Try something along the lines of

With Member [Measures].[Thing Count YTD] As

Sum(YTD([Effective Date].[Year-Week].CurrentMember)

, [Measures].[Thing Count] )

SELECT

[Measures].[Thing Count YTD] ON 0,

[Effective Date].[Year-Week].[Week].[2013 Week 6] ON 1

FROM

[Cube]

Mack