Measures of Association (Biostats) Flashcards
Precision takes into account a measurement’s (or set of measurement’s) … ?
Reliability
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The consistency and reproducibility of a test.
The absence of random variation in a test.
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Reliability refers to how similar the data points are to each other: when reliability is low, the data points are more widely dispersed. When reliability is high, the data points are more close together. An analyzer can be “reliably wrong” or “precisely wrong.”
What does the precision do to the standard deviation (SD)?
SD decreases when the measurements are more precise
Accuracy takes into account a measurement’s (or set of measurement’s) … ?
Validity
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The closeness of test results to the true values.
The absence of systematic error or bias in a test.
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Validity refers to how close the data points are to the true value: when validity is low, the data points do not approximate the true.
An analysis that renders values such as these would have (high/low) precision/accuracy?
Low reliability and High validity
An analysis that renders values such as these would have (high/low) precision/accuracy?
High reliability and Low validity
An analysis that renders values such as these would have (high/low) precision/accuracy?
Low reliability and Low validity
An analysis that renders values such as these would have (high/low) precision/accuracy?
High reliability and High validity
Random error will impact the ________ of a test?
precision
Systemic error will impact the ________ of a test?
accuracy
Specificity and sensitivity would relate to precision or accuracy?
Both of these measures (using standardized values) are of tests of validity and refers to the ability of a test to correctly identify those who do not have a certain disease (specificity) or the ability of a test to correctly identify those who have the disease (sensitivity).
What does the absolute risk help to measure?
There will be two absolute risk categories, one for the exposure group and another for the unexposed group.
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Taking these in isolation is equivalent to measuring the incidence of disease in that group or population.
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When taking the quotient between these two absolute risk groups, then the relative risk can be obtained.
What is typically used in studies where participants are followed prospectively to observe outcomes?
What type of study is this?
Relative Risk is used in a cohort study where people are followed and their “risk” of developing a disease later in the future refers to the probability of disease (or an event) occurring over a certain period of time.
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These are prospective study designs.
When two groups of interest are compared in a study over time, how (generally) is the ratio set up that functions to compare the group at risk vs the group not at risk ?
A ratio, called “relative risk,” analyzes the risk associated to the exposed group over the risk associated to the unexposed group. The rate at which the exposed group experiences disease is the numerator and the rate at which the unexposed group experiences disease is in the denominator.
What is the complete formula for calculating Relative Risk (RR)?
RR = [a/(a+b)] / [c/(c+d)]
[a/(a+b)] = the risk in the exposed group
(a+b) = all the members in the exposed group
a = diseased cases in exposed group
b = non-diseased cases in the exposed group
[c/(c+d)] = the risk in the unexposed group
(c+d) = all the members in the unexposed group
c = diseased cases in unexposed groups
d = non-diseased cases in the unexposed group
What is Attributable Risk?
The excess incidence of a disease due to a particular factor (exposure).
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Attributable risk is also known as the ‘risk difference’ and is the absolute value in terms of risk between the exposed and unexposed groups.
What is the Attributable Risk (AR) if out of 100 people, 60 were exposed and out of these 60 people, 30 developed the disease of interest, while only 10 from the unexposed group developed the disease of interest?
AR = | (Incidence in Exposed) - (Incidence in Unexposed) |
For example, 100 people are analyzed.
60 were exposed and 40 were not exposed.
In the exposed group, 50% of the members experienced disease (30 out of 60).
In the unexposed group, 25% of the members experienced disease (10 out of 40).
The AR = (30/60) - (10/40) = 0.5 - 0.25 = 0.25 (or 25%).
When the attributable risk is referring to the beneficial effects of an intervention, this is … ?
Absolute risk reduction (ARR).
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The difference in risk attributable to an exposure as compared to non-exposure.
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Absolute risk reduction (ARR) = risk in non-exposed group – risk in exposed group
If the risk of developing lung cancer in heavy smokers is 28% and the risk in non-smokers is 6%, what is the absolute risk reduction in lung cancer for individuals who do not smoke?
22%
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This is derived in the same way as attributable risk, which is the excess in after taking the difference between the absolute risk in the exposed group and the unexposed group. In this case, the absolute risk of developing lung cancer in smokers is 28%, while in non-smokers, it is 6%. Calculating the difference (excess) between these two values (28% - 6%). This also determines the attributable risk that represents the absolute risk reduction in lung cancer for individuals who do not smoke, which equals 22%, meaning not smoking is the intervention, which provides an absolute risk reduction of 22%.
