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Math
Statistics
Hypothesis Testing
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Gravity
Terms in this set (106)
Morbidity
"Any departure, subjective or objective, from a state of physiological or psychological wellbeing"
Two measures of morbidity (disease frequency in the population):
Prevalence
Incidence
Prevalence
a proportion or fraction of a population that has a disease or condition at a certain point of time
Mathematical equation for prevalence
# people with disease at a point in time/ # people in the study population
Incidence
A number of new cases of disease that develop during a specified time period in a population of individuals who are potentially at risk of developing a disease
what is incidence a measure of?
risk
mathematical equation for incidence
# of new cases of disease in a specified period/ people at risk in the study population
For the incidence equation what does the denominator represent?
people at risk
what group does people at risk not include
- people who already have a disease
- People who cannot get a disease (too old, too young, previously immunized, had previous surgery)
What does prevalence depend on?
depends on how many new cases occur & how long they remain cases
What is the mathematical equation for prevalence?
Incidence * Duration
Duration
time from occurrence to cure or death
When should you choose to to use incidence
- For studies of causes of disease (not affected by treatment, case-fatality rates)
- To estimate burden of diseases with short duration (e.g., IDs) - prevalence will miss recovered and dead cases
When should you choose to to use prevalence
- To estimate burden of diseases with long duration
what looking at the number of deaths in a specified time period what measures of mortality do you look at?
- All cause mortality
- Age-specific mortality
- Mortality rates from selected causes
Crude Mortality Rate
Total number of deaths from all causes per 1,000 persons in a population
What is the mathematical calculation for Crude Mortality Rate
# of deaths for all causes during a specific period/ # of persons in the population during that period x1000
Cause-Specific Mortality Rate
- Total number of deaths from a specific cause
What is the mathematical calculation for Cause-Specific Mortality Rate
# of deaths for a specific cause during a specific period/ # of persons in the population during that period x1000
Case-fatality rate:
Number of deaths from a specific disease by the total number of cases of that disease (measure of severity)
Infant mortality rate
Number of deaths in children under 1 year of age occurring during a one year period per 1,000 live births
For Relative Risk what is exposure (independent variable)?
(variable with potential causal characteristics):
- Risk factors
- Preventive factors
- Certain treatments
- Demographic/behavioral characteristics
For Relative Risk what is outcome (dependent variable)?
- Disease
- Side effects, Complications
- Death
- Cure
Relative Risk
comparison of the incidence in one group vs. another group
What is the mathematical calculation for Relative Risk
Incidence in exposed/ Incidence in unexposed
Strength of association for Relative Risk<1 means it has what effect?
Protective effect
Strength of association for Relative Risk=1 means it has what effect?
No association
Strength of association for Relative Risk>1 means it has what effect?
Positive association
How to convert relative risk to percents
(relative risk-1)*100
define Population
The general group of interest in a study
define Sample
A portion of the population that is selected
define Sample statistic
Sample statistic
define Population parameters
Quantities related to the population of interest
define Statistical estimation
Estimation of population parameters from sample statistics
Inferential statistics
consist of techniques that allow us to study samples and then make generalizations about the populations from which they are selected
Hypothesis testing
is a statistical method that uses sample data to evaluate a research hypothesis about a population parameter.
When the inferences about the population are made based on the sample there is always a possibility that a CHANCE (random variation due to sample selection) that what could be affected?
the results
Null hypothesis (Ho)
states that there is no change, no effect, no difference, or no relationship.
Alternative hypothesis (H1)
states that there is a change, a difference, or a relationship for the general population.
Non-directional Alternative hypothesis
(does not specify a direction of the effect) - most commonly used, more conservative
Directional or one-tailed test Alternative hypothesis
(specifies direction of association)
level of significance (alpha) for the hypothesis test.
- Probability of erroneously rejecting Ho when Ho is true (P of convicting an innocent defendant)
- Erroneously concluding that there is an association when one does not exist
What is the alpha usually set at?
alpha=0.05 (5%)
What is the alpha level?
