Biostatistics-Epidemiology Flashcards
Wilcoxon Signed Rank Test
Wilcoxon rank-sum test is used to compare two independent samples, while Wilcoxon signed-rank test is used to compare two related samples, matched samples, or to conduct a paired difference test of repeated measurements on a single sample to assess whether their population mean ranks differ.
Fischer Test
is a statistical significance test used in analysis of contingency tables. Useful for categorical data that results from classifying objects in two different ways.
Although in practice it is employed when sample sizes are small, it is valid for all sample sizes. It is named after its inventor, Ronald Fisher, and is one of a class of exact tests, so called because the significance of the deviation from a null hypothesis (e.g., p-value) can be calculated exactly, rather than relying on an approximation that becomes exact in the limit as the sample size grows to infinity, as with many statistical tests.
Fisher is said to have devised the test following a comment from Muriel Bristol, who claimed to be able to detect whether the tea or the milk was added first to her cup. He tested her claim in the “lady tasting tea” experimen
Factorial trial
Factorial trial evaluates two or more treatments simultaneously
Example - ISIS-2 trial which evaluated Aspirin and Streptokinase in STEMI.
In statistics, a full factorial experiment is an experiment whose design consists of two or more factors, each with discrete possible values or “levels”, and whose experimental units take on all possible combinations of these levels across all such factors. A full factorial design may also be called a fully crossed design. Such an experiment allows the investigator to study the effect of each factor on the response variable, as well as the effects of interactions between factors on the response variable.
For the vast majority of factorial experiments, each factor has only two levels. For example, with two factors each taking two levels, a factorial experiment would have four treatment combinations in total, and is usually called a 2×2 factorial design. In such a design, the interaction between the variables is often the most important. This applies even to scenarios where a main effect and an interaction are present.
If the number of combinations in a full factorial design is too high to be logistically feasible, a fractional factorial design may be done, in which some of the possible combinations (usually at least half) are omitted.
Other terms for “treatment combinations” are often used, such as runs (of an experiment), points (viewing the combinations as vertices of a graph, and cells (arising as intersections of rows and columns).
Confidence interval
percentage chance within which true value lies.
Example -
95% CI means - ranges within which there is a 95% chance that true value lies
similarly
95% CI around a difference are the range in which there is 95% chance that true difference lies.
Forest Plot
Forest plots are most commonly used in meta-analysis of many individual trials for data presentation. Separate trials are compared using it. Horizontal lines emerging from squares represent confidence intervals. Largest studies have narrow confidence intervals.
Area of squares is proportional to the number of events in each study.
Bradford Hill Criteria
The Bradford Hill criteria, otherwise known as Hill’s criteria for causation, are a group of nine principles that can be useful in establishing epidemiologic evidence of a causal relationship between a presumed cause and an observed effect and have been widely used in public health research. They were established in 1965 by the English epidemiologist Sir Austin Bradford Hill.
In 1996, David Fredricks and David Relman remarked on Hill’s criteria in their seminal paper on microbial pathogenesis.
9 Criterias in Bradford Hill Causation
In 1965, the English statistician Sir Austin Bradford Hill proposed a set of nine criteria to provide epidemiologic evidence of a causal relationship between a presumed cause and an observed effect. (For example, he demonstrated the connection between cigarette smoking and lung cancer.) The list of the criteria is as follows:
01 Strength (effect size): A small association does not mean that there is not a causal effect, though the larger the association, the more likely that it is causal.
02 Consistency (reproducibility): Consistent findings observed by different persons in different places with different samples strengthens the likelihood of an effect.
03 Specificity Causation is likely if there is a very specific population at a specific site and disease with no other likely explanation. The more specific an association between a factor and an effect is, the bigger the probability of a causal relationship.[1]
04 Temporality The effect has to occur after the cause (and if there is an expected delay between the cause and expected effect, then the effect must occur after that delay).
05 Biological gradient (dose–response relationship): Greater exposure should generally lead to greater incidence of the effect. However, in some cases, the mere presence of the factor can trigger the effect. In other cases, an inverse proportion is observed: greater exposure leads to lower incidence.[1]
06 Plausibility A plausible mechanism between cause and effect is helpful (but Hill noted that knowledge of the mechanism is limited by current knowledge).
07 Coherence: Coherence between epidemiological and laboratory findings increases the likelihood of an effect. However, Hill noted that “lack of such [laboratory] evidence cannot nullify the epidemiological effect on associations”.
08 Experiment: “Occasionally it is possible to appeal to experimental evidence”.
09 Analogy: The use of analogies or similarities between the observed association and any other associations.
Some authors consider, also, Reversibility If the cause is deleted then the effect should disappear as well.
Scatter Plot
Can suggests various kind of correlation between variables with a certain comfidence interval.
