Why maths matters more in MedTech than in many other sectors

MedTech is high accountability engineering. You are not just building something that works once. You are building something that works reliably for real people under real constraints.

In the UK you are also working inside a regulated environment. GOV.UK guidance explains that manufacturers must comply with product marking & conformity assessment requirements for medical devices including UKCA in Great Britain plus CE marking routes where applicable. GOV.UK For many teams this reality shapes day to day work: requirements, traceability, testing, risk files, post market data.

Maths matters because it helps you:

• design tests that actually prove performance

• interpret results without fooling yourself

• quantify uncertainty so decisions are defensible

• connect hazards to controls in a risk process

• justify thresholds, alarms, sensitivity, specificity

• communicate evidence clearly to quality, regulatory, clinicians & auditors

The only maths topics you actually need

1) Measurement maths: units, tolerances, uncertainty & repeatability

This is the single most useful maths area for MedTech job readiness because testing drives everything: verification, validation, clinical performance, complaint investigation, supplier control.

What you actually need

• unit conversions (mm ↔ µm, °C ↔ K, mg ↔ g, mV ↔ V)

• tolerances & worst case thinking

• mean, standard deviation, coefficient of variation

• repeatability vs reproducibility at a practical level

• uncertainty statements that match lab reality

A strong UK aligned starting point is NPL’s beginner guide on measurement uncertainty which is explicitly aimed at beginners including laboratories preparing for UKAS style contexts. National Physical Laboratory

Where it shows up in real MedTech work

• test method development

• gauge selection & calibration conversations

• pass/fail criteria definition

• trending drift over time

• supplier verification & incoming inspection

• “is this change real or noise” discussions

Micro exercises

1. Take 20 repeated measurements of a dimension or sensor output. Report the mean, SD & an uncertainty statement in plain English.

2. Create a pass/fail threshold then show how measurement uncertainty could cause borderline misclassification.

3. Write a short note: “What would I do to reduce uncertainty” with practical actions.

2) Statistics for verification, validation & clinical evidence

Most MedTech teams do not need you to be a full biostatistician. They do need you to be comfortable interpreting performance with uncertainty.

What you actually need

• distributions & outliers

• confidence intervals as “plausible range”

• hypothesis tests as a decision tool not a magic stamp

• sample size intuition (power thinking)

• sensitivity, specificity, PPV, NPV for diagnostic style outputs

• agreement metrics basics (when comparing devices or methods)

If your product is digital health or evidence facing you will also see structured evidence expectations. NICE’s Evidence Standards Framework for digital health technologies sets out evidence standards to help evaluators & decision makers assess benefits. NICE

Where it shows up

• verification plans: how many samples, what conditions, what acceptance criteria

• validation: does it meet user needs & intended use

• clinical performance evaluation support

• post market surveillance trend analysis

• usability studies: task success rates, error rates, confidence in findings

Micro exercises

1. Build a simple “test summary report” that includes confidence intervals rather than only averages.

2. For a binary outcome, compute sensitivity & specificity then explain what changes when disease prevalence changes.

3. Write a one page decision note: “Does the evidence support releasing this change”

3) Probability & risk thinking for hazard analysis

Risk work is not abstract in MedTech. It is core. If you can think clearly about probability, severity & control effectiveness you become valuable across engineering & quality.

ISO 14971:2019 specifies terminology, principles & a comprehensive process for risk management of medical devices including software as a medical device. ISO

What you actually need

• probability language: likelihood vs frequency vs detectability

• conditional thinking: “given X failure, what is the chance of harm”

• base rate intuition: rare events can still matter if severity is high

• risk control logic: how controls reduce probability or severity or both

• residual risk & benefit risk thinking in plain English

Where it shows up

• FMEA style work

• hazard analysis & risk control traceability

• complaint investigations & CAPA

• cybersecurity risk discussions for connected devices

• alarms & alert thresholds where false positives matter

Micro exercises

1. Take a simple device scenario (eg pulse oximeter reading drift). List hazards, causes, harms, controls.

2. Write how each control changes the risk story with numbers where possible.

3. Create a “residual risk communication” paragraph that is clear & non alarmist.

4) Curve fitting & modelling: the everyday maths skill

If you only learn one “engineering maths” capability for MedTech learn this: how to fit a simple model to data then sanity check it.

What you actually need

• linear regression basics

• log transforms when behaviour is exponential

• calibration curves: offset, gain, non linearity

• residuals: how to see when the model is lying

• interpolation vs extrapolation awareness

Where it shows up

• sensor calibration & drift compensation

• temperature effects & correction curves

• dose response style relationships

• mechanical testing correlations

• algorithm threshold tuning

Micro exercises

1. Fit a calibration curve then plot residuals & identify where the error grows.

2. Add measurement uncertainty bars & explain what changes in interpretation.

3. Write a short “model limitations” section like you would in a technical file.

5) Signal basics for sensors, wearables & monitoring devices

Many medical technology jobs involve signals even if the role title does not say it.

