Matt,
 Probably the easiest way to get 0.5*(E1 + E2) is

0.5*(E[-length(E)] + E[-1])

  The easiest way to get the delta Ts is using the function diff().
Dave

From:	Matthew Peng <matthewpeng80 <at> gmail.com>
To:	s-news <at> lists.biostat.wustl.edu
Date:	08/26/2011 04:58 PM
Subject:	[S] Area Under Curve
Sent by:	s-news-owner <at> lists.biostat.wustl.edu

Dear All,
I was wondering if someone could help me implement the following in S-Plus.
I need to calculate the AUC (Area Under Curve) using the trapezoidal method (0.5*(E1+E2)*T) and it goes as follows:

Time Exposure
1     10
2     20
3     30
4     40
5     50

I need to do the following in S-Plus:

ID Time  E Time1 E1 T E AUC (0.5*T*E)
1 1     10 0         0 1 10 5
1 2     20 1        10 1 30 15
1 3     30 2        20 1 50 25
1 4     40 3        30 1 70 35
1 5     50 4        40 1 90 45
2 1     10 0         0 1 10 5
2 2     20 1        10 1 30 15
2 3     30 2        20 1 50 25
2 4     40 3        30 1 70 35
2 5     50 4        40 1 90 45

where;
T=Time1-Time
E=E+E1

Mainly I am having trouble implementing the "lag" columns (Time1 and E1).

Appreciate any inputs I can get.

Best Regards,
Matt