Download Understanding Statistics in Research Articles

Understanding Statistics in Research Articles
Elizabeth Crabtree, MPH, PhD (c)
Director of Evidence-Based Practice, Quality Management
Assistant Professor, Library
Statistics – definition and concepts
Statistics are used to describe something, or to examine
differences among groups, or relationships among characteristics
– Descriptive Statistics
• Mean and median
• Standard deviation
– Inferential Statistics
•
•
•
•
•
•
Statistical significance – p-value
Confidence intervals
Odds ratio
Relative Risk
Sensitivity/Specificity
Positive/Negative Predictive Values
Mean and Median
What’s the average cost of a house in this neighborhood?
Mean and Median
What’s the average cost of a house in this neighborhood?
Mean value: $1,009,000
Mean and Median
What’s the average cost of a house in this neighborhood?
Median value: $10,000
Standard Deviation
How spread out is the data from the mean?
The P value
Taking statistics to the next level…
“factors that raise your chance of divorce
include living in a red state, having twins, and
contracting cervical or testicular cancer…”
differences between groups
relationships between things
Testing for significance
Sample size
Findings
Characteristics of population
Testing for significance
Sample size
Findings
Characteristics of population
Confidence Intervals: another (and maybe
better?) test for statistical significance
Confidence intervals provide information about a range in which the true value
lies with a certain degree of probability
Risk Factors for Deep Vein Thrombosis and
Pulmonary Embolism (Heit et al., 2000)
Objective: To identify independent risk factors
for deep vein thrombosis and pulmonary
embolism and to estimate the magnitude of risk
for each.
Results: “Independent risk factors for VTE included
surgery (odds ratio [OR], 21.7; 95% confidence
interval [CI], 9.4-49.9), ….”
Interpreting the Results
What does odds ratio 21.7 (95% CI 9.4-49.9)
mean?
– We can be 95% confident that the odds ratio will
fall between 9.4 and 49.9 if the study were
replicated
– OR if we performed the study 100 times, the odds
ratio would be between 9.4 and 49.9 in 95 of the
studies
P-values vs. Confidence Intervals
P-values
Confidence Intervals
Clearer than confidence
intervals
Result given directly at level of
data measurement
Allow for rapid decision as to
whether a value is statistically
significant (binary response)
Provide info about statistical
significance as well as direction
and STRENGTH of effect
May be overly simplistic (really Allow for assessment of
much difference between 0.04 clinical relevance
and 0.06???)
Statistical significance and clinical relevance: one in the same?
Odds ratio compares whether the odds of a certain
event happening is the same for two groups
The odds of an event happening is found by taking the odds the event will
happen/odds the event will not happen
– An odds ratio of 1 implies the event is equally likely in both groups
– An odds ratio > 1 implies the event is more likely in the first group
– An odds ratio < 1 implies that the event is less likely in the first group
Males and Females on the Titanic
Alive
Dead
Total
Female
308
154
462
Male
142
709
851
Total
450
863
1313
The odds ratio compares the relative odds of death in each group. For females
the odds were 154/308=0.5 (or 2 to 1 against dying). For males the odds were
almost 5 to 1 in favor of death (709/142=4.993). The odds ratio then is
4.993/0.5=9.986. There is a 10 fold greater odds of death for males than for
females.
Relative Risk (sometimes called the risk ratio)
compares the probability of death in each group
Alive
Dead
Total
Female
308
154
462
Male
142
709
851
Total
450
863
1313
Relative Risk comes closer to
what most people think of when
they compare the relative
likelihood of events, but
sometimes it is not possible to
compute RR in a research
design.
In the case of our
Titanic example,
the probability of
death for females
is
154/462=0.3333.
For males the
probability is
709/851=0.8331.
The RR is then
0.8331/0.3333=
2.5. There is a 2.5
greater
probability of
death for males
than females.
Interpreting Relative Risk
Relative
risk=1
When the relative risk is one, the risk in the exposed group is the
same as the risk in the unexposed group. There is indication of
neither benefit nor harm.
