Medical statistics is one of the main areas of statistical work and has had a considerable influence on clinical medicine and public health through its applications, for example, to the design and analysis of clinical trials and to the epidemiology of chronic and infectious diseases. At present, a large number of statistical tools are used for medical decision-making in the main activities of diagnosis, treatment and prognosis in medical theses. These tools provide undeniable help in improving medical outcomes.
These include the measurement of uncertainty by probability, medical indicators and indices, reference ranges and scoring systems. In addition, there are tools such as the Odds Ratio, sensitivity, specificity and predictivities, the area under the ROC (Receiver Operating Characteristic Curve)), probability ratios and cost-benefit analysis, which are commonly applied in medical research but have implications for clinical activities of daily living. These tools have been so fully integrated into medical practice that statistical medicine can be considered by itself a medical specialty.
Examples of Research with the use of Medical Statistics
Some examples of research topics using medical statistics are:
Analysis of clinical trial data
Survival time modelling
Detection of factors associated with hypertension
Predictors of tobacco cessation
Identification of danger signs among newborns and mothers
Modelling pain sensitivity in healthy individuals
Exploration of the genetic basis and biological pathway of pain perception
Enable learning when evaluating new health technologies
Consideration of recall bias in the analysis of case-control studies
Case-only study designs in epidemiology
Estimation of reproduction number and other epidemiological parameters of infectious diseases
Evaluation and extension of the self-controlled case series method
Infectious disease inference from multivariate serological survey data
Methodological development of syndromic and laboratory statistical surveillance systems
Statistical methods for assessing the safety of vaccines and other medicines
Statistical methods for frailty models in survival analysis
Evaluation of quality of life measures
Diagnostic Test Statistics
Surgical site infection analysis
Statistical methods for unique case studies in neuropsychology
Statistical methods for surveillance of mass vaccination programmes
Whether in clinical practice or in a clinical research laboratory, doctors often make observations that lead to questions about a particular exposure and a specific disease. For example, it can be observed in clinical practice that several patients taking a certain antihypertensive treatment develop pulmonary symptoms within two weeks of taking the drug.
These types of questions can give rise to formal hypotheses that can then be tested with appropriate research study designs and analytical methods. Identifying the study question or hypothesis is a critical first step in planning a study or reviewing the medical literature.
Identification of the Objectives of the Study
It is important to understand in advance what the objectives of the study are. Below are some questions that can facilitate the process of identifying study objectives:
Is the goal to determine the efficacy of a drug or device under ideal conditions?
How well does a drug or device work in a free-living population (i.e., effectiveness)?
Causes or risk factors of a disease
The burden of a disease in the community
Is the aim of the study to provide information for a quality management activity?
Will the study explore the cost-effectiveness of a particular treatment or diagnostic tool? The hypotheses and objectives of a study are the keys to determining the study design and the most appropriate statistical tests.
Once the question(s) and objectives of the study have been identified, it is important to select the appropriate study design.
The main classification scheme of epidemiological studies distinguishes between descriptive and analytical studies. Descriptive epidemiology focuses on the distribution of diseases by populations, by geographical locations and by frequency over time. Analytical epidemiology deals with the determinants, or etiology, of the disease and tests the hypotheses generated by descriptive studies.
Correlational studies, also called ecological studies, use measures that represent the characteristics of entire populations to describe a given disease in relation to some variable of interest (e.g., medication use, age, healthcare utilization). A correlation coefficient (i.e., Pearson’s “r,” Spearman’s “T,” or Kendall’s “K”) quantifies the degree of linear relationship between the exposure of interest or “predictor” and the disease or “outcome” studied.
Case reports and case series are commonly published and describe the experience of a single patient or a series of patients with similar diagnoses. A key limitation of the design of case report and case series studies is the lack of a comparison group. However, these study designs are often useful for the recognition of new diseases and the formulation of hypotheses about possible risk factors.
Cross-sectional studies are also known as prevalence studies. In this type of study, exposure and disease status among people in a well-defined population are assessed at the same time. Cross-sectional studies are especially useful for estimating the population burden of the disease.
In observational studies, researchers record participants’ exposures (e.g., smoking, cholesterol level) and outcomes (e.g., suffering a myocardial infarction). Instead, an experimental study involves assigning one group of patients to one treatment and another group of patients to a different treatment or none. There are two fundamental types of observational studies: case-control and cohort studies. A case-control study is one in which participants are chosen based on whether or not they have (cases) (controls) the disease of interest.
Ideally, the cases should be representative of all the people who develop the disease and that the controls should be representative of all the people who do not suffer from it. Cases and controls are then compared as to whether or not they have the exposure of interest. The difference in the prevalence of exposure between the groups with and without disease can be verified. In these types of studies, the Odds Ratio is the appropriate statistical measure that reflects the differences in exposure between groups.
In prospective studies, the disease/outcome has not yet occurred. The study investigator should follow participants in the future to assess any differences in disease incidence/outcome between types of exposure. Disease incidence/outcome is compared between exposed and unexposed groups using relative risk (RR) calculation.
