Interpreting results Flashcards
Define descriptive statistics
Used to organise or summarise data collected from a sample population
Define inferential statistics
Uses data collected from a sample population to make generalisations about the target population
Define independent variable
An entity that is manipulated in the study
- Also known as experimental variable
Define dependent variable
An entity that is affected by the change in the value of the independent variable
- Also known as outcome variable
How do you calculate incidence?
Incidence = Number of new cases / population size
- Measure of the risk of a disease
How do you calculate point prevalence?
Point prevalence = Number of people with disease at a given time / size of population at the same time
Define intention to treat analysis
All participants are included in the analysis regardless of whether they completed the study
- Pragmatic approach
- Mirrors real life scenario
Define last observation carried forward
Last recorded results of individual who drop out are incorporated into the results
- Used in intention to treat analysis
Define worst case scenario analysis
Subjects who drop out are recorded as non responders with worst possible outcomes
- Used in intention to treat analysis
Define imputation
Missing data is substituted with plausible values to allow data analysis to proceed
- Used in intention to treat analysis
Define sensitivity anaylsis
Assumptions are made when the missing values are put in
Define risk
The probability of something happening
- Expressed as p (number between 0-1) or percentage
- Number of times event occurs / total number of possible events
Define odds
Way of expressing chance
- Expressed as ratio or fraction
- Odds is the ratio of the number of times an event is likely to occur / number of times it is likely not to occur
What is a contingency table?
2x2 table comparing risk and odds across 2 groups
- Rows consist of exposure
- Columns consist of outcome event status
Define control event rate (CER)
Outcome event rate in control group
- outcome event in controls / outcome event in controls + no outcome event in controls
Define experimental event rate (EER)
Outcome event rate in experimental group
- outcome event in experimental subjects / outcome event in experimental subjects / no outcome event in experimental subjects
Define absolute risk reduction (ARR)
Control event rate - experimental event rate
- Also known as absolute benefit increase
- If negative number, then called absolute risk increase
Define relative risk (RR)
Experimental event rate / control event rate
Define relative risk reduction (RRR)
Control event rate - experimental event rate / control event rate
- Also known as relative benefit increase
- If negative number, then called relative risk increase
Define number needed to treat (NNT)
1 / absolute risk reduction
ARR = CER - EER
- Number of subjects who must be treated with intervention compared with control for one additional subject to experience the beneficial outcome
- If negative number, then can be expressed as NNH
Define odds ratio
odds of outcome in exposed group / odds of outcome in control group
What does it mean if the relative risk is equal to 1?
No risk difference between the two groups
What does it mean if the relative risk is >1?
Increased risk of the outcome in the experimental group
What does it mean if the relative risk is <1?
Reduced risk of the outcome in the experimental group
Define number needed to harm (NNH)
1 / absolute risk increase
- Number of subjects treated for one extra subject to have an adverse outcome compared with the control intervention
How can risk/benefit ratio be calculated?
NNH:NNT
What does an odds ratio of 1 mean?
Same outcome in both groups i.e no effect
- If expressed as a log odds ratio then 0 means no effect
What does an odds ratio of >1 mean?
Indicates likelihood of developing the outcome is greater among those in the experimental arm
What does an odds ratio of <1 mean?
Indicates likelihood of developing the outcome is less among the experimental arm
What are the 4 types of measurement scales?
Nominal scales
Ordinal scales
Interval scales
Ratio scales
Define nominal scales
Organised into categories
- No inherent order
- No mathematical relationship to one another
- Usually qualitative data
e. g male, female
Define ordinal scales
Organised into categories in a meaningful way
- Difference between points being equal across the scale
- Not given numerical value
- Usually qualitative data
e. g Mild, moderate, severe
Define interval scales
Organised in a meaningful way with differences between points bring equal across the scale
- No true zero
- Usually quantitative data
e. g degrees Celsius
Define ratio scales
Similar to interval scale but there is a true zero
- Usually quantitative data
e. g Kelvin
Nominal and ordinal data is analysed with non-parametric statistics (True/False)
True
Interval and ratio data is analysed with parametric statistics (True/False)
True
Define Gaussian distribution
A normal distribution, perfectly symmetrical, bell shaped curve on a graph
- Mean, median and mode are of equal value and lie in the center of the distribution
Define weighted mean
Some variables are more important than others therefore a weight is attached to reflect this
- If all values are equally weighted then the mean will be unaffected
Define variance
Indicates dispersion of values around the mean
Define standard deviation
Describes the degree of data spread about the mean
- Measure of precision
- Square root of variance
What percentage of observations are included in a range covered by 1 standard deviation above and below the mean?
