Re: Basis for Taguchi Loss Function 2

[Carl Betterton <carl.betterton@gmail.com>]

I have read the two very thoughtful and highly interesting posts by
Jonathan Siegel on the Taguchi Loss Function issue. As the poster of
the original question, I wnted to express my appreciation for
Jonathan's insight and examples. Every loss function is created by a
human, and so has values imbeded, whether we like it or not. I think
Jonathan shows the emphatic need to make the values explicit if we
can.

Sincerely,

Carl Betterton



On Mon, 25 Oct 2004 23:53:01 -0400, Jonathan Siegel <jmsiegel@umich.edu> wrote:
> Some further thoughts on non-Taguchi loss functions:
> 
> In recent years, I have been working as a statistician on drug trials,
> primarily in oncology. Many chemotherapies are essentially poisons which
> hopefully kill cancer cells faster than the rest of the body. Using them
> in the body is a risky undertaking. If one overshoots one may cause
> anything from nausea and diarrhea through death; if one undershoots, any
> residual cancer will grow exponentially. One of the first tasks in
> introducing a cancer drug into human therapy is to calculate an
> appropriate dose.
> 
> The traditional approach is to start at a very low dose and go up in
> fixed intervals until one reaches a dose which causes side effects that
> injure patients too severely. The modern approach involves
> Bayesian-influenced  methods based on loss functions, using mathematics
> somewhat similar to the pricing of stock options and derivatives. Both
> the financial and the medical applications involved address a similar
> concept of how high to go before one should stop.
> 
> A useful loss function in cancer research must incorporate the practical
> consequences of over- and under-dosing and must generally be guided by a
> theory of ethics.
> 
> One possible candidate for an ethical approach would be Hippocrates'
> dictum "first above all, do no harm." The dictum cannot be followed
> strictly, however, because when therapy is risky the only way to
> guarantee doing nothing harmful is to do nothing. One way one might
> generalize Hippocrates's principle, however, would be to implement the
> idea that doing too much is worse than doing too little. The idea
> results in an asymmetric loss function, where the overshooting side has
> a steeper curve than undershooting.
> 
> Hippocrates dictum, while a useful rule of thumb, does not turn out to
> apply all the time, and cancer therapy can sometimes present a
> counterexample. The practical consequences of undershooting and
> overshooting are very different. Cancer which is not killed off grows
> exponentially; side effects can sometimes be as little as mild nausea
> and diarrhea, although extreme nausea and diarrhea can be deadly.
> 
> Patients' perception of their losses varies. Some patients would rather
> be treated to an inch of their lives in the hope that the damage will be
> temporary and the therapy will work; others would rather deal with the
> cancer than anything more than modest side effects of the drugs. It is
> not necessarily for us to tell people what we think their losses should
> be.
> 
> Cancer research also creates an additional problem with estimating.
> People who enter the earliest phases of cancer research do so because
> they have tried and survived other, unsuccessful therapies. Such people
> are sometimes exceptionally tolerant of, and sometimes resistant to,
> chemotherapies. For this reason, a useful loss function may need to take
> into account and be somewhat insensitive to this tolerance. At the same
> time, some people may be especially sensitive to the therapy, and if
> this causes significant safety problems such people cannot be ignored.
> Only a percentage of the people who try a therapy ever respond to it.
> Therefore, one must consider the possible effect of the drug on outlying
> minorities when considering a loss function. It will not do to simply
> add or average everybody's. Some people's needs are more important than
> others. Considerations of especially sensitive and tolerant groups will
> generally result in an asymmetric loss function.
> 
> The surest approach would be an empirically-based loss function, a loss
> function specific to the therapy and patient population which attempts
> to assess the risks of overshooting and undershooting of the specific
> therapy in accordance with the desires and ethics of the specific
> population.
> 
> We generally have to suffice with something much less than such a
> method. It would take too long to gather the data needed. It is also
> hard to ask people what they would do in a way that is easily
> quantifiable and aggregable into a loss function. What one must do
> instead is a series of judgment calls, basing the loss function on past
> experience with the therapy and, especially at the beginning, therapies
> one believes to be similar.
> 
> These considerations should help explain how important it is to base
> loss functions on empirical criteria, evidence about practical
> consequences and people's value systems. There is simply no substitute
> for doing so. The fact that knowledge is imperfect, and that loss
> functions are often based on guesstimations and judgment calls, does not
> alter their empirical nature. Loss functions embody ones knowledge of
> the practical and ethical consequences of ones actions. For a
> statistician who follows the participant-observer paradigm, ones impact
> is of critical importance. Thinking about ones impact means that loss
> functions will often be asymmetrical. They will also often be
> discontinuous. Irreversible damage is on a different plane from
> reversible damage, and death is on a different plane altogether.
> 
> I have personally seen the results of trials which had to be stopped
> because the statistician devising the trial used an inappropriate loss
> function, one based, not on careful observation or sound judgment about
> the consequences of the experiment's actions, but on some sort of
> abstract mathematical properties which either make the calculations
> easier for the statistician, or were simply considered pretty. This can
> result in serious damage to patients if the experiment overshoots, or
> serious costs and possible cancellation of an effective product if the
> drug is tried at too low doses and fails to show efficacy.
> 
> Easing the statistician's calculation burden is, when all is said and
> done, simply not particularly important in the scheme of things.
> 
> Sincerely,
> 
> Jonathan Siegel
> jmsiegel@yahoo.com
> 
> 


-- 
Carl E. Betterton, P.E.