Which is the happiest nation on the planet? Fans of the original series of The Killing may be surprised to learn that it is Denmark. Nordic noir offers us a claustrophobic country shrouded in fog and lashed by icy rain, stalked by serial killers and riddled with corruption: a land from which noble souls such as detective Sarah Lund are compelled to flee, never – sadly – to be seen again.

In stark contrast, the World Happiness Report 2013, written by leading academics, finds that levels of self-reported happiness are higher in Denmark than anywhere else, with fellow Scandinavian countries Norway and Sweden also in the top five. The US is 17th and the UK 22nd. The lowest ranked nations – out of 156 – are Rwanda, Burundi, the Central African Republic, Benin, and last of all Togo.

Why are the Danish so happy? The World Happiness Report cites factors such as healthy life expectancy, GDP per capita, levels of social support, freedom to make life choices, perceptions of corruption, and the degree of generosity shown by citizens. Other experts have highlighted Denmark's high degree of income equality: this is a country, it seems, where people truly are "in it together".

Given that levels of happiness are so high in Denmark, it is reasonable to assume that Danes also enjoy good mental health. But a study published this month by the American Medical Association tells a very different story – one that demonstrates just how common mental health problems are, regardless of where people happen to live.

One of the many positive aspects of life in Denmark is its universal health care system. As part of that system, treatment for mental illness is recorded in the Danish Psychiatric Research Register: a resource that provides scientists with a treasure trove of data. Since 1969, for every person living in Denmark the register has logged admissions to psychiatric hospitals, visits to outpatient psychiatric clinics, attendance at psychiatric emergency departments, and all diagnoses. As such, it provides a comprehensive and uniquely detailed picture of treatment for psychological problems in the country.

On the basis of the register's data, researchers estimated that 38% of Danish women and 32% of Danish men will receive treatment for a mental disorder at some point during their lifetime. Remember: these statistics only include cases serious enough for professional help to be required. Of course, there are likely to be many more people with mental health conditions who for one reason or another don't seek treatment. This is why representative epidemiological surveys often produce even higher estimates for mental ill health than the Danish study. But for all those who criticise such surveys for including problems that are mild or transient, this latest research constitutes a forceful riposte. Mental illness is not a figment of over-eager clinicians' imagination; the problem is real and widespread.

The Danish results contain fascinating details. As we have noted previously for Psychology Today, women are more likely than men to develop a mental health problem, and this pattern is certainly evident in Denmark. We also see the classic dichotomy in the types of mental health problem experienced by men and women. When it comes to so-called "internalising" conditions, rates for Danish women are higher than for Danish men: for anxiety disorders 19% of women will receive treatment compared with 13% of men; for depression the figures are 16% and 9% respectively. Men, on the other hand, are more vulnerable to "externalising" disorders: in Denmark 8% of men will receive treatment for alcohol or drug problems, twice the figure for women.

Eating disorders such as anorexia nervosa and bulimia are much more prevalent among females (3%) than males (0.2%). Boys, however, show higher rates than girls of problems in early childhood such as autism (0.9%, 0.2%) and learning disabilities (1.8%, 1.2%).

The Danish study also gives us a very clear sense of when mental health problems tend to arise. For both sexes and for most conditions, it usually manifests during adolescence and early adulthood. The statistics show a substantial increase in cases from ages 10 to 20, a peak in the early 20s, and then a steady decrease with age. Mood disorders such as depression, however, become more prevalent again after the age of 65, and another obvious exception to this pattern are organic problems such as dementia, for which rates rise dramatically from the age of about 70 (the lifetime risk of organic mental health problems in Denmark was 12% for women and 9% for men).

There is no reason to believe that the Danish statistics are anomalous. In the US, the National Comorbidity Study (Replication) – the biggest and most reliable epidemiological survey of the population – found that in any one year 32% of Americans experience a psychological disorder, with anxiety disorders the most commonly experienced problem. That equates to around 70 million people. Yet only a third of these individuals receive at least minimally adequate treatment.

In the light of this timely reminder of how common mental illness is – even in the happiest countries – the stigma still attached to these conditions is remarkable. Pretty much everyone can expect either to experience a problem themselves or to know someone who has, discrimination against people with mental health problems is all too common, with much of that hostility coming from family and friends.

As a society, it is high time we faced up to the fact that mental illness is just as routine as physical illness (and assuredly no more shameful), and provided the high-quality, timely care that these conditions require.

Follow @ProfDFreeman and @JasonFreeman100 on Twitter. A version of this article appeared on the Guardian website: http://www.theguardian.com/science/blog/2014/may/14/mental-illness-happi....

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