Critical numbers🔢 Flashcards

Question

What do risk/odds ratios <1 indicate?

Answer 1

A lower risk/odds in the group of interest

Answer 2

1/risk difference = x This means x patients at risk would need to be treated with aspirin to prevent 1 additional case of hypertension.

Answer 3

Calculate the risk ratio then take away 1 from it and multiply by 100 to get the % reduction in risk

Answer 4

Need it for probability Odds = Probability/(1 − risk) Odds have symmetry so Y is the inverse of the odds for the outcome not-y

Answer 5

Population-level data

Answer 6

· Can look at trends between regions or over time · Data collection fairly easy (tends to be routinely-collected) · Fast · Inexpensive · Few ethical issues

Answer 7

· Cannot determine individual-level associations (ecological fallacy) · Cannot demonstrate cause and effect · Lack of control over variables collected

Answer 8

Outcome and exposure status measured simultaneously

Answer 9

· Can look at associations – hypothesis-generating · Data collection fairly easy · Can study multiple exposures and outcomes · Fast · Inexpensive

Answer 10

· Cannot demonstrate cause and effect · Prone to bias and confounding · Not useful for rare exposures or outcomes

Answer 11

Participants selected on the basis of outcome

Answer 12

· Can look at association between outcome and prior exposures · Fast · Inexpensive · Good for studying rare outcomes · Can study multiple exposures

Answer 13

· Cannot determine incidence/risk of outcome · Limited control over data quality – poor historic records or recall bias · Retrospective nature limits ability to determine causality · Not useful for rare exposures

Answer 14

Participants selected on the basis of exposure

Answer 15

· Can look at incident cases and associations with exposure · Good for studying rare exposures · Can study multiple outcomes · Control over data collected · Exposure determined before outcome occurs so can demonstrate temporality for potential cause and effect

Answer 16

· Mostly prospective which can be time consuming · Risk of loss to follow-up · Expensive · Not useful for rare outcomes

Answer 17

Participants randomly allocated to interventions then followed up to compare outcomes

Answer 18

· Can study intervention effects on outcome(s) · Random allocation means confounding factors should be evenly distributed · Control over variables collected · Comparator group means ability to account for placebo/temporal effects · Less prone to bias, particularly where blinding and objective outcome assessment used · Gold standard for establishing causality

Answer 19

· Time consuming · Expensive · Require expertise to run · Can only be used where ethics and participant willingness permit randomisation to intervention · Overly strict eligibility criteria may render sample not fully representative of population

Answer 20

Population Intervention Comparator Outcome

Answer 21

The stronger an association, the more likely it is to be causal

Answer 22

Association shown across different studies in different locations, populations, using different methods, etc

Answer 23

specific exposure-outcome relationship, e.g. asbestos and asbestosis

Answer 24

– exposure must precede outcome

Answer 25

dose-response, i.e. increase in exposure = increase in outcome

Answer 26

biological mechanism that would explain outcome development

Answer 27

compatible with existing theories

Answer 28

Outcome altered with experimentation, e.g. reversible

Answer 29

Similar cause-effect relationships established

Answer 30

The average or typical values

Answer 31

How spread out the data are around these values

Answer 32

What the minimum and maximum observed values are

Answer 33

Mean, median and mode

Answer 34

The dispersion around the mean

Answer 35

Mean reported with standard deviation Median reported with a central range

Answer 36

Calculate difference between each observation and the mean Square them (to make them all positive values) Sum them Divide by the number of observations minus 1 Take the square root (to reverse the earlier squaring)

Answer 37

Standard deviation squared

Answer 38

The lowest value to the highest value

Answer 39

The median is the 50th centile. We can describe spread using centiles around that, e.g. 5th to 95th centile gives the 90% central range.

Answer 40

The 25th to the 75th centile, which gives the central 50% range.

