This is going to be a tough statistic to find for two reasons.

The first being that typically if a soldier were killed in the front line the exact cause of death was not recorded in any official source. While the soldier's friends may have noted in their personal diaries that a comrade committed suicide, the officer in charge of maintaining a log of the unit's actions would likely just record it as "killed in action" or lump it in with trench wastage - men killed by snipers and artillery fire on a daily basis. I took a quick look at the War Diary for the Canadian 10th Infantry Brigade and found in Appendix C that casualty figures for a given period are simply listed with little to no detail given. Furthermore, the body of the diary may describe how Raid A resulted in X number of casualties, but the figures for "wastage" are lumped in with battle casualties in the weekly reports.

The second reason that these figures would be difficult to determine is the negative stigma surrounding suicide that was prevalent at the time. While those at home could speculate that soldiers probably did commit suicide in the trenches - Siegfried Sassoon's poem Suicide in the Trenches provides a good literary example - this stark look at the grim realities of trench warfare was not the view of the mainstream during the war years. It is this stigma that would almost certainly lead a commanding officer to simply record a suicide as "killed in action" or wastage. Nobody wants to get a letter saying their son, husband, or father took his own life.

These two factors aside, the soldier's chosen method of suicide would also make complicate your search. A suicidal soldier could simply decide to volunteer for every trench raid and take enormous risks or sneak over the top in the dead of night to disappear into No-Man's Land. With millions of mobilised soldiers in four years of conflict you can be sure a fair number ended their own lives through "indirect" methods.

As a side note, a study published in the June 2010 edition of the International Journal of Epidemiology found suicide rates in men and women actually decreased during the First World War.