A scatter plot (aka scatter chart, scatter graph) uses dots to represent values for two different numeric variables. The position of each dot on the horizontal and vertical axis indicates values for an individual data point. Scatter plots are used to observe relationships between variables.
Correlates may be rising, falling or null
Student t Test
The Student’s t test (also called T test) is used to compare the means between two groups and there is no need of multiple comparisons as unique P value is observed, whereas ANOVA is used to compare the means among three or more groups. In ANOVA, the first gets a common P value.
Unpaired t Test: used to compare the average values of the two independent groups , Ex - Patients with disease and without it.
Paired t Test: used if members of the groups are paired. Ex - disease person with healthy person of same sex/age etc
Sensitivity
Numbers of true positives detected by the test divided by the numbers of all true positives in the population tested
Number needed to Treat (NNT)
Number needed to treat to prevent death
Example:
Patients dying on Aspirin Rx - 9.4%
Patients dying not on aspirin - 11.8%
Absolute Risk reduction = 11.8 - 9.4 = 2.4%
Relative Risk reduction = 2.4/11.8 = 0.21 = 21%
NNT = 1/0.024 = 42
means 42 patients needed to treat with aspirin to prevent 1 death
P value
probability of obscuring a difference of the observed magnitude if the null hypothesis is true ie it measures compatibility of the data with null hypothesis.
between 0 and 1
near to 0 = low compatibility with null hypothesis
Chi Square test
type of parametric test
used when - data is binary, samples not paired,
N cell > 5
Any statistical hypothesis test in which sample distribution of the test statistic is chi-square distribution when the null hypothesis is true - is used to determine whether there is significant difference between the expected frequencies and observed frequencies in one or more categories.
Spearman’s Rank Correlation
a non parametric measure of statistical dependance between two variables. It assesses how well the relationship between two variables can be described using a monotoni function.
Pearson Co-efficient of Linear Co-relation
a type of parametric test
used when - linear association between two variables denoted by gamma’. Inidcates how closely point lie to a line. Takes values between -1 and +4
Closer to zero, less linear association.
Negative values of gamma indicates one variable decreases as other increases (Example - CD count falls with increasing age)
Positive Predictive Value
Proportion of those who test positive to who actually have the disease
formula = a/a+b
Likelyhood Ratio
Ratio of the probability of a +ve or -ve test results in subjects that have the disease to those that do not.
Positive LR =Sensitivity/1-Specificity
Negative LR = (1 - Sensitivity)/ Specificity
Do not depend on disease prevalence
Randomized Trials
Parallel Group Study:
most common, pts are allocated to a single exposure group for the duration of the study.
Cross Over:
Participants switch exposures at a defined point
Factorial:
When more than two exposures can be defined, patients are randomly exposed to one or another.
Cluster:
participants are not randomized individually but instead by pre existing groups, Ex - dialysis units
Superiority Trial:
Study that aims to prove now treatment results are better as patient outcomes.
Non-inferiority, Equivalence studies:
aim to demonstrate that a new treatment is no worse than the current standard.
Negative Predictive Value
Proportion of those who test negative to those who do not have the disease
Formula = d/c+d
Power of Study
Power of study is the probability of correctly rejecting the null hypothesis ie avoiding a type II error
Odds Ratio
represents tje probability of an outcome event in one exposure group relative to the other over a specific time frame
> 1 = increased risk
< 1 = reduced risk
Hazard Ratio
interpreted in the same manner as odds ratio (probability of an outcome in one group relative to other group over a specific time frame) but can be more useful because information on survival time for each patient conserved.
This allows patients with greatly different times in study to be compared.
Prevalence
Proportion of patients in a given patient population with a disease at any given time point. Affected by:
duration of disease
rate of new events
rate of cure
rate of death
Incidence rate
describes the number of end points that occur over a specific time period, as no of events per patient years.
Event Rate per 100 Pt yrs = Total no of observed events / Total no of observed pt yrs x 100
McNemar’s Test
Statistical test used on paired norminal/numerical data.
It is applied to 2x2 contingency tables with a dichomatous trait with matched pairs of subjects, to determine whether the row & column marginal frequencies are equal.
Test requires some subjects to be included in before and after measurements.
Crossover trial
Priinciple of crossover trial is that a patient has one drug of treatment - then a washout period - and then another drug and the effect is compared between the two in a single individual.
Good for study of treatment of chronic conditions. Because each person is acting as their own control, it is usually possible to use smalled numbers to get the same power.
Specificity
Definition: Number of true negatives detected by the test divided by number of all true negatives in the population tested.
Example -
75% specificity means that 75% of all true negatives will test negative OR conversely that 25% of true negatives will test positive.