Answer 41

AKA Gausian distribution or Bell shaped curve Standard deviation gives us info on the shape of the distribution

Answer 42

This sample has the same mean but the median is lower Mean pulled out to the extremes It allows us to inspect it Usually report median and centiles with it

Answer 43

Sometimes need the

Answer 44

Make distributional assumptions

Answer 45

Make no assumptions (distribution free)

Answer 46

Symmetric (mean, median and mode are equal) The empirical or 68–95–99.7 rule: 68% of values lie within 1 SD of the mean 95% of values lie within 2 SD of the mean 99.7% of values lie within 3 SD of the mean

Answer 47

Compare measures of central tendency E.g mean of one vs mean of another

Answer 48

A measure of linear relationship between variables Quantified by the correlation coefficient r

Answer 49

r is bound between -1 and 1 The closer to |1|, the stronger the correlation The closer to 0, the weaker the correlation Can be positive or negative correlation

Answer 50

We can perform a statistical test to determine how likely the result we have observed is ‘real’ Or if it is more likely there is in fact no true difference and we are just seeing chance sampling variation To do this we test the hypothesis of no difference between groups We then weigh up the strength of the evidence against that hypothesis And decide if we should reject that hyothesis

Answer 51

But first, let’s recap probabilities… Probability values range from 0 to 1 (though as you’ve seen we often x100 to express as a percentage) A probability of 0 means an event is impossible A probability of 1 means an event is certain So the smaller the probability the less likely the outcome The probability of heads from a fair coin toss is 1/2 = 0.5 The probability of rolling a 3 on a die is 1/6 = 0.17 The probability of 7 from a single roll is 0/6 = 0

Answer 52

Define the null hypothesis: This is typically the theory we want to disprove The cynic’s belief “The null is dull” We will assume this hypothesis is true until we see sufficient evidence to the contrary Denoted H0 In our example: H0 = no difference in mean IQ between groups

Answer 53

Define the alternative hypothesis: This is the opposite theory to the null Denoted HA or H1 In our example: HA = there is a difference in mean IQ between groups Using statistical notation… H0: μSHEF – μMU = 0 HA: μSHEF – μMU does not equal 0

Answer 54

Choose a significance level for the test: This is how we determine whether our result is statistically significant It is also the probability we make a false positive conclusion and reject the null hypothesis when it is in fact true So we need to minimise this risk Typically it is set around 0.05 (so 5%)

Answer 55

Perform an appropriate statistical test: Panic not - we won’t be performing these tests by hand! But for information… we use the sample data from our two groups to calculate a test statistic This effectively reduces all of our data down to a single value We then compare that test statistic against the distribution we would expect under the null hypothesis and work out the probability of our result if the null were true Hypothesis tests are basically a comparison of that which we observed versus that which we expect under the null Some examples of statistical tests (journal articles should state which test has been performed) For numeric outcomes: t-test, ANOVA/ANCOVA, linear regression For categorical outcomes: Chi-squared test, logistic regression

Answer 56

Decision time: We use the probability value from the statistical test to weigh up the strength of the evidence against the null hypothesis We call this probability value the p-value The p-value is the probability of seeing an effect of the observed magnitude or greater if the null hypothesis were true If the p-value is high the result is probable under the null hypothesis… so it is likely the null hypothesis is true The smaller the p-value, the less likely it is we would see our observed result under the null hypothesis If the p-value is smaller than our significance level (so < 0.05 in our example) we reject the null hypothesis and declare the result statistically significant

Answer 57

In our example we had a mean difference in IQ of 9 points We performed a statistical test on the difference in means The p-value from that test was p = 0.003 This means the probability of seeing a difference of 9+ points on the IQ scale under the assumption the two groups are the same is 0.003 (or 0.3%) So pretty unlikely 0.003 is lower than 0.05 so we reject the null hypothesis of no difference Our conclusion would be there is evidence to suggest University of Sheffield students have higher average IQ than MadeUp University students

Answer 58

The standard Deviation is for Describing The standard Error is for Estimating

Answer 59

The standard error indicates how different a sample mean is likely to be from the population mean It tells us the precision of estimation The smaller the standard error of the mean, the more precise our estimate of the mean i.e. the closer it is likely to be to the true population mean We estimate the standard error using our sample size (n) and standard deviation (SD) Standard error of the mean = SD/√n

Answer 60

This means our precision is affected by these two things: how variable our data are (the SD) and how large our sample is (n) This makes sense because the less variable the data are, the more precise our estimation. The more people we sample, the better the representation and therefore the more precise our estimation.

