I hate double consonants.

First, my last name is waldmann (I guess you know that if you got here) and most people spell it Waldman. On the other hand, I think I would be about the 10th most prominent progressive political addict blogger named Waldman, but, as far as I know, fairly high ranking among Waldmann's.

Second in Italian double consonants are used. Italians claim they can hear the difference between single and double consonants (they even agree on which consonants are double and do so even before they learn how to read). I absolutely can't (like japanese with r and l say). So I can't spell in Italian either. This is serious, because Italian is so phonetic that it is very unusual for functionally literate people to be bad spellers.

Finally, I got scared reading soon after reading this post at Atrios about Lt. Gov. David Paterson of New York who might replace client 9 any time now. He is African American.

Then I looked at Atrios's post about a totally idiotic accusation that the Clinton campaign is as racist as D.W. Griffith. I highlighted the link
http://www.nytimes.com/2008/03/11/opinion/11patterson.html?_r=1&ref=opinion&oref=slogin
and saw the word Patterson. I was afraid of stupid conflict between the governor and junior senator of New York.

Then I clicked the link and found that it was just Orlando Patterson being Orlando Patterson (let's just say that among the Harvard faculty he is outstandingly dick-headed)

damnn I gott tto llearnn to readd.

I do prefer double letters to triple letters. Nothing against AAA. PPP is just a false hypothesis, but the triple letter in the headline of Atrios's post is too obscene for a family blot.

Personal chat with pj

updated

Pyjamas in bananas and I are trying to figure out what Kirsch et al did in Kirsch et al 2008. I have a thought on one of the deepest mysteries -- why are their confidence intervals on d so huge ?

notation: Change is the average change in the Hamilton scale of depression for patients who got an SSRI. Pchange is the average change for those who got a placebo. N is the number of patients who got ssri's (pn the number who got placebo).
d is change divided by the estimated standard deviation of the changes in the study so the t-statistic to test the hypothesis that the true expected change is zero is
d times the square root of n. pd same for placebo. Range is the difference between the upper and lower bounds of the 95% confidence interval for d. Prange same for pd.
rnrange = range times the square root of n, pnrprange prange times squar toot of pn.

some more regressions

reg rnrange change

Source | SS df MS Number of obs = 35
-------------+------------------------------ F( 1, 33) = 39.43
Model | 4.65045538 1 4.65045538 Prob > F = 0.0000
Residual | 3.89223357 33 .117946472 R-squared = 0.5444
-------------+------------------------------ Adj R-squared = 0.5306
Total | 8.54268895 34 .251255557 Root MSE = .34343

------------------------------------------------------------------------------
rnrange | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
change | .1834387 .0292136 6.28 0.000 .1240031 .2428743
_cons | 3.590184 .3110234 11.54 0.000 2.957402 4.222966
------------------------------------------------------------------------------


My isn't that a large t-statistic.

Also


. reg pnrprange pchange

Source | SS df MS Number of obs = 35
-------------+------------------------------ F( 1, 33) = 81.05
Model | 3.92402808 1 3.92402808 Prob > F = 0.0000
Residual | 1.59773718 33 .048416278 R-squared = 0.7106
-------------+------------------------------ Adj R-squared = 0.7019
Total | 5.52176525 34 .16240486 Root MSE = .22004

------------------------------------------------------------------------------
pnrprange | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
pchange | .1676368 .0186208 9.00 0.000 .1297524 .2055211
_cons | 3.652399 .1451204 25.17 0.000 3.357149 3.947648
------------------------------------------------------------------------------


Oh my that is even huger. Oh I guess I should control for the size of the sample as for small samples the t-distribution has tails much fatter than the normal. OK

. reg pnrprange pchange pn

Source | SS df MS Number of obs = 35
-------------+------------------------------ F( 2, 32) = 54.22
Model | 4.2636823 2 2.13184115 Prob > F = 0.0000
Residual | 1.25808295 32 .039315092 R-squared = 0.7722
-------------+------------------------------ Adj R-squared = 0.7579
Total | 5.52176525 34 .16240486 Root MSE = .19828

------------------------------------------------------------------------------
pnrprange | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
pchange | .1825164 .0175267 10.41 0.000 .1468158 .2182171
pn | -.0035427 .0012053 -2.94 0.006 -.0059978 -.0010876
_cons | 3.726652 .1331891 27.98 0.000 3.455355 3.99795
------------------------------------------------------------------------------


I stress the placebo results, because I know that the sample variance of the change of those who got placebo is not very correlated with pchange. Still pchange has a t-statistic which, to put it mildly is HUGE.

How about weighting by the number who received the placebo in the trial ?

. reg pnrprange pchange pn [pweight = pn]
(sum of wgt is 1.8410e+03)

Linear regression Number of obs = 35
F( 2, 32) = 87.57
Prob > F = 0.0000
R-squared = 0.7761
Root MSE = .17404

------------------------------------------------------------------------------
| Robust
pnrprange | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
pchange | .1833535 .01469 12.48 0.000 .1534309 .2132761
pn | -.0029935 .0004081 -7.33 0.000 -.0038248 -.0021622
_cons | 3.682386 .1179811 31.21 0.000 3.442067 3.922706
------------------------------------------------------------------------------


OK it is clear that larger average change implies a broader confidence interval of d.

Hmmm why ? If true d were zero, then d times root n would have a t-distribution and the confidence interval of d*n^0.5 would rapidly converge to 2*(1.96) = 3.92.
Clearly the confidence intervals are calculated using the non centered t-like distribution, that is calculated using estimated change not under the null of change = 0.

Hmm d = change/sdhat. as n goes to infinity change goes to the population mean (m) and sdhat goes to sd. Linearizing around m/sd gives
d - m/sd is approximately equal to (change-mean)/sd - m(sdhat-sd)/sd^2

If this is calculated substituting estimates for nuisance parameters it becomes
(change-mean)/sdhat - change(sdhat-sd)/sd^2.

