Applied Statistics Flashcards
What are the characteristics of the question used to test the hypothesis
PICOT
Patients or Population Intervention(s) or Exposure(s) Comparator Outcome Time
What are the 5 fundamental types of clinical questions
- Therapy
- Harm
- Differential diagnosis
- Diagnosis
- Prognosis
Summarise and classify the different types of study designs
EXPERIMENTAL
- RCT
- Pseudo - / Quasi - RCT
- Non-RCT
OBSERVATIONAL
- Descriptive
- Analytical
- –> Cohort
- –> Cross-sectional
- –> Case-control
What type of studies are the lowest level of evidence and what are these studies used for. What are its advantages and disadvantages
Animal studies
- lowest level of evidence
- Used as hypothesis generating studies
ADV
- Cheaper
- Adequate physiological/metabolic surrogate
- Limits human suffering due to experimentation
DISADV
- Metabolic pathways / pharmacokinetics differ
- Young/no comorbidities
- Defects of methodology (less rigorous / slowly manifesting effects)
Distinguish
- Ecological study
- Case report/series
- Cross sectional surveys
- Case-controlled studies
- Cohort studies
- Randomised Controlled Trials
- Systematic review
- Meta-analysis
- Ecological
- Observational
- Retrospective
- Looks at occurrence and associations in groups - Case report/series
- Observational
- Descriptive
- No control group - Cross sectional surveys (snap-shot)
- Observational
- Descriptive / Analytical / Diagnostic
- Large series of case reports
- No control group - Case-controlled studies
- Observational
- Retrospective
- Historical controls used
- Essentially: choose a group with a shared feature and compare it to another group without that feature.
- Uses Odd’s ratio to quantify risk - Cohort Studies
- Observational
- Longitudinal: Retrospective, Concurrent, Prospective
- Observes exposure, then observes development of disease
- Observes identical control group without exposure
- Uses relative risk to quantify risk - Randomised Controlled Trial
- Experimental
- Randomised
- Prospective
- Interventional
- Analytical - Systematic review
- Answers a defined research question by collecting and summarising all empirical evidence that fits pre-specified eligibility criteria - Meta-analysis
- Use of statistical methods to summarise the results of these studies
What are cross-over trials?
Each patient acts as their own control
Patients ‘cross-over’ from one treatment to the next following a ‘washout period’ between treatments
There is usually randomization
What are self controlled studies
Each patient is their own control
Post treatment measurements in each patient are compared to pre-treatment measurements
With regards to data collection (sampling), What two principles are paramount
- Internal validity
- Sampling should be free from selection bias - External validity
- Sample should represent broader real-world population
Describe and define 4 sampling strategies
- Simple random - Everyone has equal chance of being picked
- Stratified random - Divide into subgroups 1st then random selection
- Clustered random - Treat people as groups (School vs. ICU)
- Convenience sample - non-random selection: just as they come
What does randomisation mean
A representative sample can be chosen by RANDOM sampling, whereby each person is equally likely to be selected.
It means that no systematic bias is introduced and the samples selected should be representative of the populations of interest
What is the CONSORT or STROBE diagram
STROBE - STrengthening the Reporting of OBservational studies in Epidemiology
CONSORT - CONsolidated Standards of Reporting Trials
Figure 1 in any published study –> total number of patients eligible vs total number of patients included. If number included is low vs number eligible then this is strongly suspicious that the subset is biased , either through who is in the study, or who declined to participate
What is sampling error
If a study is repeated different sample chosen with slightly different characteristics and as such the result will differ slightly.
Sampling error becomes smaller as the sample size increases
What is the difference between a parameter and a statistic
A parameter refers to a property of a population
A statistic refers to a property of a sample
What are the conventional symbols for the mean and standard deviation of a population vs a sample
Population
- Mean: mu
- SD : sigma
Sample
- Mean: X-bar (x with a bar on top)
- SD: S
What is a histogram. List and describes the 3 main shapes of this entity
This is a graph that gives an indication of the distribution of data.
- Normally distributed = Gaussian = Bell shaped
- Left skew = long left tail = negative skew
- Right skew = long right tail = positive skew
On what types of data can parametric tests be used
Normally distributed data
(This includes log transformed right skewed data –> Gaussian)
Unfortunately, Left skewed data cannot be transformed easily.
What is the purpose of a histogram
To show the frequency and shape of continuous data.
Determining whether the data is normally distributed (or can be transformed to normality) allows for the use of parametric tests in data analysis.
