過去完了の分詞構文

Having been sick for about a week, Lisa had lost some weight.

この分詞構文を元に戻すと、As she had been sick for about a week, Lisa had lost some weight.になると教わりました。でもこれだと、主節も副詞節も同じ時制なので、分詞構文にするなら
Being sick for about a week, Lisa had lost some weight. でいいのではないかと思ったのですが、どうなのでしょうか。