U5

(ppt, p. 4-5)

Relative Risk (RR)

(probability)

• AKA: probability (of a good or bad result) (Cullum, 2000 p111)
•  
• Term used when referring o the probability of either a good or bad event
• The risk of an event in the intervention group (Rⁱ) is simply the proportion of people in that group who experience the event.
• The strength of the association between the intervention and the outcome is usually represented y the relative risks or adds ratios
• Relative Risk or Risk Ratio (RR) is the proportion of the original risk that is still present when patients receive the intervention
• The proportion of risk that is still present when patients receive the intervention or exposure.
• Studies providde estimates of the true risk of an outcome
  • An RR provides and estimate of the risk of a given outcome
  • tells the relative benefit of treatment, NOT the “actual” benefit
  • not consider # Ss who would developed outcome anyways
• The risk of patients in the intervention or exposed group experiencing the outcome divided by the risk of patients in the control or unexposed group experiencing the outcome
• Proportion of patients experiencing an outcome in the treated (or exposed) group divided by the proportion experiencing the outcome in the control (or unexposed) group (text, glossary)
• Risk of Ri group divided by risk Rc group (Sheldon, 2000 p76)
• Equations
  • [a/(a+b)] / [c/(c+d)]
  • Also… Ri / Rc  
  • Also… EER / CER
• Calculate the risk of readmission in the Intervention Group:    a / (a+b) = 12 / 84 = 0.143 or 14.3%
• Calculate the risk of readmission in the Control Group:           c / (c+d) = 26 / 81 = 0.321 or 32.1%
• Now, compare the two by dividing Intervention by Control       = 0.143 / 0.321 = 0.445 or 44.5%
  • (If RR=1.0 then there is no difference between groups; the risk of event/outcome is the same in both groups).
  • If RR is on the right side of vertical line (RR >1) would favour the CTRL condition
• o   RR on the left (RR <1) favours the treatment.
• If the risk of a bad outcome is reduced by the intervention compared to the control group, then RR < 1.0.
• If risk of a bad outcome is increased by the intervention compare to the control group, then RR > 1.0.
• The further away the RR is from 1.0, the greater the strength of the association between the intervention and outcome
• Statement: The relative risk of readmission of the Intervention group is 44.5% compared to the Controls
• Statement: over 7 years, the risk of dying after admission to a stroke unit was 0.67 or 67% of the risk of dying after admission to a medical ward.
•  

U5

(text p.77-8, 79, 180-2, 189-90, 198-200, 174) (ppt, p. 5-2)

Odds Ratio (OR)

[(a/b) - (c/d)]

• • Describes the odds of a patient in the Ri group having an event divided by the odds of a patient is the Rc having the event

  • Or the odds that a patient was exposed to a given risk factor divided by the odds of that a control patient was exposed to the risk factor

  an estimate of the odds of having an event versus not having an event

   • The odds of an event in the intervention or exposed group divided by the odds of the event in the control or unexposed group

  • If (OR = 1.0) then there is no difference between groups; the odds of the event is the same in both groups).

  • If (OR < 1.0) then the outcome/event is less likely in the intervention or exposed group compared to the control or unexposed group

  • The odds of the outcome (event) in the Ri group divided by the odds of the Rc group

  First, calculate the odds of readmission for the Intervention = a / b = 12 / 72 = 0.167

  Then, calculate the odds of readmission for the Control = c / d =    26 / 55 = 0.473

  Finally, divide the odds of the Ri by the Rc = (a / b) / (c / d) = 0.167 / 0.473 = 0.353

  So, the odds of readmission for the intervention group are 0.353 times that of the control group (or 35.3% of the odds of the control group)

  • (a/b) / (c/d)

  • Also… (ad) / (bc)

• a measure of the strength of association between the Tx and the outcome
• a measure of effect in studies of causation
• The odds of an event in the intervention/exposed group divided by the odds of the event in the control/unexposed group 
• the odds that a Ss was exposed to a given risk factor divided by the odds that a Ctrl was exposed to the risk factor.