Ohooo that explains it. There is a term proportional to change. Now if I knew the plim of n((sdhat-sd)/sd)^2 I could recalculate the intervals. Odd Gauss tells me it is 0.98 so I guess it is really 1.
gauss program
i = 0;
c=0;
niter = 100000;
do while i < niter;
i = i+1;
a = rndn(10000,1);
c = c+((a'a)^0.5-1)^2/10000;

endo;
c= c/niter;
c;
gauss output
0.98001977


so for large n ((sdhat-sd)/sd)n^0.5 is roughly a unit normal as is ((sdhat-sd)/sdhat)n^0.5. so ((sdhat-sd)/sdhat^2)n^0.5 converges to a normal with variance sd^(-2)

((change-mean)/sdhat)n^0.5 converges to a unit normal so (d-(m/sd) converges to a normal with variance 1 + (m/sd)^2

A very rough sample approximation would be a normal with variance 1+d^2
so this crude confidence interval would be
range = 3.92*(1+d^2)^0.5/n^0.5

OK back to stata



. gen guess = 3.92*(1+d^2)^0.5

. reg rnrange guess

Source | SS df MS Number of obs = 35
-------------+------------------------------ F( 1, 33) = 193.71
Model | 7.29918489 1 7.29918489 Prob > F = 0.0000
Residual | 1.24350406 33 .037681941 R-squared = 0.8544
-------------+------------------------------ Adj R-squared = 0.8500
Total | 8.54268895 34 .251255557 Root MSE = .19412

------------------------------------------------------------------------------
rnrange | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
guess | .6250211 .044908 13.92 0.000 .533655 .7163872
_cons | 1.534459 .2874405 5.34 0.000 .9496573 2.119261
------------------------------------------------------------------------------

. reg rnrange guess [pweight = n]
(sum of wgt is 3.2920e+03)

Linear regression Number of obs = 35
F( 1, 33) = 412.96
Prob > F = 0.0000
R-squared = 0.8869
Root MSE = .13623

------------------------------------------------------------------------------
| Robust
rnrange | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
guess | .6686736 .0329047 20.32 0.000 .6017285 .7356187
_cons | 1.12118 .2094582 5.35 0.000 .6950337 1.547325
------------------------------------------------------------------------------

. reg rnrange guess if n>100

Source | SS df MS Number of obs = 10
-------------+------------------------------ F( 1, 8) = 198.03
Model | .678477025 1 .678477025 Prob > F = 0.0000
Residual | .027409729 8 .003426216 R-squared = 0.9612
-------------+------------------------------ Adj R-squared = 0.9563
Total | .705886753 9 .078431861 Root MSE = .05853

------------------------------------------------------------------------------
rnrange | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
guess | .6539925 .0464743 14.07 0.000 .5468227 .7611624
_cons | 1.159944 .2917518 3.98 0.004 .4871627 1.832725
------------------------------------------------------------------------------

Well that is a large R squared isn't it. I'm using large n because my formula is asymptotic. However. the coefficient is not 1 at all is it ?

It looks as if the confidence interval isn't +/- 1.96 standard deviations. dividing rnrange by guess averaging and multiplying by 1.96 I get that the confidence interval is +/- 1.7 standard deviations of d. In other words it is a 90% interval not a 95% interval.

The fit isn't perfect, because I used a normal approximation and the range is larger than I guess for small samples as it should be. Maybe they did something like a t distribution with n-1 degrees of freedom plus a normal with variance d^2 or something.

Also the difference between n^2* the size of the interval and my guess isn't strictly a decreasing function of n. I guess this is due to rounding of d and the limits of the interval.

Now the square size of the confidence interval should *NOT* be used to calculate a precision weighted average of d. Such an average would obviously be biased down.

update:
Hmm there is no reason for the confidence interval to be centered around d given the squewy destribution of 1/sdhat. Is it.

duced is the upper limit - d and range is upper limit minus lower limit
reg duced range

Source | SS df MS Number of obs = 35
-------------+------------------------------ F( 1, 33) =55765.08
Model | 1.02594697 1 1.02594697 Prob > F = 0.0000
Residual | .000607123 33 .000018398 R-squared = 0.9994
-------------+------------------------------ Adj R-squared = 0.9994
Total | 1.02655409 34 .030192767 Root MSE = .00429

------------------------------------------------------------------------------
duced | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
range | .4999338 .0021171 236.15 0.000 .4956267 .504241
_cons | -.0006627 .0018018 -0.37 0.715 -.0043285 .003003
------------------------------------------------------------------------------


Now that is a really bit t-statistic. The confidence interval is symmetric.

My guess is that the finiteness of the sample is considered when calculating the 90% interval of (change-mean)/sdhat and not when calculating the 90% interval of change(sdhat-sd)/sd^2 (which is even further from normal for a given finite sample but not a distribution written into a software package so let's assume a squewed distribution is normal and insist on the non-normality of the t distribution.)

Thus new guess is the interval is d +/- ((t(.95,n-1))^2 + (1.645d)^2)^0.5
where 1.645= n(.95) and t(95,n-1) is the 95th percentile of the t with n-1 degrees of freedom. This makes no particular sense as it has nothing to do with the 90% interval of a t plus a normal.

And, in fact, my new guess works little better than my old guess.

Weibull analysis

As no one seems to have noticed, I am displaying google ads here. Google tries to guess what you might find interesting from the content of my posts. It is known that some key words imply valuable ads, that is ads such that the blogger gets a lot of money when they are clicked (mesothelioma is the most valuable word).

I just got a bit technical, and the great Google has punished me. My latest ad was
Weibull Handbook & Software Ask Dr. Bob - Free Shipping
BobAbernethy.com. Oh yeah lots of people are interested in Weibull distributions.

Beware the Ides of March
Total confusion and political prostitution ahead.

Italian polls
Interested in the day after the Italian election, that is, the Ides of March 2741 years after the foundation of Rome (3/15/08 for uncultured Americans that is 15/2/08 for uncultured Europeans) ? I have found a site which collects polls

The background is that the last election was a virtual tie marginally won by the center left. Romano Prodi became prime minister for the second time. The 2nd Prodi government was brought down when Clement Mastella a prominent unprincipled turncoat traitor and epitome of Italian politics withdrew his support for Prodi because the center left did not denounce investigating magistrates for investigating his wife's corruption firmly enough. I thought he was slimy but sly. However, now he is not even running for parliament. It seems he decided to betray Prodi before reaching and agreement with Berlusconi (the sacker of Rome). Berlusconi (who had been betrayed by Mastella the last time a Prodi government was falling) decided he was more trouble than he is worth. This is the first time Berlusconi has done something I like.

To read the polls one must understand the electoral law. There are two houses of parliament the camera dei deputati (camer) and the Senato. To survive a government must maintain the confidence of both. The Camera is elected with proportional representation plus the "coalition" with the most votes gets 30 seats. Last time the center left coalition beat the center right coalition by 0.07 % and gained a solid majority in the Camera. To count a coalition must be declared before the election.
Only people over 25 can vote for Senators. They are assigned pretty much strictly proportionally. Prodi lost the confidence of the Senato.

The Senato has two very odd sets of senators. There are 6 senators elected by "Italians abroad". This does *not* mean Italian citizens who live abroad. It means people with Italian ancestors and Italian last names. Officially people with unbroken male line of descent from an Italian citizen. Last election the center left won the North American constituency only because of Canadians. This counts (Prodi only won a majority in the Senato because the center left won 4 out of 6 seats representing Italians abroad). Finally there are the senators for life. They include former Presidents of the Republic and a few eminent Italians named life senator by the President of the Republic. They give the Senato a tiny touch of the House of Lords. Out of respect for Democracy, the opposition tends to say life senators don't count when their votes are critical for the survival of a government. Out of respect for the constitution, the government accepts their votes.

