Linear regression is a basic and commonly used type of predictive analysis. The overall idea of regression is to examine two things: (1) do a set of predictor variables do a good job in predicting an outcome (dependent) variable? (2) Which variables, in particular, are significant predictors of the outcome variable, and in what way do they–indicated by the magnitude and sign of the beta estimates–impact the outcome variable.These regression estimates are used to explain the relationship between one dependent variable and one or more independent variables. Three major uses for regression analysis are (1) determining the strength of predictors, (2) forecasting an effect, and (3) trend forecasting

Case control studies are used to determine the relationship between exposure to a risk factor and the resultant outcomes. It finds patients in the general population who have a certain condition and retrospectively searches for past exposure to possible risk factors for the disease. Controls are people who do not have the disease found in the general population. This type of study is useful for rare diseases, and is less time consuming to conduct. While cohort studies can be used to study rare diseases they measure the relative risk of developing the disease over time based on exposure. Ecological or cross-sectional studies attempt take a snapshot of a whole population, and thus are inappropriate for rare diseases as larger sample numbers are needed. A randomised control trial is better suited to determine the effect of an intervention.

A case–control study (also known as case–referent study) is a type of observational study in which two existing groups differing in outcome are identified and compared on the basis of some supposed causal attribute. Case–control studies are often used to identify factors that may contribute to a medical condition by comparing subjects who have that condition/disease (the cases) with patients who do not have the condition/disease but are otherwise similar (the controls).
An odds ratio (OR) is a statistic that quantifies the strength of the association between two events, A and B. The odds ratio is defined as the ratio of the odds of A in the presence of B and the odds of A in the absence of B or vice versa.

Crossover trials are characterized by the switching of study participants throughout the treatment groups, keeping a random order of switching. This randomization is important to determine any carry-over effect of different treatment modalities. The benefit of this study is the evaluation of the efficacy of various short-term treatment options for the relief of chronic conditions. The washout period is small in this type of study. Crossover studies are more efficient than the parallel studies, but they should be used according to the treatment options and outcomes.

To quantify differences between percentages you can use Fisher’s exact test.Odds ratios, relative risks and number needed to treat are ways of quantifying differences between percentages in two groups, however are not in themselves significance tests.

While the results of this before and after study can provide some preliminary insight into the effects of the dietary intervention, the results should be viewed with great caution as they may be considered merely anecdotal. The lack of a control group contributes to confounding the data. Therefore, while the difference may be statistically significant and the confidence interval is compatible with a fall in the number of seizures after therapy, the results cannot be introduced as the standard without a control group to compare with.

Logistic regression analysis is an easy to use regression that can serve to estimate how a binary or dichotomous dependent variable, for example whether or not a student passes or fails a medical exam, is related to the number of hours the student studies for the exam. This regression is able to yield an odds ratio, i.e. the probability of passing the exam based on each additional hour of study. As stated, the outcome does not need to be normally distributed but is usually binary. This type of analysis is not complex and does not need to be avoided as it is available most statistical packages.

The main result of a correlation is called the correlation coefficient (or r). It ranges from -1.0 to +1.0. The closer r is to +1 or -1, the more closely the two variables are related.If r is close to 0, it means there is no relationship between the variables. If r is positive, it means that as one variable gets larger the other gets larger. If r is negative it means that as one gets larger, the other gets smaller (often called an inverse correlation).

The Chi squared test is used to find the relationship between two variables, determining whether they are not independent of each other. This test of statistical significance allows you to determine the degree of confidence with which you can accept or reject the null hypothesis. The student t test compares the significant differences in data means, while rank correlation, linear regression and the correlation coefficient all help to measure the linear relationship between variables.

The main aim of randomisation in a clinical trial is to remove the bias and avoid any potential confounding variables. While in double blind studies both the investigators and the patients are not aware of which group they belong in, being blind is not essential in carrying out a randomized study, nor is it essential that the randomisation be done away from the study centre. A placebo also does not facilitate randomisation, which can be done in single centre and multi-centre trials.

