update.3.6.19

README.md

@@ -71,7 +71,7 @@ MALF is supported by the Spanish National Institute of Health Carlos III Miguel
 
 #### Appendix
 
-In order to be able to consistently estimate the MOR, the data must satisfy the following assumptions [8]: i) Cancer treatment is independent of the potential mortality outcomes (Y(0), Y(1)) after conditioning on W. This assumption is often referred to as “conditional exchangeability” and one cannot test it using the observed data. It implies that (within the strata of W) the mortality risk under the potential treatment A=1, i.e. P(Y(1)=1|A=1,W) equals the one under treatment A=0, i.e. P(Y(1)=1|A=0,W). In other words: the risk of death for those treated would have been the same as for those untreated if untreated subjects had received, contrary to the fact, the treatment. This assumption requires that all confounders have been measured. ii) We also assume that within strata of W every patient had a nonzero probability of receiving either of the two treatment conditions, i.e. 0 <P(A=1|W)<1 (positivity). iii) We assume consistency, which states that we observe the potential outcome corresponding with the observed outcome, i.e. for any individual, Y = AY(1) + (1 – A)Y(0). Also, iv) in defining an individual’s counterfactual outcome as only a function of their own treatment, we assume non-interference, meaning that the counterfactual outcome of one subject was not influenced by the treatment of any other. If our estimate of the MOR is x (>1) then we can give, for example, an interpretation that says that the chances of one year mortality are x times higher if everyone had received dual treatment compared to if everyone had received single therapy.  
+In order to be able to consistently estimate the MOR, the data must satisfy the following assumptions [8]: i) Cancer treatment is independent of the potential mortality outcomes (Y(0), Y(1)) after conditioning on W. This assumption is often referred to as “conditional exchangeability” and one cannot test it using the observed data. It implies that (within the strata of W) the mortality risk under the potential treatment A=1, i.e. P(Y(1)=1|A=1,W) equals the one under treatment A=0, i.e. P(Y(1)=1|A=0,W). In other words: the risk of death for those treated would have been the same as for those untreated if untreated subjects had received, contrary to the fact, the treatment. This assumption requires that all confounders have been measured. ii) We also assume that within strata of W every patient had a nonzero probability of receiving either of the two treatment conditions, i.e. 0 <P(A=1|W)<1 (positivity). iii) We assume consistency, which states that the counterfactuals equal the observed data under assignment to the treatment actually taken, i.e. for any individual, Y = AY(1) + (1 – A)Y(0). Also, iv) in defining an individual’s counterfactual outcome as only a function of their own treatment, we assume non-interference, meaning that the counterfactual outcome of one subject was not influenced by the treatment of any other. If our estimate of the MOR is x (>1) then we can give, for example, an interpretation that says that the chances of one year mortality are x times higher if everyone had received dual treatment compared to if everyone had received single therapy.  
 
 #### Thank you  
 
@@ -91,7 +91,7 @@ Luque-Fernandez MA, Daniel Redondo Sanchez, Michael Schomaker (2018). Effect mod
 
 The article by Spiegelman and Zhou can be found [here](https://ajph.aphapublications.org/doi/full/10.2105/AJPH.2018.304530), their reply to our letter can be found [here](https://ajph.aphapublications.org/doi/full/10.2105/AJPH.2018.304917).
 
-Spiegelman and Zhou agree that noncollapsibility and effect modification can be a threat when using regression but argue that the examples given by us are unrealistic and not relevant in practice. Below we give a brief reply regarding these comments:
+Spiegelman and Zhou agree that noncollapsibility can be a threat when using regression but argue that the examples given by us are unrealistic and not relevant in practice. Below we give a brief reply regarding these comments:
 
 **Effect modification**
 
@@ -115,7 +115,7 @@ Our simulations contain four different cases. The probability of dying after one
 
 - "Although theoretically there is no question that the odds ratio is noncollapsible […] it is rarely the case that this matters in practice”
 
-The MOR and COR are typically not identical, no matter what example such as references [2,3]. In some applications the difference between them might be small, in some large, but we can not say beforehand how big. Using modern causal inference techniques avoids making assumptions about the difference between MOR and COR, which is a big advantage.  
+The MOR and COR are typically not identical, no matter what examples [2,3]. In some applications the difference between them might be small, in some large, but we can not say beforehand how big. Using modern causal inference techniques avoids making assumptions about the difference between MOR and COR, which is a big advantage.  
 
 In summary, we believe that the effort of using the G-formula (less than five lines of code in R or Stata) or doubly robust techniques one line of code after loading a library ([TMLE](https://cran.r-project.org/web/packages/tmle/index.html), [ELTMLE](https://github.com/migariane/eltmle)) is minimal, and one has the advantage of not making any (possibly unrealistic) assumptions about effect modification and collapsibility. In our opinion, it does not matter if the “bias” is small or big, a method that avoids a certain type of bias should be preferred over one that does not.