21.3 Biostatistics, Study Design & Critical Appraisal
Key Takeaways
- The randomized controlled trial is the strongest single study design for establishing that an intervention causes an effect, and systematic reviews of such trials sit above it in the evidence hierarchy
- A case-control study yields an odds ratio and a cohort study yields relative risk, which is why odds ratios appear in studies of rare outcomes
- A p-value below 0.05 indicates statistical significance but says nothing about clinical importance or effect size
- A 95 percent confidence interval for a relative risk or odds ratio that includes 1.0 indicates a non-significant result
- Number needed to treat is the reciprocal of the absolute risk reduction, and relative risk reduction alone systematically overstates benefit
Biostatistics, Study Design & Critical Appraisal
Why this matters on the INBDE: FK10 carries 10% of examination items — roughly 50 items — and it is the area candidates most often skip entirely. The content is finite and highly learnable, which makes it one of the best returns on study time available.
The Evidence Hierarchy
| Level | Design | Strength and use |
|---|---|---|
| 1 | Systematic review / meta-analysis of randomized controlled trials | Highest level for therapy questions; a meta-analysis statistically pools results |
| 2 | Randomized controlled trial (RCT) | The only design that reliably establishes causation, because randomization balances known and unknown confounders |
| 3 | Cohort study | Follows exposed and unexposed groups forward; yields relative risk and incidence |
| 4 | Case-control study | Starts with the outcome and looks backward at exposure; yields an odds ratio; efficient for rare outcomes and long latency |
| 5 | Cross-sectional study | A snapshot at one point in time; yields prevalence; cannot establish temporality |
| 6 | Case series / case report | Descriptive; hypothesis-generating only |
| 7 | Expert opinion, bench research, animal studies | Lowest for clinical decisions |
A critical distinction: the hierarchy applies to therapy questions. For a prognosis question the best design is a cohort study; for diagnostic accuracy it is a cross-sectional study comparing the test against a reference standard in an appropriate spectrum of patients; for harm from a rare event it is often a case-control study, because an RCT would be unethical or impossibly large.
Features that make a trial trustworthy
- Randomization — allocation by chance, balancing confounders.
- Allocation concealment — the person enrolling cannot know the next assignment.
- Blinding — single (patient), double (patient and clinician/assessor), or triple (including the analyst). Placebo control where feasible.
- Intention-to-treat analysis — participants are analyzed in the group to which they were randomized, regardless of what they actually received. This preserves randomization and is the conservative analysis; per-protocol analysis exaggerates benefit.
- Adequate power and a pre-specified primary outcome.
- Accounting for all participants — high or differential loss to follow-up undermines the result.
Descriptive Statistics
| Measure | Definition | When to prefer it |
|---|---|---|
| Mean | Arithmetic average | Symmetric, normally distributed data |
| Median | Middle value | Skewed data or outliers — income, waiting times, pocket depths in a diseased population |
| Mode | Most frequent value | Categorical data |
| Range | Maximum minus minimum | Crude spread; sensitive to outliers |
| Standard deviation | Average deviation from the mean | Spread of the data |
| Standard error of the mean | SD divided by the square root of n | Precision of the estimate; always smaller than SD |
In a normal distribution, approximately 68% of values fall within one standard deviation of the mean, 95% within two, and 99.7% within three. In a right-skewed distribution the mean exceeds the median; in a left-skewed distribution the median exceeds the mean.
Levels of measurement
| Scale | Definition | Dental example |
|---|---|---|
| Nominal | Categories without order | Tooth type, sex, material used |
| Ordinal | Ordered categories with unequal intervals | Mobility Class I/II/III, plaque index, pain 0–10 |
| Interval | Equal intervals, arbitrary zero | Temperature in Celsius |
| Ratio | Equal intervals, true zero | Probing depth in millimeters, age, DMFT count |
Inferential Statistics
Hypothesis testing
- The null hypothesis states there is no difference. Statistics test whether the observed data are compatible with it.
- The p-value is the probability of obtaining a result at least as extreme as the observed one if the null hypothesis were true. A p-value below the conventional alpha of 0.05 is called statistically significant.
- A p-value is not the probability that the null hypothesis is true, and it says nothing about effect size or clinical importance. With a large enough sample, a clinically trivial difference becomes statistically significant.
| Error | Definition | Controlled by |
|---|---|---|
| Type I (alpha) | Rejecting a true null — a false positive finding | Setting alpha, usually 0.05; correcting for multiple comparisons |
| Type II (beta) | Failing to reject a false null — a false negative | Power = 1 − beta, conventionally 0.80 or higher; achieved chiefly through sample size |
Confidence intervals
A 95% confidence interval is the range that would contain the true population value in 95% of repeated samples. It is more informative than a p-value because it conveys both significance and precision.
