Statistics, epidemiology and study design

Question 1

What formular should be used to calculate combined sensitivity or specificities for multiple diagnostic tests?

Answer 1

Combined probablity (specificty or sensitivity):

= 1 - (1- spec/sen 1) x (1 - spec/sen 2)

E.g. A test has a specificity of 60%. Another test has a specificity of 80%. If both tests are performed, the specificity of the result is:

= 1- (1-0.6) x (1-0.8)
= 1 - (0.4 x 0.2)
= 1 - 0.08
= 0.92
= 92%

Question 2

What is the geometirc mean? It’s a measure of central tendency.

Answer 2

A special type of mean that corrects better for very large a very small numbers. It’s calculate by multiplying n values together, then taking the nth root of the results.

E.g. geometric mean of 2, 3 and 10 (n = 3)

= cubed root of(10 x 2 x 3)
= 3.91

Compare with the arithemetic mean:

(10+2+3)/3

= 5 (shifted much more greatly towards the 10)

Question 3

What’s the arithemtic mean?

Answer 3

It’s the normal mean - (1+2+3+… + x) / n (where n = number of numbers)

Question 4

What is the mode?

Answer 4

The value that occurs the most often in a set of numbers. It’s a meausre of central tendency.

Question 5

What are non-parametric tests used for?

Answer 5

Statistical tests to be used when data is nor noramlly distributed.

Question 6

What has more statistical power, parametric or non-parametric testing, for discovering significant effects?

Answer 6

Parametric tests on normally distributed date.

Question 7

What might lead to data not being normally distributed and therefore requiring non-parametric stastical tests?

Answer 7

When the data is ranked (aka ordinal data, when central tendency is better represented by the median (many or large outliers), when the sample size is too small, when the outliers cannot be removed.

Question 8

What some examples of parametric statistical tests?

Answer 8

T-test and ANOVA

Question 9

What are you comparing with a T-test? How does this compare to ANOVA?

Answer 9

You are comparing the means of 2 normally distributed data sets to look for a meanful difference between the two. If you wanted to compare the means of more than 2 groups, you need to do a ANOVA.

Question 10

What’s a paired t-test used for?

Answer 10

When each value in one dataset corresponds meaningully to a value in the the other dataset. E.g. when dataset 1 is a measurement before a durg is given, and dataset 2 is a measurement after the drug was given on the same set of people.

Question 11

What is 1 tailed t-test ued for?

Answer 11

When you need to no if the mean you are interested in was higher (or lower) than the mean you are comparing to. A 2 tailed t-test will only tell you mean 1 is significantly different to mean 2 or not.

Question 12

What are some examples of non-parametric statistical test?

Answer 12

Chi-square test, Kruskal Willis test (ANOVA equivalent for non-parametric datat), and the Mann Whitney tests (the equivalent to the

Question 13

What are some examples of non-parametric statistical test?

Answer 13

Chi-square test, Kruskal Willis test (ANOVA equivalent for non-parametric datat), and the Mann Whitney tests.

Question 14

What is the purpose of comparative statistical tests?

Answer 14

Comparing the same measure of central tendency (e.g. mean/median/mode) from 2 or more data sets to establish whether or not there is a significant difference between the two groups with respect to 1 or more outcomes.

Question 15

When two data sets are normally distributed, and parametric testing is indicated to establish if there is a significantly different measure of central tendency present or not, what measure of central tendency should be compared?

Answer 15

Mean

Question 16

What are the data types that are important before choosing a statistical test?

Answer 16

Quantitative (might be continuous or discrete) data is that which is made up of numbers on an infinite scale that can be added, subtrated and divivded. Categorical data is that which falls into discrete buckets - it can be nominal (e.g. yes, no, maybe,) Ordinal (ranked, e.g. unlikley, likely, very likely), interval (ranked and with fixed intervals - e.g. scores 1-10, 11-20, 21-30).

Question 17

Which comparative statistical test can be used for non-normally distributed data that is catagorical to compare two datasets?

