risk between the two groups -it might just be that the sample size was too small to demonstrate a difference.
what is the confidence intervals?
It is difficult to use standard errors in a study thus they are converted to Confidence intervals which describe a range of values either side of the observed study result Because it is known that sampling variability leads to a normal distribution of test results (with the variability given by standard error) we use the knowledge we have about the normal distribution to compute confidence intervals. (remember that 95% of observations lie within 1.96 SD's of the mean and 99% of observations lie within 2.58 SD's of the mean) 95% Confidence interval=The range of values that lie between 1.96 standard error below the result and 1.96 standard errors above the result-we can be 95% sure that the true value of effect lies within this interval 99% confidence interval=the range of values that lie between 2.58 standard errors below the result and 2.58 standard errors above the result. we can be 99% sure that the true value of effect lies within this interval.
what is the difference between standard deviation and standard error? where will these be recorded on the study?
STANDAR ERROR=basically the same as standard deviation, it also describes variability but instead of variability in patient characteristics it describes variability of the treatment effect so tells how certain our estimate of treatment/exposure effects is you'll find standard error in the results table (if anywhere, often hidden as Confidence intervals) -tells us how far on average the true value (say of treament effect) is likely to be from the study result. -Standard error also uses the normal distribution so 95% of observations lie within 1.96 standard deviations of the mean) STANDARD DEVIATION=used to describe variation in patient characteristics-youll find this in the baseline/patient characteristics table e.g. if we measured the birth weight of 100 newborn full term infants we would observe that the mean birth weight is close to 3.5kg and the standard deviation is 0.5kg so from these quantities we could say that 68% of the sample had a birth weight between 3kg and 4kg (ie. within 1 SD of the mean)
what is the standard error?
basically when we do a study, is the sample that is studied is representative it is then assumed that results observed in the study will occur in the long run when the treatments are used in future patients like those used in the study. However, if the study is repeated it is highly likely that the result observed would be close to but not exactly the same as the first study this is because different people will be studied who have different responses to the intervention- this is called SAMPLING VARIABILITY The consequences of this is that we cannot exactly predict what will happen in the long run BUT we can work out how close to the truth we are likely to be. The variability of repeated study results represented with the standard error