Boy that was boring. Anyway it means there are two issues 1) which coalition gets the most votes and 2) which agglomeration of coalitions parties and life senators makes up a majority in the Senate.

There are two large coalitions -- the center right (pdl+lega) owned by Berlusconi and the center left (partito democratico + Antonio di Pietro). There are also two small coalitions which are critical for control of the senate. One is the Rainbow left (roughly communists + greens) who refuse to be counted with the center left coalition and thus guarantee that Berlusconi will win the plurality prize. The other is the UDC or central centrists or Resurrected Christian Democrats.

Italy still has fairly strong party loyalty (which is odd given how parties fuse and split and change names all the time). Thus polls are very stable. It is clear that the center right coalition will get the plurality of votes and the prize. They have the support of about 43% of people who respond to pollsters. The center left has about 36.5% and the objectively pro Berlusconi left deviationists have about 8 or 8.5%. That is, it would be waaaaay to close to call if the "antagonistic" left wasn't a bunch of egomaniac idiots (Berlusconi won the election of 2001 and was prime minister for 5 years, smashing the old record, because the still communists were being teste di ca**i then too).

Then the central center or UDC has about 7%. In the senate the UDC will hold the balance of power (be the "pointer of the balance"). They may go back with Berlusconi , but I think that being a junior partner to Berlusconi has been a very humiliating experience. More likely they will sell themselves to the highest bidder.

I don't like to make political predictions, but I think it is clear that after the election Italian politics will be dominated by total confusion and sordid bordellos. That is, in Italian prevedo Casini.

Caveat Lector

For the past 2 days I have been interested in meta-analysis, that is, mostly criticizing the meta-analysis of trials of modern anti depressants (SSRI's).
I have attempted some calculations based on the arguments in the post below and the one after the one after that. It is very possible that I have not understood the paper which I am criticizing as the description of statistical methods is brief and the technical terms used by psychologists when talking about statistics are different from the technical terms used by economists when talking about statistics.

Also many of my calculations were performed with a spreadsheet (good for making errors), I typed in the raw data from a *.gif file (ditto) and may have made anynumber of booboos including conceptual errors. I consider this blog post like a conversation in the corridor and not like a draft paper, working paper or heaven forfend journal submission.

OK that said, I have the impression that I was right.

My concern in the post below is that precision* weighted means of means may be biased and inconsistent if the data are drawn from a distribution such that the sample variance is higher when the sample mean is higher.

The example I gave was estimating the distribution of a variable which takes values 0 or 1, that is estimating the probability that the variable is equal to one. If there are many samples drawn from the same distribution, the best asymptotically normal estimate of the probability is the overall frequency. This is equal to the weighted average of the estimates of the probability for each subsample weighted by the sample size. It is not equal to the average of the estimates of the probability for each subsample each weighted by the inverse of the estimated variance of that estimate of the probability. The inverse of the estimated variance of an estimate is called the precision. For a frequency estimate with a sample size of Ni it is Ni/(pe*(1-pe)) where pe is the frequency of ones in the sample (that is the sample freequency).
This puts lower weight on estimates close to 0.5. In particular, if the true probability is less than 0.5, the precision weighted mean estimate of the probability will be biased down.

I think this is relevant to estimating the effects of anti-depressants, because, IIRC the general view of clinicians is that a minority of patients experience a dramatic benefit from anti-depressants and the majority much less benefit (or maybe zero benefit).

It is important to stress two things. First it is not an unusual property of the binary distribution that estimated means and variances are not independent. Rather it is an extraordinary feature of the normal distribution that estimates of the mean and estimates of the variance are independent. To have confidence that sample means and sample variances are independent, we must be confident that the distribution is one of the few such that this is the case.

Second, it is not sufficient that freequencies, that is estimates of the probability, are normally distributed. This is almost exactly the case for freequencies calculated with more than 30 observations. However, the problem depends on the distribution from which each individual observation is drawn.


Now I am attempting to see whether this theoretical problem really is a problem analyzing the data collected by

Irving Kirsch, Brett J. Deacon, Tania B. Huedo-Medina, Alan Scoboria, Thomas J. Moore, Blair T. Johnson in table 1 of "Initial Severity and Antidepressant Benefits: A Meta-Analysis of Data Submitted to the Food and Drug Administration"

I should point out that Kirsch et al did not use a precision weighted mean. They decided that one study had an absurdly low sample variance and imposed a higher value.

column 3 of table 1 reports the average improvement in the Hamilton rating scale of depression (HRSD) for 35 trials of SSRI's submitted to the FDA (change). Column 4 reports "d" which (if I understand correctly) is the average improvement divided by the sample standard deviation of the improvement. The the estimate of the standard deviation (sd) of the effect is the ratio of column 3 divided by column 4. If I am confused about the definition of d, the rest of this post is worthless.

is it true that studies with a higher mean improvement have a higher standard deviation of improvements ? To see first I ran an OLS regression of sd . This is embarrassing as I am stressing that not all variables are normal and, in this case sd definitely isn't normally distributed. Still it is somewhat interesting that the coefficient is very slightly over 0.25 with an estimated standard error of a tiny bit less less than 0.1. The ratio definitely does not have a t-distribution, which is a pity, because STATA naively thinks that the null that the true coefficient is zero is rejected at the 2% level. When the estimated variance of the effect is regressed on change the t-like statistic (which does not have a t-distribution) is 2.25.

In practice, the means are not weighted by the inverse of the estimated variance but rather by the inverse of the estimated variance of the mean, that is they are weighted by the sample size divided by the estimated variance. Thus it makes more sense to regress the estimated variance on the average improvement (change) weighting by the number of observations. This gives a t-ratio of 5.2 and that is overwhelming.

When sd is regressed on change using sample sizes as weights (pweights for STATA and I checked by hand STATA does what I think it does with pweights) I get a coefficient of over 0.38 and a standard error of under 0.079 and a ratio of 4.95. This is huge.

Now I ask is the precision weighted mean improvement significantly lower than the sample size weighted estimated mean ? Here the sample size weighted estimate is unbiased and consistent if each study is unbiased (the standard hypothesis in meta analysis). It is also consistent if a finite number of studies are no good at all (for example fraudulent). That is, as the number of valid studies goes to infinity, the sample size weighted mean result will converge to the true expected value even if there is a fixed number of worthless totally wrong or fraudulent studies.

