Statistics Akt

Knowing how likely an event is given knowledge about pre-existing conditions.

Numerical description of something quantifiable - average.

Allows us to understand how representative the data set is of the population we are interested in.

The larger the sample size - more useful it is.

The chance of an event occuring given certain parameters.

Useful when impractical to have all the data for a population you are interested in.

Used to generate or test hypotheses about particular populations - opinion poll.

Make conclusions about the available data but those conclusions reach beyond what the data shows.

Result is unlikely to have arisen by chance alone.

Dependent on there being a real relationship between the variables being measured.

Hypothesis that there is no relationship between variables.

Rejected if a significantly significant result is found.

The chance of obtaining a result at least as extreme if the null hypothesis were true.

< 0.05 = < 5 % chance that the result of a study would have occurred if there were no relationship between the varibales being studied.

False rejection of null hypothesis when there is not a relationship between the variables being studied.

Occurs if you perform +++ studies.

False positive.

Failing to reject the null hypothesis when it is false - not finding a relationship between the variables when there is one.

False negative

How likely a result from a study is to be consistently replicated when repeated in a similar manner.

Different types of data - hierarchy within data types - some are more useful than others.

Simplest data type.

Data that are a name for something.

Only mathematical operation that can be performed is mode.

Can be put into a meaningful order but the degree of difference between data points is unknown - ranking of preferences to a medication.

Able to use median and mode.

Fixed mathmatical difference between each point - temperature.

Data doesn not have a zero point.

Cannot multiply data.

Definite zero point.

Open to all mathematical manipulation.

Arithmetical average.

Every number is added together and then divided by how many numbers there are.

Value that falls in the middle of the data set if all the values are put in order of size.

Use to describe skewed distributions.

Most frequently occuring value in a data set.

If bimodal distribution - 2 values.

Used for non-numerical data.

Difference between the largest and smallest values in a data set.

Dispersion of the values.

Number of data points divided by 100 with the data set out in order, normally from smallest to largest.

25th centile

50th centile

75th centile

100th centile

Interquartile range - middle 50% of the date between 25th and 75th centiles.

Theoretical distribution that is a bell-shaped curve that is symmetrical around the mean value of the sample or population.

Median = mean = mode.

68.3 % of data will lie within 1 STD of mean.

95.4 % of data will lie within 2 STDs of mean.

99.7 % of data will lie within 3 STDs of mean.

Data with a longer tail to one side of the central measure when plotted.

Negative skew - mode > mean and median.

Positive skew - mode < mean and median.

The length of bars is proportional to the values they represent.

Compare the frequency of variables.

Display continuous data such as interval and ratio data.

Show the shape of the distribution of the data.

Continuous data are split into ranges known as bins.

The area of a bar represents the number of data points falling within that range.

Show continuous data.

Often used for time series data.

Distribution of interval data with the central value and variability shown.

Central box:

- Central line = median.

- Lower edge of box = lower quartile.

- Upper edge of box = upper quartile.

- Line to left = minimum value.

- Line to right = maximum value.

Measure of the extent to which one variable changes as another variable changes.

If positive - both variables change in the same direction - increase pollution = increase asthma.

If negative - one variable increases as one variable decreases - increase age = decrease renal function.

Estimate of the range of values within which the true parameter lies.

Range within which the population parameter can be expected to be found in a proportion of samples - usually set at 95 %.

99 % - true population parameter is 99 % likely to fall within that range.

Values that describe a complete population - statistic is a value calculated from a sample.

Statistical methods used when the population we are studying fits into a normal/related distribution.

Useful if we want to infer something about a population and more complicated modeling.

Used to compare observed data with an expected outcome - ie according to the null hypothesis.

Non-parametric test for nominal data.

Proportions same in two groups if there is no effect of a variable.

E.g. Compare smokers and non-smokers.

Non-parametric test.

Investigates whether differences in the median for 2 groups could have occurred by chance.

Ordinal data.

E.g. Patients using a rating scale for pain/depression are subjected to different interventions.

Tests whether the mean valuable in the dependent variable is the same for each of the two groups.

Parametric test - equivalent of Mann-Whitney U Test.

Paired version - tests whether the mean scores for a single group vary significantly under 2 different conditions - 2 results for each research participant - pre and post exposure.

Ordinal or interval data.

Gives a correlation coefficient between -1 and +1.

No correlation between the values = 0.

E.g. relationship to how depression changes with exercise.

Parametric test - both variables are interval level data.

Gives a value for how strong the relationship is between the 2 variables.

Used with linear regression - measure of the linear correlation between the variables.

Used when you have two interval-level variables whereby you have two readings for each research participant.

E.g. Calorie intake and weight change are measures to determine relationship between increased calorie intake and weight gain.

Plot the points on a scatter plot and fit with line of regression.

Used when dependent variable is nominal with 2 values - yes or no.

Similar to linear regression except that the dependent variable is nominal rather than interval.

Combining methods can improve out knowledge more than a single method.

Using a 2nd method can help confirm or refute what has been found.

