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Knowing medical statistics can help you find career work in medical service provider organizations that use data to grow quality improvement throughout the organization. When you take online courses on Coursera about medical statistics, you can learn key concepts about research models and statistical analysis along with how to apply and measure statistical hypothesis testing, binary data, variability regression, and confidence intervals.

You have the opportunity to discover how to read and understand mathematical formulas that will give you greater confidence to understand medical statistics as well as explore public health policy issues and assess how they impact the medical community at large. Learn a job-relevant skill that you can use today in under 2 hours through an interactive experience guided by a subject matter expert. Access everything you need right in your browser and complete your project confidently with step-by-step instructions.

Take courses from the world's best instructors and universities. Courses include recorded auto-graded and peer-reviewed assignments, video lectures, and community discussion forums. Enroll in a Specialization to master a specific career skill. Learn at your own pace from top companies and universities, apply your new skills to hands-on projects that showcase your expertise to potential employers, and earn a career credential to kickstart your new career. Benefit from a deeply engaging learning experience with real-world projects and live, expert instruction.

If you are accepted to the full Master's program, your MasterTrack coursework counts towards your degree. Transform your resume with a degree from a top university for a breakthrough price. Our modular degree learning experience gives you the ability to study online anytime and earn credit as you complete your course assignments. You'll receive the same credential as students who attend class on campus.

Coursera degrees cost much less than comparable on-campus programs. Showing total results for "medical statistics". Biostatistics in Public Health. Beginner Level Beginner. Understanding Clinical Research: Behind the Statistics. Mixed Level Mixed. Design and Interpretation of Clinical Trials.

Statistical Analysis with R for Public Health. Intermediate Level Intermediate. Introduction to Systematic Review and Meta-Analysis. AI in Healthcare. Because the physician may believe that although initial costs are greater, the follow-up costs are less, he or she may question if there would be a difference by specialist versus non-specialist if all costs were assessed. Questions like these can lead to formal hypotheses that can then be tested with appropriate research study designs and analytic methods.

Identifying the study question or hypothesis is a critical first step in planning a study or reviewing the medical literature. It is also important to understand up front what the related study goals are. Some questions that may facilitate the process of identifying the study goals follow:. Will the study explore cost-effectiveness of a particular treatment or diagnostic tool? The hypotheses and the goals of a study are the keys to determining the study design and statistical tests that are most appropriate to use.

Once the study question s and goals have been identified, it is important to select the appropriate study design. Although the key classification scheme utilizes descriptive and analytic terminology, other terminology is also in vogue in evaluating health services and will be briefly described at the end of this section. The primary classification scheme of epidemiological studies distinguishes between descriptive and analytic studies. Descriptive epidemiology focuses on the distribution of disease by populations, by geographic locations, and by frequency over time.

Analytic epidemiology is concerned with the determinants, or etiology, of disease and tests the hypotheses generated from descriptive studies. Table 1 lists the study design strategies for descriptive and analytic studies. Below is a brief description of the various design strategies. The strengths and limitations of these study designs are compared in Table 2. Correlational studies, also called ecologic studies, employ measures that represent characteristics of entire populations to describe a given disease in relation to some variable of interest e.

A correlation coefficient i. The value of the coefficient ranges between positive 1 and negative 1. Positive 1 reflects a perfect correlation where as the predictor increases, the outcome or risk of outcome increases. Negative 1 reflects a perfect inverse correlation where as the predictor increases the outcome or risk of outcome decreases. An example of a correlation study would be that of St Leger and colleagues who studied the relationship between mean wine consumption and ischemic heart disease mortality 7.

Across 18 developed countries, a strong inverse relationship was present. Specifically, countries with higher wine consumption had lower rates of ischemic heart disease and countries with lower wine consumption had higher rates of ischemic heart disease. Although correlation studies provide an indication of a relationship between an exposure and an outcome, this study design does not tell us whether people who consume high quantities of wine are protected from heart disease.

Thus, inferences from correlation studies are limited. Case reports and case series are commonly published and describe the experience of a unique patient or series of patients with similar diagnoses. A key limitation of the case report and case series study design is the lack of a comparison group. Nonetheless, these study designs are often useful in the recognition of new diseases and formulation of hypotheses concerning possible risk factors.