The same is not necessarily true of the precision weighted average effect. It is however, a more precise (or efficient) estimate of the mean. This means that I can perform Wu-Hausman test. If both estimates are unbiased, the expected difference of the estimates is zero and the variance of the difference in the estimates is equal to the estimated variance of the sample size weighted average minus the variance of the efficient precision weighted average. This means that the square of the difference in the estimates divided by the difference of the variances should have a chi squared(1) distribution.

I calculated the averages in excel (warning). I get the sample size weighted average is 10.04 and the precision weighted average is 9.59. My estimate of the variance of the sample size weighted average is 0.01947 and my estimate of the variance of the precision weighted average is 0.01799 so the difference is 0.001485. This gives a Wu-Hausman test statistic of 0.45^2/0.001485) = 133.1 which is, to use a technical term hubongous.

I don't like the Wu-Hausman test which is unreliable in small samples. For my purposes the sample size is the sum of the sample sizes minus 35 parameter estimates or 3257 which is rather large. However, I feel more comfortable using a modified Wu-Hausman test which has low power but definitely no size distortion. Personally, I prefer to divide by the larger of the two estimated variances. That gives a modified statistic of 10.15 which is still overwhelmingly significant.

The precision weighted mean estimate of the effect of SSRI's on the HRSD is definitely biased down (unless I made a mistake).

Now the interest in the studies is not the average change with SSRI's but the difference between that average and the average change with a placebo.

For the placebo parts of the studies, the regression coefficient of the estimated standard deviation (psd) on the average change (pchange) is less than 0.0131 with a t-ratio of 0.13. The regression of the estimated variance on pchange has coefficient
less than 0.0344 with t-ratio 0.02. The sample size weighted regression of psd on pchange has coefficient -0.0251 and t-ratio -0.21. The sample size weighted regression of the estimated variance on pchange has coefficient -0.810 and t-ratio -0.40

There is essentially no evidence of a positive correlation of mean change and sample variance for depressed people who received the placebo.

I almost dare predict that the Wu-Hausman test might not reject the null that the precision weighted mean placebo effect is unbiased. I am now off to calculate (see how long it takes me).

update: I have now calculated the Wu-Hausman statistic for the precision weighted mean change in the placebo treated patients and the sample size weighted change in the Placebo treated patients. The precision weighted mean change is 7.81 the sample size weighte mean is 7.852 and the Wu-Hausman statistic is 0.649. The expected value of the statistic under the null is 1. There is no evidence that the precision weighted mean of the change HRSD in patients receiving the Placebo is biased.

update 2: a robustness check. One experiment was quite unlike the others. It was experiment 62 mild, reported in row 4 of table 1. It is unique in thet the patients had relatively mild depression (average inititial HRSD of 17). The reduction of the HRSD score of patients who received Prozac was very low compared to the reduction of treated patients in most studies. The sample variance of the change in HTSD was also very low. This single totally atypical study is responsible for a considerable part of the difference between the precision weighted average aand the sample size weighted average change of HRSD of patients who received SSRI's.

As a robustness check, I replaced the estimated variance from the study with the sample size weighted average estimated variance of 64.79. Naturally, this has no effect on the sample size weighted mean. The precision weighted mean rises to 9.906 and the Wu-Hausman test statistic declines to 20.57 which is still overwhelmingly significant.

Kirsch et al wrote " One trial reported SDcs for its drug and placebo groups that were less than 25% the size of the other trials; because preliminary analyses also revealed that this trial was an outlier, these two standard deviations were treated as missing and imputed." They don't write which trial, but the description fits 62 mild. Interestingly, my results using the suspect SDcs are very similar to those reported by Kirsch et al with a difference of precision weighted means drug minus placebo of 1.78, while if I impute using the average variance (SDcs squared) I get a difference of over 2.09. Kirsch et al imputing using (among other variables) the baseline HRSD and not a simple mean. I guess that their imputed value was also fairly small, because the initial HRSD was low.

update 3: More meta-analysis.

A simple OLS regression across studies of the average change in HRSD of patients who received placebo on the average change in HRSD of patients who received SSRI's gives a large coefficient 0.288 with a t-ratio of 1.72 significant at the 10% level (5 % one tailed). when the regression is weighted by the precision of the estimates of the change for those who received the placebo (number who received the placebo divided by estimated variance) the coefficient rises to over 4.19 with a t-ratio of 5.1. The logic of this weighting is that the placebo samples are generally smaller than the SSRI samples so the precision of the change for those who received the placebo is lower.

This suggests that there are experiment effects on the change in HRSD. They may be due to different patient populations, in particular different baseline HRSD. They may also be due to the fact that the Hamilton test is partly subjective and might be applied differently by different teams of psychologists. Unfortunately such differences affect the estimated difference between SSRI and Placebo as different fractions of patients received placebos in different trials.

To avoid this, the analysis can be conducted by first , for each trial, taking the difference in the change of HRSD for patients receiving SSRI and patients receiving the placebo and then averaging this difference across trials.

The weights for such an average can be determined by analogy with sample size weights. Sample size weights would give an efficient estimate of the overall difference in changes of HRSD if the true variance of the changes was the same for all different trials. If it is assumed also to be the same for placebo and SSRI parts of trials, the resulting weights are 1/((1/Ndi)+(1/Npi)) where Ndi is the number of patients receiving SSRI in trial i and Npi is the number of patients receiving placebo in trial i. These weights are correct because the variance of a difference of two independent variables is the sum of the variances.

This approach will give an unbiased estimate of the difference of effects if each study is unbiased, because the weights are exogenous.

This approach gives an estimate of the additional benefit of SSRI's over placebos of over 2.65. excluding the one study with mildly depressed patients (protocol 62 mild) causes the estimate to increase to 2.77.

And just to leave no doubt that I am fiddling till I get the estimate over 3, I note that if only the 27 studies with an average baseline HRSD over 24 are included the estimate increases to over 3.31.

But hey just for fun and I said I was doing it and this is my blog.

pulled back from comments. PJ himself writes

Hi, interesting stuff, but I'm not sure if you can explain the findings of Kirsch et al by this alone - essentially you are pointing out fairly subtle differences in detected effect sizes, but Kirsch et al find an effect size that is substantially different from you, or me.

As I discuss here, I'm not convinced that Kirsch et al found their effect size measure 'd' by dividing the change score by the SD of the change, even though it does indeed look like that is what they are claiming in the paper - which is why I derived my estimates for the SD of the change from the confidence intervals.

What is interesting is that you find pretty similar effect sizes to me, and I just can't see how Kirsch et al arrived at their figure of a change of 1.8 in the HRSD - just looking at the numbers for the studies I can't see how you could combine them together to reach their figure, and look at the scatter plot and regression here, how are they getting an estimated effect size that seems so far outside the region of the data?