What you actually need

• sampling rate & Nyquist intuition

• noise vs signal plus filtering basics (moving average, low pass intuition)

• drift vs step changes

• time windows & features: mean, variance, peak to peak, frequency band energy at a basic level

• artefacts: motion, ambient interference, poor contact

Where it shows up

• ECG, PPG, EEG, spirometry, pressure sensors, inertial sensors

• wearable data cleaning & feature extraction

• alert threshold logic where noise drives false alarms

• validation: “does it perform under motion”

Micro exercises

1. Take a public wearable dataset & demonstrate how filtering reduces noise but can also distort peaks.

2. Show how changing sampling rate changes what you can detect.

3. Build a simple artefact detector using rolling window stats.

6) Linear algebra essentials for imaging & ML enabled devices

Not every MedTech job needs this. If you are aiming at imaging, computer vision, AI enabled SaMD, decision support or algorithmic pipelines it helps a lot.

What you actually need

• vectors & matrices

• dot product & cosine similarity

• matrix multiplication shape reasoning

• PCA intuition for dimensionality reduction

• confusion matrix metrics for classifiers

This is often enough to understand how embeddings, image features, model outputs & evaluation behave.

7) Optimisation thinking: thresholds, trade offs & performance

Most MedTech optimisation is not calculus heavy. It is practical decision making with constraints.

What you actually need

• how to choose a threshold based on cost of false positives vs false negatives

• multi objective trade offs: accuracy vs latency vs battery vs interpretability

• understanding loss functions conceptually

• basic hyperparameter tuning mindset: change one variable, measure again

Where it shows up

• alarm design: avoid alert fatigue but catch real risk

• on device processing: latency & power budgets

• triage support tools: sensitivity vs specificity trade offs

• manufacturing: process window optimisation

The standards shaped reality: why they matter to your maths choices

Even if you are not in regulatory, standards shape how teams work.

• ISO 13485 is a widely used QMS standard for medical devices that sets requirements for a quality management system in the industry. ISO

• ISO 14971 sets out a risk management process for medical devices across the lifecycle. ISO

• IEC 62304 defines life cycle requirements for medical device software & provides a framework for software life cycle processes. ISO

You do not need to memorise these standards for a junior role but you should know what they are for & how your evidence or testing supports them.

A 6 week maths plan for MedTech job readiness

Aim for 4 to 5 sessions per week of 30 to 60 minutes. Each week produces something you can publish in a portfolio.

Week 1: Measurement uncertainty basics

Learn

• mean, SD, uncertainty, repeatability
  Build

• a notebook that calculates uncertainty for repeated measurements
  Output

• a one page report style summary
  Resource: NPL beginner guide to measurement uncertainty. National Physical Laboratory

Week 2: Test design & acceptance criteria

Learn

• distributions, percentiles, confidence intervals
  Build

• a simulated verification dataset with acceptance criteria
  Output

• a verification style summary: what passed, what failed, what is borderline

Week 3: Risk maths & hazard thinking

Learn

• likelihood, severity, controls, residual risk
  Build

• a mini ISO 14971 style hazard analysis on a simple device scenario
  Output

• a risk file excerpt with clear reasoning
  Resource: ISO 14971 overview. ISO

Week 4: Calibration curves & model fit

Learn

• linear regression, residuals, log transforms
  Build

• a calibration model with residual analysis
  Output

• a calibration report with limitations section

Week 5: Signals & filtering for wearables

Learn

• sampling, noise, filtering intuition
  Build

• clean a signal, extract features, compare before vs after
  Output

• a short “signal quality” note with evidence

Week 6: Evidence facing capstone

Pick one capstone that matches your target jobs:

• digital health evidence pack mapped to NICE ESF levels

• SaMD mini lifecycle pack: requirements, tests, traceability

• connected device risk & performance pack: reliability, alarms, thresholds

If clinical investigation is relevant to your direction, MHRA has guidance for manufacturers on clinical investigations. GOV.UK Assets
NICE ESF is useful if you are building or evaluating digital health tech for the UK system. NICE

Portfolio projects that translate maths into hiring signals

Project 1: Verification dataset + uncertainty statement

What you show

• you can run a test study & report uncertainty like a professional
  Resource: NPL uncertainty guide. National Physical Laboratory

Project 2: Risk management mini file

What you show

• you can connect hazards to controls & evidence
  Resource: ISO 14971 overview. ISO

Project 3: Calibration & drift compensation

What you show

• you can build a simple calibration model, test it & explain limitations

Project 4: Alarm threshold tuning with a confusion matrix

What you show

• you understand false positives, false negatives & base rate effects
  Bonus: add a stakeholder paragraph on alert fatigue & safety.

Project 5: SaMD documentation starter pack

What you show

• you can structure work in a standards shaped environment
  Resource anchors: ISO 13485 QMS context plus IEC 62304 software lifecycle context. ISO

Resources section

UK regulation & market access context

• GOV.UK regulating medical devices in the UK. GOV.UK

• GOV.UK conformity assessment & UKCA mark guidance. GOV.UK

• NHS Digital regulations guidance on getting a UKCA mark for medical devices. digitalregulations.innovation.nhs.uk

Quality & risk standards

• ISO 13485 overview for medical device QMS. ISO

• ISO 14971 overview for medical device risk management. ISO

• IEC 62304 overview for medical device software lifecycle. ISO

Measurement uncertainty

• NPL GPG11 beginner guide to uncertainty of measurement. National Physical Laboratory

Evidence & clinical evaluation

• NICE Evidence Standards Framework for digital health technologies. NICE

• MHRA guidance for manufacturers on clinical investigations October 2025.