In a case series study reported by Kwon and colleagues 8 , 47 patients were examined who developed new or worsening heart failure during treatment with tumor necrosis factor TNF antagonist therapy for inflammatory bowel disease or rheumatoid arthritis.

From this descriptive study, the authors concluded that TNF antagonist might induce new-onset heart failure or exacerbate existing disease 8. Cross-sectional surveys are also known as prevalence surveys. In this type of study, both exposure and disease status are assessed at the same time among persons in a well-defined population.

These types of studies have become more common recently with the development and validation of survey tools such as the Short Form 36 SF 36 functional status questionnaire and the Kansas City Cardiomyopathy Questionnaire KCCQ functional status survey. Cross-sectional studies are especially useful for estimating the population burden of disease. The prevalence of many chronic diseases in the United States is calculated using the National Health and Nutrition Examination Survey, an interview and physical examination study including thousands of non-institutionalized citizens of the United States.

For example, Ford and colleagues estimated that 47 million Americans have the metabolic syndrome using the Third National Health and Nutrition Examination Survey 9. Of note, in special circumstances where one can easily deduce an exposure variable preceding the outcome or disease, cross sectional surveys can be used to test epidemiologic hypotheses and thus can be used as an analytic study.

For example, Bazzano and colleagues used data collected from a cross-sectional study to conclude that cigarette smoking may raise levels of serum C-reactive protein A cross-sectional study is useful in this situation because it is unlikely that having high levels of C-reactive protein would cause one to smoke cigarettes. Analytic studies can be observational or experimental. In observational studies, the researchers record participants' exposures e.

In contrast, an experimental study involves assigning one group of patients to one treatment and another group of patients to a different or no treatment. There are two fundamental types of observational studies: case control and cohort. A case control study is one in which participants are chosen based on whether they do cases or do not controls have the disease of interest. Ideally, cases should be representative of all persons developing the disease and controls representative of all persons without the disease.

The cases and controls are then compared as to whether or not they have the exposure of interest. In these types of studies, the odds ratio is the appropriate statistical measure that reflects the differences in exposure between the groups. The defining characteristic of a cohort study, also known as a follow-up study, is the observation of a group of participants over a period of time during which outcomes e.

Participants must be free from the disease of interest at the initiation of the study. Subsequently, eligible participants are followed over a period of time to assess the occurrence of the disease or outcome. Retrospective cohort studies refer to those in which all pertinent events both exposure and disease have already occurred at the time the study has begun. The study investigators rely on previously collected data on exposure and disease. They analyzed the data to see if blood pressure at each patient's first hypertension clinic encounter was associated with a subsequent deterioration in renal function.

The advantages of retrospective cohort studies, relative to prospective, include reduced cost and time expenditures as all outcomes have already occurred. There are two additional sub-classifications for cohort studies. First, cohort studies may include a random sample of the general population, e.

In these latter studies, a sample of all individuals or individuals with a specific demographic, geographic, or clinical characteristic is included. Second, cohort studies may begin by identifying a group of persons with an exposure and a comparison group without the exposure. This type of cohort study is usually performed in the situation of a rare exposure. Experimental or intervention studies are commonly referred to as clinical trials. In these studies, participants are randomly assigned to an exposure such as a drug, device, or procedure.

Experimental studies are generally considered either therapeutic or preventive. Therapeutic trials target patients with a particular disease to determine the ability of a treatment to reduce symptoms, prevent recurrence or decrease risk of death from the disorder. Prevention trials involve the assessment of particular therapies on reducing the development of disease in participants without the disease at the time of enrollment.

Some other classification schemes in use today are based on the use of epidemiology to evaluate health services. Epidemiological and statistical principles and methodologies are used to assess health care outcomes and services and provide the foundation for evidence-based medicine.

There are different ways to classify studies that evaluate health care services. One such scheme distinguishes between process and outcomes studies. Process studies assess whether what is done in the medical care encounters constitutes quality care e. An example of a process study would be one that evaluated the percentage of patients with chronic heart failure in a given population who have filled prescriptions for angiotensin converting enzyme inhibitors ACE — Inhibitors.