I'd also point out that their measure 'd', is a pretty odd measure of effect size, if it is the HRSD change/change SD that is a very strange measure indeed, but even a properly formed SMD (dividing by estimates of the SD of the HRSD score, not the change in the HRSD score) makes it difficult to assign any meaning to subtracting the drug 'd' from the placebo 'd' to come up with an effect size, and it is difficult to compare such a measure with the Cohen d, which is a true SMD.

But even then, a cursory look at the relationship between the difference between 'd's and the difference between change scores still suggests an effect size much larger than 1.8 HRSD points, indeed more like the 2.7 points that every other method of analysis seems to suggest.

In actual fact I find that calculating a true meta-analytic SMD (where it is the difference in change scores that is normalised to the SDs of the change scores) that can be compared with a Cohen d showed quite a small effect size (.25) so I don't know why, if they sought to deliberately underestimate the 'clinical efficacy' of anti-depressants, they didn't just compare that to NICE's Cohen d > .5 criterion.

You'd think, in these days of online open access journals they'd have given a bit more detail and supplemental material so us obsessive types could tell exactly what it was they did - and then slag it off!
# posted by Blogger pj : 2:40 PM

The Simplest Meta-Analysis Problem

This is relevant to understanding the fascinating work of pyjamas in bananas


Let us say we are interested in finding the probability p that outcome A occurs when we perform experiment B. The natural approach is to perform experiment B N times and calculate the frequency of A occurring pe (pe for probability estimate which is equal to the mean of a variable which is 1 if A happens and zero otherwise). This approach has much going for it. The estimate is consistent by definition, since the limit of this estimate as N goes to infinity is Fisher's definition of probability. Also it is unbiased (for any sample size the expected value of the estimate is equal to the true probability) and is the maximum likelihood estimate so it is the best asymptotically normal estimate of the probability.

Now let us say that various groups indexed by i have done experiment B and group i has done it Ni times. Note I have assumed that each have done identical experiments, so I assume that group 10 did not just make up the data (it happens). Further I explicitly assume that they perform B identically as described in the protocol with no slips (that is I personally am not working in any of the groups) and measure whether A happened the same way.

What do we do with all the data ? Well given my assumptions we already know. The best estimate of p is the total number of cases in which A occurred divided by the total number of times which B was performed. That is, we should just pool the data as if they came from one big experiment.

Now what if they don't report all of their raw data but just pe (the frequency) and Ni the sample size ? No problem. The best estimate of p given all of the data is equal to the weighted average of the frequencies (pei) weighted by the sample sizes.

Now what if they don't report the sample sizes (never happens but what if) but do report estimated standard errors esei of their estimate pei of p ? No problem. The square of the estimated standard error is pei(1-pei)/N so we weight by
1) weighti = 1/(esei^2pei(1-pei)).

This is all obvious so far. However, it appears that there can be a temptation to do something wrong. The misleading anology is as follows. What should we do if we have a bunch of parameter estimates and each has a KNOWN standard deviation sei ? Here the best overall estimate of the parameter is the weighted average weighted by 1/sei^2. 1/sei^2 is called the precision so this is a precision weighted average.

One might make a mistake and decide to pretend that the estimated standard errors are exact so esei = sei. This would be a mistake, since, by assumption, in the example sei is the same for all i and equal to the square root of p(1-p)/N. In fact, it would be a very bad mistake. The average weighted by estimated precision will give a biased estimate of p unless p = 0.5. Futhermore, if the number of experiments performed by each group i (Ni) is drawn from a stationary distribution, the probability limit of the overall estimate of p as the number of groups goes to infinity is not p, that is the overall estimate is inconsistent.

How do I know this ? Well I know that the sample size weighted average is an unbiased consistent asymptotically efficient estimate of p and I can compare the expected values of this correct overall estimate to the expected value of the weighted average with weights equal to the estimated precision. Assume that Ni = N for each group, that is, that each group performs the experiment the same number of times (please this is just to make things easier to type). Then we see that the best unbiased asymptotically normal estimate of p is the unweighted average of pei. The weighted average with weights based on estimated precision will put less weight on experiments where pei is close to 0.5. If p is less than 0.5, this means that, on average, experiments with high pei have lower weight than experiments with high pei. This means that, the expected value of the (estimated precision) weighted average will be lower than p equals the expected value of the unweighted average. This is true for any number of groups and therefore true asymptotically too.

So is this mistake even possible ? It sure is. Is it not possible that a data analyst will assume it is OK to act as if an estimate is exactly true even when knowing it isn't, but there is at least one case in which the (estimated precision) weighted average is the best over all estimate of a parameter. The problem is that most meta-analysts consider only the second simplest problem -- estimating the mean of a variable which is normally distributed. In this case, the estimated mean and the estimated standard deviation are independent. Therefore weighting by the inverse of the estimated standard deviation can not bias the overall mean.

Even in the case of pooling estimates of the mean of a normally distributed variable, the sample size weighted mean of means is the most efficient estimate if we are sure that each group's measurement is drawn from an identical distribution so we know that the true standard errors of their estimated means are one over the square root of the sample size. However, the (estimated precision) weighted mean is a better estimate if the variance of the normals observed by different groups are different, as it would be if some were better at measuring than others.

There is no general theory in statistics that says that estimated means and estiamated standard deviations are, in general or usually, independent. That is a particular property of estimates of the parameters of the normal distribution. However applied statistics is unfortunately often based on the assumption that all random variables are normally distributed. The binary distribution of the example above is just one of many cases in which estimated means are not independent of estimated standard deviations even if every group is reported data drawn from the same distribution.

OK so what to do about real world problems ? I think it is unwise to assume that estimated means and estimated standard deviations are independent -- not all variables are normally distributed. It is also unwise to assume that all experimental groups produce data of identical quality. My preferred solution is to calculated a sample size weighted average and give a standard error for that overall average which is robust to variable quality of measurements by different groups (for example assuming that esei = sei when calculating the standard error of the overall sample size weighted average).

Such an estimate is unbiased if each experimental result is unbiased (pretty much a necessary assumption for meta analysis) and consistent in the number of groups. It is robust to the incompetence of one group (although not to scientific fraud).

Also, the estimated precision weighted average is efficient unbiased and consistent if the estimated precision is independent of the estimated mean. The sample size weighted average is not efficient but it is unbiased and consistent even if the estimated precision is not independent of the estimated mean. This means that a Wu-Hausman test can be used to test the null that the (estimated precision) weighted mean is unbiased.

