Stats continued

Question 1

What do survival analysis techniques do?

Answer 1

Concerned with representing time until a single event (e.g. death) occurs. Able to deal with situations in which event has not happened in every patient or when info on a case is only known for a limited duration - known as ‘censored’ observations

Question 2

What is a life table?

Answer 2

Table of proportion of patients surviving over time

Look at data at a number of fixed time points and calculate survival rate at those times. Most commonly used method is Kaplan-Meier.

Question 3

What is the Kaplan-Meier approach?

Answer 3

A survival analysis should usually be accompanied by Kaplan-Meier survival curves, a special plot based on similar methods to those used to calculate the HR. This allows a visual assessment of the pattern of survival over time, something which is impossible to capture in a single summary statistic. The survival curves can be used to estimate the proportions surviving at any given timepoint and the median survival in each group.

Recalculates survival rate every time an end event (e.g. death) occurs in the data set i.e. when a change happens rather than at fixed intervals. Loss to follow-up does not therefore affect the estimate of survival probability.

Question 4

What happens each time an observation is censored in a Kaplan-Meier curve?

Answer 4

The remaining cohort gets smaller, so the reliability of survival estimates reduces with time.

Question 5

What test is used to compare survival between two groups on a Kaplan-Meier curve?

Answer 5

Log rank test - p value will tell you how significant result is

Question 6

What is a Kaplan-Meier curve?

Answer 6

A non-parametric estimate of survival function
Built directly from observed event times
Accounts explicitly for censoring
Stepwise drops occur only at event times
DOES NOT adjust for covariates!!!

Question 7

How would you interpret a hazard ratio of 0.75?

Answer 7

25% lower event rate at any given time in intervention group

Question 8

What does persistent separation of KM curves suggest?

Answer 8

Difference in survival experience

Question 9

What does the log-rank test test?

Answer 9

• Null hypothesis - no difference in survival functions
• Compares observed vs expected events over time
• Gives global p-value

DOES NOT give effect size, adjust for covariates, or give info on how big the difference is!

Question 10

What does ‘hazard’ mean?

Answer 10

Instantaneous event rate at a given time - Not a risk or probability

Question 11

What does proportional hazards mean?

Answer 11

Ratio of hazards between groups constant over time i.e. one group consistently ‘riskier’ than the other, the relative difference does not change over time

The proportional hazards assumption states that the ratio of hazards in two groups remains constant over time, even if underlying hazards change.

If the proportional hazards assumption is correct then graphs of the log
of the cumulative hazard function in the exposed and unexposed groups will be
parallel.

Question 12

When might one deem proportional hazards to be plausible?

Answer 12

If on KM curves:
- Curves separate early
- Curves remain roughly parallel
- Curves do not cross

E.g. The roughly parallel separation of the curves suggests that the
proportional hazards assumption is reasonable (or vice versa)

Question 13

What does Cox regression do?

Answer 13

Cox regression analyses
the effect of exposure variables on survival. The output is the log hazards ratio, which can then be exponentiated into a hazard ratio.

Models time to event
Estimates HZ comparing groups
Allows adjustment for multiple covariates
Does not require specifying baseline hazard
Semi-parametric model

Question 14

What does the hazard ratio from Cox mean?

Answer 14

HR represents relative event rate at any given time, averaged over the f-u period, assuming proportional hazards

E.g. HR of 0.70 indicates 30% lower event rate at any given time in the exposed group, assuming proportional hazards

 Hazard ratios – the ratio of the hazard of an event in one group of observations divided by the hazard in another.
Measure the strength of the relationship between a predictor variable and
outcome
 HR = 1 – the risk is the same in both group (i.e. no difference in risk)
 HR >1 – adverse effect / risk of outcome is increased
 HR <1 – protective effect / risk of outcome decreased
 Assumes that the hazard is constant over time
 Factors / predictor variables that can be used can be binary, categorical or continuous

Question 15

What is the proportional hazards assumption?

