I have a question on the formulation used in the function `coxph`, in particular on the of the different ways of entering time of the observations in the `Surv` function.

My results are different if I enter the time when each observation started and stopped:

```
a. Surv (time =start_ind, time2 = stop_ind, event = death)

```

As opposed to only adding information of the interval during which the observation took place:

```
b. Surv (time =stop_ind - start_ind , event = death)

```

An example of the output for **a** is `(11.215,26.167+]` and for **b** `14.952`.

I initially thought that both approaches should give me the same outcome as I expected the interval to be used in **a**. However, as the results differ I understand that in **a** the model may also use the information on how the different events (deaths) are distributed along the study period. For instance, let’s say that in the first two years of the study I have a lot of death related to on given risk factor but after that this was not so important. I understand that the effect of such a risk factor will be less strong in **a** as it is constrained to one particular period.

In my analysis, I know that there is a lot of temporal variation in the risk factors because the origin of the data varies over time as well as some external factors. In this case I believe it is an important information to add both, *time* and *time2*.

Is my interpretation correct? If not, what is the difference between **a** and **b**?