Answer 61

Just because a result is statistically significant doesn’t mean it is clinically important! Statistical significance just means an observed result is unlikely under the null hypothesis Clinical importance means the result is practically important/meaningful in the real world A very large study may find a very small effect to be statistically significant… but is it meaningful? e.g. a reduction in flu symptoms from 72 to 70 hours? Meh a reduction from 72 to 24 hours? Noticeable improvement The magnitude of the effect itself is important and we can use confidence intervals to help judge clinical importance

Answer 62

Quantifies the linear association between two numeric variables Variable order doesn’t matter (correlate x~y or y~x)

Answer 63

Allows one variable to be predicted from the other Order matters (predict y from x) Can handle multiple predictors (predict y from x1, x2, x3…) Variables don’t have to be numeric

Answer 64

y= mx+ c or y=a+ bx y and x just represent the variables we are looking at a and b explain the linear relationship between them

Answer 65

Variable being predicted The “response” or “outcome” or “dependent” variable (its value depends on x)

Answer 66

The intercept of the regression line Also known as the ‘constant’ This is the point at which the line crosses the y axis when x = 0

Answer 67

The regression coefficient The slope (gradient) of the regression line The larger the value the steeper the slope The sign indicates the direction of effect It is the change in y associated with a unit change in x

Answer 68

The “predictor” or “explanatory” or “independent” variable It is the variable we are using to predict y

Answer 69

More than one predictor For example, FEV1 is typically predicted from characteristics such as height AND age AND sex AND ethnicity We can extend our regression model y= α+β1x1+ β2x2 + … FEV1=a+b1height+ b2age + Modelling multiple variables together is: More realistic More efficient More accurate We can include multiple predictors, categorical or numeric, and create more useful models.

Answer 70

We can adjust or control for the effects of other variables. Remember confounding from lecture 1? Incorporating multiple variables in a model means we can adjust our variables of interest for the effects of potential confounders. We can analyse the simultaneous effects of multiple variables on an outcome and look for independent predictors or interaction effects We can make predictions based on combinations of risk factors – this is essential in clinical prediction modelling

Answer 71

Outcome at follow-up = a + b₁(outcome at baseline) + b₂(sex) + b₃(age) + b₄(treatment) The b₄ coefficient tells us the adjusted treatment effect, e.g. adjusted between-group difference in means.

Answer 72

Prognostic modelling uses advanced regression techniques to predict the risk of illness or future course of illness for an individual based on their individual combination of clinical and non-clinical characteristics Move towards stratified medicine Informs clinical decision-making Healthcare professionals use statements about prognosis to: Inform patients and families about likely future outcomes Guide decisions regarding course of treatment

Answer 73

Did the study address clear research question(s)? Were appropriate methods used to answer question(s)? Are the results valid? Low risk of bias? Correctly interpreted? If so, what are the potential implications for practice? So we need to consider all aspects of a study: Question, design, conduct, analysis, interpretation, reporting

Answer 74

Is the research question clear and focussed? Is the study design appropriate? - Is the research question clear and focussed? - Is the study design appropriate? - What are the strengths/weaknesses? - Is there potential for bias? Has it been addressed? - Are the analysis methods appropriate? - Have the results been interpreted correctly? - Are the findings relevant to your practice?

Answer 75

Did the study address a clearly focussed research question/hypothesis? From the information provided can you identify the PICO/PECO elements? Population Intervention or Exposure Comparator Outcomes

Answer 76

Is the design appropriate given the research question? Strengths/limitations? Where does it sit in the hierarchy of evidence? Was the methodology sound? The design may technically be high in the hierarchy but if not well executed, the strength of the evidence may still be low. E.g. We put RCTs above cohort studies in the hierarchy of evidence But if an RCT is very poorly conducted and has extremely high risk of bias… Would we consider it better than very well executed prospective cohort studies?

