I was requested by a friend's mother to analyze her data from her past treatment. Since she got leukemia two years ago, she had been instutionlized for various periods and underwent various treatments. So I can download a data chart with time points and measurement after medicine A, B,C,D, E, etc. However the measurements were not on a level enable me to comparing them with one another via a simple graph, but more like heart rate and blood pressure which must be somewhat related, however having a different mean and standard deviation. With 5-6 medicine at hand and 2 years data available to me, I could not really analyze the data properly as I am a mathematican without proper training in statistics. But now I want to ask about this in general, because the friend had died from the leukemia, and I wish I could have been making some difference, despite the fact that there is absolutely no cure for her type.

The question I want to ask out of this personal experience is: to what extent can we help (real) patients via statistical methods? How can we manage to extract the hidden relation behind a not so large discrete set of data (300-600 data points, say) and have reasonable confidence this might mean something? Suppose we had all the programming power available and money issue is not really a concern, is there any real hope we can garner personal data to help a patient on an indivudal level? I was not a statistican, and I tried linear regression between the variables, which failed miserably as there seemed to be no obvious relationship between them. So I want to ask a professional's viewpoint on this.

(I had read at least 100+ leukemia papers to try find something that might help either biologically or via mathematical biology like population dynamics, but I failed)


I forgot to write that metamed (a medical start-up company) does offer individual tailored medical analysis, seems mostly based on patients' genetic data. They charge an extremely high price. However I do not know if their service is reliable. In my personal case, my friends' family decided against seeking their help. I do not really know if this would make any difference, for in her case all the therapeutic (experimental or well-established) methods has been exhausted. Since this thread may be of interest to others, I decided to include this 25c at here.

  • $\begingroup$ I've wanted to give an answer to this since it was posted but I find it difficult to formulate quite the response I want to give. I think some of the answers are far too pessimistic. Longitudinal statistics can be informative about one subject over time, allowing us (for example) to classify them into a specific group/subpopulation, or to identify characteristic patterns of growth or change in various measurements; such things could inform individually tailored treatment, for example. However, such approaches are completely in their infancy, both in medicine and in statistics. ... (ctd) $\endgroup$ – Glen_b Dec 30 '13 at 22:25
  • $\begingroup$ (ctd) ... not being medically trained, I'd need the researchers in medicine to help guide the statistical research (to help with what questions need to be answered, what information might be useful, and so on). The statistics might then later inform the direction of medical research, but at this early stage I think the medicine needs to drive the statistical methodology more than the other way around. $\endgroup$ – Glen_b Dec 30 '13 at 22:27

@user32240, first of all, I am sorry for your loss. It is quite difficult and painful to watch people we love fail in treatment or watch a friend's family member fail in treatment. I think we are a pattern seeking species and that trait is part of what helped us evolve. For example, we were able to recognize a pattern in weather that translated into knowing when to best protect ourselves from floods. Patients will seek a pattern and blame the event closest to the change. This is why the scientific method developed, to ensure that we weren't exposing patients to risky procedures simply due to anecdotal evidence.

On an individual basis, we might find someone's symptoms are exacerbated by a irritant or relieved by a treatment, but it is only after multiple exposure or withdrawal that we can comfortable arrive at a conclusion of association. It seems impossible to find anything meaningful with a sample size of 1 and no repeated exposures. Sometimes the best we can do is to not lose that data and combine it with the experience with other patients. Perhaps in the future someone will be helped.

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Never, NEVER, apply statistics on health matters of a single person. Not because of ethical reasons, but because the processes that drive our biology are still very poorly understood, especially in their interactions. They are so complex that the level of sophistication of our current statistical knowledge is a laugh compared to them. Of course medicine depends a lot on statistics but not to analyze a single person's health data, but in order to assess and evaluate this person's health data based on accumulated knowledge (including statistical results) from many-many patients...

I understand that this is more of a viewpoint rather than an answer, but I tried to offer also some arguments for my viewpoint. I love statistics, and I don't want to see them being implicated in murder.