Shows:
- Gaps
- Outliers
- Skewed data
What is the kurtosis of the data
This refers to the flat or pointed nature of the distribution of the data
How do you calculate a 95% confidence interval and why is this necessary
95% CI = Mean ± 2SD
Used to determine if the data presented is plausible
What is the indication for a Box and Whisker Plot
To graphically represent the median and interquartile range in non-normally distributed data.
Describe the data organisation of a box and whisker plot
Median - thick horizontal line within the box
Length of box represents the interquartile range (25% –> 75%)
Whiskers represent range
Outliers shown when they are more than 3 box lengths from the upper or lower end of the box
What is the most common transformation of non-normally distributed data?
Log transformation of positively skewed (right skewed) data. Creates a normal distribution curve for which parametric tests during data analysis.
What is the purpose of scatterplots
To provide a visual representation of the relationship between two variables
- Strength of the relationship
- Degree of linearity
- Association positive or negative
- Presence of outliers
What is the indication to use a scatterplot
To understand the nature of the relationship between two continuous variables
What is the correlation coefficient
Numerical value depicting the correlation between two continuous variables:
Expresses both the magnitude (0- 1) and the direction of the correlation (positive or negative)
What is the coefficient of determination and how is it calculated. Give an example
Coefficient of determination is the square of the correlation coefficient. If r = 0.7 then coefficient of determination = 0.49.
0.49 means that 49% of the variation can be explained by the two variables and 51% is due to other factors.
What are the criteria required for causation
- Causative occurrence must precede the effect
- If cause occurs then effect should occur
- If cause does not occur then effect should not occur
Correlation does not imply causality
What are the limitations of correlation and scatterplots
- Correlation does not imply causation
2. Lack of correlation does not mean that the variables are not correlated in a non-linear way
What is the difference between ordinal and continuous data
Ordinal data is categorical data with a set order it. The interval between categorical data is not known
Continuous data is not categorical and exists on an increasing or decreasing scale with known interval
What are the different types of correlation coefficients
Pearson’s (r) correlation coefficient
- Plots two continuous variables
Spearman’s (rho) correlation coefficient
- Plots two ordinal variables OR 1 continous and 1 ranked variable
Kendall’s correlation coefficient
- Plots two categorical variables
With regard to scatterplots what is more important the p-value or the r
The r (the correlation coeeficient)
Which is on a linear scale r or r^2. What is r^2
r^2
This is the coefficient of determination.
A coefficient of determination of 0.49 means that 49% of the variation can be explained by the relationship between the variables and therefore 51% explained by other factors
True or false: A significant p-value and a high r value on a scatterplot imply causation
False
What are Altman-Bland Plots
These plots quantify the agreement between 2 readings.
Which methods cannot be used to quantify the agreement between two readings
- comparing the means (and finding no significant difference)
- The correlation coefficient is measure of association, not agreement
Altman-Bland Plots can be used to measure agreement between two readings
When are you most likely to use the Altman-Bland plot
Comparing a measurement by a new device/monitor against the gold standard
Define the axes for the altman-bland plot. How is this plot interpreted
Y-axis –> Difference between methods (A - B)
X-axis –> Average of methods x axis [(A+B)/2]
Interpretation:
- The mean of the difference A - B is the relative bias.
- The SD is the estimate of the error
Classify variables
CATEGORICAL
- Ordinal (ordered)
- Nominal (non-ordered)
CONTINUOUS (familiar constant and computable differences between variables)
- Interval scale
- ratio scale
What is frequency in statistics
The number of times (N) or proportion (%) of times a variable (data item) has been observed to occur.
Distinguish the measures of central tendency
Mean: the average
Median: The middle value
Mode: The most common value
What is the dispersion
Dispersion tests are tests for the normality of the data distribution. tests of skewness and kurtosis
How should asymmetrical data be represented?
By Box and Whisker plots:
- Range: minimum to maximum value within the fence
- Interquartile range: 25th to 75 percentile
- Quartiles: Four equal groups of 25 %
Fences are calculated as follows
Lower fence is Q1 - 1.5 x IQR
Upper fence is Q3 + 1.5 x IQR
How is a normal or Gaussian distribution described
Mean (mu population and x-bar sample)
Standard deviation
Demonstrate how the standard deviation is calculated
X - mean
S - Standard Deviation
- Calculate X
- Subtract the mean from each data point (x - X)
- Square the result to make all differences positive
(x - X)^2 - Sum all the differences SUM [(x-X)^2]
- Divide the result by n = 1 –> gives you the variance
- Take the square root of the variance and you get the standard deviation
What is the point of the standard deviation and what does it mean
Allows you to determine the distribution in relationship to the mean.
