When the association among any two classes of object is defined by the presence of a third entity it is termed as indirect association. For an instance, the age of the employee may affect the rate of pay, which would have implications on job satisfaction. So, in this example, an indirect relationship between age and job satisfaction exists due to a third party i.e. rate of pay.

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.

Being the part of a meta analysis, forest plots are more valued as evidence then randomised control trials.

The notion that forest plots can only be used if the results are substantial is not true. They are good indicators of the significance of the data. If the diamond intersects the central line, the data is rendered significant. It also aggregates means and confidence intervals from studies conducted in the past which makes the study much more reliable as errors associated with individual studies tend to have less of an impact in this way.

The suggestion that forest plots are primarily used for qualitative data is factually incorrect. Forest plots require numerical values to function.

All in all, forest plots help us in determining whether or not there is a significant trend in that particular field of study.

Randomisation can be used to provide control over the confounding variables during the design stage of a study however during analytical stage a technique called stratification is used for controlling confounding variables. Since the question asks for the information that is factually incorrect.

The normal distribution is a symmetrical, bell-shaped distribution in which the mean, median and mode are all equal.

Boyle’s law is correctly stated as it states that the volume of a gas of known mass is inversely proportional with absolute pressure, at a constant temperature.

Beer’s law states that radiation absorption by a solution of known thickness and concentration is identical to that of a solution of double thickness and half concentration.

Bougner’s (or Lambert’s) law states that every layer with the same thickness will absorb the same amount of radiation as it passes through.

Graham’s law states that the diffusion rate of a gas is inversely related to the square root of its molecular weight.

Raoult’s law states that the reduction of a solvent’s vapour pressure is directly proportional to the solute’s molar concentration.

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.

Incidence tells us about the number of new cases that have been reported while prevalence gives us the idea of existing cases.

In this particular instance, the parameter of the study i.e. the total number of cases has not changed thus the prevalence of the disease remains same. Although, more cases have been reported in the second instance as a result of which incidence has increased.

The level of statistical significance required influences the sample size used. This is because sample size is used in the calculation of SD/SE.

Sample size does not affect

The level of acceptance
The alternative hypothesis with a general level set at p<0.05
The test to be used.

Experience of the investigator and the type of patient recruited should have no bearing on the required sample size.

Chi-square test is used to determine the statistically significant different between categorical variables. It also determines the difference between expected frequencies and the observed frequencies.

Mann Whitney U test is used to determine the statistically significant different between two independent groups.

Wilcoxon’s test is the test of dependency. it determines the statistically significant difference between two dependent groups.

Student t-test is one of the most commonly used method to test the hypothesis. It determines the significant difference between the means of two different groups.

ANOVA (analysis of variance) is similar to student’s t-test.

ANOVA is a statistical method used to determines the statistically significant difference between the mean of more than two group. In this experiment as we are dealing with three different group, ANOVA is most suitable test to determine the difference between each groups.

Randomized controlled trails will be analysed by the intention-to-treat (ITT) approach. It provides unbiased comparisons among the treatment groups. ITT analyses are done to avoid the effects of dropout, which may break the random assignment to the treatment groups in a study.

ITT analysis is a comparison of the treatment groups that includes all patients as originally allocated after randomization.

In order to include such participants in an analysis, outcome data could be imputed which involves making assumptions about the outcomes in the lost participants.

The process used in the study is Delphi method. 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.

Randomisation allows for performance of experimental trials in a random order. Using this method gives us control over the confounding variables that are not supposed to be held constant.

For an instance, by employing randomisation we get to control biological differences among individual human beings during experimental trials.

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.

Absolute risk reduction = (Control event rate) – (Experimental event rate)

Experimental event rate = 24 / 120 = 0.2

Control event rate = 60 / 240 = 0.25

Absolute risk reduction = 0.25 – 0.2 = 0.05 = 5% reduction

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.

Tests are used to confirm the presence of a particular disease. However the results can be misleading at times since most of the tests have some limitations associated with them.
Sensitivity is the correct term that refers to the probability of a positive test. The others are explained below:

False Positive rates refer to the proportion of the patients who don’t have the condition being detected as positive.

False Negative rates refer to the proportion of the patients who have the condition being detected as negative (like the 20% of the patients that went undetected by the Ca-125 test).

Specificity describes the ability of a test to detect and pick up people without the disease. Absolute risk ratio compares the rate of two separate outcomes.

The question mentions a quantitative, ratio scale data set. The use of mean would be ideal under normal circumstances, however, in this situation median is preferred as it is less sensitive to the skewness of data. The median is usually preferred to other measures of central tendency when your data set is skewed (i.e., forms a skewed distribution)

Standard error can be calculated by the following formula:

Standard Error= (Standard Deviation)/√(Sample Size)
= (12) / √(64)
= 12 / 8
= 1.5

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..

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

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.

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).

where ARR= (Risk factor associated with the new drug group) — (Risk factor associated with the currently available drug)

So,

ARR= (165/1050)-(132/1044)

ARR= (0.157-0.126)

ARR= 0.031

NNT= 1/0.031

NNT=32.3

Variance and standard deviation indicate the dispersion of the plot from mean value and thus are not really helpful in summarizing the mean.

Range is the difference between maximum and minimum value that is 45 in this case.

The mean in this case is 6.2 due to the presence of an outlier 45. In the presence of outlier mean can be misleading as it is quite sensitive to skewness in data.

Mode is the most frequent value. In this case mode has 4 values: 0,1,2,4.

In case of skewedness, median is the most apt representative of the mean as it is not affected by outliers. In this case since the data set has even values i.e. 10. Median is the average of the 5th & 6th entry after arranging the data in ascending order like that in case of the question (0,0,1,1,2,2,3,4,4,45). This turns out to be 2.

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.

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

Hawthorne effect explains the change in any behavioural aspect owing to the awareness that the person is being observed.
Simpson’s Paradox explains the association developed when the data from several groups is combined to form a single larger group.

The remaining terms are made up.

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.

The Delphi is a group facilitation technique that seeks to obtain consensus on the opinions of `experts’ through a series of structured questionnaires (commonly referred to as rounds). By using successive questionnaires, opinions are considered in a non-adversarial manner, with the current status of the groups’ collective opinion being repeatedly fed back. Studies employing the Delphi make use of individuals who have knowledge of the topic being investigated

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