A criticism of process studies is that although they document whether or not appropriate processes were done, they don't indicate if the patient actually benefited or had a positive outcome as a result of the medical processes. Outcomes studies assess the actual effect on the patient e. An example of this type of study would be one that assessed the percentage of patients with a myocardial infarction MI who were placed on a beta blocker medication and subsequently had another MI.

For some diseases, there may be a significant time lag between the process event and the outcome of interest. In reviewing the medical literature, one often encounters other terms that deal with the evaluation of medical services: efficacy, effectiveness, or efficiency. Efficacy is determined with randomized controlled clinical trials where the eligible study participants are randomly assigned to a treatment or non-treatment, or treatment 1 versus treatment 2, group.

Effectiveness assesses how well a test, medication, program or procedure works under usual circumstances. In other words, effectiveness determines to what extent a specific healthcare intervention does what it is intended to do when applied to the general population.

For example, although certain anti-retroviral therapies work well using direct observed therapy in the controlled setting of a clinical trial i. Finally, efficiency evaluates the costs and benefits of a medical intervention. Once the appropriate design is determined for a particular study question, it is important to consider the appropriate statistical tests that must be or have been performed on the data collected.

This is relevant whether one is reviewing a scientific article or planning a clinical study. To begin, we will look at terms and calculations that are used primarily to describe measures of central tendency and dispersion. These measures are important in understanding key aspects of any given dataset. There are three commonly referred to measures of central location: mean, median, and mode.

The arithmetic mean or average is calculated by summing the values of the observations in the sample and then dividing the sum by the number of observations in the sample. This measure is frequently reported for continuous variables: age, blood pressure, pulse, body mass index BMI , to name a few. The median is the value of the central observation after all of the observations have been ordered from least to greatest.

It is most useful for ordinal or non-normally distributed data. For data sets with an odd number of observations, we would determine the central observation with the following formula:. For datasets with an even number of observations, we would select the case that was the average of the following observations' values:.

The mode is the most commonly occurring value among all the observations in the dataset. There can be more than one mode. The mode is most useful in nominal or categorical data. Typically no more than two bimodal are described for any given dataset.

Example 1: A patient records his systolic blood pressure every day for one week. In calculating the median, the values must be ordered from least to greatest: 98, , , , , , There are 7 observations in this dataset, an odd number. Therefore, the formula is used to determine that the fourth observation will be the median. The value of the fourth observation is mmHg.

Therefore, the median is mmHg. In the example, the mode is also mmHg. This is the only value that occurs more than once; hence it is the most commonly occurring value. Investigators and practitioners are often confused which measure of centrality is most relevant to a given dataset.

Table 3 outlines key advantages and disadvantages to the choice of measure of central location. It is interesting to note that if the dataset consists of continuous variables with unimodal and symmetric distribution, then the mean, median, and mode are the same. Measures of dispersion or variability provide information regarding the relative position of other data points in the sample. Such measures include the following: range, inter-quartile range, standard deviation, standard error of the mean SEM , and the coefficient of variation.

Range is a simple descriptive measure of variability. It is calculated by subtracting the lowest observed value from the highest. Using the blood pressure data in example 1, the range of blood pressure would be mmHg minus 98 mmHg or 62 mmHg. Often given with the median i. The most commonly used measures of dispersion include variance and its related function, standard deviation, both of which provide a summary of variability around the mean. Variance is calculated as the sum of the squared deviations divided by the total number of observations minus one:.

The standard deviation is the square root of the variance. Table 4 presents calculations of variance and standard deviation for the systolic blood pressures given in example 1. The coefficient of variation CV is a measure that expresses the SD as a proportion of the mean:. This measure is useful if the clinician wants to compare 2 distributions that have means of very different magnitudes.

From the data provided in example 1, the coefficient of variation would be calculated as follows:. The standard error of the mean SEM measures the dispersion of the mean of a sample as an estimate of the true value of the population mean from which the sample was drawn. It is related to, but different from, the standard deviation. The formula is as follows:. SEM can be used to describe an interval within which the true sample population mean lies, with a given level of certainty. Which measure of dispersion to use is dependent on the study purpose.

Table 3 provides some information which may facilitate the selection of the appropriate measure or measures. Once central tendency and dispersion are measured, it follows that a comparison between various groups e. If working with continuous variables that are normally distributed, the comparison is between means. The first step is to simply look at the means and see which is larger or smaller and how much difference lies between the two.