-The level of statistical significance (maximum probability of making Type 1 error)
-Test statistic is compared to a pre-defined 'significance' level
Out of a one sided or two sided test which is more convention?
two-sided test
Why is a two sided test used
-It is more conservative
-No need to 'guess' the direction of association
-Even if an association occurred in the direction opposite from expected (e.g., aspirin increased the risk of MI), it will be tested
What does it mean when we Reject the null hypothesis
conclude that there is an association between independent & dependent variables (e.g., treatment had an effect)
What does it mean when we Fail to reject the null hypothesis
treatment doesn't appear to have an effect
What is a type 1 error (alpha)?
Rejecting null hypothesis when null hypothesis is true
What is a type 2 error (beta)?
Failure to reject a false Ho
What is power?
Probability of rejecting Ho when Ho is false (right action)
How do you calculate power?
1-beta
What is a p-value?
Probability of the result occurring by chance
The smaller the p-value the ________ results to be due to _______
less likely; chance
What does it mean if p<alpha?
rejects null hypothesis
Since the alpha is often set up at 5% (error rate) would a value of p<0.05 be significant or not?
it would be a statistically significant result
What is defined by priori (before you look at the data) and the probability f erroneously rejecting null due to chance?
alpha
What is found by a posteriori (result of data analysis)
p-value
P-value is compared with the ________ a to determine if the observed data are statistically significantly different from the null hypothesis
alpha
What does it mean if the p < 0.05 (when α = 5%)
reject Ho, results are statistically significant
What does it mean if the p greater than or equal to 0.05 (when α = 5%)
fail to reject Ho, results are not statistically significant
What does it mean when...
- when the null hypothesis has been rejected
- obtained result is unlikely to be due to chance
- No information about magnitude of association (effect size)!
- No information about clinical significance
When results are Statistically Significant
What are the 3 factors which influence p-values
1. Magnitude of association (e.g., how big is the difference between the study groups)
2. Sample size
3. Variation in the observed outcome
What are some things to remember about the factors that influence p-Values
• A cutoff of ≤ 0.05 for significance is arbitrary;
• No p-value, however small, excludes chance;
• No p-value, however large, mandates chance.
T or F: A statistically significant test never provides a clear 'yes' or 'no' answer to a question. It calculates probability.
True
T or F: A statistically significant association does imply causality
False
Is Statistical significance the same as clinical significance
no it is not necessarily the same
Factor that determine or impact the power of the study
• Sample size (n)
- Greater power for larger sample size
• Level of significance, Alpha value (α)
- Power decreases as alpha gets smaller (usually 0.05)
• Beta (type II error)
• Choice of statistical test used
• Variability (precision) of the outcome variable
- Greater power if variability is lower (smaller s.d.)
• Effect size
- Greater power for large difference between groups
Confidence Interval (CI)
-is a range of values that are likely to cover the true parameter
- is build around the point estimate (our best single number estimate)
- point estimate ± margin of error
What can a 95% Confidence Interval be used for?
- Can be used for hypothesis testing - Confidence Interval can indicate whether the results are statistically significant or not
95% CI provides an index of the variability in the group mean differences that would be expected by _______
chance
Difference b/w means = 0 means what?
no association (Ho is true)
If '0' is not included, with 95% confidence what can we conclude
conclude that means are different
Is the Mean difference = 30 mm Hg (95% CI: 12; 38) statistically significant?
statistically significant
IS the Mean difference = 30 mm Hg (-5; 40) statistically significant ?
not statistically significant because it goes through zero
What does a wide width of the confidence interval mean?
the wider the less precise
What are the Factors Affecting the Width of confidence interval?
