Epidemiology, calculations, bias and surveillance

Epidemiological Metrics, Clinical Study Designs & Notifiable Communicable Diseases

Evidence-based clinical decision-making requires medical practitioners to critically evaluate diagnostic test accuracy, interpret biostatistical parameters, synthesize research study designs, and fulfill statutory obligations in communicable disease surveillance. Mastery of these public health concepts is essential for hospital practice and primary care across Australia.

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Diagnostic Test Accuracy & The 2x2 Contingency Matrix

The diagnostic utility of any clinical sign, bedside investigation, or laboratory test is evaluated using a standard $2 \times 2$ contingency table comparing test results against a gold-standard diagnostic reference.

Intrinsic Test Parameters: Sensitivity & Specificity

• Sensitivity: The probability that a diseased person tests positive:

$$\text{Sensitivity} = \frac{TP}{TP + FN}$$

• Clinical Rule: SnNOut (A test with very high Sn-sitivity, when N-egative, rules Out the disease). Highly sensitive tests produce very few false negatives and are ideal for screening (e.g., D-dimer in low-risk deep vein thrombosis, HIV antibody/antigen testing).
• Specificity: The probability that a non-diseased person tests negative:

$$\text{Specificity} = \frac{TN}{TN + FP}$$

• Clinical Rule: SpPIn (A test with very high Sp-ecificity, when P-ositive, rules In the disease). Highly specific tests produce very few false positives and are ideal for confirmation (e.g., Western blot, biopsy histopathology, target-specific PCR).
• Test characteristics: Sensitivity and specificity are conditional on disease status rather than calculated directly from prevalence. They can nevertheless vary across populations because of disease spectrum, threshold, sampling and verification. Predictive-value comparisons assume the operating characteristics are held constant.

Extrinsic Test Parameters: Predictive Values & Prevalence

Unlike sensitivity and specificity, predictive values depend heavily on the prevalence of the disease in the population being tested:

• Positive Predictive Value (PPV): The probability that a patient with a positive test result truly has the disease:

$$\text{PPV} = \frac{TP}{TP + FP}$$

• Negative Predictive Value (NPV): The probability that a patient with a negative test result is truly disease-free:

$$\text{NPV} = \frac{TN}{TN + FN}$$

Likelihood Ratios & Fagan's Nomogram

Likelihood ratios (LRs) quantify the degree to which a given diagnostic test result shifts the pre-test odds into post-test odds. Unlike predictive values, likelihood ratios are independent of disease prevalence:

• Positive Likelihood Ratio ($\text{LR}^+$): How much the odds of disease increase when a test is positive:

$$\text{LR}^+ = \frac{\text{Sensitivity}}{1 - \text{Specificity}} = \frac{\text{True Positive Rate}}{\text{False Positive Rate}}$$

• Likelihood-ratio interpretation: A large LR shifts odds substantially, but the resulting probability still depends on the pre-test odds. A positive LR above 10 does not make a rare diagnosis certain, and a negative LR below 0.1 does not erase a very high prior probability.
  • An $\text{LR}^+$ between 5 and 10 generates moderate diagnostic shifts.
  • An $\text{LR}^+$ between 2 and 5 generates small, borderline shifts.
• Negative Likelihood Ratio ($\text{LR}^-$): How much the odds of disease decrease when a test is negative:

$$\text{LR}^- = \frac{1 - \text{Sensitivity}}{\text{Specificity}} = \frac{\text{False Negative Rate}}{\text{True Negative Rate}}$$

• An $\text{LR}^-$ between 0.1 and 0.2 generates moderate diagnostic reductions.
• Clinical Application: $\text{Post-test Odds} = \text{Pre-test Odds} \times \text{LR}$. Clinicians can map pre-test probability to post-test probability at the bedside using a Fagan nomogram.

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Clinical Study Designs & Measures of Association

Evidence-based practice stratifies clinical research along an established hierarchy of methodological rigor.

1. Randomized Controlled Trials (RCTs)

• Randomisation: Balances confounders in expectation, not necessarily exactly in a finite trial. Allocation concealment prevents foreknowledge influencing recruitment; blinding addresses other biases. Describe who was blinded rather than relying on an ambiguous “double-blind” label.
• Blinding: Single-blind (participants unaware), double-blind (participants and investigators/clinicians unaware), or triple-blind (participants, clinicians, and data analysts unaware). Prevents performance bias and detection bias.
• Intention to treat: Analyse according to randomised assignment where possible, but report missing outcomes and sensitivity analyses. ITT alone does not eliminate bias from differential loss to follow-up; per-protocol analyses answer a different question and can be confounded.

2. Cohort Studies (Prospective or Retrospective)

• Design: Participants are classified according to their exposure status (exposed vs unexposed) and followed forward in time to observe the incidence of the outcome/disease.
• Strengths: Best design to establish temporality, calculate true disease incidence, and evaluate rare exposures or multiple outcomes from a single exposure.
• Measure of Association: Relative Risk (Risk Ratio, RR):

$$\text{RR} = \frac{\text{Incidence in exposed}}{\text{Incidence in unexposed}} = \frac{a / (a+b)}{c / (c+d)}$$

• $\text{RR} = 1$: No association between exposure and outcome.
  • $\text{RR} > 1$: Exposure increases disease risk.
  • $\text{RR} < 1$: Exposure is protective against the disease.

