Medical Statistics

Statistical inference focuses on quantifying uncertainty. It is primarily used to generalise information from samples by estimating unobservable parameters and testing hypotheses about the properties of a population that cannot be observed in its entirety. Data science, which many statisticians consider to be part of statistical science (machine learning), is mainly about exploring patterns in data and developing predictions. For example, to answer the question, "How well will this treatment work for the next patient?" a machine learning approach may be useful, and the answer should include the risk of an erroneous classification. If the question is instead, "What is the average effect of this treatment?" statistical inference is necessary, and the answer should include an assessment of the uncertainty of the presented treatment effect estimate. The two approaches often use the same statistical methods, such as logistic regression analysis, but the methods are typic...

As treatment is not assigned randomly in observational studies, patients receiving a particular exposure (or treatment) may differ systematically from patients receiving other exposures or no exposure at all. Consequentially, when investigating the effects of an exposure, the effect of the systematic differences (confounders) needs to be taken into account, preferably be adjusted away in the statistical analysis. Traditionally, this has been made by stratifying on the confounders or including them in a regression model. More recently, adjustment using propensity scores has become increasingly popular (1). A propensity score is a subject’s estimated probability of receiving a particular exposure or treatment, given their observed baseline characteristics. The propensity score thus condenses several measured baseline covariates into a single score. The purpose of this score is to balance the groups receiving different exposures or treatments. Given the score, the covariates included in t...

  Confounding is a distortion of the estimated effect of an exposure on an outcome. The distortion is caused by a confounder that impacts both exposure and outcome. Exposure <- Confounder -> Outcome An observed exposure effect may then reflect the effect of the confounder rather than exposure. For example, when studying the effect of alcohol consumption on cardiovascular disease risk, prior health status, is a confounder if it affects both alcohol consumption and the risk of a cardiovascular event. Confounding can be dealt with in two ways. The first is to perform an experiment with randomised assignment of subjects to exposure and a control group. The advantage with this strategy is that it prevents against confounding from all confounders, known as well as unknown. However, the disadvantage is that it cannot be used to investigate effects of harmful exposures as that would be unethical and in many cases practically impossible. Other disadvantages are that trials are expensi...

  To produce valid results, both observational studies and randomised trials depend on correct classifications of exposure (or treatment) and follow-up. Immortal time bias is a time-related misclassification that can seriously bias the outcome of an investigation. The phenomenon occurs when either the exposed group is assigned a follow-up period that could not have included the events under study (like time on a treatment waiting list). Or when exposed subjects with early events are excluded from the evaluation, ensuring corresponding survival among the remaining. For example, it was reported (1) from a randomised trial of the effect of a radiation sensitiser on the survival of inoperable lung cancer patients, that the subgroup of patients (36%) who completed the course of radiation therapy augmented by the sensitiser survived a median of 22 months, twice as long as the patients in the control group. However, the median survival for the entire treatment group was only 13 ...

  One of the terms most frequently misused in medical publications is ‘correlation’. It is often used to describe any kind of relationship or interaction between variables. However, the term is very specific and using it arbitrarily may be misleading. Apart from non-parametric alternatives and minor variants, two major types of correlation coefficients have been developed: Pearson's correlation coefficient and the intraclass correlation coefficient. The first one measures the linear association between two variables, the second one the resemblance of measurements made within the same unit (repeated measurements) or cluster. Pearson's correlation coefficient Pearson's correlation coefficient ( ρ ) for the two variables X and Y is the covariance of the two variables divided by the product of their standard deviations: ρ  = cov(X,Y)/(σ X σ Y ) Pearson's correlation coefficient ranges from −1 to 1. The value 1 implies that a linear equation describes the relationship bet...

One common misunderstanding demonstrated in medical publications is the testing of normal distribution as part of a decision process: If Shapiro-Wilk Test or Kolmogorov-Smirnov Test indicates that a variable has a statistically significant departure from normal distribution, group mean differences are tested using the Mann-Whitney Test instead of Student's t-test. This decision rule may sound rock solid, but it may be a serious mistake. First, the practice treats absence of evidence as evidence of absence. A statistically nonsignificant normality test is simply not evidence of a normal distribution. Second, for a two-sample t-test or a linear statistical model, the relevant distributional issue concerns the difference or model residual conditional on covariates, not whether each observed treatment group's raw outcome values are exactly normal. Third, with small sample sizes, where the normality assumption may be important, the normality test has low power to detect non-normalit...

  In early clinical trials patients were allocated to treatment and control groups by alternation, i.e. patients were assigned to the treatment group and control group in a strict order. The advantage with this method was that it produced groups with equal size. The two groups would also be fairly compared if the order of the patients included in the trial was random. However, the group allocation for a patient was predictable, which could potentially introduce selection bias into the trial's outcome through differential invitations to participate. The only way to avoid this issue was, of course, to make the group assignment concealed, which necessitated a non-systematic group assignment sequence. D'Arcy Hart (1) describes the development with two trials from the 1940s. The first one investigating the effects of patulin (a mycotoxin) on the common cold in 1943-1944 with strict alternation. The second one, having a randomised group assignment, investigating the effects of strept...