1SD - 68% of people fall within 1 SD
1.96SD - 95% of people fall within 1.96 SD
2SD - 95.4% of people fall within 2 SD
3SD - 99.7% of people fall within 3SD
What is the standard error of the mean and why is it used. How is it calculated
If the study was repeated, you would get different patients and hence different results.
You can estimate the error in your sample by calculating the standard error of the mean.
SE = SD/ √n
What is the 95% confidence interval. How is the 95% confidence interval calculated
This is the range of values within which the true population mean is likely to lie
95% CI = X + 1.96 (SE) to X - 1.96 (SE)
Where SE = SD/ √n
Thus the SE becomes smaller with increasing sample size. As SE gets larger with increasing sample size, the 95%CI gets smaller indicating greater certainty in the precision of the result.
i.e. the larger the sample size –> the smaller the SE –> the more precise the result –> the narrower the distribution.
How are the SD and the SE interpreted differently
The standard deviation (and reference range) describes the amount of variability between individuals within a single sample
The standard error of the mean (and confidence interval) measure the precision with which a population value (e.g. mean (mu)) is estimated by a single sample.
What is a Z score. How is it calculated?
It is the number of standard deviations that a value (x) is above or below the mean
Z = (observed value - population mean)/(population SD)
Z = (x - mu) / (sigma)
Define the Null hypothesis (H0)
There is no difference between the groups.
H0: X = mu
We assume that the groups that are being compared are being drawn from the same population, and hence the population parameters mew and sigma are known
Define the alternative hypothesis (H1)
There is a difference between the groups
H1: X does not equal mu
An alternative hypothesis states that there is a difference between the groups.
What is the P value and how is it interpreted
The p-value is the probability of the observed result arising by chance (If H0 is true).
The p-value is the chance of getting the reported study result when the null hypothesis is actually true.
The smaller the p-value, the stronger the finding.
What does a p value of > than 0.05 mean
This means that there is a 1 in 20 chance that the study result occurred by chance despite the null hypothesis actually being true.
If this is the case the null hypothesis is accepted and the alternative hypothesis (H1) rejected.
A p value of less than 5% is statistically significant meaning that there is less than 5% chance that the study result occurred by chance if the null hypothesis is actually true.
What is a type 1 error and distinguish the alpha value from the p - value
- A false positive
- The null hypothesis is incorrectly rejected (there really is no treatment effect, but the study finds one)
- the alpha-value determines the risk of this happening.
An alpha-value of 0.05 - same as the p - value - so there is a 5 % chance of making a type 1 error
p-value is the probability of the observed result arising by chance alone (if the H0 is actually true)
a -value is the chance that the null hypothesis is incorrectly rejected ( a false positive / a type 1 error)
What is a type 2 error
- This is a false negative
- The null hypothesis is incorrectly accepted (there is a treatment effect, but the study finds none)
- The (1 - beta) determines the risk of this happening
- At a Beta is 0.8, so there is a 20% chance of making a type 2 error
What is the power of a statistical test? What is the point of calculating the power of a statistical test and how is it calculated?
The power of a statistical test is the probability of CORRECTLY REJECTING the null hypothesis
It is the chance of the study demonstrating a true result.
You can use ‘the power’ to calculate a sufficient sample size, and not run the risk of performing a pointless negative study.
Power = 1 - false negative rate
Power = 1 - Beta error
Normally power is 80% (i.e. a 20% chance of false negative result)
Which factors are required for the calculation of the an adequate sample size?
- Alpha value: level of significance (normally 0.05)
- Beta value: the power (normally 0.2)
- The statistical test you plan to use
- The variance of the population (the greater the variance, the larger the sample size)
- The effect size (the smaller the effect size, the larger the sample required)
Differentiate statistical significance from clinical significance
STATISTICAL SIGNIFICANCE
- the likelihood othat the results obtained were not due to chance
- data which do not reach statistical significance are too weak to reach any conclusion
CLINICAL SIGNIFICANCE
- the practical importance of a treatment effect
- clinical significance implies that the difference between treatmnes in effectiveness is clinically important, and it is possible that clinical practice will change if such a difference is seen.
Statistical significance is used to inform clinical significance
Define the primary outcome
Only the primary outcome can change practice, if the study findings are found to be both statistically and clinically significant
Define secondary outcomes
Secondary outcomes are only hypothesis generating. They need further investigation to ensure that this was not just a chance finding
Compare the standard deviation formula to the Chi squared test formula
S = √ [ Σ(x - X)^2 / (n-1) ]
x - obsrervation
X - mean
n = total number
Chi squared (X^2) = Σ(Oi - Ei)^2 / Ei
Oi - Observed value
Ei - Expected value
What is the Chi squared test used for, what does it calculate and how is it interpreted?