If 8% of people who receive a placebo vaccine develop the flu vs 2% of people who receive a flu vaccine, then the absolute risk reduction is … ?
8%–2% = 6% = 0.06
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This is equivalent to saying that the vaccine (intervention) had an absolute risk reduction of 6%.
What is Number Needed to Treat (NNT)?
The number of patients that need to be treated to prevent one additional adverse outcome.
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Formula: NNT = 1 / Absolute Risk Reduction (ARR)
What insight does Number Needed to Treat (NNT) provide?
Practical insight into the effectiveness of a treatment.
How is Number Needed to Treat (NNT) calculated?
1) First determine the absolute risk reduction, ARR = (Mortality Rate in Control - Mortality Rate in Treatment).
2) Then take the reciprocle of this value.
For example if a new treatment regimen now has a death rate of 25/50 = 0.5 over 5 years, whereas in patients kept on the conventional regimen had a mortality rate of 75/100 = 0.75, then the absolute risk difference between the two groups would be 0.75 - 0.5 = 0.25. Taking the reciprocal (1/0.25 = 4) of the absolute risk difference allows for the NNT to be determined.
Example: = 0.75 - 0.5 = 0.25; NNT = 1 / 0.25 = 4.
Based on this result, we can conclude that we need to treat 4 patients with the new regimen as opposed to the conventional regimen in order for one more patient to survive 5 years without relapse.
NNT = 1 / Absolute Risk Reduction (ARR)
What is the epidemiological measure of risk that refers to the proportion of decreased risk due to an intervention compared to the control group.
This is the relative risk reduction
What is the significance of ( 1 - RR ) ?
This is how the relative risk reduction is expressed mathematically, where the proportion of risk reduction attributable to the intervention/treatment is compared to the control (non-intervention or non-treatment).
When can ( 1 - RR ) be used?
When RR is less than 1, the RRR is determined by ( 1 - RR )
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What is used when the RR is above 1 is ( RR - 1 ) .
Can relative risk reduction be expressed as a percent?
Yes:
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When RR is less than 1:
% risk reduction = (1 - RR) x 100
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When RR is more than 1:
% risk increase = (RR - 1) x 100
If the insight of interest is to determine the RR and the RRR, where, 2% of patients who receive a flu shot develop the flu, while 8% of unvaccinated patients develop the flu, then what is the RR and RRR?
RR = 2/8 = 0.25
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RRR = (1 - 0.25) = 0.75
If a study needed to determine how much an exposure or risk factor has contributed to the incidence of a disease, and the relative risk was provided, what measure of assoication would be appropriate and how would this be calculated?
This would require the Attributable Risk Percent (AR%), which is the proportion of disease incidence in the exposed group attributable to the exposure.
Formula: AR% = [ ( RR - 1) / ( RR ) ] x 100 = (Attributable Risk / Incidence in Exposed) × 100
How is Attributable Risk Percent (AR%) calculated?
AR% = ( [Attributable Risk] / [Incidence in Exposed] ) × 100.
AR% = [ ( RR - 1) / ( RR ) ] x 100.
What is Population Attributable Risk Percent (PAR%)?
The proportion of disease incidence in the total population attributable to the exposure.
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[(incidence of disease in the total population) - (incidence of disease among the unexposed group)] / (incidence of disease in the total population)
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In order to determine this, the incidence of the disease within the entire population (irrespective of whether they were exposed to the risk factor) is subtracted by the incidence of developing the disease in the unexposed group (which is assuming random chance of developing the disease). That value is then placed within a ratio to the entire population’s incidence where the numerator is the value obtained from subtracting out the random chance and the denominator is the incidence of the entire population.
How is Population Attributable Risk Percent (PAR%) calculated?
To determine population attributable risk percent:
1) First calculate the incidence of the disease in the study population as a whole. For example, if a study population of 100 people (where 60 were smokers and 40 were non-smokers) had 30 individuals from the smoker group and 10 individuals from the non-smoker group who developed respiratory disease or symptoms, then the overall incidence of developing respiratory disease or symptoms in this study population would be 40/100.
