Tests of significance

Two questions arise about any hypothetical relationship between two variables:

1. what is the probability that the relationship exists;
2. if it does, how strong is the relationship

There are two types of tools that are used to address these questions: the first is addressed by tests for statistical significance; and the second is addressed by Measures of Association.

Steps in Testing for Statistical Significance:

1) State the Research Hypothesis
2) State the Null Hypothesis
3) Select a probability of error level (alpha level)
4) Select and compute the test for statistical significance 

Chi Square TestàFor nominal and ordinal data, Chi Square is used as a test for statistical significance.

T-Testsà are tests for statistical significance that are used with interval and ratio data. 

NOIR: Nom/Ordà chi sq, Int/ratioàT-test

5) Interpret the resultsà

                    I.            the hypothesis

                  II.            the test statistic used and its value

                III.            the degrees of freedom

                IV.            the value for alpha (p-value)

blinding in anaesthesia (statistics)

Blinding refers to the concealment of group allocation from one or more individuals involved in a clinical research study.The French Academy of Sciences originated the first recorded blind experiments in 1784: the Academy set up a commission to investigate the claims of animal magnetism proposed by Franz Mesmer.


Reason for blinding a study:
Blind testing is used wherever items are to be compared without influences from testers' preferences or expectations, for example in clinical trials to evaluate the effectiveness of medicinal drugs and procedures without placebo effect, nocebo effect, observer bias, or conscious deception.

Types of Blinding:

1. In a single-blind experiment, the individual subjects do not know whether they are so-called "test" subjects or members of an "experimental control" group. Single-blind experimental design is used where the experimenters either must know the full facts (for example, when comparing sham to real surgery) and so the experimenters cannot themselves be blind, or where the experimenters will not introduce further bias and so the experimenters need not be blind. However, there is a risk that subjects are influenced by interaction with the researchers – known as the experimenter's bias.
2. In double-blind experiments, neither the participants nor the researchers know which participants belong to the control group, nor the test group. They help to lessen the power of preconceived notions or physical cues (e.g., the placebo effect, observer bias, experimenter's bias) to distort the results.The key that identifies the subjects and which group they belonged to is kept by a third party, and is not revealed to the researchers until the study is over.
3. A triple-blind study is an extension of the double-blind design; the committee monitoring response variables is not told the identity of the groups. The committee is simply given data for groups A and B. A triple-blind study has the theoretical advantage of allowing the monitoring committee to evaluate the response variable results more objectively. However, in a trial where the monitoring committee has an ethical responsibility to ensure participant safety and by the time monitoring committees receive data, often the emergency situation has long passed where the monitoring was usually guided by a constellation of trends and their directions.

Uses in Anaesthesia: Double-blinding is relatively easy to achieve in drug studies, by formulating the investigational drug and the control (either a placebo or an established drug) to have identical appearance (color, taste, etc.).

Comments:
Effective blinding can be difficult to achieve where the treatment is notably effective (in cases where the tested drug combinations were so effective that it was deemed unethical to continue withholding the findings from the control group, and the general population), or where the treatment is very distinctive in taste or has unusual side-effects that allow the researcher and/or the subject to guess which group they were assigned to.

Type I and type II errors

Also called  α and β error.

Type I error, α (alpha), is defined as the probability of rejecting a true null hypothesis which means detecting an effect that is not present. Usually a type I error leads one to conclude that a supposed effect or relationship exists when in fact it doesn't. Examples of type I errors include a test that shows a patient to have a disease when in fact the patient does not have the disease.(False positive cases)

Type II error, β (beta), is defined as the probability of failing to reject a false null hypothesis which means failing to detect an effect that is present. Example of type II error would be a blood test failing to detect the disease it was designed to detect, in a patient who really has the disease. (False negative cases)

Any statistical hypothesis test has a probability of making type I and type II errors. For example, all blood tests for a disease will falsely detect the disease in some proportion of people who don't have it, and will fail to detect the disease in some proportion of people who do have it.  

These error rates are traded off against each other: for any given sample set, the effort to reduce one type of error generally results in increasing the other type of error. Therefore, for a given test, the only way to reduce both error rates together is to increase the sample size.

Tabularised relations between truth/falseness of the null hypothesis and outcomes of the test:

Table of error types		Null hypothesis (H0) is
		Valid/True	Invalid/False
Judgment of Null Hypothesis (H0)	Reject	Type I error (False Positive)	Correct inference (True Positive)
	Fail to reject	Correct inference (True Negative)	Type II error (False Negative)
Type-1 = True H0 but reject it (False Positive) Type-2 = False H0 but accept it (False Negative)

P-Value in Anesthesia

P-values in scientific studies are used to determine whether a null hypothesis formulated before the performance of the study is to be accepted or rejected. The p-value is a probability calculation. It reflects the measure of evidence against the null hypothesis. Small p-values correspond to strong evidence. If the p-value is below a predefined limit, the results are designated as "statistically significant" 

For example, If it is to be shown that a new drug is better than an old one, the first step is to show that the two drugs are not equivalent. Thus, the hypothesis of equality is to be rejected.