This step is the basis of deductive inference. In comparing the means, and, preferably before calculating any p-values, the clinician or investigator must answer the question: is the observed difference clinically important? If the magnitude of the observed difference is not clinically important, then the statistical significance becomes irrelevant in most cases.

If the observed difference is clinically important, even without statistical significance, the finding may be important and should be pursued perhaps with a larger and better powered study; Table 5. Once a deductive inference is made on the magnitude of the observed differences, statistical inference follows to validate or invalidate the conclusion from the deductive inference.

To illustrate: if two people each threw one dart at a dartboard, would one conclude that whoever landed closer to the center was the more skilled dart thrower? Such a conclusion would not be reasonable even after one game or one match as the result may be due to chance. Concluding who is a better player would have to be based on many games, against many players, and over a period of time. There are many reasons for inconsistencies good day, bad day, etc. Because in clinical research we rely on a sample of the patient population, variance is a key consideration in the evaluation of observed differences.

The observed difference between exposed and unexposed groups can be large, but one must consider how it stands next to the variation in the data. Since these parameters are highly quantifiable, the probability that the means are different or similar can be calculated. The details of this process are beyond the scope of this chapter; nevertheless, ANOVA is a fundamental statistical methodology and is found in many texts and is performed by many statistical software packages.

In essence, the ANOVA answers the question: are differences between the study groups' mean values substantial relative to the overall variance all groups together? Therefore, further analysis with multiple comparison tests must be performed to determine which means are significantly different.

Portney and Watkins 19 provide a good overview of these procedures. In the special case where one and only one comparison can be made, the t-test can be done. It was developed to be a shortcut comparison of only two means between groups with small sample sizes less than Armed with a basic understanding of algebra and user-friendly statistical software, most clinicians and clinical researchers can follow the cookbook method of statistical inference.

Problems quickly arise because the vast majority of medical research is not designed as simply as the examples given in basic statistics textbooks nor analyzed as simply as the shortcut methods often programmed beneath the layers of menus in easy-to-use software. Violations of assumptions that are necessary for a classic statistical method to be valid are more the rule than the exception. However, avoiding the misinterpretation of statistical conclusions does not require advanced mastery of the mathematics of probability at the level of calculus.

An effort to understand, at least qualitatively, how to measure the degree of belief that an event will occur will go a long way in allowing non-mathematicians to make confident conclusions with valid methods. Two practical concepts should be understood up front: first, understanding that every probability, or rate, has a quantifiable uncertainty that is usually expressed as a range or confidence interval. Second, that comparing different rates observed between two populations, or groups, must be done relative to the error terms.

This is the essence of statistical inference. The final rate of an event that is measured, as the size of the sample being measured grows to include the entire population, is the probability that any individual in the population will experience the event.

For example, one analyzes a database of heart transplant patients who received hearts from donors over the age of 35 to determine the rate of cardiac death within a 5-year post-transplant follow-up period No one would accept an estimate from a sample of one. However, as the sample size increases, the event rate will migrate towards truth. When written as a probability, one can say that the probability is 0.

It may be more relevant to use the data to predict that the next patient seen in clinic and added to the database will have a probability of 0. The illustration just described is that of a binomial probability. That is, the outcome is one of two possible levels binary : survival or death. To complete the estimate of a probability of an event in this population, a measure of uncertainty must be placed around this point estimate. In this case, the standard error SE, not to be confused with the SEM described earlier is calculated with the classic formula.

This formula indicates that the square root of the function of the probability of event p , times the probability of no event 1-p , divided by the sample size n is the standard error SE of the event rate. These yield the range. Thus, if this observation were repeated times in similar populations of the same sample size, 95 of the sampled death rates would fall between. In order to understand disease etiology and to provide appropriate and effective health care for persons with a given disease, it is essential to distinguish between persons in the population who do and do not have the disease of interest.

Typically, we rely on screening and diagnostic tests that are available in medical facilities to provide us information regarding the disease status of our patients. However, it is important to assess the quality of these tests in order to make reasonable decisions regarding their interpretation and use in clinical decision-making 1. In evaluating the quality of diagnostic and screening tests, it is important to consider the validity i. These are conditional probabilities.