Experimental or interventional studies are often referred to as clinical trials. In these studies, participants are randomly assigned to an exposure (such as a drug, device, or procedure). “The main advantage of this feature (ed: randomized controlled trials) is that if treatments are randomly assigned to a sufficiently large sample, intervention studies have the potential to provide a degree of assurance about the validity of an outcome that is simply not possible with any observational design option.” Experimental studies are usually considered therapeutic or preventive.
Outcome studies assess the actual effect on the patient (e.g. morbidity, mortality, functional ability, satisfaction, return to work or school) over time, as a result of their encounter(s) with healthcare processes and systems. An example of this type of study would be one that evaluated the percentage of patients with a myocardial infarction (MI) who were given a beta-blocker medication and subsequently had another MI.
In the case of some diseases, there may be a significant time lapse between the process event and the outcome of interest. This often causes some patients to get lost during follow-up, which can lead to erroneous conclusions unless methods are used that “censor” or otherwise adjust missing and time-dependent covariates.
What are the appropriate statistical tests?
Once the appropriate design has been determined for a particular issue of the study, it is important to consider the appropriate statistical tests that need to be performed (or have been performed) with the data collected. This is relevant whether a scientific article is reviewed or a clinical study is planned. To begin with, we will examine the terms and calculations that are primarily used to describe measures of central tendency and dispersion. These measures are important for understanding key aspects of any dataset.
Measures of central tendency
There are three commonly known measures of central tendency: the mean, the median, and fashion. The arithmetic mean or mean is calculated by adding the values of the sample observations and dividing the sum by the number of observations in the sample. This measure is frequently reported for the continuous variables: age, blood pressure, pulse, body mass index (BMI), to name a few. The median is the value of central observation after ordering all observations from lowest to highest. It is very useful for ordinal or undistributed data normally.
Fashion is the most prevalent value among all dataset observations. There may be more than one fad. Fashion is more useful in nominal or categorical data. Typically no more than two (bimodal) are described for a given dataset.
Measures of dispersion or variability provide information about the relative position of other data points in the sample. These measures include the following: range, interquartile range, standard deviation, mean standard error (SEM), and coefficient of variation.
Evaluation of diagnostic tests
In order to understand the etiology of the disease and to provide adequate and effective health care to people suffering from a certain disease, it is essential to distinguish between people in the population who suffer from and those who do not suffer from the disease of interest. Typically, we rely on the screening and diagnostic tests available at medical centers to obtain information about the disease status of our patients.
However, it is important to assess the quality of these tests in order to make reasonable decisions about their interpretation and use in clinical decision-making. When assessing the quality of diagnostic and screening tests, it is important to take into account the validity (i.e. sensitivity and specificity) as well as the predictive value (i.e. positive and negative predictive values) of the test.
The odds ratio (OR) is a measure of effect size and is commonly used to compare the results of clinical trials. It is the probability that an event will occur in one group compared to the probability that it will occur in another group.
For example, one research study compared two groups of women who developed diabetes during their pregnancies. One group was treated with metformin and the other with insulin. The researchers recorded how many of the mothers gave birth ahead of schedule (less than 37 weeks after becoming pregnant). When they calculated the odds of preterm birth, the odds ratio (OR) of metformin was 1.06. This means that women taking metformin had a small (1.06-fold) increase in the odds of having a preterm birth compared to women taking insulin.
Receiver Operating Characteristics (ROC) curves were developed to assess radar quality. In medicine, ROC curves are a way to analyze the accuracy of diagnostic tests and to determine the best threshold or “cut-off” value to distinguish between positive and negative test results.
Diagnostic tests are almost always a compromise between sensitivity and specificity. ROC curves provide a graphical representation of this commitment. Setting a cut-off value too low can produce very high sensitivity (i.e. no disease would be lost) but at the cost of specificity (i.e. many false positive results). If a cut-off value is set too high, high specificity will be obtained at the expense of sensitivity.
Consider a study that measures the accuracy of B-type natriuretic peptide (BNP) as a test for impaired left ventricular function. They measured BNP levels in 155 elderly patients, who also underwent echocardiography (the gold standard for diagnosis). An ROC curve was created plotting the sensitivity versus specificity of 1 for different BNP cut values. The sensitivity and specificity of the BNP test were calculated and represented, assuming a level of 19.8 pmol/L as the cut-off point for a positive test.
On the other hand, the best cut-off point has the highest sensitivity and lowest specificity, so it sits as high as possible on the vertical axis and as far left on the horizontal axis. The area under an ROC curve is a measure of the usefulness or “discriminatory” value of a test in general. Also, the larger the area, the more useful the test will be. The maximum possible area under the curve is simply a perfect square and has an area of 1.0. The curve has an area of 0.85. Finally, the diagonal line of 45° represents a test that has no discriminative value, that is, it is completely useless.
Relative Risk (RR)
Relative risk is the relationship between the risks of an event for the exposure group and the risks for the non-exposure group. Therefore, relative risk provides an increase or decrease in the probability of an event based on a certain exposure. Relative risk has the advantage of being a risk ratio, which means that it can be applied to populations with different disease prevalences. Relative risk does not specify the absolute risk of the event occurring.
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