Limitations of P value:

The p-value refers only to a single hypothesis, called the null hypothesis, and does not make reference to any other hypotheses. One instead one computes the rate of Type I and type II errors as α and β. However, the p-value cannot be directly compared to these error rates α and β – instead it is fed into a decision function.

Shortcomings of P value:

1. The significance level, such as 0.05, is not determined by the p-value. Rather, the significance level is decided by the person conducting the experiment (with the value 0.05 widely used by the scientific community) before the data are viewed, and is compared against the calculated p-value after the test has been performed.

                                I.            Criticismsà criterion used to decide "statistical significance" is based on an arbitrary choice of level (often set at 0.05). If significance testing is applied to hypotheses that are known to be false in advance, a non-significant result will simply reflect an insufficient sample size

                              II.            The p-value is incompatible with the likelihood principle, and p-value depends on the experiment design.

                            III.            p-value is sometimes portrayed as the main result of statistical significance testing, rather than the acceptance or rejection of the null hypothesis at a pre-prescribed significance level.

                            IV.            Due to these criticisms, scientific articles which use p-value are now, not accepted by some organizations

2. The p-value is not the probability that the null hypothesis is true, nor is it the probability that the alternative hypothesis is false – it is not connected to either of these. (it can simply accept or reject hull hypothesis at a particular significance level)
3. The p-value is not the probability that a finding is "merely a fluke." Calculating the p-value is based on the assumption that every finding is a fluke, that is, the result of chance alone.
4. The p-value is not the probability of falsely rejecting the null hypothesisà prosecutor's fallacy.
5. The p-value cannot predict if replicating the experiment would yield the same conclusion. 
6.  The p-value does not indicate the size or importance of the observed effectà the larger the effect, the smaller sample size will be required to get a significant p-value      

ANOVA

The Analysis Of Variance can be used in cases where there are more than two groups for comparison. (ANOVA) simultaneously compares the differences among sample means of more than two groups for a one-factor experiment.

Example:

• Hypothesis 1 : μ1 = μ2= μ3 (there is no difference between the three means)
• Hypothesis 2: μ1 ≠ μ2 ≠ μ3 (there is a difference between the three means)

Example: You might use ANOVA to compare mean morphine consumption between total knee replacement patients that received a femoral nerve block, those that received a femoral and a popliteal nerve block, and those that did not receive a nerve block of any kind.

Why Not Multiple T-Tests?

t-test can only be used to test differences between two means. When there are more than two means conducting such multiple t-tests makes the study complicated especially if there are large number of population groups and in such circumstances we use ANOVA.

Assumptions

There are four basic assumptions used in ANOVA.

1. the expected values of the errors are zero
2. the variances of all errors are equal to each other
3. the errors are independent
4. they are normally distributed

Chi-square test

A categorical variable (sometimes called a nominal variable) is one that has two or more categories, but there is no intrinsic ordering to the categories (example, gender: male/ female). So, categorical variable is one that allows us to assign categories but cannot clearly order the variables in a particular manner. For example, Hair color is a categorical variable having a number of categories (blonde, brown, brunette, red, etc.) but there is no agreed way to order these from highest to lowest. The central tendency of categorical variables is given by its mode, since median and mean can only be computed on numerical data. Therefore, it does not follow a normal bell-curve distribution, and cannot be analyzed with tests that rely on a normal distribution such as the t-test or ANOVA.

A chi-squared test is a statistical hypothesis test wherein the sampling distribution of the test statistic is in a chi-square distribution when the null hypothesis is true.Chi-square is used most commonly to compare the incidence (or proportion) of a characteristic in one group to the incidence (or proportion) of a characteristic in other group(s). The Chi-Square (χ2) test is used for categorical variables which determines whether there is a difference in the population proportions between two or more groups.The Chi Square distribution is the distribution of the sum of squared standard normal deviates. The degrees of freedom of the distribution is equal to the number of standard normal deviates being summed.

Types:

1. Pearson's chi-square test
2. Yates's correction for continuity
3. Cochran–Mantel–Haenszel chi-squared test.
4. McNemar's test
5. Tukey's test of additivity
6. The portmanteau test in time-series analysis, testing for the presence of auto-correlation
7. Likelihood-ratio tests

In anaesthesia, Chi square test is commonly used to compare a group with a value, or to compare two or more groups, but with categorical data.

Class note on ECG for Diploma Critical Care

Electrocardiography

Electrocardiography is the process of recording the electrical activity of the heart by  electrodes placed on the skin. These electrodes detect the tiny electrical changes on the skin that arise from the heart’s electrophysiological activity during each heartbeat.