  ---

• the outcome expressed as the ____ of the event (a/b)
• The ____ ____ is the odds of the event in the Tx group (a/b) devided by the odds of the event in the Ctrl group (c/d)

• an ____ ____ of 1.0 means there is no difference between groups
  • the odds of an even are the same
• an ____ ____ <1.0 means the event is less likely in the Tx group than the control group

  ---

• When the event being measured is quite rare, the OR and RR are numerically similar because the values of a and c are insignificantly small

• odds of death in Tx group
• odds of death in Ctrl group

U5

(ppt, p. 5-3)

Number Needed To Treat (NTT)

• The number of ppl needed to treat with the intervention, over a specific period of time, to prevent one additional adverse outcome; or promo one additional good outcome
• Number of patients who need to be treated to prevent one additional negative outcome (or to promote one additional positive evenT)
• This is calculated as 1/ARR (rounded to the next whole number), accompanied by the 95% confidence interval.

• How many people would we need to treat to prevent one adverse event (or improve one patient’s outcome)?
• In other words, how many asthmatics would have to see the Specialist Nurse in order to prevent one of them from being readmitted?

  ---

• We calculated the ARR to be 17.8% (which we will round to 18)
• This means, that for every 100 patients who see the Specialist Nurse, 18 will avoid readmission
• How many will we have to treat to avoid 1 readmission?
• NNT = 1 / ARR = 1 / 0.18 = 5.6 
  • (always round up)
• So, for every 6 asthmatics who see the Specialist Nurse, we prevent 1 of them from being readmitted

U5

(ppt, p. 6-3)

Confidence Intervals (CI)

• AKA: confidence limits (Cullum, 2000 p112)
• A 95% CI > Rr is 95% sure of the true treatment effect. (Cullum, 2000 p112)
• If larger sample size > higher precision > narrower width of 95% CI. (Cullum, 2000 p112)

  ---

• Instead of p-values, many studies are now reporting ____ ____
• ____ ____ also help us understand whether a study finding is statistically significant or not
• The benefit of confidence intervals is that they help us to interpret the clinical significance of the findings as well
• When we observe a difference between the Intervention and Control Groups, the Confidence Interval asks “What is the range of differences between the two groups within which the we would find the true difference?”

  ---

•  If we go back to our original Weight Loss example, we provided a point estimate (means) for both the Drug Group and the Control Group
• We ran a t-test to see if those means were statistically different
• But instead of comparing 2 points, we can expand the results and compare 2 intervals
• These intervals will take into account 95% of the variance represented by our Means
•  We are 95% confident that this interval contains the population mean

• Our Drug Group had a Mean weight loss of 14.4 lbs
• The 95% CI is 10.9 to 17.9
• We are 95% confident that this interval contains the true weight loss of the whole population if they took the drug

[image]

• Our Placebo Group had a Mean weight loss of 7.3 lbs
• The 95% CI is 5.4 to 9.2
• So, we are 95% confident that this interval contains the true weight loss of the population without the drug

[image] 

• Now we compare the confidence intervals to each other
• Drug Group = 10.9 to 17.9
• Placebo Group = 5.4 to 9.2
• Because the Upper Limit of the Placebo Group fails to exceed the Lower Limit of the Drug Group, we can conclude that there is a difference between the two groups

U5

(pp, 2-6)

Mean Difference

(aka: mean effect size)

• Mean is the “average value” from a data set
  • It is a single number that summarized a mass of data points and allows for easy comparison between groups.However, it is sensitive to extreme scores

U5

(Chapt 12)

Statistical Significance

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()

Clinical Importance

U5

(ppt, p.2-6) (Cullum, 2000 p73)

Mean

(mean effect size)

• Mean is the “average value” from a data set
• It is a single number that summarized a mass of data points 
• _____ allows easy comparison between groups.

