439:) symbol. Also, while the Newton-Raphson method is certainly applicable, many other numerical optimization routines might be applied. In particular, the BHHH optimization algorithm is applicable, making use of only the outer product of the score vectors in approximating the Hessian. Moreover, it doesn't seem very pedagogical to present the Cox Proportional Hazards model with the partial likelihood function without ever mentioning what the full likelihood for this model is (the full likelihood would need a parametric specification of the baseline function
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As of August 2022, this article was very focused on the mathematics of a very important tool in survival analysis¹. Most of the page was dedicated to the likelihood, which is never used by practitioners (instead the likelihood is implemented by software, and users use that software instead of working
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I just donated $ 35 to
Knowledge, then I went looking for an understandable explantation of what a "Cox proportional hazard model" is; unfortunately, I got sent to this entry, which has succeeded only in deepening my mystification. Please, somebody, take pity on those of us who need more fundamental
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I came to
Knowledge looking for an accessible information about the Cox proportional hazards model. What is here is completely un-understadable to an average reader. Please add common language or example explanation. There must be dozens of such readable explanations in various better statistical
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Once on a conference I heard such presentation of a mathematical equations about some economic phenomena, then the presenter asked “Are there any questions?” silence… then someone started to ask about the phenomena also used some A(t)+I etc…. The presenter kept silence one minute looked on his
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Assume I have observed a throw of a dice. I am absolutely sure, one hundred percent sure, about the outcome. But I also know this outcome only had a probability of 1 in 6. I have tried to express this in the phrase "The probability that this happened .." (Revision
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The main assumption is the first equal sign in the first equation of the section "The Cox model". Must this be stated explicitly like this? Another assumption, which holds quite general, is the treating of the subjects as statistically independent from each other.
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books. It is not a spirit of
Knowledge to include only a dry mathematical model, which seems to be rewritten from a student exercise book from a technical university, which author did not understand mathemetics very well himself. your Reader
326:, but it does not mention proportional hazards. I hope that this article will supplement that article; and I hope that it will be useful to users who search for proportional hazards, and fail to find even the survival analysis page.
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Agree. I've written some more friendly texts about the Cox model. I've started editing this page to make it less math dense. I imagine the median reader of this page is coming _not_ from a statistics background.
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I've taken the first steps to iteratively make this page better able to be understood for more people, especially students. Additional content to be included over the next year (fingers-crossed):
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understanding, and write an introduction to this subject that would be useful and graspable by anybody with the basic interest to look it up. That's how to make
Knowledge better; make it useful.
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The section describing how to deal with tied times used unclear notation. In particular, it is unknown what the parameters l and m stand for. Furthermore, what does |H| stand for?
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It seems that the sections "Multiple and mixed covariates" and "Calculating the baseline hazard" are empty. The sections should either be filled in or removed / moved to drafts.
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584:= 1 is 1, and not the Cox formula given. The only condition about t, is that some event happens for any subject at risk at this time and that indeed subject i is at risk (C
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Can we make this clearer by adding a phrasing such as: "the probability that the event occurred in subject i out of all the other subjects that survived till time t is"?
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I added a description of the summation in the denominator, paraphrased from Cox, "Partial likelihood" (Biometrika 1975), above his equation (5).
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deemphasizing the mathematics, including the likelihood work, by pushing it further down the article (Not that it isn't important, it's just
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It's not at all clear to me what "PH models" and "GLM models". Can someone familiar with these things clarify that sentence?
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of Cox (with specified baseline hazard). Also there is new work in time-dependent covariates. Updating.
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I also hope this page will be expanded by another editor, or merged with the survival analysis page. --
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with the likelihood). It's often a biology or medical students first encounter with regression, too.
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on
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as well but maximizing over the partial likelihood gives valid estimates of the parameters).
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formulas and said “Well…. Actually I used another model…” – very fruitful discussion …
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I've just expanded those initialisms, giving "proportional hazards models" and "
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The probability that the event occurs for subject i under the condition that Y
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The score "function" is called the score vector and it should use a nabla (
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Add an inuition for the probability that the event occurs in the subject i
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adding first-class software implementations, as this is how people will
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There should be a description of the assumptions needed for this model
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how do I check the PH assumptions? What to do if the assumptions fail?
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Missing frailty model which connects this to mixed-effects models
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focusing on interpretations, including common misinterpretations.
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93:and see a list of open tasks.
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