Statistics Flashcards
NNT
1/ARR
ARR = absolute reduction risk ARR = CER (Control Event Rate) – EER (Experimental Event Rate)
i.e
mortality without intervention =30%
mortality with intervention = 25%
30%-25% = 5% = 0.05 1/0.05 = 20
Note: if the ARR changes so will the NNT
Case control studies
- Case control studies are the most widely conducted type of epidemiologic study because they are relatively cheap, powerful, and adaptable to many settings.
- persons with infection or disease are compared with controls
- Restrospective in nature
- Such comparison allows for the study of associations between exposure and disease even when the disease is a rare outcome of the exposure
Benefits of case control studies
Benefits:
- Efficient in terms of time and cost
- Efficient in design for study of RARE diseases
- Requires FEWER SUBJECTs than other studies
- Best design for diseases with LONG LATENCY periods
- Can evaluate multiple possible/potential EXPOSURES
- Calculates indirect estimate of risk:odds ratio
Disadvantages:
- Both exposure and disease occurred ‘prior to’ the study (retrospective), hence more POTENTIAL FOR BIAS, and the temporal relationships may be unclear
- Can not directly calculate incidence
- Recall or interviewer bias can be problematic; can over or underestimate odds ratio
- Confounding factors
- Selection of controls from population sub-group can be difficult
calculating likelihood ratio
Assesses the value of performing a diagnostic tes
-uses sensitivity and specificity
LR of a positive test is probability of TRUE POSITIVES (given disease) to FALSE POSITIVES (w/o disease)
–>positive LR = sensitivity/(1-specificity)
LR of a negative test is the probability of a FALSE NEGATIVE (with disease) to a TRUE NEGATIVE (w/o disease
negative LR = (1-sensitivity)/specificity
Pre-test probability
The probability of a condition before a test
–> The PREVALENCE of the disease, which may have to be chosen if no other characteristic is known for the individua
Post-test probability
The probability of a condition AFTER a test
Uses Bayes’ normogram with pre-test probability and LR
-multiple the pre-test probability with the LR
Positive predictive value
If the test is POSITIVE what is the chance of the patient having the disease
Need to take into account the PREVALANCE
PPV= True positives / (True positives + False positives)
Negative predictive values
If the test is NEGATIVE what is the chance of the patient NOT having the disease
Need to take into account the PREVALENCE
TPV = True negative/ (True negatives + False negatives)
Sensitivity
Indicator of how good a test is for the condition of interest
- True positive rate
- If the sensitivity is HIGH this means a NEGATIVE result is useful for ruling OUT a disease
Sensitivity = True positives/ (True positives + false negatives)
Specificity
Indicator of how good a test is for the condition of interest
- True negative rate
- If the Specificity is HIGH this means a POSITIVE result is useful for ruling IN a disease
Specificity = True negatives / (true negatives + false positives)
Prevalence and PPV
Prevalence = pre-test probability
The prevalence and PPV are directly related
The lower the prevalence the LOWER the PPV (The LESS sure a positive means the person has the disease) BUT the HIGHER the NPV
Null hypothesis
= no effect
Type I error
we reject the null hypothesis when it is TRUE and conclude there is an effect when there is in fact none
This is the SIGNIFICANCE level of the test; we reject the null hypothesis if the p value is less than the signifcance value
p value < alpha
alpha is the significance value chosen before the trial which is usually 0.05 or <0.01
Our CHANCE of type 1 error will never exceed our chosen significance level say alpha = 0.05 because if p >0.05 we will not reject the null hypothesis and therefore not make a type 1 error
Type II error
we do not reject the null hypothesis when it is FALSE and conclude there is not an effect when ONE really EXISTS
The chance of making a type II error is based on beta
and POWER which is 1- beta
The power is therefore the probability of rejecting the null hypothesis when it is false (a percentage) –> it is the chance of detecting, as statistically significant, a real treatment effect of a given size
- the greater the sample size, the greater the power = the small the chance of making a type II error
Cohort study
A group or groups of individuals are defined on the basis of presence or absence of exposure to a suspected risk factor for a disease, and are then followed for a specified period of time to determine the development of disease in each exposure group
- at the time the exposure status is defined all the potential subjects must be free from the disease under investigation.
- eligible participants are then followed over a period of time to assess the occurrence of that of that outcome.