  ---

• However, _____ is sensitive to extreme scores 

U5

()

Median

U5

(pp, slide 2-6)

Standard Deviation

• Average amount individual values differ from the mean of the group (Cullum, 2000 p73)
• ____ ____ (SD) is the most common measure of variance
• SD describes how far the values stray from the Mean
• A small SD will indicates scores are closer to the Mean
• a large SD indicates scores are scattered over a wider range around the mean
• Smaller is better! Watch to see how close the SD value is to the mean
• Lower SD = smaller spread of values (Cullum, 2000 p73)

U5

(ppt, p. 4-1) (Text p.73)

Discrete Outcome

• To compute ____ ____ measures of association, we “count bodies” that belong to different categories
• We look at these variables in terms of proportions and we use a 2 x 2 table

• measures used for discrete outcomes:
• Relative Risk (RR)
• Relative Risk Reduction (RRR)
• Absolute Risk Reduction (ARR)
• Odds Ratio (OR)
• Number Needed to Treat (NNT)
• Number Needed to Harm (NNH)

U5

(ppt, p2-5) (Cullum, 2000 p72)

Continuous Outcome

• The weight loss study example involves continuous data 
  • (i.e., body weight measured in lbs or kilo)
• To analyze our results, we would look at the two groups as a whole by calculating the Mean and Standard Deviation (SD) for each group
• Our Drug (Intervention) Group of 25 people had a mean weight loss of 14.4 lbs (SD=8.5)
• Our Placebo (Control) Group of 25 people had a mean weight loss of 7.3 lbs (SD=4.5)
• It looks like there is a difference, but is it a True difference?

U5

(text p104, 142, )

Precise (precision)

• How precise is the estimate of treatment effect? (Cullum, p104)
• A large number of subjects increases precision (Cullum, p104)
• CI’s around the RR and the RRR indicate
  • The precision of the estimate of true treatment effect
  • Wide CIs = less precision in the estimate
• Precision increases with larger sample size

U5

(ppt, p9-2)

What is Precision of

the study Findings?

• Precision of study findings is indicated by the width of the CI:
  • The wider the CI, the less precise our study finding
  • The narrower the CI, the more precise our study finding
• Precision of study findings depends on the Sample Size of the study:
  • The smaller the Sample Size, the wider the CI and the less precise the study finding
  • The larger the Sample Size, the narrower the CI and the more precise the study finding

U5

(ppt 1-2)

Null Hypothesis

U5

()

Alternative (research) hypothesis

U5

(ppt 1-6) (glossary)

p-value

U5

(ppt 1-6)

Type I error

(false-positive)

• A mistake some researchers make is claiming there is a difference between their groups when there isn’t one. This is called Type I Error
• To help combat this, researchers will declare a statistic called the alpha level, which is the probability they accept of making this error (e.g., <0.05, or < 5%)
• If we can produce a small enough alpha level, we will be more confident that there is no Type I error, and therefore, that the difference between groups is a true difference that is related to our intervention.

U5

(ppt 2-3,4)

Type II error

(false-negative)

• AKA “False-Negative”
• Occurs when we conclude the tx has no effect, when it really does
• This is called Type ___ Error
  • E.g., It is possible at the end of our weight loss study that the Drug Group lost more weight than the Placebo Group, and this difference occurred because of the drug
  • But, to our disappointment, p = 0.06
• The most common reason for Type II error is a Sample Size that is too small
  • Most statistical tests require a large number of observations in order to detect a true difference
• The ability to properly detect a true difference when it exists is called Power
• The easiest way to increase Power is to increase Sample Size 
  • The larger the Sample Size, the greater the Power, which results in less risk of Type II

U5

(ppt 2-4) (glossary)

Power

• The ability to properly detect a true difference when it exists is called Power
• The easiest way to increase Power is to increase Sample Size 
  • The larger the Sample Size, the greater the Power, which results in less risk of Type II