Research findings are strengthened if different methods lead to similar results.

Can have > 1 observer rather than 2 methods.

Randomly select participants from a population - patients within a GP surgery.

Risk that sample does not reflect the population in certain attributes.

Sometimes desirable to have research participants with particular attributes.

Splitting the population into subgroups with similar characteristics (age/gender) and taking a sample that includes members from all subgroups.

Population is split into subgroups like stratified sampling, but quotas are set in each group.

Non-probability technique - not random - greater chance that some people will be selected than others.

Large population that is split into groups and then samples are taken from within those groups - used when cost of random sampling would be an issue.

Often multistage.

Individuals are selected through convenience without any randomization.

Initial contact is made with an individual/group and associated of them are also asked to take part in the research

Can give very misleading results - may not reflect the whole population.

Reached when no new data are collected over a predetermined number of interviews.

Alternatively it may be reached when no more study participants can be found without taking up considerable resources.

Study of what can be known in terms of which beliefs can be justified and which are simply opinion.

E.g. If someone believes a bridge is safe but when crossing it, it collapses the belief is only an opinion. But if on crossing it, it holds his weight the belief is justified.

Methods, principles and rules that are used in undertaking research.

About how epistemology and theoretical underpinnings are applied to answer a research question.

Systemic study of a social group or culture.

Observation and participant observation and possibly interviews.

Should be undertaken in the naturally occurring setting of the study subjects.

Aim to construct the narrative from the viewpoint of the studied subject.

Tries to avoid preconceived ideas and instead allows theories to develop from the research data.

In-depth interviews, focus groups and observation groups.

Useful when there is little previous exploration of a particular research setting.

Study of subjective experience.

Trying to understand the different ways that people think about something.

Participant observation and interviews.

Explore the motivations and perceptions of the research participants and investigate them in depth.

Aims to solve a problem.

Enacting change and gauging the results of that change.

Involves careful planning, observation and critical reflection.

Evaluating public health interventions.

Not a single neat qualitative research methodology.

All research methods and methodologies have limitations - aims to circumvent these.

Uses several methods that are applied appropriately.

Needs to have a well thought out research question.

Aim to deliver data that are consistent and do not vary depending on the interviewer.

Mask individual variety and do not target a depth of understanding.

1) Systemic reviews and meta-analyses

2) Randomised controlled trials

3) Cohort studies

4) Case-control studies

5) Case series and case studies

6) Expert opinion, editorials

Gold standard for medical trials

Study participants are randomly allocated to one or more interventions.

Most useful - compare an intervention to current gold-standard.

Combining the results of RCTs

Secondary research.

Looks at a particular subject or question - searching for all the relevant studies with an explicit search strategy and evaluating studies using predetermined criteria.

Assessing studies.

Combining the selected studies from a systematic review by mathematical means.

Increases the number of people studied.

Reduces confidence interval.

Each study can be given a weighting based on how reliable the study is.

Forest plot.

Graphical representation of meta-analysis.

Size or weighting of study.

Confidence interval for the results of each trial.

Overall result.

Studies on left of graph.

Square on horizontal line is centred on the relative risk/odds ratio of the effect.

Width of horizontal line - 95 % confidence interval of relative risk/odds ratio.

If line crosses the solid vertical line - no significant effect.

Solid vertical line - line of no effect.

Diamond - pooled result.

Looks for publication bias in systematic reviews and meta-analysis - not all data has been published.

Based on assumption that larger studies will be more powerful and precise - nearer the true value than smaller studies.

Intervention effect - plotted on log relative risk on x-axis.

Estimates are plotted against measure of studies precision or size - standard error.

If assymtetrical - suggests that not all studies have been published.

Measure of how different studies are.

Measure of how similar studies are.

Modified RCT - gives a group of participants an intervention and then after an appropriate time period gives them another intervention.

Cheaper than RCT and useful when thought unethical to not give a certain treatment.

Washout period - time allowed to allow the effects of the previous intervention to have disappeared.

Probability of a particular event occurring.

Can be positive - reduction in cardiovascular disease in those taking metoformin.

Comparison is made to something other than zero - usually a control group.

RR = EER/CER

Chance or actual risk of developing a condition with zero meaning there is no risk.

ARR = CER-EER.

CER - control event rate - how often the event of interest occurs in the control group.

EER - experimental event rate - how often that event occurs in the group given the intervention being studied.

If > 0 - risk reduction.

If < 0 - risk increase.

Ratio of the probability of an outcome in the experimental group compared with the probability of the same outcome in the control or comparison group.

RRR = (CER - EER) / CER

RRR= ARR/CER

Value of 1 = no difference between the 2 groups being studied.

Similar to relative risk ratios but it takes into account the timing of events.

Once a patient has reached the end point of a study - cure or death they are removed from the analysis.

Hazard - rate at which events happen.

If = 1 - relative probability in the 2 groups being equal over time.

If < 1 - decreased hazard for treatment group.

If > 1 - increase hazard for the treatment group.

Inverse of absolute risk reduction - 1/ARR.

