Phase 0 trials assist the scientists in studying the behaviour of drugs in humans by micro dosing patients. They are used to speed up the developmental process. They have no measurable therapeutic effect and efficiency.

Phase 1 is associated with assessing whether a drug is safe to use or not. The process is extensive and can take up to several months. It also involves healthy participants (less than 100) that are paid to take part in the study. The side effects upon increasing dosage are also addressed by the study. The effects the drug has on humans including how its absorbed, metabolized and excreted are studied. Approximately 70% of the drugs pass this phase.

Phase 2 trials involve patients that are suffering from the disease under study and are associated with determining the efficiency and the optimum dosage of the drug.

Phase 3 also assesses the efficacy but at a higher scale with larger population sample.

Phase 4 trials are involved with the long term effects and side effects of the drug.

Number needed to treat can be defined as the number of patients who need to be treated to prevent one additional bad outcome.

It can be found as:

NNT=1/Absolute Risk Reduction (rounded to the next integer since number of patients can be integer only).

A ‘double blind crossover study’ happens when every patient receive both treatments.

It is incorrect to say that only half of the patients do not know which treatment they receive because in a double blind placebo control clinical trial ALL of the patients are blind to their treatment choice .

If some of the patients are not treated, they would be aware that they were not being treated and it could not be considered a blind trial.

In a double blind placebo control clinical trial both the clinician and the patient are blind to the treatment choice. The clinician assessing the effects of the treatment, therefore, does not know which treatment the patient has been given.

The hazard ratio (HR) is simply a comparison of two hazards in a study. It provides an estimate of the ratio of the hazard rates between the experimental group and a control group over the entire study duration. It is typically used when analysing survival over time, hence is the most suitable statistical method in this case.

An odds ratio is a statistic that quantifies the strength of the association between two events, A and B. It is the “measure of association” for a case-control study.

The Pearson product-moment correlation coefficient (Pearson’s correlation, for short) is a measure of the strength and direction of association that exists between two variables. An example would be if scientists wanted to evaluate the relationship between quality of certain population of rice and their genetic make-up.

Relative risk is the ratio of the risks for an event for the exposure group to the risks for the non-exposure group. Thus relative risk provides an increase or decrease in the likelihood of an event based on some exposure. Relative risk measures the association between the exposure and the outcome.

Absolute risk reduction is the number of percentage points your own risk goes down if you do a preventive act such as stop drinking alcohol. It depends on what your risk factors are to begin with.

The Delphi method relies on expert consensus. This method kicks off with an open ended questionnaire and uses its responses as a survey instrument for the next round in which each of the participants is asked to rate the items that the investigators have summarized on the basis of the data collected in the first round. Any disagreement is further discussed in phases to come on the basis of information obtained from previous phases.

Phase IIa studies are usually pilot studies designed to demonstrate clinical efficacy or biological activity (‘proof of concept’ studies) whereas phase IIb studies determine the optimal dose at which the drug shows biological activity with minimal side-effects (definite dose-finding studies).

Phase III and Phase IV studies are performed on larger set of participants (usually hundreds to thousands) when safety and efficacy have been established.

An epidemic is declared when the increase in a give disease is above a certain level in a specific interval of time.

An endemic is the general, usual level of a disease in a population at a particular time.

A pandemic is an epidemic that is spread across many countries and continents.

The standard error of the mean (SEM) is a measure of the spread expected for the mean of the observations – i.e. how ‘accurate’ the calculated sample mean is from the true population mean. The relationship between the standard error of the mean and the standard deviation is such that, for a given sample size, the standard error of the mean equals the standard deviation divided by the square root of the sample size.

SEM = SD / square root (n)

where SD = standard deviation and n = sample size

For establishing a cause effect relationship, following criteria must be met:

1. Coherence & Consistency

2. Temporal Precedence

3. Specificity

As can be seen, sensitivity (The probability of a positive test) is not among these deciding factors..

99.7% of the values within 3 standard deviations of the mean.

For 99.7% confidence interval, you can find the range as follows:

1. Multiply the standard error by 3.

2. Subtract the answer from mean value to get the lower limit.

3. Add the answer obtained in step 1 from the mean value to get the upper limit.

For a confidence interval of 68%, multiply the standard error with 1 and repeat the process. For a 95% confidence interval, Standard Error is multiplied by 1.96 to get the interval.

Its known that 68.3% of the total values of a normally distributed variable are found within a range of 1 standard deviation from the mean which makes the range to be 4.3 to 4.9 mmol/L.

