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A) What do you mean by "this situation?" If the issue is calculating sample size for a non-inferiority trial with a time-to-event outcome, I suggest chapter 7 of "Chow SC, Wang H and Shao J, 2007. Sample size calculations in clinical research. CRC press." For a software implementation, dunno what software you use, but if Stata, I suggest ...


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No. You will end up with biased results, in general. The Cox model gets its information from comparing the covariate for person who gets the event at a particular time with the covariates for people under follow-up who do not get the event at that time. If you drop censored people, the comparison group is restricted to those who did not get the event at that ...


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With a semi-parametric Cox model, the hazard function is discontinuous/discrete. At times between events, the hazard is zero: according to the data you have on hand, there is no risk of an event during those time intervals. At each event time, the hazard is determined from the case that had the event versus all the other cases at risk at that time. That's ...


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... will the effect and hazard ratio for the biomarker alone ... be the same in both models? Almost certainly not, particularly if the association of the biomarker with outcome differs depending on the type of treatment. Say that there is no association of the biomarker with outcome under treatment R but there is under treatment C, and you use treatment R ...


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The time-dependent vignette for the survival package recommends examining the shape of the plot of scaled Schoenfeld residuals over time and using a function that captures the shape of that relationship; see Section 4.2 of the vignette. That's why different situations might be handled best by different functional forms for the change over time. For this ...


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Your specific result has little to do with Cox regression itself but a lot to do with regression in general, when predictors are correlated. As @chl notes, in your data (and also in real life) smoking behavior and alcohol intake are highly correlated. A search on this site for "correlated predictor" just turned up 2500 hits. This is a very common ...


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As the salt exposure varies from year to year, it is best to represent it in some way as a time-dependent covariate. This vignette shows how to accomplish that in R, by using one row of data for each structure and period of time, with start and stop times and status indicated for each row. You should consider, based on your understanding of the subject ...


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The classic book by Terry Therneau and Patricia Grambsch, "Modeling Survival Data: Extending the Cox Model," devotes chapter 8 to modeling multiple events per subject. It covers recurrent events of the same type, ordered and unordered events, competing events, and multi-state models. If you can't get a copy, much of that material is also in a Mayo ...


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It turns out that Nelson-Aalen estimator is the estimator for recurrent events. More precisely: the estimator, initially developed by Nelson for survival analysis, was adapted to recurrent events by Aalen. My answer relies on this document.


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have to add the coefficient estimates from the Cox model in sch2. sch2 <- sresid %*% res.cox$var*ndead + rep(res.cox$coefficients, each = nrow(sresid)) would give the same thing as sch1.


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In a competing risks setting you observe only time to the first event. If you can observe types of events which don't prevent observation of the event of focal type, you can use a Cox model with a variable indicating whether the event you are not interested in was observed. The variable will be time-dependent, so the data should be transformed into a form (...


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First, with your experimental design for the underwater group you are estimating the cumulative survival from the beginning of the study up to the time of capture. That insight might give you a different, potentially simpler way to describe the survival of that group. You can, however, accommodate left censoring in survival models. The Surv() function in the ...


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The difference might come from the handling of tied survival times in the two approaches. The Kaplan-Meier estimator simply uses the number of events at each event time in its calculations. To accommodate the multiple covariates that need to be evaluated in general in a Cox model, there needs to be special handling of multiple events occurring at the same ...


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It is OK to stratify a continuous predictor to deal with violation of proportional hazards (PH). Harrell says on page 501 of the second edition of Regression Modeling Strategies: When a factor violates the PH assumption and a test of association is not needed, the factor can be adjusted for through stratification ... For continuous predictors, one may want ...


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