OK so why am I thinking about this ? It is related to meta-analysis of the effects of anti-depressants. Different results are obtained by using different weights when averaging across studies. The differences are large compared to the estimated standard errors of the overall averages. Why might the effect of an anti-depressant be like a binary ? Let's say event A is the patient recovers. Sad to say, this happens less than half of the time during the test period even with modern anti-depressants (also it often happens with just a placebo). A study in which more patients recovered will have a larger variance of the patient outcome 1 = recovery 0 = still depressed, even if the results of all studies are drawn from the same distribution. Using the variance of patient outcomes as well as the sample size to calculate estimated standard deviations of the effect will bias the estimated precision weighted average effect away from curing half of the patients which means (I think) towards zero.

Of course the data are not 1 no longer depressed and 0 still depressed. Instead they are scores on a scale. However, I honestly believe that, in practice, the response to anti depressants is bimodal with chance of being roughly cured less than 50% and chance of no effect of the antidepressant more than 50%. In any case, it is easy to test the hypothesis that estimated means and estimated standard deviations are independent and it is easy to test the hypothesis that the expected value of the sample size weighted mean and the estimated precision weighted mean are the same.
There is, I think, a very strong presumption that, if one of the two is biased, it is the (estimated precision) weighted mean.

And it Couldn't have happened to a nicer guy

Iraq's elusive Shiite cleric Moqtada Sadr has decided to drop out of politics for the time being because his disillusionment with the political scene in Iraq has left him sick and anxious, he said in an unusually personal letter to his followers released Friday.

The best news I've heard from Iraq in months (since October).

Come on Moqtada, you've been working too hard. You deserve a break. A nice longgg vacation.

Via tpm.

Prozac Fan Talks Back
1.8>0.

Update 2: DeLongians and missing links If you are still clicking links and getting here, don't stop clicking. The really good stuff is just one click away at Pyjamas in Bananas.

I am going to comment on a controversy from February 25, the stone age in Blogtime. I had a thought (which turns out to have been wrong) and it got me to click links in a post by Kevin always click the link Drum.

I get emotional and run on. My points, if any, are that the study which is described as showing that SSRI's (modern anti depressants) don't work, in fact finds a positive effect of SSRI's on measured depression which is overwhelmingly statistically significant. Journalists, including Sarah Boseley, health editor
# The Guardian made claims about the results of this study which are absolutely totally false. The authors of the study put great evidence on a standard for clinical significance, which seems to me to be very high and very poorly conceived.

Like Kevin Drum, I find it hard to believe this claim In an article by Sarah Boseley in "The Guardian" "The study examined all available data on the drugs, including results from clinical trials that the manufacturers chose not to publish at the time. The trials compared the effect on patients taking the drugs with those given a placebo or sugar pill.

When all the data was pulled together, it appeared that patients had improved - but those on placebo improved just as much as those on the drugs."

Drum notes extensive anecdotal evidence. I am much more strongly convinced based on my personal experience (I should note that according to my "don't do this at home kids" application of the Hamilton Rating Scale to my recollection of my state when I first took Prozac, I was severely depressed and the study finds a larger difference between drug an placebo for the severely depressed). Also, Boseley's claim about the study she claims to be summarizing is absolutely totally false.

Interestingly, I got to the guardian article clicking the following link in Drum's post: "Compared to a placebo, they improved patients' scores on the most widely used depression scale by only 1.8 points:" Clearly Sarah Boseley, health editor
# The Guardian is totally dishonesnt, totally innumerate or both. 1.8>0. Patients on Placebo did not improve just as much as patients on SSRI's. Furthermore, this isn't even a case of treating a statistically insignificant difference from as evidence (or proof) that the true value is zero.
In fact, pooling the studies "Irving Kirsch, Brett J. Deacon, Tania B. Huedo-Medina, Alan Scoboria, Thomas J. Moore & Blair T. Johnson" find a significant additional benefit of taking a SSRI rejecting the null of no benefit with a p value of "<0.001". The standard level for statistical significance is p <0.05. In fact, as shown in their paper Kirsch, Deacon, Huedo-Medina, Scoboria, Moore & Johnson find overwhelmingly strong evidence that SSRI's cause improvement in depression.

They stress the novel result that the estimate of the magnitude of the effect is smaller than that based on published trials. Researchers tend stress the novelty of their results. Oddly big Pharma, which spends huge amounts of money on advertizing, doesn't seem to have managed to hire anyone intelligent enough to point out that 1.8>0.

Kirsch, Deacon, Huedo-Medina, Scoboria, Moore & Johnson note that it is lower than 3 and that "National Institute for Clinical Excellence (NICE) used a drug–placebo difference of three points as a criterion for clinical significance when establishing guidelines for the treatment of depression in the United Kingdom." Thus the opinion of a bureaucratic organization is held to be the truth. What do this 1.8 and this 3 mean ? I quote from the background information for non experts provided by the journal.

Doctors measure the severity of depression using the “Hamilton Rating Scale of Depression” (HRSD), a 17–21 item questionnaire. The answers to each question are given a score and a total score for the questionnaire of more than 18 indicates severe depression.

It sure appears to me that 1.8 is a tenth of the way from the best possible score (which I would guess is very rare) to severe depression. But the NICE says it's clinically insignificant and the NICE must know.

Now the NICE clearly has no clue what it is talking about. I dare write this, because I am about to talk about math.

I quote from the article

"standardized mean difference (d), which divides change by the standard deviation of the change score (SDc) [10], and another using each study's drug and placebo groups' arithmetic mean (weighted for the inverse of the variance) as the meta-analytic “effect size” [11].

The first analysis permitted a determination of the absolute magnitude of change in both the placebo and treatment groups. Results permitted a determination of overall trends, analyses of baseline scores in relation to change, and for both types of models, tests of model specification, which assess the extent to which only sampling error remains unexplained. The results in raw metric are presented comparing both groups, but because of the variation of the SDcs, the standardized mean difference was used in moderator analyses in order to attain better-fitting models [12]. These results are compared to the criterion for clinical significance used by NICE, which is a three-point difference in Hamilton Rating Scale of Depression (HRSD) scores or a standardized mean difference (d) of 0.50 [1]."

Now the standardized mean difference is not used to test the hypothesis that the true difference is zero (that implies dividing by the standard deviation of the mean not the standard deviation) nor is it used to calculate a confidence interval around the estimated effect. NICE suggests it be used as a measure of the magnitude of an effect "clinical significance" for no good reason at all.

Take two studies of two different drugs, both show a positive effect say 2.9 for drug 1 and 1.5 for drug 2. The sample sizes are large enough that these effects are statistically significantly different not only from zero but from each other. Hell I'm pretending so make the sample size 400 in each case. The sd of the effect drug 1 is 10 and the sd of the effect of drug 2 is 2. Hmm the sd of the means are 0.5 and 0.2 so the z-scores testing whether each drug is effective are 5.8 and 15 both strongly significant. The sd of the difference in means is the square root of the sum of the squares of the sd's of them means or ... uhm roughly 0.50990195 so the z score for the difference is more than 2.7, that is statistically significant.