2) Next, calculate the difference in risk of developing respiratory disease among the study population as a whole and among non-smokers (40/100 - 10/40 = 0.4 - 0.25 = 0.15). To explain this further, 40/100 accounted for the incidence of developing disease or symptoms in the entire population while 10/40 was the risk based on random chance.
3) Divide the difference in risk between the two groups by the incidence of respiratory disease in the population as a whole (0.15/0.4 = 0.375) to determine that Based on the calculation, 37.5% of the yearly respiratory disease in the study population is attributable to smoking.
PAR% = [(Incidence in Total Population - Incidence in Unexposed) / Incidence in Total Population] × 100.
What does Attributable Risk Percent (AR%) show?
The proportion of disease incidence in exposed individuals that is due to the exposure.
What does Population Attributable Risk Percent (PAR%) demonstrate?
The impact of exposure on disease incidence in the entire population.
The number needed to harm is determined by … ?
Attributable risk (AR)
When you take the past exposures and compare those exposures to those who were not exposed, this is a(n) ________ study that uses a(n) ________ to make the comparison.
When you take the past exposures and compare those exposures to those who were not exposed, this is a(n) case-control study that uses a(n) odds ratio to make the comparison.
Odds ratio (OR) is the measure of association used in case-control studies. It compares the odds of exposure in cases to the odds of exposure in controls. A case-control study is retrospective in nature. It starts with individuals who have a specific outcome (cases) and those who do not (controls). The study then looks back in time to compare exposure histories between the two groups. Case-control studies are particularly useful for studying rare diseases or outcomes because they focus on individuals who already have the outcome of interest. The odds ratio in these studies provides an estimate of the relative risk, especially when the outcome is rare.
What is the formula for calculating Odds Ratio (OR)?
OR = (a/c) / (b/d) = (ad) / (bc), using the 2×2 table structure.
a = Exposed and Diseased
c = Unexposed and Diseased
b = Exposed and Non-Diseased
d = Unexposed and Non-Diseased
What is the key difference between cohort studies and case-control studies in terms of risk measures?
Cohort studies measure incidence prospectively and calculates the relative risk. The relative risk compares the probability of developing an outcome between two groups over a certain period of time. It implies a prospective study design because the patients are followed over time to see whether or not they develop an outcome. Relative risk determines within certain period of time, how many times are exposed people likely to develop a disease compared to those who have remianed unexposed.
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Case-control studies makes use of retrospective data and calculates the odds ratio. The odds ratio compares the chance of exposure to a particular risk factor in cases and controls. Cases have developed the disease and controls remain disease free. “Risk,” in it’s purest sense is not calculated, instead infered indirectly in case-control studies, because the anaylsis is retrospective. Odds ratio answers how many times are diseased people more likely to have been exposed to a particular factor in comparion to those who have not developed disease.
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Both relative risk and odds ratio are measured on a scale from 0 to infinity. The value of 1.0 indicates no difference between the two groups being compared.
What is the ‘rare disease assumption’?
The ‘rare disease assumption’ states that when a disease is rare, the Odds Ratio approximates the Relative Risk.
What does a Relative Risk (RR) or Odds Ratio (OR) of 1 indicate?
An RR or OR of 1 indicates no difference in risk between the exposed and unexposed groups.
A Relative Risk (RR) > 1 would mean that …
Indicates that the exposure is associated with an increased risk of the outcome. For example, an RR of 2.0 means the exposed group is twice as likely to develop the outcome compared to the unexposed group.
A Relative Risk (RR) < 1 would mean that …
Indicates that the exposure is associated with a reduced risk of the outcome. An RR of 0.5 means the exposed group has half the risk of developing the outcome compared to the unexposed group.
An Odds Ratio (OR) = 1 would indicate that …
Indicates that there is no association between the exposure and the outcome. The odds of the outcome are the same in both the exposed and unexposed groups.
How do you interpret an Odds Ratio (OR) > 1?
An OR > 1 suggests that exposure is associated with higher odds of the outcome occurring. For example, an OR of 2.0 means the odds of the outcome are twice as high in the exposed group compared to the unexposed group.
Odds Ratio (OR) < 1 would indicate that …
This indicates that the exposure is associated with lower odds of the outcome. For example, an OR of 0.5 means the odds of the outcome are half as likely in the exposed group compared to the unexposed group.