U5

(pp, p3-1)

t-Test

• ___ ___ Used to compare [variable] between 2 groups (e.g. males or females; Drug or Placebo) in terms of some continuous variable (e.g. mean weight or height)
• A t-Test is designed to determine & compare if the difference between mean values of 2 groups is statistically significant

•  used to compare a [variable] b/w 2 groups
  • Limitation: only looks at 2 groups

U5

(ppt, p. 3-6)

Chi-Squared Test

(c2)

• the most common nonparametric test 
• used to measure the statistical significance of an association between 2 nominal (categorical or dichotomous) variables
• It determines the difference between the observed and expected frequencies of the occurrence of the variables and creating a variance term
• deals with dichotomous variables (yes / no)

U5

(ppt p3-2)

ANOVA

(Analysis of Variance)

• ANOVA: Used to compare 3 or more groups 
  • (e.g. single/married/widowed; Drug 1/Drug 2/Placebo) when their variable is continuous (e.g. mean weight or height)

• ---

• t-Test used when only two groups

U5

(ppt, p.4-6) (U43,4,6,7,8) Statistic Summary)

Relative Risk Reduction

• ____ ____ ____ = (1.0 - RR)
• An estimate of the proportion of baseline risk that is reduced by the intervention
• Easy to calculate
• 1.0 – Relative Risk = 1.0 – 0.445 = 0.555 or 55.5%
• This means that the Specialist Nurse (Intervention) decreased the risk of hospital readmission by 55.5% compared with Regular Care 

U5

U3,4.5.7,8) statistics summary

(ppt, p. 5-1 (text, p. 78, 79, 122-3))

Absolute Risk Reduction (ARR)

 [c/(c+d)] - [a/(a+b)]

• The absolute arithmetic difference in rates of harmful outcomes between Ri and Rc groups
• takes into account the basement risk of patients 
• provides more detailed info than RRR
• The proportion of patients that will be spared an adverse outcome if they receive the intervention
  • I.E. the risk of a bad outcome is reduced this much by the intervention
• NOTE:  ARR uses absolute value (no sign)
• Telss us what percent of patients  will be spared the adverse outcome if they receive the intervention
• Caluculate th risk of readmission in the Control group: c/(c+d)
• Calculate the risk of readmission in the Intervention group: a/a+b
• Now > subtract the Intervention from the Ctrl: Ri - Rc
• statement: _x_% of asthma patients will not be readmitted to the hospital if they receive the special nursing care
• ** be aware of the ___ ___ ___ of an event when trying to assess the importance of a finding expressed as an RR or RRR.

• ---

U5

(ppt, p. 5-4)

Number Needed to Harm (NNH)

• •             the number of patients who, if they receive the intervention, would result in one additional patient being “harmed”

  •               The number of people who, if treated with the intervention, would lead to one additional adverse event or peron being harmed over a specific period of time

  •               Could be the case if the intervention is LESS effective than the control condition

  •               Could be used to express harmful effect of an otherwise beneficial intervention

  •                

  •               Calculation is the same as NNT (1/ARR)

  •               (remember we use the absolute number for ARR)

  •               To decide whether you are calculating NNT or NNH, you need to look at the event rates in each group (e.g., your 2X2 table) and determine whether:

      a) a higher proportion of patients in the intervention group experienced a good outcome:  calculate an NNT

      b) a higher proportion of patients in the intervention group experienced a bad outcome: calculate an NNH

  •               NNH is used in conjunction with NNT because while treatments may be designed to have positive outcomes, they are often also associated with adverse effects (or negative outcomes)

  ◦                                 EXAMPLE: Daily aspirin is often recommended for those at risk of stroke to reduce their risk (a positive outcome); however, daily use of aspirin may also cause internal bleeding (a negative outcome)

  •               Consider that a common way to decrease the chances of a stroke is to take blood thinners

  •               Two common blood thinners are Warfarin and Aspirin, both of which have been proven to reduce the risk of stroke

  •               The NNT for Warfarin is 37 while for Aspirin it is 67

  •               Which is better? Warfarin, because it has a positive impact on every 37 people who take it while Aspirin has a positive impact on every 67 people

  •                However, this is only one side of the picture

  •               What if the NNH of Warfarin is 10 while the NNH of Aspirin is 90?