assuming observations follow a normal distribution
68%
i.e area under the curve
What percentage of observations are included in a range covered by 2 standard deviations above and below the mean?
assuming observations follow a normal distribution
96%
What percentage of observations are included in a range covered by 3 standard deviations above and below the mean?
assuming observations follow a normal distribution
99.7%
Define co-efficient of variation
Measure of spread which is independent of the unit of measurement
- Compares studies using different units
coefficient of variation = standard deviation / mean x 100
What is the median if there is an even number of data values?
An average of the two values that lie on either side of the middle
Define geometric mean
Used when distribution is positively skewed
Each value is replaced by its logarithm in a log normal distribution
Define interquartile range
Focus on the spread of the middle 50% of data
Not influenced by outliers
What percentage of values lie below the 10th percentile?
10%
What percentage of values lie below the 20th percentile?
20%
What percentage of values lie below the 50th percentile?
50%
Define coefficient of skewness
Measure of symmetry
Define coefficient of kurtosis
Measure of peakedness of distribution
Define positively skewed distribution
The distribution has an extended tail to the right
- Has a positive coefficient of skewness
Is the mean larger or smaller than the median in a positively skewed distribution?
Mean > Median > Mode
Define negatively skewed distribution
The distribution has an extended tail to the left
- Has a negative coefficient of skewness
Is the mean larger or smaller than the median in a negatively skewed distribution?
Mean < Median < Mode
Define symmetrical distribution
Coefficient of skewness is zero
Define standard error of the mean
Measure of the precision of the sample
- More observations = smaller the standard error will be
Standard error of a sample of size n = standard deviation / square root of number of observations in the sample
Define confidence interval
A range of values that express the degree of uncertainty around an estimate
- Width of a CI indicates the precision of the estimate
What does a p value of 0.05 mean?
Chance of results being due to chance is 5% meaning the null hypothesis can be rejected
- Results are deemed statistically significant
Define a type 1 error
Null hypothesis is rejected when it is true
- False positive result recorded
- Usually attributable to bias, confounding or multiple hypothesis testing
Define a type 2 error
Null hypothesis is accepted when it is false
- False negative result recorded
- Usually happens when the sample size is not large enough or measurement variance is too large
Define alternative hypothesis
Proposed experimental hypothesis that runs opposite to the null hypothesis
Define a two tailed test
Exists if the alternative hypothesis does not offer a direction for the difference between the groups
Define a one tailed test
Alternative hypothesis specifies a direction for difference
Not used often
Define Bonferroni correction
Safeguards against multiple tests of statistical significance on the same data which may give a false appearance of significance
- If excessive, it will increase the risk of making a type 2 error
If the confidence intervals overlap, the result is statistically significant (True/False)
False
- If the confidence intervals do not overlap, the result is significant
Define unpaired data
Data from two groups with different members
Define paired data
Data from the same individuals at different time points
Which statistical test can be used when comparing two or more groups of categorical data?
Chi-squared test (unpaired)
McNemar’s test (paired)
Which statistical test can be used when comparing two groups of non-normal data?
Mann-Whitney U test (unpaired)
Which statistical test can be used when comparing one group of non-normal data?
Sign test
Wilcoxon’s signed rank test
Which statistical test can be used when comparing more than two groups of non-normal data?
Kruskal-Wallis ANOVA test (unpaired)
Friedman’s test (paired)
Which statistical test can be used when comparing one group of normal data?
One sample t test
Which statistical test can be used when comparing two groups of normal data?
t test (paired or unpaired)
Which statistical test can be used when comparing more than two groups of normal data?