- For a ratio measure (relative risk, odds ratio, hazard ratio), an interval that includes 1.0 is not significant.
- For a difference measure (mean difference, risk difference), an interval that includes 0 is not significant.
- A wide interval signals imprecision, usually from a small sample.
Common tests
| Comparison | Test |
|---|---|
| Two independent group means, continuous data | Independent t-test |
| Paired measurements (before/after in the same subjects) | Paired t-test |
| Three or more group means | ANOVA |
| Categorical proportions | Chi-square (Fisher exact test for small expected counts) |
| Relationship between two continuous variables | Correlation (r), then regression for prediction |
| Time to an event | Kaplan-Meier survival analysis, log-rank test, Cox regression |
| Non-normal or ordinal data | Non-parametric equivalents — Mann-Whitney U, Wilcoxon signed-rank, Kruskal-Wallis |
Correlation coefficients run from −1 to +1. Correlation does not establish causation, and the coefficient describes only a linear relationship.
Measures of Effect
| Measure | Formula in words | Note |
|---|---|---|
| Incidence | New cases in a population at risk over a period | Requires follow-up |
| Prevalence | Existing cases at a point in time | From cross-sectional data |
| Relative risk (RR) | Risk in exposed divided by risk in unexposed | Cohort studies and RCTs |
| Odds ratio (OR) | Odds of exposure in cases divided by odds in controls | Case-control studies; approximates RR when the outcome is rare |
| Absolute risk reduction (ARR) | Control event rate minus treated event rate | The clinically meaningful magnitude |
| Relative risk reduction (RRR) | ARR divided by control event rate | Systematically sounds larger than it is |
| Number needed to treat (NNT) | 1 divided by the ARR | Number of patients treated to prevent one event; smaller is better |
The classic appraisal trap: a paper reports a "50% reduction in caries." If the control incidence was 2% and the treated incidence 1%, the relative reduction is 50% but the absolute reduction is 1 percentage point, and the NNT is 100. Always ask for the absolute numbers.
Diagnostic Test Measures
| Measure | Definition |
|---|---|
| Sensitivity | True positives divided by all who have the disease — SnNout |
| Specificity | True negatives divided by all without the disease — SpPin |
| Positive predictive value | True positives divided by all who test positive — falls as prevalence falls |
| Negative predictive value | True negatives divided by all who test negative — rises as prevalence falls |
| Reliability | Reproducibility — kappa for categorical agreement, intraclass correlation for continuous |
| Validity | Whether the test measures what it claims |
Kappa corrects agreement for chance: values above roughly 0.80 represent excellent agreement, 0.60–0.80 substantial, 0.40–0.60 moderate, and below 0.40 poor.
Bias and Confounding
| Problem | Description | Remedy |
|---|---|---|
| Selection bias | The sample is not representative of the target population | Random sampling, consecutive enrollment, clear eligibility criteria |
| Information / measurement bias | Systematic error in measuring exposure or outcome | Calibration, standardized instruments, blinding |
| Recall bias | Cases remember exposures differently from controls | Prospective design, records-based exposure |
| Observer bias | The assessor's expectation influences measurement | Blinded outcome assessment |
| Attrition bias | Differential loss to follow-up between groups | Intention-to-treat, sensitivity analysis |
| Publication bias | Positive studies are more likely to be published | Trial registries, funnel plots |
| Confounding | A third variable is associated with both exposure and outcome | Randomization (best), restriction, matching, stratification, multivariable adjustment |
The classic dental confounder is smoking, which is associated with both periodontal disease and many exposures of interest. A study reporting an association between periodontitis and an outcome that does not adjust for smoking has not answered the question.
Research Ethics
Human-subjects research requires Institutional Review Board (IRB) approval, informed consent for research that is distinct from clinical consent, protection of vulnerable populations (children, prisoners, cognitively impaired adults), an independent data safety monitoring board for higher-risk trials, and disclosure of conflicts of interest and funding sources. Equipoise — genuine uncertainty about which arm is superior — is the ethical precondition for randomizing patients at all.
Investigators identify 200 patients with oral squamous cell carcinoma and 200 matched patients without it, then compare their prior areca nut use. What study design is this, and which measure of association does it produce?
A trial reports that a varnish reduces caries incidence from 4 percent to 2 percent over two years. What is the number needed to treat?
A study reports a relative risk of 1.35 with a 95 percent confidence interval of 0.88 to 2.07. How should this be interpreted?
Which analytic approach preserves the benefit of randomization when some trial participants do not receive their assigned treatment?