  •               Now, Warfarin is not looking too good

  •               In words, this means that for every 10 people treated with Warfarin, one will have internal bleeding

  •               If the NNH is substantially lower than the NNT, the risk-benefit ratio  would argue against the use of that drug or treatment

  •               1.0/ARI ARI (absolute risk increase); the risk of a bad outcome is increased by the intervention

  •               also, 1.0/[c/(c+d)] - [a/(a+b)]

  •               also, 1/[CER-EER]

U5

(ppt, p. 7-3)

Interpreting CI's

• When we look at CIs OF CONTINUOUS DATA, we need to think of three things:
  • 1) Does it cross 0?     
  • 2) How wide is it?     
  • 3) Where are the limits?

Line A

• Does not cross 0 à there is a difference; statistically significant
• The width is quite narrow à the sample size is large and the results are more precise
• The lower limit is not far from the upper limit à the true value falls within a tight range which increases precision

• Does not cross 0 à there is a difference; statistically significant
• The width is quite wide à the sample size is small and the results are less precise
• The lower limit is far from the upper limit à the true value falls within a wide range which decreases precision; hard to make a clinical decision because the true value may be close to 0 or it may be very large

• Does cross 0 à there is NOT a difference
• The width is quite wide à the sample size is small and the results are less precise
• The lower limit is far from the upper limit à the true value falls within a wide range which decreases precision; but, the upper limit is very positive so there may be something to this intervention

• Does cross 0 à there is NOT a difference
• The width is quite narrow à the sample size is large and the results are more precise
• The lower limit is not far from the upper limit à the true value falls within a tight range which increases precision
• §The concept is the same for Dichotomous Data like Relative Risk

U5

(ppt, p. 7-3)

Interpreting CI's

• When we look at CIs OF CONTINUOUS DATA, we need to think of three things:
  • 1) Does it cross 0?     
  • 2) How wide is it?     
  • 3) Where are the limits?

Line A

• Does not cross 0 à there is a difference; statistically significant
• The width is quite narrow à the sample size is large and the results are more precise
• The lower limit is not far from the upper limit à the true value falls within a tight range which increases precision

Line B

• Does not cross 0 à there is a difference; statistically significant
• The width is quite wide à the sample size is small and the results are less precise
• The lower limit is far from the upper limit à the true value falls within a wide range which decreases precision; hard to make a clinical decision because the true value may be close to 0 or it may be very large

Line C

• Does cross 0 à there is NOT a difference
• The width is quite wide à the sample size is small and the results are less precise
• The lower limit is far from the upper limit à the true value falls within a wide range which decreases precision; but, the upper limit is very positive so there may be something to this intervention

Line D

• Does cross 0 à there is NOT a difference
• The width is quite narrow à the sample size is large and the results are more precise
• The lower limit is not far from the upper limit à the true value falls within a tight range which increases precision
• The concept is the same for Dichotomous Data like Relative Risk

[image]

• The three questions of interpretation are the same but with one slight change:
  • 1) Does it cross 1?     
  • 2) How wide is it?     
  • 3) Where is the lower limit or upper limit?
• Remember, for statistics like Relative Risk and Odds Ratio, the “no difference” line is 1.0
• On our previous slide, only two CIs are significant
• Notice that the larger the sample size, the more narrow the CI which means the results are more precise
• And note that the wide CIs make it difficult for us to decide if the Intervention actually works

U5

(ppt, p8-2)