The graph of voltage versus time thus printed by the ECG machine is called electrocardiogram

In a conventional 12 lead ECG, ten electrodes are connected to the patient.

The overall magnitude of the heart's electrical potential is then measured from twelve different angles ("leads") and is recorded over a period of time (usually 10 seconds).

Electrodes and leads:

An electrode is the conductive pad in contact with the body that makes an electrical circuit with the electrocardiograph.

A lead is the source of measurement of a vector.  [A vector is a geometric object that has magnitude (or length) and direction and can be added to other vectors according to vector algebra]

Leads are of two types:

1.       Bipolar leads: they limb leads and are used for comparison between two electrodes.

2.       Unipolar leads: they are Precordial leads and compared to a common lead (commonly the Wilson's central terminal)

The common lead, Wilson's central terminal V_W, is produced by averaging the measurements from the electrodes RA, LA, and LL to give an average potential across the body:

 

Leads are arranged in three sets:

1.       3 limb leads and 3 augmented limbs are arranged like spokes of a wheel in the coronal plane (vertical). They view the heart from a vertical plane.

2.       6 precordial leads that lie on the perpendicular transverse plane (horizontal). They view the heart from a horizontal plane.

Precordium is the region of the thorax immediately in front of the heart.

Limb leads: Leads I, II and III are called the limb leads. The electrodes that form these signals are located on the limbs—one on each arm and one on the left leg. The limb leads form the points of what is known as Einthoven's triangle.

Augmented limb leads: Leads aVR, aVL, and aVF are the augmented limb leads. They are derived from the same three electrodes as leads I, II, and III, but they use Goldberger's central terminal as their negative pole which is a combination of inputs from other two limb electrodes.

Precordial leads: The precordial leads lie in the transverse (horizontal) plane, perpendicular to the other six leads. The six precordial electrodes act as the positive poles for the six corresponding precordial leads: (V₁, V₂, V₃, V₄, V₅ and V₆). Wilson's central terminal is used as the negative pole.

The 12 leads in a 12-lead ECG are listed below: 

LEAD			VIEW OF HEART
Lead I			Lateral
Lead II			Inferior
Lead III			Inferior
aVR			None
aVL			Lateral
aVF			Inferior
V1			Septal
V2			Septal
V3			Anterior
V4			Anterior
V5			Lateral
V6			Lateral

Electrode name	Electrode placement
RA	On the right arm, avoiding thick muscle.
LA	On the left arm, avoiding thick muscle.
RL	On the right leg, lateral calf muscle.
LL	On the left leg, lateral calf muscle.
V1	In the fourth intercostal space (between ribs 4 and 5) just to the right of the sternum (breastbone).
V2	In the fourth intercostal space (between ribs 4 and 5) just to the left of the sternum.
V3	Between leads V2 and V4.
V4	5th Intercostal space at the midclavicular line
V5	Anterior axillary line at the same level as V4
V6	Midaxillary line at the same level as V4 and V5

Artefacts on ECG:

An ECG tracing is affected by patient’s motion. Some rhythmic motions (such as shivering or tremors) can create the illusion of arrhythmia. Artefacts are distorted signals caused by secondary internal or external sources, such as muscle movement or interference from an electrical device.

Accurately separating the ECG artefacts from the true ECG signal can have a significant impact on patient’s diagnosis, treatment, outcome of therapy and legal liabilities.

Reducing Artefacts while measuring an ECG:

Below is a list of guidelines that will help reduce artefacts when performing ECG’s.

Patient Positioning

• Place the patient in a supine or semi-Fowler’s position. If the patient cannot tolerate being flat, you can do the ECG in a more upright position.
• Instruct the patient to place their arms down by their side and to relax their shoulders.
• Make sure the patient’s legs are uncrossed.
• Move any electrical devices, such as cell phones, away from the patient as they may interfere with the machine.

Skin Preparation

• Dry the skin if it’s moist or diaphoretic.
• Shave any hair that interferes with electrode placement. This will ensure a better electrode contact with the skin.
• Rub an alcohol prep pad or benzoin tincture on the skin to remove any oils and help with electrode adhesion.

Electrode Application

• Check the electrodes to make sure the gel is still moist.
• Do not place the electrodes over bones.
• Do not place the electrodes over areas where there is a lot of muscle movement.

Electrocardiogram grid

ECG's are normally printed on a grid. The horizontal axis represents time and the vertical axis represents voltage. The standard values on this grid are shown in the image to the right:

• A small box is 1 mm x 1 mm big and represents 0.1 mV x 0.04 seconds.
• A large box is 5 mm x 5mm big and represents 0.5 mV x 0.2 seconds wide.

The "large" box is represented by a heavier line weight than the small boxes.