How can Relative Risk (RR) and Odds Ratio (OR) be applied in clinical practice?
RR and OR help assess the strength of association between an exposure and an outcome, aiding in clinical decision-making.
What makes the relative risk and odds ratio similar?
Relative risk and odds ratio are measures of association which provide point estimates of effect. They are useful in describing the magnitude of an effect.
What are the two measures of dispersion?
Standard deviation
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Standard error
How is a normal distribution set?
1 sd = 68 % of all values (+/- 1 sd from the mean is +/- 34%)
2 sd = 95% of all values (+ / - 2 sd from the mean is +/- 14%)
3 sd = 99% of all values (+ / - 3 sd from the mean is +/- 2 %)
What is used to determine the accuracy of the mean?
The likelihood of the estimated mean to be accurate is “standard error of the mean (SEM)”
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The standard error of the mean is a specific kind of standard deviation: while SD describes the dispersion of sample data in relation to its mean, SEM describes the dispersion of means of different samples from a population mean. As the SD increases and the sample size decreases, SEM will increase.
How is the standard error of the mean (SEM) calculated and what is the purpose?
SEM = SD/ sqrt(n)
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Once this is calculated, then SEM is multiplied by the z-score.
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for a 99% CI this is 2.58
for a 96% CI this is 1.96
How does sample size alter the confidence interval?
Sample size is a part of the calculation for determining the confidence interval, the bigger the sample size, the tighter the confidence interval.
What elements are needed to calculate the limits of a confidence interval?
To calculate the Cl around the mean you must know the following: the mean, standard deviation (SD), z-score and sample size (n). A Cl can be calculated to correspond with the mean of any continuous variable.
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Mean +/- 1.96 * [SD/(sqrt(n))]
Would increasing the amount of measurements alter the standard deviation?
No, the standard deviation measures the dispersion or spread in data and is an intrinsic property of the population from which the sample is drawn. Increasing the sample size may increase the accuracy of estimating the standard deviation, but it will not change the standard deviation itself.
Would increasing the amount of measurements alter the standard error of the mean?
Yes, the standard error of the mean (SEM) is a measure of the dispersion of a random set of sample means around the true population mean. It is dependent on the variability (i.e., standard deviation) of the measured values and the sample size (SEM = SD/√n). By increasing the sample size, the sample means approach the true population mean, resulting in a smaller SEM.
How would a larger standard deviation alter the standard error of the mean?
A greater standard deviation will increase the SEM, resulting in a less accurate estimate.
How would a smaller sample size affect the standard error of the mean?
A smaller sample size will increase the SEM, resulting in a less accurate estimate.
When a sample is measured and population mean is then subtracted from the sample measurement and this result is then divided by the standard deviation, what is this value if we assume that all measurements follow a normal distribution?
Z-score
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This value is used to express data in terms of units of standard deviation and how many standard deviations from the mean a particular value is is represented in its value. With a z-score a research can compare values between other populations with different means and standard deviations.
How are confidence intervals (CIs) calculated?
CIs are defined as the mean ± standard error of the mean, which is calculated by multiplying a Z-score (for 95% confidence intervals this is always 2) by the standard deviation (SD) divided by the square root of the sample size (Mean +/- Z-score (SD/√sample size)). A larger sample size or a decreased SD (based on data precision) will decrease the standard error. Including more disparate data or reducing the sample size, will increase the standard error, thus expand the CI.
With negatively skewed distributions, the mean is displaced to the ______ on a distribution curve.
left
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The Peak is to the right and the tail is to the left.
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Going left to right is mean (“-“ tail), median, mode (apex).
With positively skewed distributions, the mean is displaced to the ______ on a distribution curve.
right
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The peak is to the left and the tail is to the right.
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Going left to right is mode (apex), median, and mean (“+” tail).
When a study uses the means to compare two independent variables, what is used to compare them?
Two-sided sample T (student’s T test)
When the same individual mean is followed over time, what is used to study any comparison?
paired T test
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In a paired t-test, data is derived from study subjects who have been measured at two different points in time (e.g., before and after a treatment). The difference between the means of a continuous outcome variable of this group is compared. The null hypothesis is that the group mean is equal at these two different times. A statistically significant difference rejects the null hypothesis.