Using CI's to interp 

Positive Results

• Consider a trial to determine the effect of calcium supplementation (taken to reduce fractures) on myocardial infarctions (MI) in healthy postmenopausal women
• Results indicate that MI is more common in the calcium group than in the placebo group
• Relative risk is 3.5 and the 95% CI is 2.10 to 4.47
• This means that the risk of MI in the calcium group is 3.5 times higher than in the placebo group but that the true RR may be as low as 2.10 or as high as 4.47
• The CI does not include an RR of 1.0 which means the result is statistically significant
• Having determined that it is statistically significant, we next ask is it clinically significant?
• Here, we look at the smallest plausible effect of the intervention [i.e., lower limit of the CI (2.10)].
• This means that women who take calcium are twice as likely to have an MI than those who don’t.
• This still represents an important clinical difference and we would want to inform our patients about this risk.

U5

(ppt, p8-4)

Using CI's to Interp

Negative Results

• Consider a trial in a neonatal intensive care unit that compared mortality rates of infants cared for by nurse practitioners (NPs) or pediatric residents
• The results show that 4.6% of the NP patients died while 5.9% of the residents’ patients died
• The RR is 0.78 and the 95% CI is 0.43 to 1.40
• This means that the risk of neonatal mortality is reduced in the NP group by 22%, but that the true RR could be consistent with a 57% reduction or a 40% increase in neonatal mortality in the NP group  
•  
• The CI includes an RR of 1 so the difference between groups is not statistically significant (negative trial)
• The trial failed to show differences between the 2 groups, BUT it also failed to exclude the possibility of important differences in neonatal mortality (because the CI was so large)
• Therefore, the recommendation would be that a larger study be conducted to address this question which would provide a more precise study finding
• In a negative trial, the CI can help determine whether the trial was definitely negative
  • If the boundary of the CI most in favour of the intervention excludes any important benefit, then the trial is definitely negative
  • If this boundary includes an important benefit, the trial has not ruled out the possibility that the intervention may be beneficial & a larger study is needed

U5

(ppt, p8-6)

Summary: Interpreting

Confidence Intervals

• CIs can tell us 3 things:
  • Is the difference between groups significant?
  • What is the precision of the study finding?
  • What is the clinical significance of the study findings?

U5

(ppt, 9-1)

is the difference

between groups Significant? 

• If comparing continuous data, ‘no difference’ in mean values is 0 
  • (e.g., 0 difference in mean weight loss indicates the 2 groups are the same)
• Since 0 indicates no difference, a CI containing 0 would indicate a non significant mean difference
• If comparing dichotomous data, then a “no difference” in RRs or ORs is 1.0 
  • (e.g., RR = 1.0 means that the risk of neonatal death in the NP group is the same as the risk of neonatal death in the resident group)
• Since 1.0 indicates no difference, a CI containing 1.0 would indicate a non significant ratio (RR or OR)

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(ppt, p. 9-3)

What is the Clinical Signif 

of the study findings?

• Once statistical significance has been established, the confidence interval is more informative than a p-value in helping us determine whether the difference between groups is clinically important
• Clinical importance is determined by examining the limits of the CI for the smallest plausible effect of the intervention and deciding whether this effect is large enough to warrant a change in practice

U5

(text p67, glossary)

(U3,5,6,8 Statistics Summary)

Nominal Variables

• Type of data: Discrete
• Nominal (categorical) variables are simply names of categories with no specific order.
• “data that exist as unordered, qualitative categories” (text, p297)
  • sex
  • ethnicity
  • religion
• Nominal variables that have only two possible values are referered to as dichotomous variables (text p67)
  • male/female/transgender (not dichotomous)
  • dead/alive
  • brown eyes/blue eyes
• Appropriate Statistics/Tests
  • Relative Risk / Relative Risk Reduction
  • Absolute Risk / Odds Ratio
  • Number Needed to Treat
  • Chi-squared test (X2 test)