The evaluation of treatments in medicine is often made through the Kaplan-Meier Survival Curves. The curves evaluate the probability of survival of patients treated with some medicine in relation of a time series.
My question is if the time variable can be, for instance, be replaced by a dosage variable, e.g., the idea is to evaluate the probability of survival of tree alien species applying different tree-girdling depths, evaluating this variable instead of the time series.
As the tree ring depths are a surrogate for time, this should be valid. It would not matter if the time (depth) intervals are non uniform.
Dear James: your reasoning is interesting, nevertheless I´m not sure if applies in my case.
Perhaps another (medical) example: as researcher you might want to evaluate through a Kaplan-Meier curve the response of an antibiotic (a fix dosage) over a population of patients with sepsis. You´ll evaluate the probability at a time x of people getting cured (1) or staying sick (0) (I apologize if the example is not technically correct...)
My question would be if it is possible to apply the Kaplan-Meier curves for the following study: the evaluation of the probabilities of getting cured (1) or stay sick (0) in patients with different dosages of the antibiotic (shown in the x axis) in only one moment of the experiment.
What you would need is Cox survival analysis allowing for time varying co variates.
I dont think you could do this with KM (only fixed covariates possible)
I suppose you could display the relation between survival and dose at certain time points, depending on other covariates.
the attached papers are a good introduction.
Dear James. Very enlightning! I'll read the papers you recommend. Thank you very much
As far as I know, a survival study is a type of medical research that assesses the impact of an interventions, esp. a medicine or substance, or a risk factor on the mortality (or growth) of a patient group or living organisms over a long period of time, usually life-long. This cannot be achieved by normal clinical trials, e.g. RCT, or observational studies. It normally consists of three components, i.e. the Cox proportional model, KM plot and log rank test for hazard ratios. Therefore, the x axis of the KM curve always denotes time observed in the study. If you vary your substance with three doses (e.g. a, b and c), you can plot three separate KM curves or one KM curve with three lines to present the effect of three doses on the mortality or growth of one alien species over the time period. Then do the same for the two remaining species.
I agree with Win Winit-watjana. After do the calculation of KM to each doses, you can to use theLog rank to compare the KM curves.
We commenters, as I see it, have all understand the problem differently. My version is this.
The dose (= depth x) serves as a censoring variable. Meaning: if the infestation of a given tree survives this dose, we cannot know how much deeper we would have had to cut to eliminate the infestation. However if the infestation is cured by this dose, we would not only (1) know this - BUT WE ARE ALSO able to observe(2) what lower dose (depth < x) would have sufficed to cure it (in KM terms, an observed death before timex).
However, as observation (2) is probably impossible, KM cannot be drawn; and we are left wqith a simple dose-->binary response dataset.
Am I right?
Thank you Win, Poliana and Jørgen.
Indeed, Jørgen, the "dose" is a censored variable, however I believe I´m still not explaining myself very well with this case. The objective here is to eliminate the "patients" (because these are invasive alien species), we do not want to cure the trees, therefore the statistical analysis traits dead individuals as success ("0" in our case).
The other aspect is that the "dose" (in our case mean depth of cut over the tree) is not fixed because the treatment is freehand made, the trunk has irregularities and little differences in depth made with the chainsaw are sufficient to produce different effects.
Yes, in other words, good and bad outcomes are interchanged in a sense. But in the treatment of stomach cancer the good outcome also has two desriptions: the patient successfully survives, the unwanted species of cancer cells are eradicated.
Yes, the dose is freehand-made, but the important point is the INTENDED depth. Just as in cancer therapy RESEARCH, it is the INTENDED drug dose or radiation dose that counts. The actual drug dose is also uncertain because of individual variation in the absorption and metabolization of drugs (or variation in the patient's anatomy and cancer's location in radiotherapy research). You have to live with that fact - and base recommendations on INTENDED doses.
o.k.?
Dear Jørgen. In this case the intended dosis (cutting depth) is variable from tree to tree. It depends on the cambium depth and it cannot be seen unless the bark is removed. This is why we want to apply this modified analysis, apart from a sensibility-specificity analysis.
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