Medical Statistics

  Statistical inference is used to evaluate sampling uncertainty in medical research. The two most commonly used uncertainty measures are confidence intervals and p-values. However, it is often useful to distinguish between the uncertainty resulting from random variation (aleatoric uncertainty) and the uncertainty caused by incomplete knowledge (epistemic uncertainty). A small p-value indicates disagreement between observed data and a tested null hypothesis, but it is not in itself a direct measure of either aleatoric or epistemic uncertainty. P-values do not, by themselves, separate random variability from the uncertainty about whether the statistical model and its assumptions are appropriate. A confidence interval quantifies sampling uncertainty about an estimate under the assumed statistical model and study design. Its width is influenced by outcome variability and sample size, but it does not generally capture uncertainty from model misspecification, unmeasured confounding, or ...

While the risk (or incidence) in absolute numbers is an important measure from an individual and a public health perspective and for planning health care resources, the biological effect of a beneficial or harmful exposure is always measured and medically interpreted in terms of relative risk. With some prospective study designs, the relative risk (RR) can be measured directly from risks or indirectly from incidence density rates. Other statistical methods produce other effect measures, such as the hazard ratio (HR) or odds ratio (OR), that sometimes can be used to approximate the RR. For example, RR can be estimated from cohort data or a randomised trial using a log-binomial regression model as well as other models (1), HR using a proportional hazards regression model, and OR using a logistic regression model. However, it is a mistake to always interpret odds ratios and hazard ratios as relative risks. When common outcomes are studied, the odds ratio provides an inflated estimate of t...

  The term 'incidence' may seem straightforward, but it can refer to three distinct metrics: the total number of new cases, cumulative incidence (risk), and incidence density. The calculations of these metrics can vary in difficulty (1). As demonstrated by Havers-Borgersen et al. (2) mistakes are often published, and numerous errors probably remain undetected as a result of unclear methodological descriptions. 1. Incident numbers In the most basic form, incidence begins with the number of new cases that occur in a population over a specified period. It does not convey any information regarding risk on its own: 500 new cases in a village of 5000 is clearly not the same as in a city of 5 million. To be useful, the number of new cases of a disease needs to be compared to the number of people who are at risk. 2. Cumulative Incidence (risk) The cumulative incidence is a classic risk measure, the number of new cases divided by the number of people free of disease at the start of the ...

  Medical science is one of the youngest sciences, at least as we define science today. From 1665, when the first scientific journals were established, to the mid-20th century, when modern medical research emerged, medical research publications were primarily descriptive (case reports) or presenting subjective comments (expert opinions). It lasted until the mid-20th century, until medical research focused on empirical evidence collected from samples of patients and evaluating the uncertainty of the findings objectively, using statistical science. First, during the second half of the 19th century, some remarkable events happened. In Vienna, Ignaz Semmelweis showed that the incidence of childbed fever could be drastically reduced by requiring healthcare workers to disinfect their hands. With this procedure, the maternal mortality rate dropped from 18% to less than 2%. The finding was published in 1861 in the book, "Etiology, Concept and Prophylaxis of Childbed Fever". However, ...

  Unfortunately, the findings of confirmatory trials are often misinterpreted. There is no guarantee that a hypothesis is true just because it passes a statistically significant test. The significance level, typically 5%, represents nothing more than the likelihood of a false positive result. Hence, systematic reviews and meta-analyses, which lessen the uncertainty by integrating the findings from multiple trials of the same endpoint, play a significant role in the pursuit of truth. Conversely, confirmatory trials that fail to confirm the tested hypothesis because of statistical nonsignificance are frequently presented to the reader as negative trials. See, for example, Que et al. (1) "this was a negative trial as it failed to reach its primary endpoint." However, a negative trial offers evidence that the intervention does not have any significant impact on the outcome under investigation, and statistical nonsignificance is not such evidence. There are several other reasons w...

  Medical research is primarily performed using samples of humans, laboratory animals, or cells, but the studied phenomena are rarely limited to what can be observed in samples of these. On the contrary, the aim is almost always to learn about the population from which the sample was drawn. However, this leads to generalisation problems. Sampling variability makes the results from sample studies uncertain, and the consequences of non-random sampling may induce an uncertain amount of bias. The uncertainty can, under certain conditions, be quantified, and a sound study design may reduce it. Quantification and reduction of uncertainty are thus essential components of successful scientific research. Statistical inference is a crucial port of modern empirical science. A fundamental principle in statistical inference is that a hypothesis cannot be generated and confirmed using the same sample. Doing so induces selection bias in the confirmation testing and invalidates standard p-values a...

  Misuse of statistical terminology is very common in medical research reports. The misuse not only indicate methodological ignorance, it also threatens the consistency of the statistical terminology. For example, Nahoui et al. (1) state that in their sample of patients, those "in 3rd and 4th quartiles of median PES [esophageal pressure] had increased mortality risk compared to 1st quartile". Given that only three quartiles exist, this statement is remarkable. A quartile is defined (2) like this: "There are three values which separate the total frequency of a distribution into four equal parts. The central value is called the median and the other two the lower (first) and upper (third) quartiles respectively." The authors obviously confuse quartiles with the four quarts of the distribution defined by the three quartiles. Similar misunderstandings of other quantiles, such as tertiles and quintiles, are as frequent. Furthermore, the misunderstanding of the term quarti...

  Using the correct terminology helps to ensure that the same words are used for the same concepts, which is crucial for a clear communication and for avoiding misunderstandings. The term 'nonparametric data' appears often in the statistics section of research reports. For example, Dugan et al. (1) state that the "data from patients in the two groups were compared using Mann-Whitney U tests for nonparametric data." However, statistical tests are used to evaluate sampling uncertainty, to test a hypothesis about the properties of an unobservable population represented by a sample, in this case of patients. The hypothesis may or may not be based on an assumption about a specific data distribution (e.g. Normal) for a test of its parameters. If this is the case, the hypothesis is parametric. Such hypotheses are tested using asymptotic methods. Otherwise, the hypothesis is nonparametric, which requires a distribution-free method. The term "Nonparametric data" is a...

  The terms univariate, multivariate, univariable, and multivariable often appear in scientific medical publications. For example, Kanbaş et al., claim that they have evaluated factors prognostic for cervical cancer using multivariate Cox regression. However, Cox regression is a semi-parametric technique that they use to evaluate how a single response variable (survival time) is associated to one or more explanatory (potentially prognostic) variables. That is not a multivariate analysis. Univariate and multivariate refer to the probability distribution upon which a statistical model is based. If a model only has one response variable, a univariate probability distribution works. But if the model has more than one response variable, a multivariate probability distribution is needed. In contrast, the model's univariable or multivariable nature is determined by the number of explanatory variables. As an example, a model for evaluating the relationship between systolic blood pressure a...