The Chi squared test can be used to test the ‘goodness of fit’ between observed and expected data.
It is used similar to the p-value used for quantitative data.
Interpretation:
Calculated Chi squared > Chi square critical value (p = 0.05) –> reject your null hypothesis.
Calculated Chi squared < Chi squared critical value (p=0.05) –> accept your null hypothesis
What is the Fragility index
Measure of robustness (or fragility) of the results of a clinical trial
The fragility index is the number indicating how many patients would be required to convert a trial from being statistically significant to not significant (p>0.05)
The larger the fragility index the better
How can a study of an intervention be biased?
- Intervention and control groups may be different at the start
- Intervention and control groups may become different as the study progresses
- Intervention and control groups differ, independent of treatment at the end of the study
Give an example of bias in the case that the intervention and control groups differ from the start of the study. Suggest how this bias can be reduced with regards to therapy and harm
Treatment and control patients differ in prognosis
Therapy
- Randomisation
- Randomisation with stratification
Harm
- Statistical adjustment of prognostic factors
- Matching
Give three examples of bias in the case that the intervention and control groups become different as the study progresses. Suggest how this bias can be reduced with regards to therapy and harm
Placebo
- Therapy: Blinding of patients
- Harm: Objective outcomes (mortality)
Co-intervention
- therapy: Blinding of caregivers
- Harm: Document treatment differences and statistically adjust
Bias in assessment
- Therapy: Blinding of assessors of outcomes
- Harm: Document treatment and statistically adjust
Give 3 examples of bias in the case that the intervention and control groups differ, independent of treatment at the end of the study
Loss to follow up
- therapy: ensure complete follow up
- harm: Ensure complete follow up
Stop study early because of large effect
- therapy: complete study as initially planned
Omitting patients who did not receive assigned treatments
- therapy: include all patients in the arm to which they were randomized
Describe the levels of evidence
RCTs - HIGH QUALITY
1a - Systematic review (with homogeneity) of RCTs
1b - Individual RCT (w narrow CI)
1c - All or none ( All pts dies before Rx avail but now some survive on Rx. or some patients died before Rx avail. but now none die on it)
LOW QUALITY RCTs and COHORT STUDIES
2a - Systematic review (with homogeneity) of cohort studies
2b - Individual Cohort studies (including low quality RCT < 80% follow up)
2c - ‘Outcomes’ Research or ecological studies
3a - Systematic review (with homogeneity) of Case control studies
3b - Individual Case control studies
4 - Case series (poor quality cohort and case control)
5 - Expert opinion or based on physiology, research or first principles
What is the indication for a Forest plot
to present the summary data of a meta-analysis
Discuss the interpretation of a Forest plot
X-axis: Odd’s ratio
Y-axis: List of studies
Vertical line: Line of no effect - Odds Ratio of 1.0
Horizontal lines: confidence interval of individual study
Square position: A point estimate of odds ratio
Square size: Weight of study according to weighing rules of the meta-analysis (representing sample size and statistical power)
Diamond: Combined result of the meta-analysis
Results can be considered statistically significant if the CIs of the combined result do not cross the line of no effect
Differentiate between parametric and non-parametric tests
Parametric tests
- Rqr. Normal distribution
- Are more accurate
- Rqr. Large sample size
Non-parametric tests
- Make no assumptions about the distribution of data
- Better with smaller sample sizes (n < 30)
- Have less power than parametric tests
What is a Receiving Operating Characteristic Curve (ROC)
A curve to determine the cut -off point in continuously distributed data, the predicts the presence of an outcome.
1) Screening cut point
2) Diagnostic cut point
3) Optimal cut point
How are ROC curves interpreted
Data point at extreme top and left of the curve = perfect test i.e. 100% sensitivity and 100% specificty
X - Axis is 100 - specificity
Y - Axis is Sensitivity
Further left on the plot the more specific (Minimum false pos)
Further up on the plot the more sensitive (Minimum false neg)
When are you most likely to see a ROC test
To determine an appropriate cut point for a test e.g. at what STOP-BANG score should you consider postoperative apnoea a clinical problem.
What is a Survival plot (Kaplan-Meier curve)
To present the time to an outcome in two different groups.
Used to report the time of specific outcomes in two patient cohorts.
The utility of a survival plot is that it can indicate the time period at which the patient is most likely to be at risk of the outcome (the steepest part of the curve)
