# Goldsmiths’ 2014 Mathematics

Thursday 24th July

Medical Statistics

Professor Joan Morris

Folic Acid and Neural Tube Defects

Randomised Controlled Trial

A clinical trial is an experiment in which a treatment is administered to humans in order to evaluate its efficacy and safety

Controlled = a comparison group

Randomised = allocated to groups on basis of chance e.g. tossing a coin (ensures fair comparison)

Can folic acid reduce neural tube defects (e.g. spina bifida)?

MRC Vitamin trial – randomised controlled trial

Large: 1817 women who had had a previous NTD, 33 centres, 7 countries

The women were chosen as they had a 0.3% chance of having another NTD pregnancy.

Folic Acid vs Placebo for Neural Tube Defects – Lancet 1991

Neural Tube Defects

RR = 0.29; P = 0.008; 95% Confidence Interval: 0.10 to 0.76

Results: Women who did not receive folic acid were 3 times more likely to have a second NTD pregnancy. The fact that 6 women who took folic acid still had a NTD pregnancy shows there may be other factors involved than lack of folic acid in some pregnancies.

Impact: Women are advised to take folic acid PRIOR to becoming pregnant

http://www.nhs.uk/chq/Pages/913.aspx?categoryid=54&subcategoryid=129#close

Statisticians Involvement

Planning the study – how large should it be

Analysing the results

Stopping the study early (Independent Data Monitoring Committee) for ethical reasons perhaps (Heart surgery blockages need to be dealt with or the patient could die)

What Dose?

You want the dose to make a difference but you don’t want it to be so high it risks the life of the patient. There is a risk of heart attack on older people who take folic acid.

Women in MRC trial had had a previous NTD pregnancy and were given 4mg folic acid per day

Current recommendation is 0.4mg folic acid per day

Folic Acid and NTD Dose Response

Levels measured in blood over the pregnancy. The graph above right uses a natural log scale on the Y axis and its shape shows there is an exponential relationship between folic acid levels in the blood plasma and the incidents of NTD.

Interpretation

The same proportional increase in serum folate has the same proportional reduction in NTD

All women benefit from taking folic acid. There is not a threshold effect

Conclusions

Women planning a pregnancy should take 5mg folic acid tablets daily, instead of the 0.4mg dose presently recommended

(THE LANCET • Vol 358 • December 15, 2001)

Some people would like folic acid to be added to flour to help women increase their levels but other people are worried by possible side effects of doing this.

Use of Statistics in Screening

Screening is the identification, among apparently healthy individuals, of those who are sufficiently at risk from a specific disorder to benefit from a subsequent diagnostic test, procedure or direct preventive action.

Screening for Heart Disease

There is a strong relationship between cholesterol and heart attack

The graphs below are Gaussian curves

The graph of a Gaussian is a characteristic symmetric “bell curve” shape that quickly falls off towards d. The parameter a is the height of the curve’s peak, b is the position of the centre of the peak, c (the standard deviation, sometimes called the Gaussian RMS width) controls the width of the “bell”, and d is the value that the function asymptotically approaches far from the peak (in practice d is often set to 0).

Gaussian functions are widely used in statistics where they describe the normal distributions,

http://en.wikipedia.org/wiki/Gaussian_function

A good test will show two distinct results

False negative is when the biomarker says the patient is ok but the patient becomes ill.

Is Cholesterol any good for screening?

The graphs show this type of screening isn’t very good. There is a big overlap with the results. It may be a good idea to stop testing and just medicate everyone whether they are at risk or not.

Are there any good screening tests?

Antenatal screening for Down’s syndrome

Method: Monte Carlo Simulation

Generate a population of 500,000 people aged 0-89 years. [Use Office for National Statistics Population Data for England and Wales]

Assign risk factors (eg diabetes, smoking, blood pressure) [Use Health of the Nation Survey]

Calculate a person’s risk [Use Framingham risk equations]

Assign deaths according to people’s risks

Monte Carlo methods (or Monte Carlo experiments) are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results; typically one runs simulations many times over in order to obtain the distribution of an unknown probabilistic entity. The name comes from the resemblance of the technique to the act of playing and recording results in a real gambling casino. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to obtain a closed-form expression, or infeasible to apply a deterministic algorithm. Monte Carlo methods are mainly used in three distinct problem classes: optimization, numerical integration and generation of draws from a probability distribution.

http://en.wikipedia.org/wiki/Monte_Carlo_method

The Framingham Risk Score is a gender-specific algorithm used to estimate the 10-year cardiovascular risk of an individual. The Framingham Risk Score was first developed based on data obtained from the Framingham Heart Study, to estimate the 10-year risk of developing coronary heart disease. In order to assess the 10-year cardiovascular disease risk, cerebrovascular events, peripheral artery disease and heart failure were subsequently added as disease outcomes for the 2008 Framingham Risk Score, on top of coronary heart disease.

http://en.wikipedia.org/wiki/Framingham_Risk_Score

Conclusion

Age is as good at predicting heart disease as measuring conventional risk factors

Therefore treatment should be offered on the basis of age

Treatment to Prevent Heart Disease

Several are studies looking at the same thing

Each study may be relatively inconclusive because of too much uncertainty (too small)

Meta-analysis: statistical method of combining and presenting results from several studies will improve the conclusions

Can indicate more robust results

A reduction in blood pressure of 20mm Hg halves the risk of a CHD event or stroke regardless of the person’s original blood pressure or their level of cardiovascular risk.

This means that everyone at sufficient cardiovascular risk will benefit from a reduction in blood pressure, even if they don’t have a high blood pressure. For example all people with diabetes should be offered treatment.

Involvement of Statistician:

Study the design for the clinical trial

Analysing the data from the clinical trial

Meta-analysis from several trials

Monte Carlo simulation using results above

Conclusion

As much about collection, interpretation and presentation as calculation

Making sense out of uncertainty

At the moment the polypill isn’t licensed.

https://www.polypill.com/