Biostatistics for paediatric exams — formative SAQs

SAQ 1 (10 marks)

You are asked to interpret an abstract reporting a new therapy for a childhood illness. It states a mean difference in symptom duration with a p-value of 0.04, but the 95 percent confidence interval is wide and crosses zero. [9]

1. Explain what a 95 percent confidence interval represents and why an interval crossing zero changes the interpretation of the p-value. (4) [9] [5]
2. Define a Type I and a Type II error, statistical power, and how the sample size influences each. (3) [3]
3. Describe how you would convey this result to the family. (3) [4] [5]

Model answer

A 95 percent confidence interval is the range of values that, over many repeated samples, would capture the true population effect 95 times in 100; it expresses both the size and the precision of the estimate in a single band. When the interval crosses zero for a difference, it is compatible with both a benefit and a harm, so the result is not statistically significant at the 0.05 level, and the quoted p-value of 0.04 cannot stand alone against an interval that includes the null. The confidence interval always takes precedence, because it carries the information the p-value omits — the magnitude and the precision. [9] [5]

A Type I error is a false positive, rejecting a true null hypothesis, and its rate is alpha. A Type II error is a false negative, failing to reject a false null, and its rate is beta. Statistical power is one minus beta, the probability of detecting a true effect, and it rises as the sample size grows. The standard error of the mean shrinks with the square root of the sample size, so larger samples narrow the confidence interval and raise power; a wide, null-crossing interval is the fingerprint of a small, underpowered study. [3]

To convey the result, give the effect size and its confidence interval in absolute terms a family can weigh, explain that the interval includes both a meaningful benefit and essentially no effect, and be honest that the study was too small to be certain. Where the choice is preference-sensitive, present the uncertainty plainly and let the family share the decision, with a plan to revisit it as larger evidence appears. [4] [5]

SAQ 2 (10 marks)

A paediatric oncology abstract reports a hazard ratio of 0.6 (95 percent confidence interval 0.45 to 0.80) for relapse-free survival, and a separate abstract reports a logistic regression model predicting intensive-care mortality that ran twenty subgroup analyses. [7]

1. Explain what a hazard ratio represents, how to interpret the reported interval, and why a hazard ratio is not a ratio of median survival times. (4) [7] [5]
2. Outline how you would choose the correct statistical test for a dataset, naming the key decisions about data type, pairing, number of groups, and assumptions. (3) [3] [9]
3. Explain why the twenty subgroup analyses should be read with caution and how to correct for multiple comparisons. (3) [2] [4]

Model answer

A hazard ratio from a Cox proportional hazards model represents the relative rate of the event between two groups; a hazard ratio of 0.6 indicates about a 40 percent lower rate of the event in the intervention group. Because the 95 percent confidence interval (0.45 to 0.80) excludes the null value of one, the result is statistically significant at the 0.05 level. A hazard ratio is a relative rate of events over time, not a ratio of median survival times, which is a different and cruder summary that carries its own considerable uncertainty. [7] [5]

To choose the correct test, first classify the outcome as categorical or numerical, then ask whether the comparison is paired or independent, then count the number of groups. For numerical data with roughly normal distribution and equal variance, use a parametric test — the paired t-test for paired data, the independent t-test for two groups, one-way analysis of variance for more than two. For skewed or ordinal data, fall back to the rank-based non-parametric equivalents — Wilcoxon signed-rank, Mann-Whitney U, and Kruskal-Wallis. For categorical data, compare proportions with the chi-square test or Fisher's exact test when counts are small. Checking the assumptions before trusting a parametric test is the safeguard against a precisely wrong answer. [3] [9]

Running twenty tests inflates the chance of at least one false positive far above the nominal alpha, so a lone significant subgroup is more likely a chance artifact than a real finding. The Bonferroni correction divides alpha by the number of tests to control the family-wise error rate, and a pre-specified analysis plan prevents the data-dredging that produces false positives. The significant subgroup should be treated as hypothesis-generating and confirmed in an independent dataset before it changes practice. [2] [4]