Answer 15

• Cox regression assumes that the relative effect of exposure does not change over time (hazard ratios constant between two groups)
• Checked using visual inspection of KM curves, log-minus-log plots, and time-dependent covariates

Question 16

What might you say if proportional hazards might not hold?

Answer 16

If proportional hazards are violated, the Cox model still provides a summary estimate, but the hazard ratio should be interpreted as an average effect over time.

Question 17

How can you describe a 95% confidence interval?

Answer 17

We can be 95% confident that the true value lies in the range.

Question 18

How do you get ‘expected’ values for a chi-squared test?

Answer 18

E = (Row Total × Column Total) / Grand Total

Question 19

How do you interpret SMR?

Answer 19

SMR >100 = suggests higher mortality compared to expected/standard pop

SMR <100 = suggests lower mortality compared to expected/standard pop

Question 20

How do you calculate 95% CI for an SMR?

Answer 20

1. Approximate CI of SMR using Poisson approximation
2. Calculate ‘expected’ value from SMR and observed using E=O/SMR
3. Put ‘expected’ values into SMR calculation to obtain lower and upper confidence intervals for SMR

Question 21

What are the factors to consider when assessing the quality of a systematic review with meta-analysis?

Answer 21

Study-specific: Big meta-analysis so results are significant but may not be clinically relevant.

Methodological aspects – did the authors provide sufficient evidence that it was appropriate to combine studies? Heterogeneity – qualitative (study design, completeness and quality of data, absence of biases, population case-mix) and quantitative (extraction and analysis of the numerical data - statistical heterogeneity).

Publication bias – were smaller studies that did not demonstrate an effect not published.

Question 22

What is analysis of covariance?

Answer 22

A form of linear model with a continuous outcome variable, some categorical input variables and usually just one continuous input variable.

A special type of multiple regression, gets the same results.

ANCOVA - Is a statistical technique blending ANOVA and regression to compare group means on a dependent variable while controlling for the effect of one or more continuous, nuisance variables called covariates

Question 23

What are the assumptions of the log rank test?

Answer 23

1 - Data continuous or ordinal
2 - Risk of an event in one group relative to the other does not change over time – proportional hazards assumption.

Question 24

What is censoring?

Answer 24

Censoring is when an observation is incomplete due to a cause independent of the event of interest.

Question 25

What impact will applying a random effects model have on the pooled results?

Answer 25

A random effects model will produce a more conservative pooled odds ratio and wider confidence intervals as compared to using a fixed effect model.

Question 26

How does sensitivity analysis work?

Answer 26

A sensitivity analysis varies each input to see which are the most important drivers of the final result. Sensitivity analysis is a method used to determine how different values of an independent variable (or input) affect a particular dependent variable (or output) under a given set of ***assumptions*.**

Question 27

What is a limitation of recruiting participants opportunistically from primary care settings during periods of heightened disease activity?

Answer 27

Some children who met study eligibility criteria may not have been invited to take part

Question 28

What is informative censoring?

Answer 28

When the probability of being censored is related to the probability that the event of interest occurs (usually these are not related and such information is just 'censored')

Question 28

What are two ways of estimating the survival curve?

Answer 28

1. Life tables 2. Kaplan-Meier method

Question 29

How do cohort and period/current life tables differ?

Answer 29

Cohort: shows actual survival of group of individuals through time. Period/current: shows expected survivorship through time of a hypothetical population to which current age-specific death rates have been applied.

Question 30

When might Kaplan-Meier estimates be used over life tables?

Answer 30

When we know the exact follow-up time for each individual in the study. Means we don't need to divide survival time into discrete periods, and can therefore prevent info getting lost through grouping.

Question 31

What is Bayes theorem?

Answer 31

Bayes' Theorem is a mathematical formula used to calculate or update the probability of a hypothesis (A) based on new, incoming evidence (B). It determines the likelihood of an event by incorporating prior knowledge

Question 32

How do you undertake the Bonferroni correction?