Answer 77

Some design aspects to consider are relevant to all studies, e.g. Is the sample representative of the population of interest? Have potential sources of bias/confounding been addressed? Were clearly defined, objective outcome measures used? Other aspects will differ by study design, e.g. transparency regarding non-compliance or loss to follow-up in an RCT; control selection in observational studies. If the study was registered prior to being conducted (e.g. published protocol) did the final publication reflect the original plan? If not, were deviations transparently explained? If a study is well-reported there should be sufficient information to enable replication (or at least references/links provided to said information).

Answer 78

Are all recruited participants accounted for? Are summary statistics well reported, e.g. appropriate measures of central tendency reported with measures of dispersion? Were the authors transparent regarding missing or incomplete data? (Look for Ns on tables, flowcharts and graphs or in text) Other signs of poor reporting, e.g. unclear units of measurement, mislabelling of figures, inconsistent/truncated axes, etc.? Multiple hypothesis tests on descriptive data?

Answer 79

Are results given for all outcomes (if not in main body, in supplementary material or another paper referenced)? Any evidence of ‘cherry picking’? Any inappropriate data manipulation, e.g. arbitrary categorisation of continuous outcomes or questionable assumptions made? Were the statistical tests appropriate given the type of data and the research question? If using NHST were p-values reported correctly? i.e. not just “NS” or “p>0.05” Were confidence intervals reported? If reporting risk, is it clear whether absolute or relative? Any inappropriate reporting, e.g. incident risk from a case-control study? Was sample size estimation/power calculation performed a priori? Were assumption checks performed for statistical models? Was goodness of fit determined? Multiplicity?

Answer 80

What are the results? Was the reporting comprehensive? Are the results believable? Do they fit with other available evidence? (Can apply Bradford Hill criteria here) Do the design and analysis allow for the conclusions drawn, e.g. causality? Are the results clinically/practically important? Focus on effect size and precision rather than just statistical significance. Can the findings be used to inform practice?

Answer 81

- They also summarise available research on a given topic - The question may be broader - They do not necessarily follow such strict, standardised, transparent methodology - They are therefore less rigorous, more subjective and can be more prone to selection bias

Answer 82

They also summarise available research on a given topic The question may be broader They do not necessarily follow such strict, standardised, transparent methodology They are therefore less rigorous, more subjective and can be more prone to selection bias

Answer 83

1) Specify research question (and check recent systematic review doesn’t already exist!) 2) Develop search strategy and inclusion/exclusion criteria 3) Identify relevant studies 4) Assess quality and risk of bias 5) Extract results from each study 6) Pool results 7) Answer research question (Potential final step: update review at a later date if further primary evidence becomes available)

Answer 84

- “The analysis of analyses” - Statistical method for combining evidence from different (separate but related) sources - In the early 1900s, Karl Pearson used a meta-analytic approach in a BMJ paper - Methodological and computational advances later increased the use of these approaches - Meta-analysis is often (but not always) used in systematic reviews

Answer 85

One row per study The point estimate is shown as a square with size proportional to the size of the study The horizontal lines are confidence intervals The x axis is a measure of effect- in this case odds ratio The solid vertical line indicates the line of no effect (the null, so given these are ORs, the null value = 1) The diamond shows the pooled estimate from the meta-analysis

Answer 86

These are different approaches to meta-analysis (just for info – you won’t need to go into this level of detail).

Answer 87

A measure of variation between different studies (heterogeneous = different; homogeneous = similar).

Answer 88

Analysis to test the robustness of the findings of primary analysis – looks at the effect of assumptions or variations in approach.

Answer 89

Preferred Reporting Items for Systematic Reviews and Meta-Analyses. These are guidelines aimed to improve the reporting of systematic reviews. First published 2009; updated 2020.