<p>Token consumption by prompting strategy.</p>

We test baseline prompts (direct answer, Chain-of-Thought, and self-consistency) while introducing a new prompting method we call “prompt-chaining for continuous reflection” (PCCR) that forces inference time minimum token-generation budgets. We assess accuracy and tokens-generated, allowing us to investigate the accuracy–efficiency trade-offs across prompting, context-grounding, fine-tuning, and model scales. We discover equivalency point configurations where a smaller model’s accuracy falls within one 95% confidence interval of a larger model’s (typically within 1–4 percentage points) reached through increased reasoning budgets, context-grounding, or fine-tuning.

Specific effects are apparent and statistically supported: the benefit of medical fine-tuning grew from +4.6 to +15.7 percentage points (non-overlapping 95% CIs) when paired with self-consistency, and enforced extended reasoning raised MedGemma 27B accuracy from 58.1% to 80.1% (<i>p</i> < 10^-5) in the absence of context. We also identify an “overthinking” inflection: when high-quality context is available, extended reasoning beyond roughly 128–256 tokens degrades accuracy by 7–13 percentage points.

Using these empirical results, we formulate a general framework with equations to balance cost-benefit trade-offs when engineering LLM-based systems for medical reasoning and QA. We recommend generalizable configurations, designs, and patterns to achieve accuracy and efficiency objectives for example use-cases relevant to healthcare organizations.</p></div>