When a study compares the difference between the means of a continuous outcome variable of two or more categorical groups.
Analysis of variance (ANOVA)
When proportions of any type are used for comparison, what studies are important?
Chi-squared for big sample sizes
Fisher’s exact test for small sample sizes
What statistical analysis is used to measure of the strength and direction of a linear relationship between two continuous variables?
Pearson correlation coefficient
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This is a statistical measure of the strength and direction of a linear relationship between two variables. A near perfect relationship is when the line that best fits is “1” and ranges anywhere from -1 to +1, where -1 represents a perfectly negative linear relationship and +1 represents a perfectly positive linear relationship.
What a correlation such as this indicate?
R= 0, thus there is no correlation.
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When R = 0, the best-fit line is flat, indicating no clear relationship between the independent and dependent variables. The scattered points suggest a lack of correlation, meaning there is no association between the two variables.
What is the coefficient of determination?
This is the proportion of variability in the dependent variable.
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The coefficient of determination (r^2) represents the proportion of variance in the dependent variable explained by the independent variable.
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For example, if r = -0.8; this means r^2 = 0.64 or 64%
When analyzing a confidence interval, what are the two distinctions when determining to reject the null hypothesis or fail to reject the null hypothesis?
When the study is measuring differences, the null value is expressed with a “0,” if a “0” is within the confidence interval, fail to reject the null hypothesis, if a zero is not within the confidence interval, then reject the null hypothesis.
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When the study is using ratios, like an odds ratio or relative risk, and a “1” is within the confidence interval, this is the null value and will warrant accepting the null hypothesis (failing to reject the null hypothesis). If a “1” is not within a confidence interval when a ratio is used, then reject the null hypothesis.
If using a confidence interval, what value must the interval lack in order to fail to reject the null hypothesis?
If a null value of “0” is within the confidence interval, fail to reject the null hypothesis (accept the null). If the confidence interval does not include the null value, this means that the data provide sufficient evidence to reject the null hypothesis, suggesting that there is likely a true effect or difference.
If a study lacks sufficient statistical evidence to conclude there is a real effect or difference, what might be expected in the confidence interval?
When the CI includes the null value, it suggests that the observed effect or difference could plausibly be zero (or no effect) given the data.
What is the probability of rejecting the null hypothesis when it is actually true (the likelihood of concluding that there is an effect or association when there truly is none)?
Alpha is the probability of committing a Type I error in hypothesis testing.
What is the significance of the probability of committing a type 1 error?
This is the significance level and the probability of a type I error is denoted by alpha (α).
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This is expressed as the p-value.
What type of error occurs when the null hypothesis is rejected despite it actually being true. Consequently, the alternative hypothesis is accepted, although the observed effect is actually due to chance (Wrongfully concluding that there is an association between exposure and disease when in fact there is none)?
Type I error
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“False positive”
Falsely rejecting the null hypothesis means that a researcher committed a ____ error
Type I error
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This is the same as creating a false positive.
The probability of obtaining the observed results (or more extreme results) assuming the null hypothesis is true, is how the ____ is described.
p-value
What is the probability of not committing a Type I error?
“1-alpha”
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This represents the confidence level.
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Correctly identifying a true null hypothesis (The probability of correctly failing to reject the null hypothesis when it is true).
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“True negative”
When the null hypothesis is false (i.e., the alternative hypothesis is true), but the null is incorrectly not rejected, what type of error has occurred (wrongfully concluding that there is no association between exposure and outcome, when in fact there is one)?
Type II error (β)
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When the null hypothesis is false (i.e., the alternative hypothesis is true), but the null is incorrectly not rejected (accepted), a Type II error (β) has occurred. This means the test fails to detect a real association or difference, wrongfully concluding that there is no association between the exposure and the outcome, even though one exists.
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“False negative”
Does statistical power affect generalizability?
No, statistical power does not directly affect generalizability, but it plays an important role in the reliability of study results. Statistical power refers to the probability of correctly rejecting the null hypothesis when a true association exists (i.e., avoiding a Type II error). Generalizability, on the other hand, refers to how well the findings of a study apply to populations beyond the specific sample studied.
What method of statistical analysis pools summary data (eg, means, RRs) from multiple studies
for a more precise estimate of the size of an effect.
Meta-analysis