The correlation coefficient gives us the idea about relation between two parameters. i.e. to what extent change in parameter A could prompt a change in parameter B. The numerical value of correlation coefficient could not be greater than 1.

The null hypothesis states that there is no significant difference between two groups.

The alternative hypothesis states that there is a significant difference between two groups.

A type I error (false positive) occurs when a null hypothesis is rejected when it should be accepted.

A type II error (false negative) occurs when the alternative hypothesis is rejected when it should be accepted.

The probability determines the rejection of a null hypothesis.

The level of significance is set at p <0.05.

The dose-response curve plots the graph of the dose (drug concentration) versus the response. As doses increase, the response increment diminishes; finally, doses may be reached at which no further increase in response can be achieved. This relation between drug concentration and effect is traditionally described by a hyperbolic curve. When the x-axis is plotted in log scale, the graph yields a sigmoid curve.

Efficacy (Emax) and potency (EC50) can be derived from this curve. Emax is the maximal effect achievable, with increasing concentration of a drug. EC50 is the concentration of the drug, wherein half of the maximal effect is achieved.

When the graph is plotted using a log [response/1-response] against log dose, the sigmoid curve becomes a straight line (Hill plot). A graph that transforms from a straight line to exponential curve is mathematically incorrect. A graph that transforms from either a wash-in or wash-out exponential curve to a straight line comes from an initial set of data plotted against time, to a logarithmic transformation of the initial data set against time.

ANOVA is based upon within group variance (i.e. the variance of the mean of a sample) and between group variance (i.e. the variance between means of different samples). The test works by finding out the ratio of the two variances mentioned above. (Commonly known as F statistic).

The correct answer is the mean, median and mode of normally distributed data are the same value. This is as a result of the bell shaped curve which is equal on both sides.

The bell-shape indicates that values around the mean are more frequent in occurrence than the values farther away.

In a normal distribution:
1) +/- one standard deviation of the mean accounts for 68% of the data.
2) +/- two standard deviations of the mean accounts for 95% of the data.
3) +/- three standard deviations of the mean accounts for 99.7% of the data.

The degree of correlation is summarised by the correlation coefficient (r). This indicates how closely the points lie to a line drawn through the plotted data. In parametric data this is called Pearson’s correlation coefficient and can take any value between -1 to +1. A correlation of -1.0 indicates a perfect negative correlation, and a correlation of 1.0 indicates a perfect positive correlation.

For example

r = 1 – strong positive correlation (e.g. systolic blood pressure always increases with age)

r = 0 – no correlation (e.g. there is no correlation between systolic blood pressure and age)

r = – 1 – strong negative correlation (e.g. systolic blood pressure always decreases with age)

Whilst correlation coefficients give information about how one variable may increase or decrease as another variable increases they do not give information about how much the variable will change. They also do not provide information on cause and effect.

In contrast to the correlation coefficient, linear regression may be used to predict how much one variable changes when a second variable is changed.

Omitted variable bias occurs when a statistician passes over one or more relevant variables from the study.

Publication bias occurs in publish academic research. it occurs when the results of the study effect the decision whether to publish or not.

Expectation bias occurs when the expectation of a researcher about the results effect the behaviour of the participants. Expectations may come from communication and experiences.

Work up bias occurs in the study of diagnostic test validity, whether a gold standard procedure has been used. work up bias can seriously affect the specificity of the test.

Recall bias introduced when participants in a study are systematically more or less likely to recall and relate information on exposure depending on their outcome status. Recall bias is more potential for Case-control studies.

Correlation doesn’t justify causality. Correlation coefficient gives us an idea whether or not the two parameters provide have any relation of some sort or not i.e. does change in one prompt any change in other? It has nothing to do with predictions. For that purpose linear regression is used.

Observers may subconsciously measure or report data in a way that favours the expected study outcome. Therefore, by blinding the study we can eliminate expectation bias.

Recall bias is a systematic error that occurs when the study participants omit details or do not remember previous events or experiences accurately.

Verification can occur during investigations when there is a difference in testing strategy between groups of individuals, which might lead to biasness due to differing ways of verifying the disease of interest.

Nonresponse bias is the bias that occurs when the people who respond to a survey differ significantly from the people who do not respond to the survey.

A distortion that modifies an association between an exposure and an outcome because a factor is independently associated with the exposure and the outcome. Randomization is the best way to reduce the risk of confounding.

