[R] multistate data w/out individual ID

[Emilio A. Laca]

Dear R help community,

I have a version of the data below generated by counting the number of individuals in each state every 2-3 time units for a series of cohorts (sets).
States are A, B, C, E and T.
It is known that the following transitions are possible A->B, B->C, C->E, B->T, C->T and E->T. 
The identity of the individuals in each set was not recorded.
I am interested in estimating the transition rates or probabilities and sojourn times as a function of covariates.
We assume that rates (probabilities) are independent of time.

Is there a package to estimate those quantities?
Is there a method to estimate those quantities?
Do you think a Bayesian approach integrating over all possible paths might work?
Everything I read about multi-state modeling packages seems to indicate that it is necessary to know the identity of individuals.

time,N,A,B,C,E,T,set,cov1,cov2
199,24,22,2,0,0,0,s1,1,4.65816667
201,24,22,2,0,0,0,s1,3,0.29922222
203,24,22,1,1,0,0,s1,10,9.570125
205,24,21,2,1,0,0,s1,6,9.94370139
207,24,20,3,1,0,0,s1,4,1.34693056
209,24,15,8,1,0,0,s1,2,1.20429167
212,24,14,9,1,0,0,s1,9,8.3008125
214,24,12,10,2,0,0,s1,15,9.14613194
216,24,10,11,3,0,0,s1,8,8.94250694
219,24,4,12,8,0,0,s1,5,0.97334722
221,24,3,12,9,0,0,s1,7,7.29372917
223,24,3,6,12,2,1,s1,17,1.28570139
225,24,1,7,8,5,3,s1,16,1.41599306
227,24,1,4,5,11,3,s1,18,7.07947222
229,24,1,3,2,15,3,s1,14,6.09359028
231,24,0,4,0,17,3,s1,12,4.70666667
233,24,0,4,0,17,3,s1,13,5.31577083
235,24,0,2,0,19,3,s1,11,4.62228472
199,24,19,5,0,0,0,s2,1,4.65816667
201,24,23,1,0,0,0,s2,3,0.29922222
203,24,22,2,0,0,0,s2,10,9.570125
205,24,22,2,0,0,0,s2,6,9.94370139
207,23,21,2,0,0,0,s2,4,1.34693056
209,23,19,3,1,0,0,s2,2,1.20429167
212,23,12,10,1,0,0,s2,9,8.3008125
214,23,10,12,1,0,0,s2,15,9.14613194
216,23,3,18,2,0,0,s2,8,8.94250694
219,23,0,16,7,0,0,s2,5,0.97334722
221,23,0,14,8,0,1,s2,7,7.29372917
223,23,0,5,14,2,2,s2,17,1.28570139
225,23,0,0,18,2,3,s2,16,1.41599306
227,23,0,2,13,2,6,s2,18,7.07947222
229,23,0,0,6,7,10,s2,14,6.09359028
231,23,0,0,3,8,12,s2,12,4.70666667
233,26,0,0,1,13,12,s2,13,5.31577083
235,28,0,0,0,16,12,s2,11,4.62228472
199,24,20,4,0,0,0,s3,1,4.65816667
201,24,22,2,0,0,0,s3,3,0.29922222
203,24,18,5,1,0,0,s3,10,9.570125
205,24,16,7,1,0,0,s3,6,9.94370139
207,24,13,10,1,0,0,s3,4,1.34693056
209,24,8,12,4,0,0,s3,2,1.20429167
212,24,5,14,5,0,0,s3,9,8.3008125
214,24,4,10,10,0,0,s3,15,9.14613194
216,24,2,9,12,1,0,s3,8,8.94250694
219,24,0,8,13,3,0,s3,5,0.97334722
221,24,2,6,5,11,0,s3,7,7.29372917
223,22,0,5,4,12,1,s3,17,1.28570139
225,24,1,3,1,17,2,s3,16,1.41599306
227,24,0,2,1,18,3,s3,18,7.07947222
229,25,0,2,0,20,3,s3,14,6.09359028
231,24,0,2,0,19,3,s3,12,4.70666667
233,24,0,1,1,19,3,s3,13,5.31577083
235,24,0,1,0,20,3,s3,11,4.62228472

Any comment will be appreciated.
Regards,

Emilio A. Laca, Professor                                                
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