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.

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.

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.

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.

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

Work up bias involves comparing the novel diagnostic test with the current standard test. A portion of the patients undergo the standard test while others undergo the new test as the standard test is costly. The result can be alteration in specify and sensitivity.

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

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

When information gathering is ill suited with respect to time i.e. collecting the data regarding a fatal disease many years after the death of its patients, it is termed as Late – look bias.

The case in point is an instance of lead time bias when upon comparing two tests, one is able to detect the condition earlier than the other but the overall outcome doesn’t change. There is a possibility that this will make the survival rates for the newer test look more promising.

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 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.

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.

Selection bias is when randomisation is not achieved and is often a result of in efficient recruiting method.

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

Measurement bias can be characterized by gathering of information in a manner that is distorted.

When the participants of a research study are recruited from the hospitals rather than the general population, its called Berkson Bias.

Confounding bias is the major player here because in this case the effects of smoking can be masked behind and can be read as outcomes of lower socio economic status. This extraneous factor (Smoking), distorts the founding.

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 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.

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.

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

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.

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)

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.

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 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.

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..

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).

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.

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.

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.

Level 1 – High-quality randomised controlled trial with statistically significant difference or no statistically significant difference but narrow confidence intervals (prospective controlled)

Level 2 – Prospective comparative study (prospective uncontrolled)

Level 3 – Case-control study, retrospective comparative study (retrospective controlled)

Level 4 – Case series (retrospective uncontrolled)

Level 5 – Expert opinion.

This clinical trial consists over 1000 patients being evaluated for the response to a new treatment against a currently licensed treatment for ulcerative colitis. Therefore, it is comparing its efficacy to an established therapeutic or control in a larger population of volunteers. These are the characteristics of a phase III clinical trial.

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 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.

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.

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.

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.