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.

During analytical stage a technique called stratification is used for controlling confounding variables. This technique involves sorting out the data into discernible groups.

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.

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..

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 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.

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.

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.

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).

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.

Hypochondriasis is an illness anxiety disorder, and describes excessively worriedness about the presence of a disease. While the woman is concerned about her possibility of developing motor neurone disease, she understands that no symptoms have yet appeared. Hypochondriasis involves patients who refuse to accept that they don’t have the disease, even if the results come back negative.

Late Look Bias occurs when the data is gathered or analysed at an inappropriate time e.g. when many of the subjects suffering from a fatal disease have died. This type of biasness might occur in some retrospective studies of motor neurone disease, but is not applicable to this prospective study.

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. Of all the options, lead time-bias is a better answer.

The Hawthorne Effect refers to groups modifying their behaviour simply because they are aware of being observed. Any differences in the behaviour have not been mentioned in the question, and it is highly unlikely that a change in patient’s behaviour would have affected their length of survival in this case.

The correct option is lead-time bias. Even if the new blood test diagnoses the disease earlier, it doesn’t affect the outcome, as the survival time was still on average 43 months from the onset of symptoms in both groups. With the help of blood test, the disease was only detected 8 months earlier.

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.

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 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

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.

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.

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.

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 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

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.

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.

Being the part of a meta analysis, forest plots are more valued as evidence then randomised control trials.

The notion that forest plots can only be used if the results are substantial is not true. They are good indicators of the significance of the data. If the diamond intersects the central line, the data is rendered significant. It also aggregates means and confidence intervals from studies conducted in the past which makes the study much more reliable as errors associated with individual studies tend to have less of an impact in this way.

The suggestion that forest plots are primarily used for qualitative data is factually incorrect. Forest plots require numerical values to function.

All in all, forest plots help us in determining whether or not there is a significant trend in that particular field of study.

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.

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 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.

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.

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?

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

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.