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)

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.

Case control studies in particular are prone to recall bias, people who are suffering from COPD might sometimes relate the ailment to marijuana usage in past and hence contrary to the control group, they are more able to describe to what extent they have been using the drug in the past.

As recommended, all the doctors should make sure that there practice is based on evidence and thus it is paramount that the doctors learn to appraise the paper in a critical manner i.e. ability to detect any potential source of bias.

Detection Bias: Outcomes are more looked for in one group than the other.

Observer Bias: Subjectivity of observers regarding the outcome.

Publication bias: Not publishing the results of a valid study just because they are negative or uninteresting can be termed as publication bias.

Recall bias: Recall bias is specifically appropriate to the case control studies that is when ever the memories retrieved by the participants differ in accuracy.

Response Bias: The participants that filled out the response forms containing information that was going to be used for a trial, don’t represent the target population.

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.

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.

The positive predictive value is the ratio of patients truly diagnosed as positive to all those who had positive test results. In this case, this is 60/(60+20)=75%.

The negative predictive value is the ratio of patients truly diagnosed as negative to all those who had negative test results. In this case, this is 80/(80+40)=67%.

The sensitivity is the ratio of patients with the disease who test positive i.e. true positive patients to the total number of people with the disease. In this case, this is 60/(60+40)=60%.

The specificity is the ratio of people who don’t have the disease who test negative i.e. true negatives to the total number of people without the disease. In this case, this is 80/(20+80)=80%.

70% is not the result of any screening measurements

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

Attributable proportion is the proportion of disease that is caused due to exposure. It refers to the proportion of disease that would be eradicated from a particular population if the disease rate was diminished to match that of the unexposed group.

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. Thus two are not the same.

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 i.e. how many deaths did the exposure cause.

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..

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).

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

So,

ARR= (0.04-0.03)

ARR= 0.01

NNT= 1/0.01

NNT=100

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.

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 relative risk (also known as risk ratio [RR]) is the ratio of risk of an event in one group (e.g., exposed group) versus the risk of the event in the other group (e.g., nonexposed group).

The odds ratio (OR) is the ratio of odds of an event in one group versus the odds of the event in the other group.

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.

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.

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

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.

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)

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

So,

ARR= (24/120)-(60/240)

ARR= 0.2-0.25

ARR= 0.05 (Numerical Value)

ARR= 5%

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 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.

Linear regression, using a technique called curve fitting, allows us to make predictions regarding a certain variable.

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?

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.

68% of the population will be found in one standard deviation (SD) above plus one SD below the mean. Two SDs above plus two SDs below the mean will include 95% of the population.

The median can be greater or less than the mean as it is simply the mid point of the data after the data is arranged. Half the data are above and half below the median .

The mode is a true score, unlike the mean or the median. It is the most common score or the score obtained from the largest number of subjects in any given data.

This data is in a 2 × 2 contingency table so a chi square test can be used. There is a special chi squared formula that gives a value that can be looked up in a table giving the p value.

Since we are comparing proportions not means, the Student’s t test CANNOT be used.

There is no linear regression to plot so Pearson’s co-efficient cannot be calculated.

Nothing is so obvious that no statistical analysis is needed.

Standard error can be calculated by the following formula:

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

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.

Both incidence and prevalence are indicators of the disease frequency. While incidence tells us about the number of cases reported per population in a provided time period, prevalence is the factor you should be vigilant about as it tells us about the total number of cases that have been reported in a population at a particular point of time.

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.