NICE would conclude that drug 2 has a clinically significant benefit because it has a standardized mean difference of 0.75 while drug 1 does not have a clinically significant benefit because it has an average benefit of 2.9<3 and a standardized mean difference of 0.29 <0.5.

Thus, although the data demonstrate that the mean benefit of drug 2 is greater than the mean benefit of drug 1, NICE would conclude that the benefit of drug 2 is clinically significant while the benefit of drug 1 is clinically insignificant.

I think this is crazy. NICE developed a rule of thumb which mixes point estimates and confidence intervals. The mixed rule requires statistical significance (a 95% interval must not contain zero) and an arbitrary level of the point estimate measured effect (if there were any calculation behind it it wouldn't be exactly three) which takes no account of the fact that the point estimate is not exact.

Now some may argue that a high mean effect with a high standard deviation implies a very bad effect on many people. This is not true. It is based on assuming that the distribution of effects is normal. There is no way of calculating the probability that some patients score will drop by more than say 3 from means and standard deviations.

update: The very excellent Michael O'Hare falls for it. He writes "Antidepressants seem to be only somewhat more effective against depression than placebos," and "drugs that don't work much better than sugar pills?". He accepts the idea that 1.8 is roughly zero (note he is smart and honest and doesn't say that 1.8=0 as Sarah Boseley did). To be fair to 0'Hare, his post is not about SSRI's but about the power of placebos.

However, I am not convinced that he understands the evidence on the placebo effect.
The studies report the change in the Hamilton rating from the first interview until some period after beginning treatment with the SSRI or the placebo. There was a huge improvement among people who took the placebo. It is, however, not at all clear that this was a placebo effect. O'Hare's implicit assumption is that there would have been no improvement without the placebo. He mentions no evidence to this effect.
Another explanation of the data is that depression comes and goes. So people who are depressed when the study started might improve even if there is no treatment, not even with a placebo.

To measure the placebo effect, it would be necessary to compare it to no treatment, that is to interview some patients and ask them to come back in say 4 weeks and do nothing else. A substantial fraction of people would not cooperate with such a study, and, I would guess, a larger fraction of depressed than non depressed people.

update: I have added actual links to the article to click (sorry).
Pyjamas in Bananas seems to have done really excellent work. I pull back from comments

Putting the limitations of NICE's arbitrary criteria for 'clinical significance' to one side, I'm not at all sure how Kirsch et al arrived at an effect size of 1.8 HRSD points (my own analyses, and frankly just eye-balling the data, suggests a figure more like 2.8 points overall, with both paroxetine and venlafaxine exceeding three points of HRSD change).

By using the rather odd measure of HRSD change score normalised as the standardised mean difference for each group separately their results look rather different to what we would expect from analysing the raw HRSD change scores, and it is not clear that they can be compared to the NICE criterion of d > .5.

Adopting this measure means that a greater improvement from baseline HRSD to outcome HRSD with drug treatment can be normalised away by a greater variance in this group - and it is hardly inconceivable that outcome HRSD variance would increase with an effective, but non-uniform, response to drug treatment.

It is also worth noting that the main conclusion of this paper, at least as far as the media is concerned, that newer anti-depressants shouldn't be prescribed in 'mild' or 'moderate' depression is based on only a single 'moderate' study and extrapolation of the regression line, since the rest of the studies were in 'severe' or 'very severe' depression.

Canadian TV networks disagree*

CBC vs CTV**


CBC claims that everything Obama said in public was absolutely true and that the accusation against him was a lie based on a misunderstanding.


via

MattW at DailyKos

*Is this headline more boring that "Worthwile Canadian Initiative" ?

**CBC does not stand for Canadian Barack Committe and CTV does not stand for Clinton TV.

Jonathan Kulick is a Yellow Pig

Home Town Hero (or Heroine)

I'm from the very non-descript DC suburb of Silver Spring. Main claims to fame, one single solitary insulting and inaccurate article in "the Economist," Dominique Dawes and her biggest fan Oliver Willis. Now there is someone who tells Charlotte Allen where her article belongs.

Silver Spring, Md.: Yes, women’s reasoning is sometimes clouded by emotion, but so is men’s. Why is “swooning” so much worse than murderous rage? How are “Eat, Love, Pray” and “Grey’s Anatomy” any more self-indulgent and fantastical than “On the Road” and James Bond movies? Are romance novels a less realistic picture of male-female relations than “Big Butt Sluts #23″? In short, why do you consider men’s irrational distortions forgiveable, while women’s are a sign of lower intelligence?

Charlotte Allen: I agree that men do many dumb things, and many men have dumb tastes.

Wish I had written that (the spellling errror is forgivable).

Obama and Rezco.

I'm worried. Barack Obama did business with a crooked real esate developer named Tony Rezco. Rezco owned land next to the Obamas' house and they bought a ten foot wide strip of that land. The details of the transaction make me worry about Obama.

Obama has said that he approached Rezko personally in January of 2006 about buying some of the adjacent lot. To set the price for the 1,500-square-foot strip, which was one-sixth of the entire lot, Obama hired a firm to appraise its value. When that appraisal came in at $40,500, Obama says he judged it too low for appearance's sake and instead set the price at $104,500, which was one-sixth of the price Rezko had paid for the entire lot. There's been no suggestion that Rezko actually negotiated with Obama on the price. In any case, he accepted.

What !!! he had the property appraised then paid more than two and a half times the appraised value ?!?! For appearance's sake !! Is this really the guy we want to negotiate with Republican Senators ?

Karl Rove has Good Advice for The Democratic Candidate for President

Furthermore, the Rove recommended strategy is based on honesty. Strange but true.

The advice is "You don't attack their weaknesses. You attack their strengths." Very good advice as it is very easy to get the media to reach an inconclusion. Thus it was possible to make Kerry's war record in Vietnam a confused disputed matter and to make Gore's role in the development of the internet a weak point (my advice is don't ever dream that the press will do to your opponent what they did to Gore).

McCain's perceived strong point is that he is a straight talker. This includes two aspects. First that he is honest and second that he is resolute and does not bend with the wind. Since McCain tells unusually blatant lies and has bent all the way over for the right this year, it should be easy to attack McCain on this point. The McCain vs McCain ads write themselves (unlike the Kerry vs Kerry ads which required one distortion of the meaning of a statement by dishonest editing per video clip).

See Steve Benen, J. C. Christian and ... well it's shooting fish in a barrel so how will the Democrats manage to miss.

What is going on with FISA ?