Answer 17

Chi-square test of independence, spearman’s r

Question 18

What’s the name of the test used typically in table 1 to determine if a study population between two arms are heterogenous?

Answer 18

Chi-square test of best fit (or cochrane Q)

Question 19

Which comparative statistical test can be used for non-normally distributed data that is catagorical to compare 3
or more datasets?

Answer 19

Kruskal-Wallia (the non-parametric test version of the ANOVA).

Question 20

If you wanted to compare 3 parametric datasets with regards to 2 or more outcome variables, which statistical test would you use?

Answer 20

MANOVA (modfied ANOVA allows multiple outcomes to be tested)

Question 21

If you have wanted to compare to non-parametric quantitative data sets that are un-paired, how would you do this?

Answer 21

Wilcocon Rank-Sum test. For paired data, do the paired Wilcoxon Signed-rank test.

Question 22

What is the formular for number needed to treat?

Answer 22

The inverse of the absolute risk reduction.

So 1 / (risk 1- risk 2)

Question 23

What are odds?

Answer 23

The number of times something happened compared to the number of times something didn’t happen to members of a population expressed as a ratio.

e.g. There was a population of 100 people who went for a walk. 10 fell over. What are the odds of falling over when walking if in this population?

10 fell over
90 did not fall over

Odds of falling over

=10:90
=1:9

Question 24

What is relative risk?

Answer 24

The chance something will happen to a proprotion of the population expressed as percentage or a decimal. It is calculated by dividing the number of people who the event occured to by the total number in the population.

E.g. There was a population of 100 people who went for a walk. 10 fell over. What is the risk of falling over when walking if in this population?

Relative risk:

10 fell over
100 went walking (population)

= 10/100
= 1/10

Question 25

What is absolute risk?

Answer 25

Risk of something occuring in one data set, minus the risk of that thing occuring in another data set.

E.g.
In population A, the risk of falling was 1/10.
In population B, the risk of falling was 4/10.

The absolute risk reduction acheived by being in population A is:

4/10 - 1/10
= 3/10.

Question 26

What is the inverse of absolute risk reduction?

Answer 26

Number needed to treat.

Question 27

What type of bias to randomisation reduce?

Answer 27

Selection bias (i.e. any known or unknown biases applied to placing participatns into different arms of a trial).

Question 28

What is ascertainment bias?

Answer 28

This is the biases that originates from investigators knowning what type of intervention a participant is receiving, and threatening to distort how the results are intepreted.

Question 29

What study design model best reduces ascertainment bias?

Answer 29

Blinding the investigators (single blinding) and the participatns (double blinding)

Question 30

What is bias in handling dropouts?

Answer 30

This bias changes study outcomes when cohort characteristics change due participant drop outs.

Question 31

What is recall bias?

Answer 31

This is bias that occurs due to inaccurate recollection of events. It impacts retrospective studies.

Question 32

How is recall bias best mitigated with study design?

Answer 32

By creating a prospective study.

Question 33

How is sensitivty calculated?

Answer 33

True positive number/(true positive number + false negative number)

Question 34

Calculate sensitivity of the new test using the attached dataset.

Answer 34

True positive number/(true positive number + false negative number)

6/(6+0) = 1.

Sensitivity = 100%

Question 35

How is specificity calculated?

Answer 35

True negatives/(true negatives + false positives)

Question 36

Caculate the specificity of the new test using the attached dataset

Answer 36

True negative/(true negative + false positive)

20 / (20 +9) = 20/29

= ~69%

Question 37

How do you calculate the positive predictive value of a test assuming that the population prevalence of the disease is the same is the disease prevalence amongst the specimens used to evluate the test?

Answer 37

True positivies/(true positives + flase positives)

Question 38

How do you calculate the negative predictive value of a test assuming that the population prevalence of the disease is the same is the disease prevalence amongst the specimens used to evluate the test?

Answer 38

True negatives/(true negatives + false negatives)

Question 39

Calculate the positive predictive value of the new test using the dataset attached.

