Statistics

advantages and disadvantages of cohort study

+ eliminates reverse causality as the variable was there prior to cancer onset. - there may be unknown confounders or unmeasured confounders that are not adjusted for - time consuming and expensive and resource heavy

comparing 2 confidence intervals - how do you know if the difference is significant?

- no overlap: statistically significant - bars overlap: unsure - overlap and point estimate falls within the CI of another: no evidence of statistical difference

p value if confidence interval ends at a point where there is no benefit or harm?

0.05 (5%)

what are you assessing when looking at a baseline characteristics table?

1. is study population similar to the population you want to treat? 2. internal validity - check 2 arms are similar. if measured characteristics are balanced can assume others are balanced.

hiararchy of evidence

1. systematic review 2. critically appraised topics 3. RCT 4. cohort 5. case control 6. case series

how many standard deviations from mean is 95% data?

1.96 SD

how many SD from mean is 99% data?

2.58 SD

how to calculate 95% confidence interval?

95% CI is the range of values that lie between 1.96 standard errors below the result and 1.96 standard errors above the result. can then be 95% certain the true value of the mean lies within the range. mean +/- 1.96 x SE

features of a case series study

A case series is a type of medical research study that tracks subjects with a known exposure, such as patients who have received a similar treatment, or examines their medical records for exposure and outcome. eg observe that oesophageal cancer patients drink hot tea.

features of a randomized controlled trial

A study in which people are allocated at random to receive one of several clinical interventions. One of these interventions is the standard of comparison or control.

features of a case control study

A study that compares patients who have a disease or outcome of interest (cases) with patients who do not have the disease or outcome (controls), and looks back retrospectively to compare how frequently the exposure to a risk factor is present. eg compare groups of people with and without oesophageal cancer and notice those with cancer drink hot tea more frequently.

what does a small P value tell us?

P value is the probability of the null hypothesis being true and due to chance. if the P value is small, the chance the difference has arisen as a result of sampling variation is very small. therefore the treatment or real factor has real effect and influences outcome.

features of a cohort study

Researchers compare what happens to members of the cohort that have been exposed to a particular variable to what happens to the other members who have not been exposed. eg taking a large cohort without cancer and measuring the temperature of their tea and other confounders. then wait until some develop oesophageal cancer.

how to work out how many standard deviations something is away from the mean?

Z= (value - mean)/ SD eg bp of 75 when mean is 85 and SD 10 (75-85)/10 = -1 SD from mean, below average Z scores above or below 2SD's are atypical

frequency plot, what to observe?

can be unimodal, bimodal, symmetric (normal), Asymmetric (skewed)

whats the odds ratio and what's it used for?

can interpret an OR as a RR. odds = number with event/ number without odds intervention 960/9040 = 0.106 odds control 1200/8800 = 0.136 odds ratio is ratio of odds in the intervention group to ratio of odds in the control group. 0.106/0.136 = 0.8 (same as RR for rare events, interpret as RR (1))

how to summerise data?

categorical - percentages in each group numerical 1. average value 2. spread/variability 3. shape of distribution

types of data

catogorical: binary, nominal, ordinal numerical (continuous or discrete): measurements and counts

how to caculate the treatment effect for difference in cardiovascular events between aspirin and control groupsn in 1 month (binary outcome)

control risk = number events/number of people 1200/10000 = 0.12 or 12% (12 per 100, so 100/12 = 1 in 8 patients will have an event) treatment risk = 960/10000 = 0.096 or 10%. 10 per 100. 100/10 so 1 in 10 patients will have an event.

features of the summary statistic

diamond - result of meta analysis summary statistic. combined average, weighted estimate. small CI due to pooling and large sample size.

comparisons between treatment groups can be affected by sampling variability - observed difference may not actually be due to treatment or risk factor. how do we judge whether this is the case?