Relative
risk<1
When the relative risk is less than one then the exposure is
associated with a protective effect.
Relative
risk>1
When the relative risk is greater than one, then the exposed group
have greater risk of contracting the disease, so the exposure is
associated with harm.
Huh? Odds and Probability Explained
Example: for every 3 attempts there will be one
successful outcome
The language differs:
“one to two” is an odds; expressed as the number;
0.5
“one in three” is a probability; expressed as a
fraction; 1/3
Risk Factors for Deep Vein Thrombosis and
Pulmonary Embolism (Heit et al., 2000)
Objective: To identify independent risk factors
for deep vein thrombosis and pulmonary
embolism and to estimate the magnitude of risk
for each.
Results: “Independent risk factors for VTE included
surgery (odds ratio [OR], 21.7; 95% confidence
interval [CI], 9.4-49.9), ….”
Interpreting the Results
What does (OR 21.7, 95% CI 9.4 – 49.9) mean?
– Patients who have had surgery have a 21.7 to 1
odds of developing a venous thromboembolism,
compared to patients who have not undergone
surgery
– We can be 95% confident that the odds ratio
would be between 9.4 and 49.9 if the study were
repeated
Sensitivity and Specificity
• Sensitivity is the proportion of true positives that are
correctly identified by a test or measure (e.g., percent of
sick people correctly identified as having the condition)
• Ex: If 100 patients known to have a disease were tested, and 43
test positive, then the test has 43% sensitivity.
• Specificity is the proportion of true negatives that are
correctly identified by the test (e.g., percent of healthy
people correctly identified as not having the condition)
•
Ex: If 100 patients with no disease are tested and 96 return a
negative result, then the test has 96% specificity.
Relationship between results of liver scan and
correct diagnosis: sensitivity/specificity
Liver Scan
Abnormal
Normal
(+)
(-)
Total
Abnormal
231
32
263
Normal
27
54
81
Total
258
86
344
How good (sensitive/specific) is the liver scan at diagnosing abnormal
pathology?
There are 258 true positives and 86 true negatives. The proportions of these two groups
that were correctly diagnosed by the scan were 231/258=0.90 and 54/86=0.63.
We can expect that 90% of patients with abnormal pathology to have abnormal (positive)
liver scans: 90% sensitivity.
We can expect that 63% of the patients with normal pathology to have normal (negative)
liver scans.: 63% specificity.
Patients and clinicians have a different question…
Positive and Negative Predictive Values
• Positive predictive value is the probability that a
patient with a positive test result really does have
the condition for which the test was conducted.
• Negative predictive value is the probability that a
patient with a negative test result really is free of
the condition for which the test was conducted
• Predictive values give a direct assessment of the
usefulness of the test in practice
– influenced by the prevalence of disease in the population
that is being tested
Relationship between results of liver scan and
correct diagnosis: +/- predictive values
Liver Scan
Abnormal
Normal
(+)
(-)
Total
Abnormal
231
32
263
Normal
27
54
81
Total
258
86
344
Of the 263 patients with abnormal liver scans 231 had abnormal pathology, giving the
proportion of correct diagnoses as 231/263 = 0.88. Similarly, among the 81 patients with
normal liver scans the proportion of correct diagnoses was 54/81 = 0.67.
Prevalence, Predictive Values and Sensitivity/Specificity
Analysis of liver scan data with prevalences
of abnormality of 0.75 and 0.25
Prevalence
0.75
0.25
Sensitivity
Specificity
Positive predictive value
Negative predictive value
0.90
0.63
0.88
0.67
0.90
0.63
0.45
0.95
Total correct predictions
0.83
0.69
Acknowledgements
Dr. Charles Macias, lecture, Evidence-based
medicine: why does it matter?
Texas Children’s Hospital Evidence-Based
Outcomes Center Evidence-Based Medicine
course handouts
Texas Children’s Hospital Lean Six Sigma Green
Belt Certification material
Craig Hospital, Those Scary Statistics!