The incidence of a disease is the number of new cases of the disease in a population over a defined time period.

The prevalence of a disease is the number of cases of the disease in a population over a defined time period describes. It is NOT the number of new cases.

The number of new cases of a disease only, has no denominator (time period or population) from which to derive an incidence.

The number of new cases of a disease seeking medical treatment is the incidence of patients seeking medical treatment NOT the incidence of the disease in a population.

The death rate from a disease is the number of patients dying from the disease in a population.

Mean, also known as the average, is the most common measure of central tendency. It is the sum of all observed values divided by the number of observation. It is not useful for skewed data, which has an abnormal distribution. It is useful, instead, for numerical data that have symmetric distribution. It reflects the contributions of each data in the group, and are sensitive to outliers.

The median is the value that falls in the middle position when the observations are ranked in order from the smallest to the largest. If the number of observations is odd, the median is the middle number. If it is even, the median is the average of the two middle numbers. Unlike the mean, the median is useful on skewed data, and can be used for ordinal or numerical data if skewed.

The mode is the value that occurs with the greatest frequency in a set of observations, and is utilized for bimodal distribution.

The variance and the standard deviation are not measures of central tendency, but of dispersion.

Risk ratio (relative risk) compares the probability of an event in an exposed (experimental) group to that of an event in the unexposed (control) group.

A relative risk of 1 suggests that there is no discernible difference in the outcome whether or not it has been exposed.

A relative risk of less than 1 indicates that probability of occurrence of an event is less if there is exposure.

A relative risk of greater than 1 highlights that an event is most likely to occur if it was provided exposure. Since you believe that exposure (the new drug) would have side effects, the value should be greater than 1.

Number needed to treat is a measure of the impact of a treatment or intervention that is often used to communicate results to patients, clinicians, the public and policymakers. It states how many patients need to be treated for one additional patient to experience an adverse outcome (e.g. a death).

It is calculated as the inverse of the absolute risk reduction and is rounded to the next highest whole number.

The absolute risk reduction is 8% (16% – 8%). 100/8 = 12.5, so rounding up the next integer this gives at NNT of 13. i.e. you would need to give the new drug to 13 people to ensure that you prevented one death.

Standard error can be calculated by the following formula:
Standard Error= (Standard Deviation)/√(Sample Size)
= (16) / √(100)
= 16 / 10
= 1.6

The attributable risk is the rate of a disease in an exposed group to that of a group that has not been exposed to it. It involves the measure of association that is pertinent to making decisions for the individuals.

Half life (T½) is the time required to change the amount of drug in the body by one-half (or 50%) during elimination. The time course of a drug in the body will depend on both the volume of distribution and the clearance.

Extrapolating the values from the plasma concentration vs time:

Plasma concentration at 0 hours = 800 mcg/mL
Plasma concentration at 2 hours = 400 mcg/mL
Plasma concentration at 4 hours = 200 mcg/mL
Plasma concentration at 6 hours = 100 mcg/mL
Plasma concentration at 8 hours = 50 mcg/mL
Plasma concentration at 10 hours = 25 mcg/mL
Plasma concentration at 12 hours = 12.5 mcg/mL
Plasma concentration at 14 hours = 6.25 mcg/mL

The study is being conducted on a smaller level with only 200 participants and is determining the effectiveness of the drug in comparison to a placebo. These characteristics are in accordance with the second phase of trial.

The relationship between bacterial growth and time is a tear-away exponential. The mathematical relationship between y and x in this case is:

y = ex

Where: the power is x, and the base is e.

Euler’s number (e) is a mathematical constant that is the base for all logarithms occurring naturally. Its value is 2.718.

The statement X increasing with an increase in Y is proportional to Y refers to the change in y in terms of x when considering any exponential relationship.

This is not a build-up exponential, and that is mathematically stated as y = 1-e-kt.

The negative x axis being a horizontal asymptote and the y intercept being 0, 1 are examples of tearaway exponentials , but do not describe an exponential process.

Number needed to harm are a measure of the impact of a treatment or intervention that is often used to communicate results to patients, clinicians, the public and policymakers. It states how many patients need to be treated for one additional patient to experience an adverse outcome (e.g. a death). It is calculated as the inverse of the absolute risk reduction. It can equally well be applied to harmful outcomes as well as beneficial ones, where it becomes numbers needed to treat (NNT) instead.

In this way, they are both calculated the same but NNT usually refers to a therapeutic treatment whereas NNH refers to a risk-factor for disease.