https://en.wikipedia.org/wiki/List_of_countries_by_suicide_rate
This source puts the US at #47 worldwide:
http://www.worldlifeexpectancy.com/cause-of-death/suicide/by-country/
US Suicide rate is 2/3rds Japans. Eastern European Rates are around Japan's while Western European rates are around the US.
US is #3 in sucide by firearms, behind El Salvador and Uruguay:
https://en.wikipedia.org/wiki/List_of_countries_by_firearm-related_death_rate
Hanging is the most common method of Suicide in England and Wales and the second most common in the US:
https://en.wikipedia.org/wiki/Suicide_by_hanging
Hanging is the most common method world wide, with 90% of suicide of women in Eastern Europe being by hanging:
http://www.who.int/bulletin/volumes/86/9/07-043489/en/
Hanging was the predominant method of suicide in most countries included in the analysis (Table 1). The highest proportions were around 90% in men and 80% in women, as observed in eastern Europe (i.e. Estonia, Latvia, Lithuania, Poland and Romania). There were a number of deviations from the predominant pattern. As might be expected, firearm suicide was the most common method in the United States, but was also prevalent in Argentina, Switzerland and Uruguay, although only men used this method in Switzerland. Jumping from a height (designated as falls in the figures) plays an important role in small, predominantly urban societies such as Hong Kong SAR, Luxembourg and Malta. In contrast, in rural Latin American countries (e.g. El Salvador, Nicaragua and Peru), Asian countries (e.g. the Republic of Korea and Thailand) and also in Portugal, poisoning with pesticides was a major problem, notably among women. Poisoning with drugs was common in women from Canada, the Nordic countries and the United Kingdom. It also played an important role in male suicide in these countries.......
Correspondence analysis of all countries and of the subset of non-European countries provides evidence for a polarization between suicide methods. The poles are pesticide suicide and firearm suicide, while hanging is in an intermediate position. This polarization has several implications.
Firstly, at the poles, hanging and other more traditional suicide methods are displaced by suicide methods whose main characteristics are utilization of a technical means, ready availability, quick use and high lethality. For pesticide and firearm suicide, the impact of availability seems to be greater than for traditional suicide methods.
Secondly, the opposite slopes seen in the correspondence maps and the degree of displacement indicate that there is a substantial substitution effect: pesticide suicide and firearm suicide are not only associated with new suicide behaviour, but also tend to substitute hanging. The introduction of specific prevention programmes focusing on pesticides or firearms would be expected to reverse this substitution to some extent. In fact, this reversal was observed when firearm availability was restricted in Australia and Canada at the same time, the proportion of suicides due to hanging increased.
Readily available poisons and firearms facilitate unplanned suicide acts,22,23 which are typical of impulsive suicide. Consequently, they increase the suicide frequency. It is noteworthy that the proportion of suicides in individuals with a background of severe mental illness is distinctly below average in firearm suicide.24,25 This observation holds for both Asian and European countries.
In simple terms, hanging is the fall back position for suicide world wide. Other methods of Suicide are substitutes for hanging but only if available. Thus in Canada and Australia when access to firearms were cut back, suicide by hanging increased.
In the US over 50% of all suicides are by Firearms, 14% by hanging and 16 % by poison:
http://lostallhope.com/suicide-statistics/us-methods-suicide
In the US Men overwhelmingly perfer sucide by firearms, hanging is a distance second and only about 10% of men opt for posion. On the other hand hand over 1/3 of women prefer poison, under 1/3 opt for firearms, with just under a 1/4 of women opt to hand themselves.
Prior to 1960 the primary method of suicide was natural gas inhalation in Britain, but that fell to almost zero when non toxic natural gas was introduced:
http://actionallianceforsuicideprevention.org/sites/actionallianceforsuicideprevention.org/files/Reducing%20a%20Suicidal%20Persons%20Access%20to%20Lethal.pdf
When natural gas was no longer an option for suicide in Britain, other methods went up, but no where near in numbers as the drop in suicides by Natural Gas. The same Report noted when it comes to US Suicide rates, most but not all studies show a clear difference in rates if the Firearms are kept unloaded and the ammunition stored separately as opposed to the firearms are kept loaded Much lower rates if the firearms are kept Unloaded as is the case with most rifles and shotguns as opposed to pistols).
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