1. The level of confidence
- The larger the level of confidence (e.g., 99% vs 95%) the larger the CI
2. Sample size
- The bigger the sample size (n), the smaller the CI
When RR=1 or OR=1, no difference between proportions it means what hypothesis is true?
null hypothesis is true
The higher the confidence level
the wider the confidence interval
What is another name for a screening test
medical surveillance
screening test
is a medical test or procedure performed on members (subjects) of a defined asymptomatic population or population subgroup to assess the likelihood of their members having a particular disease
What is an example of a screening test?
• Pap smear
• Mammography
• PSA
• Cholesterol level
• X-ray
Does a screening test diagnose an illness?
no it does not and people who test positive typically require further evaluation with subsequent diagnostic tests or procedures
What are the 3 values of a perfect test?
1.All individuals without disease give one uniform value on the test
2.All individuals with disease give a different, but uniform value on the test
3.All test results coincide with either the diseased or disease free group
What are some important factor of a perfect test?
• Perfectly discriminate between individuals with and without a disease
• No ambiguous test results
• Reliable regardless of test environment or operator
• Provide accurate results in all patient subgroups
What is the "The Gold Standard" for defining disease?
-That test whose results determine disease status, e.g. autopsy, tissue biopsy, or standard classification systems (DSM-5)
- Assumed 100% accurate or True
- Many diseases lack a true gold standard test
- New tests always compared to a gold standard test
What disease status is this question asking to define?
"I know my patient has the disease. What is the chance that the test will show that my patient has it?"
sensitivity
What disease status is this question asking to define?
"I know my patient does not have the disease. What is the chance that the test will show that my patient doesn't have it?"
Specificity
Sensitivity
The proportion of people WITH the disease who have a POSITIVE test
What disease status is this question asking to define?
"I just got a positive test result back on my patient. What is the chance that my patient actually has the disease?"
PPV (positive predictive value)
What disease status is this question asking to define?
"I just got a negative test result back on my patient. What is the chance that my patient actually doesn't have the disease?"
NPV (negative predictive value)
association
is a relationship between two or more variables. However, that relationship does not automatically mean that the change in one variable is the cause of the change in the other variable.
Causation
indicates that one event is the result of the occurrence of the other event.
What are the aspects of Hills Criteria of causality
1) Temporality
2) Strength of association
3) Dose-response
4) Reversibility (Cessation of Exposure)
5) Consistency
6) Biologic Plausibility
7) Specificity of the association
8) Analogy
What is Hills Criteria of causality is this statement an example of?
ex: greater proportion of blind people own dogs - chicken or the egg?
temporality
What is Hills Criteria of causality is this?
- measured by RR, OR
- the stronger the association, the more likely to be causal
strength of association
What is Hills Criteria of causality is this?
- dose increase, the risk of disease increase - e.g., cigarette smoking (packs/day) & lung cancer - difficult to demonstrate for exposures with threshold effect, non-linear relationships
Dose-response
What is Hills Criteria of causality is this?
- reduction in the risk of disease after cessation/elimination of exposure
- in some instances the pathogenic process is irreversible
Reversibility (Cessation of Exposure)
What is Hills Criteria of causality is this?
- replication of the findings
- replication with different study designs, populations, etc
Consistency
What is Hills Criteria of causality is this?
- coherence with the current body of biologic knowledge
- in some instances clinical observations might precede basic science knowledge (e.g., Gregg's observation on rubella & congenital cataracts)
- should fit with the known facts of the natural history and biology of the disease.
Biologic Plausibility
What is Hills Criteria of causality is this?
- a specific exposure is associated with only one disease (works for infections diseases)
- unlikely for many environmental exposure
Specificity of the association
What is Hills Criteria of causality is this?
- case-and-effect relationship already established for a similar condition
- association of passive smoking with lung cancer (analogy to the risk with active smokers)
Analogy
What is the mathematical calculation for sensitivity?
A/(A+C)
What is the mathematical calculation for specificity?
D/(B+D)
What is the mathematical calculation for PV+
A/(A+B)
What is the mathematical calculation for PV-
D/(C+D)
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