There is a charming anecdote that Marianne Legato, a best-selling American author and the professor of clinical medicine at Columbia University, tells about her father. He was a short, muscular and fit man, a successful physician like his daughter, who had one other passion in his life apart from medicine: hunting. He used to take his son on frequent hunting trips and on one occasion they came to the edge of a sunflower field.

"The plants were tall and entangled together, making it very difficult to walk through them. My father, who was about 70 at the time, bent his head and simply started out, doggedly trudging through the field with no complaint, never pausing to rest and never commenting on how difficult the passage undoubtedly was.

"On another trip, my brother found him sitting on the edge of his bed, smoking, at three in the morning. 'What's the matter, Dad?' he asked. My father answered, pointing to his head: 'Too much traffic.' That was all he said. It would never have occurred to him to confide in one of his sons – or anyone else."

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This insight into the family's modus operandi appears in the opening chapter of Dr Legato's latest book, Why Men Die First. It illustrates a truth about the male psyche: a bloody-minded refusal to ask for help. Dr Legato's father took risks, had enormous confidence and dismissed anything that might be interpreted as a sign of weakness. When he died of cancer, 10 years before her mother, it was partly because he had ignored the fact that his urine was blood-tinged for two years before he asked a colleague to examine his bladder.

For Dr Legato, part of the solution is that men need to live more like women. "Men are told from an early age to 'suck it up'," she says. "They are socialised to get on with it and it is left to women to urge them to go to the doctor, usually ineffectively."

It is extraordinary, as the opening sentence of her book says, that in a society where health is an obsession, we are not investigating in more detail the most fundamental question of all – why one sex should die before the other.

On average, women live seven years longer than men. Boys die more frequently than girls in infancy and in childhood. Between the ages of 20 and 24, three times more men die than women, and men are twice as likely to die before 65. Heart disease, cancer, suicide, accidents and murder are all higher among men.

The difference in death rates between the sexes has puzzled doctors on both sides of the Atlantic. In Britain, the former chief medical officer, Sir Donald Acheson, has a single word explanation for the gender gap: hormones. Among younger, testosterone-fuelled men, accidents and violence are the chief cause of death, whereas in later life they are carried off by heart disease – against which women are protected by the female hormone, oestrogen. Men also die in larger numbers from lung cancer, because they tend to be heavier smokers than women. It is men's "rash and venturesome natures" that rendered them the weaker sex, he says.

Dr Legato agrees that hormones supply a "tremendous part of the answer". But this raises a further question. "Why are we not looking for an oestrogen-like molecule to protect men from coronary disease?" she says. "Men start to die from heart disease from the age of 35 – it should be regarded as important as breast cancer."

Twenty years ago, men and women were regarded as indistinguishable in terms of the way their bodies functioned. Gradually, that view has changed as it has become clear that the two sexes are different, not just in the obvious ways, but in every system of their bodies. In 1992, Dr Legato wrote The Female Heart, exploring the reasons why heart disease affects men and women differently. That experience led her to create a discipline of gender specific medicine.

Today, the sexes are becoming homogenised as they exchange roles – she interviewed female soldiers, firefighters and boxers for the book as well as house husbands. But it is too early to say whether these changes will shift attitudes at a deeper level. Why is it, for example, that there are more cases of melanoma (the most serious form of skin cancer) in women, but more deaths in men?

Her latest book traces what she calls the "fragility" of men throughout their lives. As well as biological differences, social pressures on men can be lethal, she says.

Now in her seventies, Dr Legato has two children of her own, a son and a daughter, whom she admits to having treated differently, sending the boy to a tough school renowned for its discipline, while the girl attended a "softer" institution.

The legacy of that decision is still evident. Her son, a lawyer in his mid-thirties, called her recently to tell her he was sick and would not be going to work. Three days later he called again and it was clear that he was seriously ill, but had done nothing about it.

She says: "If he had asked for help earlier, I think we could have made him better sooner, but he talked of soldiering on. I wish he would read my book, but I don't think he will. He is not interested in why men die first."

Health risks every man should know about

Obesity

A waist measurement over 37 inches increases your risk of health problems such as diabetes and heart disease. Eat healthily and lose that gut.

Unprotected sex

Up to 50 per cent of men (70 per cent of women) with a sexually transmitted infection don't show any symptoms. Use a condom

Too little exercise

Staying fit is the key to good health. Walking is fine (10,000 steps burns 500 calories) and if you jog or swim or play football (700 calories an hour), you burn more.

Heart disease

There are more than 200,000 deaths a year in the UK from heart disease and stroke and together they account for almost one in three premature deaths (before age 75) in men. Check your blood pressure (should be below 160/100 mmHg) and cholesterol level (ideally less than 5mmol/litre).

Smoking

Men still smoke more and die more frequently from smoking than women. It increases the risk of heart disease, half a dozen kinds of cancer and other illnesses such as bronchitis. Half of all smokers will die from their habit if they do not stop. Give it up.

Drinking

Heavy drinking is common among men. In moderation alcohol enhances enjoyment and reduces the risk of heart disease. In excess, it leads to social and psychological distress and physical damage. Three small glasses of wine or a pint and a half of beer a day is fine – more could be problematic.

Testicular cancer

Although still rare, rates have trebled in the past 25 years and it is the commonest cause of cancer deaths in men aged 15-35. Check your testicles regularly.

Prostate cancer

The commonest in men with 35,000 cases and 10,000 deaths a year. Be alert to warning signs (difficulty peeing or getting up in the night).

Other cancers

Don't ignore symptoms (persistent cough, blood in the urine or faeces) – early treatment increases the chance of a cure.

Why Men Die First by Marianne Legato, Palgrave Macmillan, £14.99