Archive for October, 2011

Purpose of life

Nihilists often sound depressed about life having no meaning or purpose.

Religious folks often say that, without god, life would have no purpose (i.e., God saves them from the state of depression that some nihilists find themselves in).

What could purpose look like?

Suppose a conscious intelligent designer (let’s call it ‘god’) creates a conscious being and gives it a specific purpose.   God might say “I created you because I wanted to see if you can get to the end of this corn maze.”   Suppose this being was even created with a very strong desire to get through the maze.  This being was created with a purpose.

But is that really objective meaning?

You could ask the meta question, “what is the purpose of the purpose?”  I conjecture that in any possible world you can find a meta-purpose question for which the answer is ‘there is none.’  Thus, there is no possible world in which life could have objective purpose or meaning (at every meta-level).

Why be depressed that we don’t live in a world that couldn’t exist?

It seems strange to be disappointed because something didn’t happen that couldn’t happen.  It seems strange to be disappointed by something having no purpose that couldn’t have a purpose.

Humans have as much purpose as any living thing in any world could have.  There are better possible worlds for sure, but I cannot imagine one with more meaning or purpose.

Complaining that life has no purpose is like complaining that salt is composed primarily of sodium chloride.

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As discussed previously, participants in randomized trials are typically blinded to treatment assignment.  This differs from the non-trial setting, where blinding patients to treatment would be considered unethical.  It is unclear the extent to which uncertainty about treatment assignment affects outcomes.  Most randomized trials are not designed to deal with this issue.

Informed consent laws prevent researchers from lying to patients about treatment assignment.  However, we can, to a large extent, affect what people believe about treatment assignment via the allocation probability.   For example, if subjects are informed that there is a 50% chance they will receive a placebo, they should believe that they have about a 50% chance of receiving placebo.  Alternatively, if we tell them that 99.999% of subjects will receive the active drug, they should be pretty confident that they will receive the active drug.  In the latter example, we will obtain something pretty close to the counterfactual we want (Y0,100%) on 0.001% of subjects.   Of course, we would need an enormous sample size to observe many people like that.  Thus, there are the usual tradeoffs between bias and efficiency.

My suggestion is to randomize subjects to one of several arms that have different allocation probabilities.  Assuming the causal effects are a smooth function of the allocation probability, we could extrapolate to obtain estimates of E(Y1,100% -Y0,100%).

For details, see here, or email for reprint (nequal1@gmail.com).

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Consider the situation where there are two treatments, T=0 or 1.  Let the variable B denote the subject’s confidence (as a percentage) that they have been assigned treatment T=1.  Finally, let the potential outcome Yt,b be the outcome that would be observed if the subject was actually assigned treatment t and were b% confident that they were assigned T=1.

For example, Y1,100% is the outcome that would be observed if the subject was assigned treatment 1 and was sure that they were assigned treatment 1.  Similarly,   Y0,0% is the outcome that would be observed if the subject was assigned treatment 0 and was sure that they were not assigned treatment 1.

I would argue that the causal effect we are most often interested in is  Y1,100% -Y0,100%   That is, the potential outcome if the subject was assigned treatment 1 and was sure they were assigned treatment 1, minus the potential outcome if the subject was assigned treatment 0 but falsely believed they were assigned treatment 1.

To illustrate the idea, imagine that treatment 1 is an active drug and treatment 0 is a placebo.  We are interested in what would happen if the subject believed they were assigned the active drug and did receive the active drug, versus the case where they were assigned placebo but believe it was the active drug.  The difference in these potential outcomes should tell us the effect of the active drug that is not strictly due to knowing that they are taking an active drug.

Using this notation, we can also formally define the placebo effect as Y0,100% -Y0,0% (the difference in potential outcomes if given a placebo, but on the one hand believe it’s an active drug and on the other had know that it’s a placebo).

The problem is that informed consent laws prevent us from directly observing Y1,0% or  Y0,100%  (because it would require lying to subjects about what treatments they are given).  Typically in randomized trials, only one of the following two potential outcomes is observed for each subject: Y1,50% or Y0,50%.  It is unclear how similar a contrast such as  Y1,50% -Y0,50% will be to the contrast we want, Y1,100% -Y0,100%

Thus, most randomized trials with human subjects are not even designed to obtain the variables that we are most interested in.

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