3. Case-Control Studies

• Design: Retrospective study where participants are selected based on outcome status (cases have the disease, controls do not); investigators examine past records to determine prior exposure.
• Strengths: Highly efficient and economical for rare diseases (e.g., rare malignancies) or diseases with very long latency periods (e.g., mesothelioma from asbestos exposure).
• Limitation: Cannot calculate true disease incidence because the ratio of cases to controls is determined arbitrarily by the investigator. Therefore, Relative Risk cannot be directly calculated.
• Measure of Association: Odds Ratio (OR):

$$\text{OR} = \frac{\text{Odds of exposure in cases}}{\text{Odds of exposure in controls}} = \frac{a / c}{b / d} = \frac{a \times d}{b \times c}$$

• The Rare Disease Assumption: When the prevalence of the disease in the general population is low ($< 5\%$), the Odds Ratio closely approximates the Relative Risk ($\text{OR} \approx \text{RR}$).

4. Cross-Sectional Studies

• Evaluates exposure status and disease status simultaneously at a single cross-sectional point in time.
• Cross-sectional measures: Estimate prevalence, not new-case incidence directly. Prevalence is approximately incidence rate × average duration only under steady-state and other assumptions; it is not a universal identity for a changing epidemic.

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Biostatistical Measures: ARR, RRR, NNT & NNH

When evaluating clinical trials comparing an intervention group (Experimental Event Rate, EER) against a control group (Control Event Rate, CER):

• Absolute Risk Reduction (ARR): The absolute difference in event rates between groups:

$$\text{ARR} = \text{CER} - \text{EER}$$

• Relative Risk Reduction (RRR): The proportional reduction in event rate relative to control:

$$\text{RRR} = \frac{\text{CER} - \text{EER}}{\text{CER}} = \frac{\text{ARR}}{\text{CER}} = 1 - \text{RR}$$

• Number Needed to Treat (NNT): The number of patients who must receive the intervention over a specified duration to prevent one additional adverse outcome:

$$\text{NNT} = \frac{1}{\text{ARR}} = \frac{1}{\text{CER} - \text{EER}}$$

• Calculation Rule: NNT must always be rounded up to the nearest whole integer.
• Number Needed to Harm (NNH): The number of patients who must receive the intervention to cause one additional adverse event:

$$\text{NNH} = \frac{1}{\text{Absolute Risk Increase (ARI)}} = \frac{1}{\text{EER} - \text{CER}}$$

• Reporting NNH: State the absolute risk increase, follow-up period and calculation transparently. Report suitable precision; rounding down is not a universal mandatory statistical convention.

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Methodological Biases in Clinical Research

• Selection Bias: Systematic difference in how participants are selected or retained in a study (e.g., Berkson bias, where hospitalized patients have higher rates of multiple comorbidities; healthy worker effect).
• Recall Bias: Differential accuracy of historical memory between cases and controls. Individuals diagnosed with severe disease (e.g., congenital malformations, cancer) search their memories and over-report past potential exposures compared to healthy controls. Major flaw of case-control studies.
• Confounding: A third variable that is independently associated with the exposure AND independently associated with the outcome, without being an intermediate step on the causal pathway. Controlled by randomization, matching, restriction, stratification, or multivariate regression.
• Lead-Time Bias: Screening detects disease earlier in its natural history without postponing the actual date of death, artificially inflating calculated survival times from diagnosis without conferring clinical survival benefit.
• Length-Time Bias: Screening preferentially detects slowly progressive, indolent conditions with long asymptomatic phases, while rapidly progressive, lethal cases manifest between screening rounds (interval cases), artificially making screened cases appear to have superior outcomes.

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Communicable disease surveillance

Notification duties originate in state/territory public-health law. Clinicians report to that health authority; it contributes to the National Notifiable Diseases Surveillance System. Required case definitions, reporter responsibilities and deadlines vary, so a single national urgent/routine timetable is misleading.

Call the PHU urgently for suspected invasive meningococcal disease or measles while beginning appropriate treatment/isolation. Do not wait for serotyping or final culture. Measles contacts can benefit from time-sensitive MMR or immunoglobulin when appropriate; the PHU determines eligibility and timing. Meningococcal prophylaxis is for defined close contacts, not everyone who shares a building.

Rabies/lyssavirus exposure needs immediate wound care and expert PEP assessment. TB, Legionella, hepatitis A and other conditions can require urgent local action rather than a routine five-to-seven-day letter. A notifiable-disease report does not replace infection control, contact precautions or clinical resuscitation. Disclose necessary information under the lawful pathway and document the advice received.

Primary references (checked 7 October 2026): Australian CDC surveillance.