Answer 32

To perform a Bonferroni correction, divide your desired significance level (α, usually 0.05) by the number of hypothesis tests or comparisons (n) you are performing. The new threshold (α/n) is used to determine significance. For example, with 5 tests at α = 0.05 , the adjusted threshold is 0.05/5 = 0.01

Question 33

How do superiority and non-inferiority trials differ and when might a non-inferiority trial be appropriate?

Answer 33

Superiority trials aim to demonstrate that one treatment is better than another Non-inferiority trials aim to show that a new treatment is not unacceptably worse than standard treatment by more than a pre-specified margin A non-inferiority design is appropriate where the new treatment may offer other advantages (e.g. reduced bleeding risk, ease of use) and similar efficacy is acceptable

Question 34

How are relative risks from a non-inferiority trial interpreted?

Answer 34

RR < 1 suggests similar or slightly reduced risk with new medication Upper CI < non-inferiority margin → non-inferiority demonstrated CI includes 1 → no evidence of superiority (if CI excludes 1 then evidence of superiority)

Question 35

When might cluster randomisation be appropriate?

Answer 35

- The intervention is being delivered at community level - High risk of contamination if individuals within the same community were randomised differently - Structural reasons make non-cluster designs difficult (e.g. changing practices within a hospital) - Cluster randomisation preserves intervention fidelity and feasibility

Question 36

When might cross-over designs be appropriate?

Answer 36

- A crossover design is appropriate because each participant acts as their own control, which reduces between-person confounding and increases statistical efficiency. - Appropriate for relatively stable, chronic conditions, where effects of intervention reversible, making carry-over less likely if an adequate washout period is used. - Where outcome (e.g. BP) can be measured repeatedly and reliably, which suits a crossover design.

Question 37

What are some important limitations of crossover designs?

Answer 37

- Carry-over effects may persist despite a washout period and bias estimates - Period effects, such as time trends or behavioural changes, may influence outcomes - Crossover trials are not suitable for progressive or irreversible conditions - Longer study duration increases the risk of dropout, which may bias results - Adherence to interventions may differ between periods - Results may be affected by order effects if treatment sequencing is imperfectly balanced

Question 38

Why might ARR or NNT be better than relative risk?

Answer 38

Absolute measures incorporate baseline risk, so they better reflect real-world impact and support decisions about resource allocation and prioritisation. Relative risks can appear impressive even when the absolute benefit is small, whereas ARR and NNT communicate the actual size of benefit and are more directly interpretable for planning and commissioning.

Question 39

What is a weighted average and how is it calculated?

Answer 39

When results are combined in a meta-analysis, a summary estimate is calculated. This value is a weighted average of the treatment effects of all of the eligible studies. Each study is assigned a weight, which determines the relative importance of that study in the meta-analysis and is based largely on the sample size. The estimate for each study is then multiplied by its weight in order to calculate the weighted average

Question 40

How would you calculate variance with a group of numbers?

Answer 40

1. Average squared deviation of each number from its mean (sample - mean) squared. 2. Sum of squared differences 3. For sample variation, do sum of squared differences/number of samples. For population variation, do sum of squared differences/N-1. 4. Can then calculate SE using formula on sheet.

Question 41

What test can be used to assess for statistical difference between two counts?

Answer 41

Z test Z = (a-b)/SQRT(a+b) Z > 1.96 is statistically significant

Question 42

What is a proportional mortality ratio?

Answer 42

A proportional mortality ratio measures the proportion of deaths occurring from a given cause for a particular occupation relative to the proportion of deaths from that cause in the whole population (or a comparison population)  A PMR is based on the underlying cause of death as recorded on the death certificate and provides little information about diseases that cause high morbidity but which are rarely fatal  Occupational information usually relates to the deceased person‟s last full-time job, but other jobs undertaken earlier in their career may be of more relevance  The PMR is not a population-based rate, and so it can be used to measure mortality where no denominator is available about the number of people who work in an occupation  The PMR of an occupational group for a specific cause depends not only on its death rate from the cause in question, but also on its death rate from all causes combined. This may be of relevance where an occupational group has particularly high or low mortality from the most common causes of death. As it is a proportional measure, the PMR can be raised in situations where the frequency of other causes of death is low