- the cohort is identified before the appearance of the disease under investigation.
The study groups, so defined, are observed over a period of time to determine the frequency of new incidence of the studied disease among them. The cohort cannot therefore be defined as a group of people who already have the disease. Distinguishing causality from mere correlation cannot usually be done with results of a cohort study alone
Disadvantage of this study is that it is not useful in identifying causative agents when the disease process is rare
Cross over trial
A crossover study is one in which two or more treatments are applied sequentially to the same subject. This type of study can only be considered for chronic conditions where treatment is not expected to cure the patient and where withdrawal of treatment leads to a return to baseline level which is relatively stable
Advantages- fewer subjects may be required as each subject then acts as his or her own control
Disadvantages- carryover effect in that the action of the second treatment is affected by the first treatment
Cross-sectional study
Cross-sectional studies (also known as cross-sectional analysis) form a class of research methods that involve observation of some subset of a population of items all at the same time, in which, groups can be compared at different ages with respect of independent variables, such as IQ and memory. The fundamental difference between cross-sectional and longitudinal studies is that cross-sectional studies take place at a single point in time and that a longitudinal study involves a series of measurements taking over a period of time. Cross-sectional studies are used in most branches of science, in the social sciences and in other fields as well.
RCT
Prospective study.
In this the subjects with the disease are randomised to one of two (or more) treatments, one of which may be a control treatment.
Wherever possible those entering the trial should be allocated to their respective groups by means of random numbers, and one such group (controls) should have no active treatment (RCT). Ideally neither the patient nor the person assessing the outcome should be aware of which therapy is allocated to which patient (blind trial), nor should the doctor responsible for treatment (double-blind trial).
Advantages:
unbiased distribution of confounders
blinding more likely
randomisation facilitates statistical analysis
Disadvantages:
expensive: time and money
volunteer bias
ethically problematic at times
Absolute risk reduction
Absolute risk reduction is a way of measuring the size of a difference between two treatments. It simply tells you how much better or worse one treatment is at reducing a particular outcome in terms of the actual numbers (or rates) of people who experience the outcome compared with another treatment.
Different studies (including comparison groups) will have a different ARR
Cost-benefit analysis
The benefits of a given situation are summed and then the costs associated with taking that action are subtracted. This will be based on the ARR and the NNT and therefore will differ between two studies.
Risk-benefit analysis
This is analysis that seeks to quantify the risk and benefits and hence their ratio.
The risk-benefit analysis of treatment effect may differ - largely depending on what method is used to quantify this e.g. NNT, ARR, RRR, adverse drug events, number needed to harm, drug-related quality adjusted life years.
Relative risk reduction
Relative risk reduction is the difference between the likelihood of an event happening in two groups, expressed as a percentage of the risk for one of the groups.
Event = outcome you are measuring
CER = control event rate EER= experimental event rate
RRR = (CER - EER)/ CER
or:
ARR/ CER
Screening programme
The Wilson-Jungner criteria for appraising the validity of a screening programme
- The condition being screened for should be an important health problem
- The natural history of the condition should be well understood
- There should be a detectable early stage
- Treatment at an early stage should be of more benefit than at a later stage
- A suitable test should be devised for the early stage
- The test should be acceptable
- Intervals for repeating the test should be determined
- Adequate health service provision should be made for the extra clinical workload resulting from screening
- The risks, both physical and psychological, should be less than the benefits
- The costs should be balanced against the benefits
Standard deviation
- The standard deviation of a probability distribution, random variable or population or multiset of values is a measure of the spread of its values. It is defined as the square root of the variance.
- Standard deviation, being the square root of that quantity, therefore measures the spread of data about the mean, measured in the same units as the data
- If many data points are close to the mean, then the standard deviation is small; if many data points are far from the mean, then the standard deviation is large. If all the data values are equal, then the standard deviation is zero
Growth chart and standard deviation
In a curve with a normal (Gaussian) distribution:
Values within 1 standard deviation account for 68% of the values
Values within 2 standard deviations account for 95% of the values
Values within 3 standard deviations account for 99.7% of the values
Assuming that height and weight is normally distributed –
Mean - 1SD = (31.7/2) = 15th percentile of a normal distribution
Mean - 2SD = (4.5/2) = 2.5th percentile of a normal distribution
