Analysis of variance (ANOVA).
A form of linear model with a continuous outcome variable and categorical input variables.
Bayesian methods.
Methods which allow parameters to have distributions. Initially the parameter ? is assigned a prior distribution P(?), and after data, X, have been collected a posterior distribution P(?|X) is obtained using Bayes’ Theorem, which links the two via the likelihood p(X| ?).
Binomial distribution.
The distribution shows frequency of events that have two possible outcomes.
When sample size is large, approximates to normal distribution.
Two parameters - n (sample size) and π (true probability)
Cluster randomised trial.
- Involves randomisation of clusters (groups) of participants as opposed to individuals
- Used to reduce contamination between control and intervention participants
- Some interventions may only be delivered at population rather than individual level (e.g. health promotion campaigns)
- Generally need a 30% larger sample size than RCT
- ICC measures the homogeniety within cluster (variation within a cluster) the higher the ICC, the higher the ICC, the less variation within a cluster and the more power is “lost”.
- Random mixed effects model assumes variation between clusters is random
- Fixed effects model assumes that differences between clusters is not random, i.e. differences between school attainment is to with systematic differences between schools and not due to chance.
- Complex to plan - need to try and account for variation
Example
- randomising schools in a trial of an intervention to reduce childhood obesity that was administered at school level and would be
hard to deliver to individual pupils with contamination of controls.
Conditional logistic regression.
Used to analyse binary data from matched case-control studies, or from cross-over trials.
Confidence Interval.
A 95% confidence interval displays the degree of uncertainty about the population parameter provided by the sample estimate
- technically, if one conducted the same study, with the same sample size, 100 times, we would expect 95% of these intervals to cover the true population parameter.
What is design effect?
The amount that a variance of an estimator has to be inflated to allow for clustering, or other aspects of the sampling scheme.
Effect modification
Given a model between an input variable and an outcome, effect modification occurs if the observed relationship is changed markedly when a third variable is included in the model.
Fixed effect vs random effect
In meta analysis:
Fixed effect: assumes treatment effect is the same (fixed) in all studies in the meta-analysis
Random effects model: allows the treatment effect to vary across studies.
FE and RE differ in the way studies are weighted and in the interpretation of the summary effect.
Forest plot
A plot used in meta analysis. Usually it comprises a series of estimates and confidence intervals from the component studies, and a summary estimate and confidence interval. Supposedly named because it appears like a set of trees.
Funnel plot
A plot used in meta analysis to try and detect publication bias. It comprises a plot of the precision of estimates of treatment effects from component studies versus the estimate itself.
Methods to account for clustering in analysis x3
- Calculating summary statistics for each cluster and then analysing these using standard techniques
- Calculating robust standard errors that account for clustering
- More sophisticated techniques, such as generalised estimating equations and multi-level models
Hazard Rate:
The probability per time unit that a case that has survived to the beginning of the respective interval will fail in that interval. Specifically, it is computed as the number of failures per time units in the respectiveinterval, divided by the average number of surviving cases at the mid-point of the interval.
Hazard Ratio (Relative Hazard):
Hazard ratio compares two groups differing in treatments or prognostic variables etc. If the hazard ratio is 2.0, then the rate of failure in one group is twice the rate in the other group. Can be interpreted as a relative risk.
Kaplan-Meier plot.
A graphical plot of the probability of survival on the y axis by survival time on the x-axis. Censored observations can be incorporated in the plot.
Likelihood:
The probability of a set of observations given a model. If the model has a single parameter θ, it is denoted P(X|θ) where X denotes the data.
e.g. Probability of B occurring given that A occurred P(B|A)
Logistic regression.
Used to analyse data where the outcome variable is binary. It uses the logistic transform of the expected probability of ‘success’.
Meta-analysis.
A method of combining results from different studies to produce a overall summary statistic, usually in clinical trials.
Multiple linear regression.
Often just known as multiple regression. Used to analyse data when the outcome is continuous and the model is linear.
Null hypothesis
�For comparing two samples the assumption under the null hypothesis is that they both came from the same population
�type 1 error: occurs when null hypothesis is true and wrongly rejected, i.e. conclude significant difference exists when in reality doesn’t
�type 2 error: occurs when null hypothesis is wrongly accepted when false, i.e. missing a true difference
Type 1 error
Type 1 error: Occurs when null hypothesis is true and wrongly rejected, i.e. conclude significant difference exists when in reality doesn’t
Type 2 error
Type 2 error: occurs when null hypothesis is wrongly accepted when false, i.e. missing a true difference
NNT:
Number Needed to Treat. An estimate of number of patients that would need to be treated under a new treatment for one more of them to achieve the desired outcome than under the standard treatment
�NNT = 1/ARR (absolute rate reduction)
�method of expressing trial outcomes
�possibly more easily applicable to clinical practice than OR/RR.
However, be aware that it is dependent on the baseline incidence rate, and so cannot be interpreted without knowledge of the baseline incidence.
Example NNT 1.2 ~ for Helicobacter eradication, NNT 40 for preventing death with aspirin after MI
NNH:
Number Needed to Harm.
Number of patients that a physician would have to treat with a new treatment to harm one extra patient who would otherwise have not been harmed.
Harm may be an adverse reaction, or treatment failure, death etc.