Risk Reduction
Absolute Risk Reduction:
Risk in group 1 - Risk in group 2
Relative Risk reduction:
Risk in group 1/Risk in group 2
Number needed to treat - 1/ absolute risk reduction
Mann Whitney U Test
is a non parametric test of null hypothesis that two samples came from same population against an alternative hypothesis especially that a particular population tends to have larger values than others.
Krauskal Wallis ANOVA (analysis of variance)
Kauskall Wallis anova by ranks is a non paramteric method for testing whether samples originate from the same distribution.
Used to comparing two or more samples that are independent and may have different sample sizes and extends Mann-Whitney U test to two more than two group.
One Way anova (analysis of variance)
One way anova is technique used to compare means of three or more samples.
It can be used only for numerical data.
Tests the null hypothesis.
Two estimates are modes of the population variance.
Produces a F-statistic, ratio of the variance calculated among the means to the variance samples.
Michealis Menten Equation
describes enzyme kinetics
E + S = ES = E + P
where,
E = Enzyme
S = substrate
P = Product
V = (Vmax x CS) /Km + S
where
Vmax = maximum reaction rate
Km = substrate concentration at which the rate is half Vmax
Statistical Tests
Parametric data: something which can be measured, normally distributed
Parametric Test: student t test: paired or unpaired: pearson’s product moment coefficient correlation
Non-Parametric Tests:
1. Mann Whittney U test = unpaired data
2. Wilcoxon Signed Rank Test : compares two sets of observations on single sample
3. Chi-Squared test: to compare proportions or percentages
4. Spearman, Kendal Rank Test: correlation
Paired data: from a single group of patients
Un-Paired data: comparing responses to different interventions in two groups
Non Parametric Test
Paired or Unpaired data
Study Types
Randomized controlled trial:
participants randomly allocated to interventions or to control group ie to drug or placebo therapy
Cohort Study:
Observational, prospective, two or more are selected at their exposure to a particular agent (drug, toxinete) and followed up to see outcome (relative risk)
Case-Control study:
observational and retrospective, patients with a particular condition are identified and matched with controls. Data is then collected on past exposure to a possible causal agent (odds ratio)
Cross Sectional Survey:
provided a snap shot of prevalence study which provided weak evidence of cause and effect
Null Hypothesis - Power of study
power of study = 1 - probability of type II error
probability of correctly rejecting the null hypothesis
Null Hypothesis:
states that two treatments are equally effective.
A significance test uses sample data to assess how likely the null hypothesis is correct.
Alternative Hypothesis:
opposite of null hypothesis ie states that there is a difference between two treatments
P value
probability (P) of obtaining a result by chance at least as extreme as the one that was actually observed, assuming that null hypothesis is true
Type I Error
null hypothesis is rejected when it is true ie showing difference between two groups when it doesnt exist ie a FALSE POSITIVE
Type II Error
failing to spot a difference when it really exists ie null hypothesis is accepted ie a FALSE NEGATIVE
Absolute-Relative measures
Prime examples of absolute measures are risk difference and incidence rate difference. It is best practice to include absolute measures in research articles.
In comparison, relative measures are those that quantify the strength of an association between an intervention, or exposure, and a disease.
Examples of relative measures are risk ratio (also known as relative risk), incidence rate ratio, and odds ratio. These measures form the bulk of those used in published public health research articles.
Example:
Let us consider the risks of smokers and nonsmokers developing lung cancer as an example. An absolute measure that could be used is the risk difference between the risks of smokers and nonsmokers developing lung cancer; a relative measure one might use is the risk ratio between the risk of smokers and nonsmokers developing cancer.
Absolute measures
Absolute measures are those that quantify excess rate or risk of disease between groups (such as exposed and unexposed).
Examples include risk difference and incidence rate difference.
It is considered best practice to report absolute measures (along with relative measures) in research articles. Absolute measures are those preferred by public health decision-makers.
Relative measures
Relative measures quantify the strength of an association between an intervention/exposure and a disease.
Examples include risk ratio, incidence rate ratio, and odds ratio.
Relative measures are most commonly reported in public health research articles.
Risk Ratio
A risk ratio (RR) (also known as relative risk) expresses how many times more, or less, likely it is that an exposed person will develop an outcome relative to an unexposed person.
It is the ratio of the risk (incidence risk) in the exposed to the risk (incidence risk) in the unexposed groups.
Risk Ratio = Risk of outcome in the Exposed
———————————————-
Risk of outcome in Unexposed
Risk ratio < 1 indicates a reduced risk in the exposed group (what you want if testing an intervention works).
Risk ratio > 1 indicates an increased risk in the exposed group.
Risk ratio = 1 is the “null effect”—there is no difference. The risk is the same in both groups.
Risk only ranges between 0 and 1, so both denominator and numerator are limited to 0–1.
However, if the risk in the numerator approaches 1 and the risk in the denominator approaches 0, then you can get exceedingly large risk ratios.
