How can the change in exposure be taken into account in the survival analysis?

We are trying to compare the impact of three bariatric surgery techniques (Surgery to treat obesity) on the occurrence of oesophageal cancer: gastric band, bypass and sleeve. We have data from national reimbursement databases. We have the dates on which the patients had their surgeries and the date on which the diagnosis was made is considered as the date of the event. We want to do a survival analysis (we have an average of 10 years of follow-up data on patients) to see if one surgical technique increases the risk of cancer compared to another. But the problem is that many patients do one surgical technique and if it doesn’t work after a few years they switch to another surgical technique. (For example, many patients switch from gastric banding to sleeve or bypass surgery). The question arises as to whether all patients who switch from one technique to another (i.e. change exposure) should be eliminated or whether there are statistical methods to deal with this problem? The first approach we thought of was to do as in intention to treat and leave the patient in his initial treatment group. What do you think about this?

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My initial reaction is that intent to treat will not answer the question of interest, and that you need to do an explicit analysis of time-dependent confounding. This requires recharacterization of patients at the time of switching, among other things. Miguel Hernan has written about this.