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If our unit of measurement is in days, will a person-period (person-day) dataset be equivalent to a more condensed data set?

For example below are the person-period data and condensed data where c1 and c2 and fixed covariates and c3 is time varying. Are the two cox models fit using these datasets equivalent?

ID  start  stop  c1  c2  c3
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 1      0     1   0   1   0
 1      1     4   0   1   0
 1      4     6   0   1   1
 1      6     7   0   1   1
 2      0     3   1   1   0
 2      3     5   1   1   1
 3      0     2   1   0   0
 3      2     5   1   0   0
 3      5     6   1   0   1


ID  start  stop  c1  c2  c3
---------------------------
 1      0     4   0   1   0
 1      4     4   0   1   1
 2      0     3   1   1   0
 2      3     5   1   1   1
 3      0     5   1   0   0
 3      5     6   1   0   1
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  • $\begingroup$ Is there an error in your stop time in the second row of the second table? Also, is there a possibility of multiple events for the same individual? $\endgroup$ – EdM Feb 2 '18 at 20:45
  • $\begingroup$ I gather the second row in the second table should be 1 4 6 0 1 1. $\endgroup$ – Benjamin Christoffersen Feb 2 '18 at 23:05
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Are the two cox models fit using these datasets equivalent?

The difference between the two table is that the first has redundant information while latter has not. The underlying data is the same so the resulting estimates are equivalent.

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