Epidemiology and measures of disease

Point prevalence is existing cases divided by the population at a specified moment. Period prevalence includes anyone who had the condition during a stated interval. Prevalence rises when incidence rises, survival lengthens or case ascertainment improves, and falls when recovery, death or out-migration removes cases. It is valuable for workload planning: the number needing asthma review today depends on prevalence, not only this year’s new diagnoses.

Cumulative incidence, or risk, is new cases during a period divided by the disease-free population at the start, assuming sufficient follow-up. Example: among 800 initially unaffected people, 32 develop disease over one year; one-year risk is 32/800 = 0.04 or 4%. Incidence rate uses person-time. If observation totals 620 person-years and 31 new events occur, the rate is 31/620 = 0.05 per person-year, often reported as 5 per 100 person-years.

An attack rate is a cumulative incidence used in outbreaks. If 45 of 180 wedding guests develop gastroenteritis, the attack rate is 25%. Food-specific attack rates compare those who ate and did not eat an item. Secondary attack rate measures spread among susceptible contacts of primary cases. Define who counts as exposed, susceptible and a case, and align the observation window with the plausible incubation period.

Mortality rate measures deaths in a population over time. Case fatality proportion measures the proportion of identified cases who die from the condition over a specified period and reflects disease severity, case definition and ascertainment. Survival is conditional on diagnosis and follow-up. Apparent improvement in survival can occur through lead-time bias when screening advances diagnosis without changing time of death, or length bias when slower disease is more likely to be detected.

Measures of association compare groups. In a cohort, if 24 of 300 exposed people and 9 of 300 unexposed people develop disease, risks are 8% and 3%; risk ratio is 0.08/0.03 = 2.67, risk difference is 5 percentage points, and attributable fraction among exposed is (2.67−1)/2.67 = 62.5%. Relative measures describe strength; absolute measures show population and clinical impact.

Odds are probability divided by one minus probability. A case-control study begins with outcome status, so disease risks cannot usually be calculated directly from sampled cases and controls; use the exposure odds ratio. For a two-by-two table, odds ratio equals ad/bc. When disease is rare, odds and risk are close. With common outcomes, describing an odds ratio as a risk ratio exaggerates the apparent effect.

Intervention effects require a time horizon and baseline risk. Suppose an event occurs in 18 of 300 controls and 9 of 300 treated participants. Control risk is 6%, treatment risk 3%, relative risk 0.5, relative risk reduction 50%, and absolute risk reduction 3 percentage points. NNT is 1/0.03 = 33.3, conventionally rounded up to 34 for that follow-up period. State the population and duration because NNT changes with baseline risk.

For harm, absolute risk increase is intervention risk minus control risk and number needed to harm is its reciprocal. Benefits and harms may have different denominators, severities and times. A composite outcome can be driven by a less important frequent component. Intention-to-treat analysis preserves randomisation and estimates effect of assignment, while per-protocol analysis answers a different question and can introduce selection bias.

A diagnostic two-by-two table compares the index test with an appropriate reference classification. Sensitivity = TP/(TP+FN); specificity = TN/(TN+FP). Positive predictive value = TP/(TP+FP); negative predictive value = TN/(TN+FN). Sensitivity and specificity can vary with spectrum and thresholds; predictive values vary with prevalence. Verify that participants received the same reference process independent of index result to avoid verification bias.

Worked numbers show prevalence effect. A test has 90% sensitivity and 90% specificity. In 1,000 people with 10% prevalence, expect 90 true positives, 10 false negatives, 90 false positives and 810 true negatives; PPV is 90/180 = 50%. At 1% prevalence, expect about 9 true positives and 99 false positives among 1,000; PPV falls to roughly 8.3%. The test characteristics did not change, but the meaning of a positive result did.

Likelihood ratios update odds. LR+ = sensitivity/(1−specificity), and LR− = (1−sensitivity)/specificity. With sensitivity 0.90 and specificity 0.90, LR+ is 9 and LR− is 0.11. Convert pre-test probability to odds, multiply by the likelihood ratio, then convert odds back to probability. Nomograms or validated tools reduce arithmetic error, but a precise output remains wrong if the pre-test estimate or study population is unsuitable.

Bias is systematic deviation. Selection bias occurs when inclusion or follow-up differs with exposure and outcome. Information bias arises from measurement or classification; non-differential misclassification often dilutes association but not invariably. Recall bias particularly threatens retrospective self-report. Confounding is a mixing of effects by a factor associated with exposure and independently with outcome, outside the causal pathway. Restriction, randomisation, matching, stratification and multivariable adjustment address different parts of the problem.

Chance and precision matter. A confidence interval describes values compatible with data under model assumptions, not the probability that a fixed true value lies within this realised interval. A p value is the probability of results at least as extreme under a specified null model, not the probability that the null hypothesis is true. Statistical significance does not establish clinical importance, validity or causality. Inspect effect size, interval, missing data, multiplicity and design.