hypothesis tests/significance tests which give us P values that help us to measure the strength of evidence that a treatment, and not sampling variability is the cause of the observed difference. allows us to determine which treatments are better.

how to interpret CI's for RR and RD?

if CI for a relative risk does not contain the the null value of 1, we can be 95% sure the difference is significant. if CI for risk difference does not contain the null value of 0 we can be 95% sure difference is significant. * can't conclude there is no difference

2b. how to summerise the variability or spread of the data with a calculated median?

interquartile range - describes where the central 50% of the data lies. range is whole spread of data.

what does a p value of less than 0.05 tell us?

is P value is less than 0.05 we can be 95% sure not due to chance. there is still a 1 in 20 (5%) chance it is due to chance. this is an arbitrary cut off point. if P value is lower it's more convincing.

how to determine whether the finding of a study is clinically important?

look at size of effect and confidence interval. for clinical significance it must be statistically significant and have a large effect.

1. how to summerise the central tendency or average?

mean and standard deviation median and interquartile range - more robust to outliers

comparing confidence intervals and reference ranges?

mean birth weight is 3.5kg 95% CI 3.3-3.6 kg using 1 standard error. 95% certain mean is in this range. 95% reference range is 2.5kg-4.5kg using 1 standard deviation. 95% births will be within range.

what is the standard error and what is it used for?

measure of certainty. used to describe the uncertainty of treatment/exposure effects. tells us how precisely we have estimated the treatment effect (how close to true result), used to assess the variability of repeated study results.

how do significance tests work?

more difficult to prove something is true so easier to prove something is not true. Firstly presume that the observed difference is caused by sampling variation and then try to falsify null hypothesis.

how to interpret a risk difference of -0.024

negative value (less than 0) shows risk is lower in treatment group. multiply to get more meaningful difference. eg 24 per 1000, can avoid 24 cardiovascular events per 1000 treated with aspirin.

whats the number needed to treat and how is it used to communicate risk differences?

number needed to treat with the new treatment in order to prevent one adverse event from occuring. NNT = 1/ absolute risk reduction NNT = 1/ -0.024 = 42 people treated to avoid on average 1 cardiovascular event.

properties of the normal distribution

on a symmetrical bell shaped curve. within 1 SD of mean - 68.27% within 2 SD of mean - 95.45% within 3 SD of mean - 99.73%

how to interpret a forrest plot

point - RR bars - 95% CI size of square indicates weight diamond - summary statistic line of no effect (if RR 1)

how to compare risk between 2 groups?

relative risk (risk ratio) where we divide the risk in the treated group by the risk in the control group. (1) absolute risk (risk difference) where we subtract the risk in the control group from the risk in the treatment group. (0)

work out the relative risk and absolute risk for the cardiovascular data risk on aspirin is 0.096 and risk without aspirin is 0.12

relative risk = risk intervention / risk control = 0.096/0.12 = 0.8 risk difference = risk intervention - risk control = 0.096-0.12 = -0.024

how to interpret a relative risk of 0.8

relative risk/risk ratio is 0.8, the fact it's less than 1 shows aspirin reduces chance of cardiovascular event. risk in treated group is 0.8 times less, risk is 80% of control group, or risk reduced by 20%.

compare use of relative risk and risk difference

relative risks can look impressive, especially when event is rare. absolute difference is preferred measure as it tells us about number of events, but doesn't look as impressive, less susceptible to misinterpretation.

why do we not expect exactly the same results when studies are repeated?

sampling variability - different people are studied and they will have different responses.

2a. how to summerise the variability or spread of the data with a calculated mean?

standard deviation is a measure of the average distance of a set of observations from the mean. 0 means no variation. also skewed by outliers.

explain evidence synthesis

systematic identificiation of all RCT's or other studies and combining the results.

studies identify a primary outcome. how does the primary outcome differ between experimental and observational studies?

treatment effects - compare outcome between control and intervention groups. exposure effect - compare the rates of exposure between those with and without the disease.