Answer 39

PPV = True positive/(true positives + false positives)

6/(6+9)

=6/15
=2/5
=4/10
=40%

Question 40

Calculate the negative predictive value of the new test using the dataset attached.

Answer 40

NPV = True negatives/(true negatives + false negatives)

20 /(20 +0)

=1
=100%

Question 41

How do you calculate the false negative rate?

Answer 41

1 - sensitivty

Question 42

How do you calculate the false positive rate?

Answer 42

1 - specificity

Question 43

What is spearman’s rank (r) correlation test used for?

Answer 43

It’s a non-parametric data statistical test that examines the dependence of two variable on one another. E.g. the amount of attendence to a class and how they relate to results in an exam.

Question 44

What is the interquartile range?

Answer 44

The middle 50% of datapoints. It’s the 75th perentile mine the 25th percentile.

Question 45

What percentage of values fall within 1 standard deviation from the mean in a normal distribution?

Answer 45

68%

Question 46

What percentage of values fall within 2 standard deviations from the mean in a normal distribution?

Answer 46

95%

Question 47

How is the variance calculated?

Answer 47

Standard deviation squared

Question 48

What is a cross-sectional study?

Answer 48

A subsection of a cohort is studied at a particular point in time. The exposure and outcome are measured at the same time. E.g. number of kids on a playground that get sunburnt (outcome) and whether or not they are wearing a hat (exposure).

Question 49

What is a case-control study?

Answer 49

Observational study that looks at two otherwise equivalent groups who have had a differing outcome. E.g. 40yo males with testicular ca vs 40yo males without testicular cancer. It then examines what might have contributed to the outcome.

Question 50

What is publication bias?

Answer 50

Over representation of studies in publication with positive or signifcant effects. This is a problem for systematic reviews.

Question 51

What is the best method to evaluate for publication bias when performing a systematic review?

Answer 51

A funnel plot

Question 52

What is a funnel plot?

Answer 52

A graphical respresnation of the size of trials plotted agains the effect size they report. As the size of the trial increases, they will converge around the true underlying effect. A symmetric inverted funnel shap indicates that publication bis is unlikely.

Question 53

What tests are used to measure heterogeniety across studies examined in a metaanlaysis?

Answer 53

Chi squared test and the I squared test. Low p-values in chi squared test reporting are consistent with low heterogeneity. I squared is reported as a percentage, with 0% indicating no heterogeneity and 100% being very heterogenous studies.

Question 54

What is case fatility?

Answer 54

The proportion of people within a population affected by a disease that die from that disease.

Question 55

What is attack rate?

Answer 55

The measure of frequency of morbitidy, or speed of spread, of disease in at risk population. Used in disease outbreaks. Calculate as number ill/ number at risk of becoming ill.

Question 56

What is the population attributable risk?

Answer 56

The proportion of incidence of disease in a population that is atributable to a particular risk of interest. It’s often used to establish the value of a public health measure to remove a risk be calculating the associated reduction in overall disease prevalence that would result.

Question 57

What are the subtypes of information bias?

Answer 57

Differential and non-differential misclassification bias

Question 58

What is differential misclassification bias?

Answer 58

Random or systematic inaccuracy of measurement of a variable during a study. Labelled ‘differential’ misclassification bias when the variable with an error is affected by the status of another variable.

Question 59

What is a non-differential misclassification bias?

Answer 59

Random or systematic inaccuracy of measurement of a variable during a study. Labelled ‘non-differential’ misclassification bias when the variable with an error is independent of other variables measured in the study.

Question 60

What’s a crossover study?

Answer 60

A prospective study in which participants recieve all the treatments. So placebo, treatment 1, treatment 2 and so on in some defined sequence. Crossovers studies help to reveal confounding factors by allowing the same individuals to be the control arm and experimental arm at some point in the study. So, if a particular group has an unknown confounding factor, it will become evidence when the crossover occurs.

Question 61

What requires fewer participants to be statistically powered: a crossover study or a non-crossover study?

Answer 61

Crossover study. They are very statistically efficient and require fewer participants to obtain meaningful power.