Two months ago Steve Jobs, the charismatic boss of Apple, received a new liver. A successful organ transplant is always cause for celebration. But when the recipient is not just the chief executive but, in many ways, the embodiment of Apple — and the operation is kept secret from shareholders — celebrations give way to serious questions: if Mr Jobs’s health is crucial to the wealth of his company, at what point does his personal illness become a matter of public concern?

Ill health is no more a bar to good judgment than robust health is a guarantee of wisdom. Many of the politicians who have led their countries into chaos, many of the bankers who helped to tilt the world into recession, appeared fit enough. But what if poor health, or depression, clouds a leader’s judgment? When does it become a leader’s duty to share his medical notes with a broader audience than just his consultant?

The dilemma becomes more stark when you see how closely the graph of Apple’s share price has mirrored rumours about the state of Mr Jobs’s health. Apple’s shareholders have been obsessed with his wellbeing since 2004, when he was treated for pancreatic cancer. Rumours in October that he had suffered a heart attack sent shares slipping 5 per cent. They rose 4 per cent in January when Mr Jobs attributed his weight loss to a hormone imbalance. One week later, he said that he would be taking six months off because of poor health, and shares fell 7 per cent.

Mr Jobs is central to the continuing success of Apple. Yet Apple twisted itself into a tangle of evasions to protect his privacy and its share price.

Tim Martin, the founder and chairman of JD Wetherspoon, revealed last month that he had prostate cancer two years ago; his condition had no demonstrable impact on performance. Steven Cranshaw, the former boss of Bradford & Bingley, resigned with a heart condition, before a profit warning. The bank was in a parlous condition, but this was due to its decision to follow its banking peers into the complex financial instruments that triggered the credit crunch. Did Mr Cranshaw’s heart condition help to weaken the bank or did the bank’s woes help to weaken Mr Cranshaw’s heart?

This is sensitive ground. The dividing line between private and public spheres is often a blurred one. In politics, the tally of world leaders is full of alcoholics and addicts. Depression, breakdowns and terminal illness have stalked the corridors of power. In his book, In Sickness and in Power, Lord Owen, the former Foreign Secretary and doctor, cites how the ill health of world statesmen has, time and again, changed the course of history. Sir Anthony Eden, already unwell on becoming Prime Minister in 1955, got worse. A routine gall bladder operation went wrong. Further operations and a diet of drugs followed. As a result, the man who decided to collude in the Suez Canal adventure was weak, lacking sleep, and stuffed with stimulants. François Mitterrand concealed that he was dying of cancer. Sir Winston Churchill grew too ill to sign papers, so his son-in-law forged his signature on his behalf.

It would be unwise to regulate for this. Individual cases need individual judgment calls.There is a fine line between transparency and intrusion. Once again, this is a matter for responsible company boards. They need to look out for the interests, in every sense of the word, of both the people who run the company and those who own it.