Funnel plot is essentially a scatterplot of the effect of treatment against a particular measure of study precision. Its primal purpose is to serve as a visual aid and help in detection of bias or systematic heterogenity.

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 Kappa Statistic or Cohen’s Kappa is a statistical measure of inter-rater reliability for categorical variables. It is used when two raters both apply a criterion based on a tool to assess whether or not some condition occur. A good example can be two doctors rating individuals for diabetes occurrence on the basis of symptoms.

It gives a quantitative measure of the magnitude of agreement between observers.

Kappa can take any value between 0 and 1. 0 implies the observers are in complete disagreement and a value of 1 implies complete agreement.

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 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.

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.

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.

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.

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.

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 Weibull distribution are used to describe various types of observed failures of the components. it is used in reliability and survival analysis.

Regression Analysis is used to measure the relationship between among two or more variable. It determines the effect of independent variables on the dependent variables.

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.

A time series is a collection of observations of well-defined data obtained at regular interval of time.

Kaplan-Meier estimator is used to estimate the survival function from lifetime data. It can be derived from maximum likelihood estimation of hazard function. It is most likely used to measure the fraction of patient’s life for a certain amount of time after treatment.

A forest plot is a graphical representation that summarizes the findings of several research, such as a meta-analysis of a series of randomized controlled trials.

The Kaplan-Meier estimate shows survival over time, for example, plotting the number of patients still alive seven years after chemotherapy for lung cancer.

Fisher’s exact test similarly uses contingency tables to assess statistical significance, however, it is typically used when sample sizes are small.

Chi-square test assesses whether an association exists between two categorical variables using the observed and expected frequencies. For instance, is social class (I-V) related to body mass index (BMI) category? Using the observed and anticipated frequencies, the Chi-square test determines whether a connection exists between two categorical variables. For example, is socio-economic status related to BMI category?

Linear regression is a technique which attempts to model the relationship between two variables by fitting a linear equation to observed data. Linear regression uses correlation between two continuous variables. As correlation only indicates the strength of an association only, it cannot be used to forecast the change in one variable when a second variable is altered.

This equation takes the form y = mx + c, where ‘y’ is the dependent variable, ‘x’ is the independent variable, ‘m’ is the slope of the line and ‘c’ is the intercept. In this example, for a range of heights, it would be possible to map a line of best fit to a scatter plot and thus predict the forced expiratory volume (FEV1) for an individual.

In statistical terms, correlation is used to denote association between two quantitative variables.

The degree of association is measured by a correlation coefficient, denoted by r. The correlation coefficient is measured on a scale that varies from + 1 through 0 to – 1. Complete correlation between two variables is expressed by either + 1 or -1. When one variable increases as the other increases the correlation is positive; when one decreases as the other increases it is negative. Complete absence of correlation is represented by 0.

The two methods are not synonymous as correlation measures the degree of relationship between two variables whereas regression analysis is about how one variable affects another or what changes it has on the other variable. Both are also shown by a different graphical representation.

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.

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.

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.

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

So,

ARR= (10/400)-(20/400)

ARR= 0.025-0.05

ARR= 0.025 (Numerical Value)

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.

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.

A prospective randomised double blind controlled trial against cyclizine in multiple centres is the most likely to change your practice.

Case controlled studies are efficient in identifying an association between a drug treatment and outcome and are usually conducted retrospectively. They are generally less valued than prospective randomised trials. They cannot generate incidence data, are subject to bias, have difficult selection of controls and can be made more difficult if note keeping is not reliable.

The gold standard in intervention-based studies is randomised controlled double blind trials. Its features are:

Treating all intervention groups identically
Reduction of bias by random allocation to intervention groups
Patients and researchers unaware of which treatment was given until at completion of study
Patients analysed within the group to which they were allocated, and
Analysis focused on estimating the size of the difference in predefined outcomes between intervention groups.

New healthcare interventions should be evaluated through properly designed randomised controlled trials (though there are some potential ethical disadvantages)

Conducting trials in multiple centres is an accepted way of evaluating a new drug as it may be the only way of recruiting sufficient number of patients within a reasonable time frame to satisfy the objectives of the trial. Type II statistical errors will occur if a small numbers of patients is used in study group.

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).

Since the data is normally distributed, 95.4% of the values lie with in 2 standard deviations from mean. The rest of the 4.6% are distributed symmetrically outside of that range which means 2.3% of the values lie above 2 standard deviations of the mean.

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 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)

Key Point: While finding out confidence intervals, standard errors are used. Standard error and Standard deviation are two distinct entities and should not be confused.

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

Multiply the standard error by 3.

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

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

The range turns out to be 1-13 mmol/L.

For a confidence interval of 68%, multiply the standard error with 1 and repeat the process. The range found for this interval is 3-11 mmol/L.

For a 95% confidence interval. Standard Error is multiplied by 1.96 which gives us the limit ranging from 3.08 to 10.92 mmol/L which could be approximated to 3-11 mmol/L.

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 Number Needed to Treat (NNT) is the number of patients you need to treat to prevent one additional bad outcome. For example, if a drug has an NNT of 5, it means you have to treat 5 people with the drug to prevent one additional bad outcome.

To calculate the NNT, you need to know the Absolute Risk Reduction (ARR); the NNT is the inverse of the ARR:

NNT = 1/ARR

Where ARR = CER (Control Event Rate) – EER (Experimental Event Rate).

NNTs are always rounded up to the nearest whole number.

In this case, the NNT can be computed as follows:

ARR = 10% – 5% = 0.05

NNT = 1/0.05 = 20

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.

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.

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.

In procedure bias, the researcher decides assignment of a treatment versus control and assigns particular patients to one group or the other non-randomly. This is unlikely to have occurred in this case, although it is not mentioned specifically.

Self Selection or volunteer bias occur when those subjects are selected to participate in the study who are not the representative of the entire target population. those subjects may be from high socio-economic status and practice those activities or lifestyle that improves their health.

Lead-time bias occurs when a disease is detected by a screening test at an earlier time point rather than it would have been diagnosed by its clinical appearance. In this bias, earlier detection improves the survival time in the intervention group.