How many people would have to be treated to prevent/cause one outcome of interest.

Assesses effectiveness of an intervention.

NNT - 1/(CER-EER)

Takes a group of people and sees what happens to them over a period of time - longitudinal study.

Used to try and see whether suspected risk factors actually have an impact on people's health and if so what size of impact.

Cohort - group of people that have something in common.

Doesn't have to have a comparison group.

Confounding variables may exist - 3rd variable that is not taken into account.

Prospective - look forward in time.

Researchers looking at the medical records of of a cohort of people to find information about variables the researchers are interested in.

Normal outcome of a cohort study.

What is the risk of an event occurring in the exposure group compared to the non-exposure (control) group.

RR = EER/CER

Relative risk reduction = 1-RR

Compares people with a condition to those that don't have it.

Evaluates potential causes of the condition/risk factors that contribute to the way it develops.

Retrospective and rely on people correctly recalling events.

Useful if condition is rare.

May have spurious correlations.

Outcome of a case-control study.

Looks at the odds in the case group and compares this with the odds within the control group.

Odds of an event are the ratio of people with the condition to people without the condition.

Ratio of events to non-events in the condition group and dividing this by the ratio of events to non-events in the control group.

OR = (a/c)/(b/d)

If < 1 - exposure is protective.

If > 1 - exposure is causative.

a = exposure and condition present.

b = exposure and no disease present.

c = no exposure and condition present.

d = no exposure and no disease present.

Study of health populations.

Patterns of health and disease within a population - causative or risk factors.

Effects of health and disease on populations.

Aims to prevent people from developing diseases or protect them from harm.

Vaccines

Weight loss/lifestyle advice

Interventions after a disease, condition or risk factor occurs before it has caused any harm.

Prescribing medication to people diagnosed with hypertension

Acting after the disease or condition has been diagnosed and has caused harm and symptoms.

Minimise harm from an acute event, improve quality of life and prevent future complications.

Treating someone following an MI with a statin, anti-platelet, beta-blocker and ACEi.

Number of new cases of a disease or condition in a particular population starting in a given period of time.

Rate of new cases in relation to a population.

Rate is given in a time period.

Incidence rate = number of new cases starting during a specified time period / average population during specified time interval.

Incidence proportion = number of new cases during specified time interval / population at start of time period.

Proportion of cases in a given population at a given time.

For short-term illnesses - prevalence = incidence

For long-term illnesses - incidence < prevalence ie less new cases than those who have the disease.

Prevalence = total number of people with a condition at a given time / population

How good a test is at detecting people with the condition.

High sensitivity = does not miss many cases of disease.

Sensitivity = true positive / number of people with the condition

Sensitivity = TP / TP + FN

How good a test is at excluding those people without the condition.

High specificity = low number of false positives

Specificity = true negatives / number of people without the condition

Specificity = TN / TN + FP

How likely someone who tests positive is to actually have the condition being tested for.

The larger the PPV, the lower the number of false positives the test will result in.

Increases as prevalence increases.

PPV = true positives / true positives + false positives

PPV = TP / TP + FP

How likely someone who tests negative is to not have the condition being tested for.

The higher the NPV the more likely someone who tests negative will not have the condition.

Decreases as prevalence increases.

NPV = true negatives / true negatives + false negatives

NPV = TN / TN + FP

Probability before the test of someone having the disease is the same as the prevalence of that disease in the population from which the person is drawn.

Revised probability of a person having a disease based on the predictive values and their test results.

Compare the probability of a test result if the patient has the condition with the probability of the same result if the patient does not have the condition.

Value > 1 test result is associated with the presence of the condition.

Value < 1 test result is associated with the absence of the condition.

Value = 1 - no diagnostic value of the test result

Likelihood Ratio = probability of finding in patients with the disease / probability of finding in patients without disease

Positive LR = sensitivity / 1 - specificity

Negative LR = 1 - sensitivity / specificity

First line - pre-test probability = disease prevalence.

Second line - likelihood ratio.

Third line - post-test probability - calculated by drawing a straight line through first and second lines.

Number of deaths in a specified population in a specified time.

Percentage of people alive at a specified time after diagnosis.

Relative survival rate = survival rate after diagnosis / survival rate observed in a similar population without the disease.

Removes people who die of other causes than the one of interest from the population.

Estimate of how long a newborn baby will live based on current age-specific mortality rates.

Annual number of deaths in children aged between 1 and 4 years - rate per 1000 children in that age group.

Children younger than 1 year of age given as a rate per 1000 liver births in that year.

Deaths in infants younger than 28 days of age.

Number of deaths due to a particular condition, compared with the number of people who contract the condition, over the course of a disease or condition.

Time when half the patients are expected to be alive.

QALY - standardised measure for comparing different treatments. It is the average of additional years of life gained multiplied by a factor that takes into account the quality of life that may be expected in those additional years of life.

One QALY is a year of life gained with perfect health.

DALY - takes the negative impact of a disability into account.

One DALY = 1 lost year of healthy life.