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.

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.

A relative risk of 1 suggests that there is no discernible difference in the outcome whether or not it has been exposed.

A relative risk of less than 1 indicates that probability of occurrence of an event is less if there is exposure.

A relative risk of greater than 1 highlights that an event is most likely to occur if it was provided exposure. Since you believe that exposure (the new drug) would have side effects, the value should be greater than 1.

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.

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.

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.

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.

Standard error can be calculated by the following formula:

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

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.

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).

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.

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 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

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.

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)

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 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.

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.

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 hazard ratio (HR) is simply a comparison of two hazards in a study. It provides an estimate of the ratio of the hazard rates between the experimental group and a control group over the entire study duration. It is typically used when analysing survival over time, hence is the most suitable statistical method in this case.

An odds ratio is a statistic that quantifies the strength of the association between two events, A and B. It is the “measure of association” for a case-control study.

The Pearson product-moment correlation coefficient (Pearson’s correlation, for short) is a measure of the strength and direction of association that exists between two variables. An example would be if scientists wanted to evaluate the relationship between quality of certain population of rice and their genetic make-up.

Relative risk is the ratio of the risks for an event for the exposure group to the risks for the non-exposure group. Thus relative risk provides an increase or decrease in the likelihood of an event based on some exposure. Relative risk measures the association between the exposure and the outcome.

Absolute risk reduction is the number of percentage points your own risk goes down if you do a preventive act such as stop drinking alcohol. It depends on what your risk factors are to begin with.

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.

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.

Observation bias occurs when the behaviour of an individual changes that results from their awareness of being observed.

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.

Attrition bias is a systematic error caused by unequal loss of participants from a randomized controlled trial (RCT). In clinical trials, participants might dropout due to unsatisfactory treatment or efficacy, intolerable adverse events, or even death.

Selection bias introduced when the individuals are not chosen randomly to take a part in the study. It usually occurs when the research decides who is going to be studied, they are not the representative of the population.

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.

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.

Correlation doesn’t justify causality. 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? It has nothing to do with predictions. For that purpose linear regression is used.

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.

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.

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

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 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