Correlation is a bivariate analysis that measures the strength of association between two variables and the direction of the relationship.Pearson r correlation: Pearson r correlation is the most widely used correlation statistic to measure the degree of the relationship between linearly related variables. Pearson’s correlation coefficient is the test that measures the statistical relationship, or association, between two continuous variables. It is known as the best method of measuring the association between variables of interest because it is based on the method of covariance. It gives information about the magnitude of the association, or correlation, as well as the direction of the relationship.The non-parametric Spearman or Kendall rank correlation coefficient is used if neither variable has a normal distribution or the sample size is small (i.e. <20).

Relative risk = (Incidence in exposed group)/incidence in unexposed group). So in this case RR = (50/100)/(50/200) = 2.

A cohort study is a particular form of longitudinal study that samples a cohort (a group of people who share a defining characteristic, typically those who experienced a common event in a selected period, such as birth or graduation), performing a cross-section at intervals through time.
The relative risk (RR) or risk ratio is the ratio of the probability of an outcome in an exposed group to the probability of an outcome in an unexposed group. Relative risk is used in the statistical analysis of the data of experimental, cohort and cross-sectional studies, to estimate the strength of the association between treatments or risk factors, and outcomes.

Power calculations are a important step in study design and preparation, but do not directly help with the interpretation of the results. They are used to determine how many subjects are needed in order to avoid errors in accepting or rejecting the null hypothesis. These calculations are not usually complex and for the best results, the power of the test should be set to above 80%.

The type of significance test used depends on whether the data is parametric (can be measured, usually normally distributed) or non-parametric.
Parametric tests:
Student’s t-test – paired or unpaired*
Pearson’s product-moment coefficient – correlation

Non-parametric tests:
Mann-Whitney U test – unpaired data
Wilcoxon signed-rank test – compares two sets of observations on a single sample
chi-squared test – used to compare proportions or percentages
Spearman, Kendall rank – correlation.

The outcome measured is not normally distributed, i.e. it is non-parametric. This excludes the Student’s t-tests. We are not comparing percentages/proportions so the chi-squared test is excluded. The Mann–Whitney U test is a nonparametric test of the null hypothesis that it is equally likely that a randomly selected value from one sample will be less than or greater than a randomly selected value from a second sample.
This test can be used to investigate whether two independent samples were selected from populations having the same distribution.

The equation, lung function = 3.2 + (1.7 x height) is linear, but this does not necessarily mean that the relationship itself is linear. The equation is able to predict that taller individuals are more likely to have greater lung functions. No information is given on whether the coefficients and the R value are statistically significant.

The selection process is based on five requirements and essentially aims to select a random representative cohort through:1.Isolating a group for which there is a greater or lesser chance of detecting a possible difference between the treatments compared|2.Establishing a homogeneous group in order to reduce the variability of response, thus making statistical comparison more sensitive and decreasing the risk of bias due to the constitution of non-homogeneous groups|3.Obtaining representative samples of the affection studied|4.Defining the rules corresponding to realistic recruitment|5.Respecting ethical obligations.

Compared to parametric tests, non parametric tests are seen to be less powerful as they often contend with fewer assumptions, and may use less information from the data. Sample sizes can be smaller. The samples do not have to follow a normal distribution as in parametric tests, and data may be ordinal, ranked or contain outliers that cannot be removed. Therefore nonparametric tests are well suited for these instances and do not need to be used as a last resort. They are not any more complex than parametric tests.

Case control studies are observational studies which retrospectively determine whether a patient might have been exposed to a risk factor for a certain disease, as compared to a control group from the general population. They can be used for a range of outcomes as well as rare diseases. One of the biggest problems with this type of study is recall bias. Research subjects may selectively remember factors that are more predictive of the disease outcome when compared to the control group. All studies should have prior power calculations before the study commences.

Observational studies fall under the category of analytic study designs and are further sub-classified as observational or experimental study designs. The goal of analytic studies is to identify and evaluate causes or risk factors of diseases or health-related events. The differentiating characteristic between observational and experimental study designs is that in the latter, the presence or absence of undergoing an intervention defines the groups. By contrast, in an observational study, the investigator does not intervene and rather simply “observes” and assesses the strength of the relationship between an exposure and disease variable.Three types of observational studies include cohort studies, case-control studies, and cross-sectional studies. Case-control and cohort studies offer specific advantages by measuring disease occurrence and its association with an exposure by offering a temporal dimension (i.e. prospective or retrospective study design). Cross-sectional studies, also known as prevalence studies, examine the data on disease and exposure at one particular time point. Because the temporal relationship between disease occurrence and exposure cannot be established, cross-sectional studies cannot assess the cause and effect relationshipDisadvantage of Cohort study is Susceptible to selection bias.

