Is coming into work when you’re so sick that you’re on the verge of collapse really something we should be praising, or encouraging? When Hillary Clinton announced last week that she was trying to work through a pneumonia diagnosis and continue her campaign schedule, her supporters were quick to use this as an opportunity to praise her strength of character. She was described as tough, determined, strong, gritty and other adjectives that suggest working through serious illness is to be admired.

It may well be viewed as heroic by some, but in reality it’s a sign of an increasingly pervasive culture that sets up work as more important than our wellbeing.

Clinton certainly isn’t the only person who has turned up sick for work recently. I suspect at one time or another we’ve all uttered the words “don’t worry, it’s nothing serious”, or struggled in only to be greeted by a concerned colleague who politely asked us to go home and stop sneezing on them.

Whether it’s guilt about letting down the team, concern your tasks won’t get covered or more likely some fear that it might be counted against you, the trend for employees to come into work or to work longer hours when they should be taking time off has been growing.

Research by Simplyhealth and the Chartered Institute of Personnel and Development (CIPD), where I work as chief executive, shows “presenteeism” is on the rise. Our 2015 survey showed that in the preceding 12 months, a third of firms reported a rise in employees working when they’re sick, and this has some pretty clear negative effects on employee wellbeing. Organisations that have noticed an increase in presenteeism are nearly twice as likely to report an increase in stress-related absence and more than twice as likely to report an increase in mental health problems among their staff too.

Greater uncertainty in the economy and regarding jobs in recent years, together with an increasingly “always on” working environment and the pressure to perform are all factors driving this trend. Many of the companies and employees we talk to cite job insecurity as a reason for increased presenteeism, with employees fearing that a competitive job market, and the growth of automation, will make them more replaceable.

But leaders and managers set the tone, and have a responsibility not just to their organisation but also to the wellbeing of their employees. As our research shows, increasing presenteeism leads to increased prevalence of stress, and there is a wealth of evidence, such as the Towers Watson 2014 Global Benefits Attitudes survey, which clearly shows that workplace stress leads to less productive employees.

So why, then, do more than half of all organisations admit that they aren’t doing anything to combat this growing problem? It may well be that they believe that promoting long-term employee wellbeing might come at the expense of the short-term success of an organisation, but it can also be a lack of awareness of the growth of a corporate culture that accepts or even encourages presenteeism.

To perform at our best, people need to be well both physically and mentally. If businesses want employees who are engaged and motivated, then employees need to feel that their organisation, their managers and bosses are supporting them, and not pressuring them to work when they are not properly fit.

How do we change this culture? It has to come from the top down. Employees won’t feel empowered to take time off when they’re sick if their manager’s behaviour runs counter to that. The second action businesses can take is to build a culture that emphasises healthy living.

Health should be promoted in the workplace, with people given the opportunity to learn more about their own health, to exercise and eat well within the workplace and beyond. At the CIPD, we host discounted zumba and yoga classes each week. TransferWise takes all its staff on annual company holidays, while the law firm Allen & Overy has GPs and dentists on site. Those are at the more expensive end of the scale, but even simple things like free fruit for staff, a perk offered by just 15% of employers, can help instil a healthier work culture.

Mental health and particularly the understanding of stress is equally important and is perhaps even more challenging. Much more needs to be done to educate managers in how to show understanding and ask the right questions, and how and where to find the right support. Leaders in this field, such as Google, have built good mental health into their culture by offering mindfulness classes to staff, while many large employers in the City, such as KPMG and Deloitte, have launched the City Mental Health Alliance, working with charities to end the stigma attached to mental health problems.

The message to business is clear; a workforce that is well, works well. Clinton may have wanted to preserve her image of strength, but she wasn’t being honest with herself. We need our leaders – in the workplace and beyond – to take responsibility for their own health and wellbeing first, to set the right example.

Only then does this damaging culture of presenteeism have any chance of changing.