Reviewer's report
Title: Flexible parametric modelling of cause-specific hazards to estimate cumulative
incidence functions
Version: 2 Date: 21 September 2012
Reviewer: Maja Pohar Perme
Reviewer's report:
This is a clearly written manuscript describing the usage of flexible parametric
models in the competing risks framework. The authors present the flexible
parametric model as an alternative to the Cox model that incorporates the timedependent effects with more ease. They advocate against using direct models for
probabilities and instead propose to model cumulative incidence functions via plug-in
models.
Comments:
1. The authors focus on clear presentation of the results that is accompanied with
easy to read graphs. Nevertheless, their advocating against the usage of direct
models for probabilities may be a bit strong - such models ask different questions
and different variables may prove to be important when talking about probabilities
than when considering cause-specific hazards.
The approach they describe therefore cannot replace direct modeling of probabilities
if such questions are of interest to the researcher, but simply offers an additional way
to present the results.
We take the reviewers point that in some situations you may want to model directly
on the cumulative incidence function. However, when all causes are of interest,
modelling directly does not restrict the sum of the probabilities to be in the range 0 to
1. We still believe that for a full understanding of how exposures impact on mortality,
in many situations both measures will be of interest. We have added an additional
paragraph to the discussion section to clarify these points.
2. The authors should perhaps focus more on what is new and specific in their work.
What are the particular issues when bringing in the flexible parametric models to the
competing risks setting as compared to their usual usage? Are there any particular
differences when calculating the cumulative incidence function as compared to
calculating it based on any other hazard based model?
There are not major differences to a standard parametric model. However, there are
very few real world examples where all of the competing events can be adequately
modelled using an exponential or Weibull model as these are not flexible enough to
model all the causes of interest. The flexible parametric model generally gives a
better fit. A sentence has been added to the start of the flexible parametric model
section to highlight this.
3. The flexible parametric models seem to have a particular advantage in large data
sets with sufficient event numbers, the authors should perhaps comment on this or
give some experience on the behaviour in smaller data sets. If one has a smaller
data set and cannot afford all the flexibility - can this importantly affect the predicted
cumulative incidence functions?
As with all models, when the data set is small there may not be sufficient information
to estimate the underlying hazard. However, we see the main advantages of the
flexible parametric model in population-based cohorts that have larger numbers but
also require the correct modelling of time-dependent effects. This has been added to
the discussion.
4. The authors should make a clearer distinction between describing and modelling
the data. In the introduction (page 4), they advocate against using non-parametric
estimates. I cannot agree with such a claim - non-parametric approaches are free
from any assumptions, that may, if not true, importantly affect the predictions made
using a model. Furthermore, the fact that such an estimate shall produce a step
function does not really seem a big disadvantage, a large step may simply indicate
that we have no information in that part of the curve. In any case, if the data set is
large enough to allow for a model that is so flexible that one no longer has to worry
about its assumptions, then the data set is large enough that even the step-wise
non-parametric estimates shall be practically smooth.
We agree that the non-parametric approach is good for describing the data or for
data exploration. There are many advantages for modelling in observational studies,
however, when there may be a number of covariates of interest that need to be
adjusted for. Yes some models do make assumptions, such as proportional hazards,
but again this is an advantage of the flexible parametric model as it is very flexible in
the assumptions is makes about the shape of the baseline hazard and it can also
easily incorporate time-dependent effects and thus relaxes the assumption of
proportional hazards. This has been made clearer in the text.
5. page 6, second paragraph: is the assumption of independent censoring really
needed? Would conditional independence not be enough?
We have clarified in the text that the assumption of independence is conditional on
covariates.
6. page 7, "it allows for simple interpretation ... under the proportional hazards
assumption". How can they be interpreted if the assumption is not true?
As with all models, when the proportional hazards assumption is not true then
interpretation of the hazard ratios becomes more complicated. This sentence has
been added to the text.
7. Results and discussion, 1st paragraph: Why must kernel smoothing be used for
the Cox model? Why can one not just use the Breslow formula and plug it in the
cumulative incidence function formula?
Thank you for highlighting this as it was unclear. Indeed the Breslow formula for the
cumulative baseline hazard can just be plugged into the cumulative incidence
function formula. However, if we require estimates of the baseline hazard then we
would need to obtain these through post-estimation techniques such as kernel
smoothing. This has been made clearer in the text.
Level of interest: An article of limited interest
Quality of written English: Acceptable
Statistical review: Yes, and I have assessed the statistics in my report.
Declaration of competing interests:
I declare that I have no competing interests