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    $\begingroup$ Never hear of $n$ of 1 trials? $\endgroup$ – Frank Harrell Aug 19 '13 at 18:32
  • $\begingroup$ @Frank Harrell: as interesting as n of 1 trials are, they certainly do not prove much and clearly are not the type of data to use to prove the efficacy of drugs. That would be unscientific and unethical. $\endgroup$ – nico Aug 19 '13 at 21:11
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    $\begingroup$ That's your opinion and you are entitled to it. Many patients and scientists would be interested to learn that you cannot learn from multiple blinded trials using multiple regimens to see what works best for one patient. [Note this does not imply that data on groups of patients are not useful for the individual patient.] $\endgroup$ – Frank Harrell Aug 19 '13 at 22:44
  • $\begingroup$ @Glen_b I am rather new here, so I am perfectly willing to take advice from experienced members of the forum. So I will transform my answer to a comment - but my point of view stands: Science is power -and especially when it comes to matters of urgent health issues, its inappropriate use may be fatal. I admit "murder" was an inexact word - "involuntary manslaughter" I believe is the correct legal term (and I am not making fun here). $\endgroup$ – Alecos Papadopoulos Aug 19 '13 at 22:48
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    $\begingroup$ It seems to me this is an actual answer to the question "to what extent can we help (real) patients via statistical methods?" Because it (at present) is put forward as an opinion with little or no factual or objective support, I would expect it to get downvotes, but (as a moderator) I see no reason to convert it to a comment. $\endgroup$ – whuber Aug 20 '13 at 19:44

I would say it is well worth the time of a person with a personal stake to investigate data on the individual level. What can be learned by comparing averages is severely limited, as was noted by Poisson et al when "numerical" methods were first being applied to medicine nearly 200 years ago:

In the field of statistics, that is to say in the various attempts at numerical assessment of facts, the first task is to lose sight of the individual seen in isolation, to consider him only as a fraction of the species. He must be stripped of his individuality so as to eliminate anything accidental that this individuality might introduce into the issue in hand.

In applied medicine, on the contrary, the problem is always individual, facts to which a solution must be found only present themselves one by one; it is always the patient's individual personality that is in question, and in the end it is always a single man with all his idiosyncrasies that the physician must treat. For us, the masses are quite irrelevant to the issue.

Calculations of probability, in general, show that, all other things being equal, the truth or the laws that are to be determined are all the better approached if the observations used embrace a large number of facts or individuals at once. These laws, then, by the very manner in which they are derived, no longer have any individual character; therefore it is impossible to apply them to the individual chances of a single man, without exposing oneself to numerous errors.

Statistical research on conditions caused by calculi by Doctor Civiale. 1835. Int J Epidemiol. 2001 Dec;30(6):1246-9. Reprint of the classical report by Poisson, Dulong, Larrey, Double.

The thing to do with individual data is to look for patterns and theorize as to what mechanisms could be responsible the patterns. Group averages often hide the individual patterns and can lead to bad inference regarding the underlying mechanism under many circumstances.

Another issue with analyzing group level data is that individual differences are treated as noise, and if it is repeated measures then the intra-individual differences are also treated as noise. The idea that biological data consists of a deterministic signal + random noise is a rather unjustified assumption. It simplifies the analysis but also has caused many researchers to ignore studying the variability which is not necessarily "random".

One field that studies variability is cardiovascular physiology:

Heart Rate Variability Standards of Measurement, Physiological Interpretation, and Clinical Use Circulation. 1996; 93: 1043-1065 doi: 10.1161/​01.CIR.93.5.1043

Another is the study of motor systems:

Variability and Determinism in Motor Behavior Michael A. Riley and M. T. Turvey Journal of Motor Behavior, 2002, Vol. 34, No. 2, 99-125

So what you could do is plot the data for each parameter over time, and investigate the structure of the variability for patterns. Even just eyeballing it may work, you may also be able to find methods from the fields mentioned above.

One of your goals is probably to compare treatments. The best "n=1" experiments are to measure baseline, give treatment, take away treatment, then give treatment again. If the treatment is doing what you expect you should expect the effect to appear, disappear, then appear again. This is not possible in your case, but perhaps there are similarities and differences of the putative mechanisms behind the treatments that could play a similar role.

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