Also known as the “product limit estimate’’, the Kaplan-Meier survival plot is used to estimate the true survival function from the collected data.

Using this plot, probabilities of occurrence of an event at a certain point in time can be computed. The successive probabilities are multiplied by any earlier computed probabilities to get the final estimate. For a given population, the survival probability at any particular time on the plot = (number of subjects living at the start – number of subjects who died)/number of subjects living at the start.

The description of a scatter plot is a graphical representation using Cartesian coordinates to display values for more than two variables for data set. It is used for to assess the relationship between 2 different variables.

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.

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

Therefore, the SEM gets smaller as the sample size (n) increases.

If we want to depict how widely scattered some measurements are, we use the standard deviation. For indicating the uncertainty around the estimate of the mean, we use the standard error of the mean. The standard error is most useful as a means of calculating a confidence interval. For a large sample, a 95% confidence interval is obtained as the values 1.96×SE either side of the mean.

A 95% confidence interval:

lower limit = mean – (1.96 * SEM)

upper limit = mean + (1.96 * SEM)

Results such as mean value are often presented along with a confidence interval. For example, in a study the mean height in a sample taken from a population is 183cm. You know that the standard error (SE) (the standard deviation of the mean) is 2cm. This gives a 95% confidence interval of 179-187cm (+/- 2 SE).

Hence, it would be wrong to say that confidence levels do not apply to standard error of the mean.

The following terms are used in medical testing:

True negative – The test is negative and the patient does not have the disease.
True positive – The test is positive and the patient has the disease.
False positive – The test is positive but the patient does not have the disease.
False negative – The test is negative but the patient has the disease.

The sensitivity of a predictive test = true positives / (true positives + false negatives).

The specificity of a test = true negatives / (false positives + true negatives).

The negative predictive value of a test = true negatives / (false negatives + true negatives).

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

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%

9 & 27 can be obtained by subtracting and adding 9 from the mean. 9 is three times the standard deviation and we know that 99.7% values lie within 3 standard deviations from the mean. We can find the interval for 99.7% to verify in the following way:

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.

4. The range turns out to be 9-27 kg.

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.

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.

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.

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.

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.

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)

In general practice, majority of phase 3 trials and some of the trials conducted in phase 2 are randomized. Because phase 4 trials require a huge sample size, they are not randomized as much. The primal reason behind conducting phase 3 trials is to test the efficiency and safety in a significant sample population. At this point it is assumed that the drug is effective up to a certain extent.

During a case-control study, subjects that exhibit outcomes of interest are compared with those who don’t show the expected outcome. The extent of exposure to a particular risk factor is then matched between cases and controls. If the exposure among cases surpasses controls, it becomes a risk factor for the outcome that is being studied.

Pilot studies are conducted on a lower and much smaller level, to assess if a randomized controlled trial of the crucial components of a study will be plausible.

Phase 4 trials are the ones that are conducted after its established that the drug is effective and is approved by the regulating authority for use. These trials are concerned with the side effects and potential risks associated with the long term usage of the drug.

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.

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.

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

Only on rare occasions has it been found that the prevalence and incidence were same. Incidence can be greater than prevalence in acute cases only. In case of chronic diseases prevalence is far greater than incidence. One needs to have a deeper understanding of both the concepts to understand the health literature.

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.

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.

Normal distribution, also called Gaussian distribution, the most common distribution function for independent, randomly generated variables, and describes the spread for many biological and clinical measurements.

Properties of the Normal distribution

symmetrical i.e. Mean = mode = median

68.3% of values lie within 1 SD of the mean

95.4% of values lie within 2 SD of the mean

99.7% of values lie within 3 SD of the mean

The empirical rule, or the 68-95-99.7 rule, tells you where most of the values lie in a normal distribution: Around 68% of values are within 1 standard deviation of the mean.

Around 95% of values are within 2 standard deviations of the mean. Around 99.7% of values are within 3 standard deviations of the mean.
the standard deviation (SD) is a measure of how much dispersion exists from the mean.

SD = square root (variance)

The empirical rule, or the 68-95-99.7 rule states where most of the values lie in a normal distribution. Around 68% of values fall within 1 S.D of the mean, about 95% within 2 S.D of the mean, and about 99.7% of values within 3 S.D of the mean. Therefore, 95.4% is the most reasonable answer if results are normally distributed.

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 Delphi technique was developed in the 1950s and is a widely used and accepted method for achieving convergence of opinion concerning real-world knowledge solicited from experts within certain topic areas. Choosing the appropriate subjects is the most important step in the entire process because it directly relates to the quality of the results generated, despite this, there is no exact criterion currently listed in the literature concerning the selection of Delphi participants.

Therefore, due to the potential scarcity of qualified participants and the relatively small number of subjects used in a Delphi study, the ability to achieve and maintain an ideal response rate can either ensure or jeopardize the validity of a Delphi study.

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).

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

The data is ideal for chi square test evaluation as it will help determine if observed outcomes are in line with expected outcomes, and also if results are significant or due to chance.

The student’s t test is not ideal as it requires comparison of means from different populations, rather than proportions.

Pearson’s coefficient of linear regression is not ideal as it requires the plotting of a linear regression.

The numbers should be analysed before determining if there are any statistical conclusions that can be drawn from the population.

Statistical analysis is always required to determine the performance of any treatment during a clinical drug trial. Conclusions cannot be drawn simply by looking at the data.

Number needed to treat (NNT) is a time specific epidemiological measure that indicates how many patients would be require for an intervention to prevent one additional bad outcome. A perfect NNT would be 1, where everyone improves with treatment, thus the higher the NNT, the less effective the treatment.

Thus if you treat 1000 patients then you will expect to have 50 fewer strokes.

Since the data is normally distributed, 95% of the values lie with in the interval 70 to 90. This can be calculated as follows:

Interval= Mean ± ( 2 times standard deviation)
= 80 ± 2(5)
= 80 ± 10
= 70 & 90

The rest of the 5% are distributed symmetrically beyond 90 and below 70 which means 2.5% of the values lie above 90.

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.