A written protocol is important in clinical research as it helps to decrease bias with early findings as the process of the trial has been documented in advance. To show that the study has been properly undertaken before commencing, the investigators must document their names| they must describe the process, detail the analysis that will be undertaken, and provide a power calculation. The ethics committee does not always need to see the protocol.

Before the test, the patient was likely to have the disease being tested for. Their pre test odds were 2, making them twice as likely to have the disease. After testing positive, their pretest odds of 2 and the likelihood ratio of 3 are multiplied to produce 6 as the post test odds. The patient is now 6 times as likely to have the disease after the test. Likelihood ratios above 10 or below 0.1 are strong evidence to rule in and rule out a diagnosis. The negative likelihood ratio is not known here, but does not subtract from the interpretation of the outcomes in this patient.

The Chi-squared test evaluates if two variables are related. The other statistical tests mentioned do not perform this function.

Standard deviation is defined as the measure of dispersion of a set of data from its mean. It measures the absolute variability of a distribution| the higher the dispersion or variability, the greater is the standard deviation and greater will be the magnitude of the deviation of the value from their mean.

Randomization is one of the ethical protocols for research work, involving unbiased sample selection. Consent is required before undertaking any research and is taken for the complete research work at once. No separate consent is required for the process of randomization. The consent should explain each and every aspect of the study, including details about the process of randomization. Only particular study designs, like Zelen design, permit the avoidance of consent to randomization but these studies have their setbacks.

Relative risk is the probability of an outcome occurring in an exposed group as compared to the probability of that outcome in an unexposed group. In the scenario given, 50% of the children exposed developed the disease while only 10% of the children who were unexposed developed the disease. The relative risk was therefore 50/10=5. There is no further information about whether the study was controlled, the confidence interval, or the type of study. It therefore cannot be confirmed whether the chemical is causative and if it should be avoided.

In case control studies, observational studies are made to compare two groups, individuals with a certain condition, to those without the condition, with all other factors being equal. In the situation presented by the question, the study was to determine whether a prior risk factor, a low birth weight, was associated with later developing adolescent hypertension, using a paired t-test to statistically determine whether there was indeed a significant association between the two conditions. Case control studies only help to draw associations between two groups and therefore cannot indicate causation. In this scenario we are also not given the p value to determine whether the association is statistically significant. Therefore there is not enough evidence to conclude whether or not birthweight affects the development of adolescent hypertension.

In the final result of this double blind study, 25% or one in four of patients who received the treatment responded positively. Though the difference is significant at P<0.05, it is better to present this as a significant difference at 0.4%. The number needed to treat (NNT) is defined as the inverse of the absolute risk reduction. Taking this as 0.25 (25%), the NNT is 1/0.25 = 4. However given the 95% confidence interval is between 10-50% for absolute risk reduction, the NNT with 95% CI is between 2 and 10. Therefore we cannot say with certainty that the NNT is at least 4.

Odds ratios are best described as the odds of an event in one group divided by the odds of the event in another. They form an alternative to the relative risk in case–control studies and are close to the relative risk when events are rare. The odds are the number of the event divided by the number without the event, which is less intuitive than the risk, which is the number with the event divided by the total. Odds ratios are therefore less intuitive than relative risks. Logistic regression analysis outputs variable coefficients which are the log of the odds ratio.

The sensitivity of a screening test can be described in a variety of ways, typically such as sensitivity being the ability of a screening test to detect a true positive, being based on the true positive rate, reflecting a test’s ability to correctly identify all people who have a condition, or, if 100%, identifying all people with a condition of interest by those people testing positive on the test.The specificity of a test is defined in a variety of ways, typically such as specificity is the ability of a screening test to detect a true negative, being based on the true negative rate, correctly identifying people who do not have a condition, or, if 100%, identifying all patients who do not have the condition of interest by those people testing negative on the test.