One way ANOVA (for unpaired)
Repeated measures ANOVA (for paired)
Define a non parametric test
Used for analysis of non-normally distributed data
Name a non parametric test
Sign test Man-Whitney U test (unpaired) Wilcoxon matched pairs (paired) Kruskal-Wallis ANOVA test (unpaired) Friedman's test (paired)
Define a parametric test
Used for data that is normally distributed
Name a parametric test
t test
Paired t test
ANOVA
What is Kendall’s correlation?
A statistical test used in analysis of categorical data
What is Spearman’s correlation?
A statistical test used in analysis of mixed categorical & continuous data
What is Pearson’s correlation?
A statistical test used in analysis of continuous data
What is ANOVA?
Used to compare three or more groups of continuous or interval scores. Can have one way, two way or repeated measures ANOVA
- Can also have MANOVA (multiple analysis of variance)
Define an equivalence study
Researcher attempts to show equivalence between drugs
Define a non-inferiority study
Researcher assesses whether a new drug is no worse within a specified margin than the standard drug
- Cheaper to run
- Require smaller sample size
Define multivariate statistics
Examine the relationship between several variables and make predictions about the data set
- Continuous data can be analysed using correlation and regression techniques
What does correlation assess?
The strength of the relationship between two quantitative variables and if there is a linear association
Define positive correlation
Y increases linearly as X increases
Define negative correlation
Y decreases linearly as X increases
Define zero correlation
Complete non association between the compared variables
What is simple linear regression?
Describing the linear relationship between a dependent variable
- Also known as univariate regression
- Stand errors can be estimated and CIs can be determined
Assumes the dependent variable is continuous
What is multiple linear regression?
The dependent outcome variable is predicted from 2 or more independent variables
- Independent variables can be continuous or categorical
- Also known as multivariable regression
Assumes the dependent variable is continuous
Define logistic regression
Used when there is a binary outcome of interest.
- Has a theoretical binomial distribution
What are the four main components to a systematic review?
Research question
Search strategy
Quality assessment
Interpretation of data
What are the key steps for a meta analysis?
Synthesis using statistical techniques (Combines results of included studies)
Calculation of pooled estimate of effect, together with P value and CIs
Check for heterogeneity
Check for publication bias
Review and interpret findings
What does the vertical line on a forest plot represent?
Line of no effect
What do the boxes on a forest plot represent?
Each box corresponds to a study
- Size of box is proportional to weight of study in meta analysis
- Position of box relates to estimate of outcome
What are the horizontal lines around boxes on a forest plot?
Represent CIs
- If touches/crosses vertical line then outcome not statistically significant or sample size was too small for confidence in result
What does the diamond on a forest plot represent?
Overall outcome of the meta anaylsis
- Centre of the diamond is the point estimate of pooled result
- Horizontal width is CIs
What is the PRISMA statement?
27 item checklist
- Aims to improve the reporting of systematic reviews and meta analysis
Define homogeneity
Studies have similar & consistent results, any observed differences are due to random variation
Define heterogeneity
More variation than would be expected by chance alone after allowing for random variation
Define clinical heterogeneity
Individuals chosen for two studies differ from one another significantly, results are difficult to collate
Define statistical heterogeneity
Results of different studies differ from one another significantly more than would be expected by chance
What are the two methods for calculating the effect size in a meta analysis?
Fixed effects model
Random effects model
Define fixed effects model
Assumes there is no heterogeneity between studies
- Used when heterogeneity has been ruled out
- Examples include Mantel-Haenszel procedure
Define random effects model
Allows for between study variations when the pooled overall effect estimate is produced
- Gives wider CIs
What methods are available to check for heterogeneity?
Forest plot (if CIs from studies do not overlap with one another)
Cochran’s Q
Galbraith plot - used when number of studies is small
What methods are available to check for homogeneity?
L’Abbe plot
Define sensitivity analysis
Assess how sensitive the results of the analysis are to changes in the way it was done
What are the different types of reporting bias?
Time-lag bias Language bias Citation bias Funding bias Outcome variable selection bias Publication bias
Define publication bias
Studies with positive findings are more likely to be submitted and published than those with negative findings
What methods are available to identify publication bias?
Funnel plots
Galbraith plot
Begg’s rank correlation test
What does it mean if there is asymmetry in a funnel plot?
There is publication bias
- Can be removed with ‘trim & fill method’