Obviously the Democrats are caving, but what exactly are they

Dismal but unsurprising. The Bush administration and Republicans had me going for a while. They were so determined to humiliate themselves getting caught lying about the effects of the lapsing of the PRotect America Act, that I almost hoped that the Democrats wouldn't have thrown them a life line.

Oddly the claims this article by Ellen Nakashima and Paul Kane in the Washington Post which are news to me are claims about the past.

The paragraph below is an amazing piece of work.

"This is not amnesty," Wainstein [assistant attorney general for national security] said at the meeting. "This is targeted immunity" for companies who meet requirements specified in the Senate bill that include having received an attorney general's certification that their assistance was determined to be lawful.

Note that the key phrase "an attorny general's certification" is not in quotation marks. The existing law protects telecom companies if they have such a certification signed by the attorney general or deputy attorney general. The issue of amnesty only arises, because the telecom companies did something which Ashcroft and Comey would not certify as legal, but rather such that they said they would resign if it weren't stopped. The key issue related to amnesty is whether an assurance from the White House Council that the Attorney General agreed that the actions were legal is good enough, although existing law makes it clear that it isn't (hence the desire to change the law). This is not a detail. We now know that the assurances that the Attorney General knew of the activities and considered them legal were lies. The law is quite clear about signatures. It is impossible to believe that the telecom companies didn't ask for a letter which would immunize them (they have lawyers). It must be that the Bush administration failed to generate such a letter when asked and the telecom companies decided to break the law.

The paragraph which suggests that the Senate bill changes telecom liability not at all (based on words chosed by Ellen Nakashima and Paul Kane and not by Wainstein) must be incorrect.

Also, it was generally agreed that some FISA fix was needed, because the FISA court had decided that FISA warrants were required to intercept foreign to foreign communications passing through the USA on wires of optical fibers. Now

But in response to a question at the meeting by David Kris, a former federal prosecutor and a FISA expert, Wainstein said FISA's current strictures did not cover strictly foreign wire and radio communications, even if acquired in the United States. The real concern, he said, is primarily e-mail, because "essentially you don't know where the recipient is going to be" and so you would not know in advance whether the communication is entirely outside the United States.

That is, the Bush administration just admitted that a justification for revising FISA, which has been accepted as valid by just about everyone including liberal bloggers and other opponents of amnesty, was a false claim. For months many people (too many for links) believed that, a recent FISA court decision, had removed the words "wire and" from the exception to FISA court authority. Now that the Democrats are caving, there is no need to imply this any more.

The Title and Author of this column convince me that Obama is more electable that Clinton.

"Why McCain Would Vote For Obama" by Stanley Fish

Professor Fish is the greatest Fukayamer of our times. Sadly, "to Fish" is already a verb.

Brad at Sadly No is Sadly naive.

he doesn't understand that Obama plans to destroy the Republican party by appointing Republican Senators to the Cabinet.

He writes stuff. I reply.


You don't get it. Don't worry, Bill Clinton didn't get it and he is a genius. Senators are very powerful. Cabinet (some)ecretaries have power somewhere between that of the average secretary (lots if their boss is dumb) and that of the average cabinet (made of wood noticed only if it catches on fire). Clinton's worst mistake was making Senator Lloyd Bentson (D-Tex) a mere secretary and giving his very precious seat to Kay Baily Forehead.

Now Nebraska and Indiana are not promising territories for Democrats, but you know semi Democrat Ben Nelson represents Indiana.

The name of the game is "get to 60" and any means are fair. Obama plans to play to win.

OK OK he should appoint Olimpia to be UN embassatrix and Collins (if, heaven forfend, she is re-elected) embassatrix to the moon, but he can't be too obvious.

Hmm this looks interesting but I will write before reading it.

Why I am not a Rawlsian - Tyler Cowen

So why am I not a Rawlsian ? Hmm well first we have to distinguish two things Rawls and Rawls as described by an economist.

Following a decision which he later described as a mistake, Rawls added a bit to "The Theory of Justice" called the difference principle. OK I admit I peeked and the first 3 words of Cowen's post are "the difference principle." The idea is that policies should be judged by the level of (roughly income or wealth) of the poorest person. This is about the most egalitarian anyone would naturally imagine. (roughly income or wealth) is the level gained by things everyone would find useful, including wealth and legal rights (if not equal for everyone) and stuff.

This is just one little bit of a lifetime of thought. Unfortunately, since it was simeple, it has become the doctrine of "Rawls" who has driven John Rawls into obscurity. OK so what do I have against the difference principle ?

It is too edgy, not smooth. A problem is that someone who is handicapped has very little real freedom. Should we devote all of societies efforts to making the life of the most severely handicapped among us less limited ? Rawls thinks not, but he has trouble explaining why. His semi desciple Sen notes that the arguments which Rawls made to avoid this conclusion which is rejected by his concience are unconvincing.

Also, I am not convinced that it makes sense to imagine society made up of individuals and try to maximize their choices (real freedom). In the real world there are helpless babies who have rights just like you and me. They need care not freedom. In the real world we shouldn't consider the distribution of wealth or income among individuals but first among families then within families. The fact that a baby has his or her own income doesn't help the baby at all, since his or her parents manage it. I think this can imply that Rawls was not egalitarian enough, as relative poverty can be bad for babies if, with the same income, parents in an unequal society imitate the super rich and consume luxuries and let their babies die. I happen to believe that this is a real problem in the real world.

Or so what about Rawls who is much more subtle than "Rawls" ? Well for one thing he is way too subtle and I can't understand what the hell he was saying (OK so maybe I shouldn't have just listened to the lectures but actually done the reading). Let's just say that I think that Rawls was a wonderful person and an excellent teacher, but he agreed with Kant on points where I personally agreed with Bentham. I absolutely disagree with "The groundwork of the Metaphysics of Morals" from the first to the last word, so I never went on to read about the first and second floors.

That Gal Sure Can't Do Math

In the article people think must be a hoax, Charlotte Allen writes

A study published in 1998 by the Johns Hopkins schools of medicine and public health revealed that women clocked 5.7 auto accidents per million miles driven, in contrast to men's 5.1, even though men drive about 74 percent more miles a year than women.

Uh Charlotte, if you have already calculated "per million miles driven," it makes no sense to write "even though" men drive more. You do remember about fractions and the meaning of the word "per". Also, if you are trying to argue that women can't drive, you shouldn't provide information that shows men are more than 2.5 times as likely to have fatal accidents.

And what is this about imagining things in 3 dimensions and philosophy "Visuospatial skills, the capacity to rotate three-dimensional objects in the mind, at which men tend to excel over women, are in turn related to a capacity for abstract thinking and reasoning, the grounding for mathematics, science and philosophy." I assume Allen knows philosophers who use visuospatieal skills. Or she is bullshitting. I would say, philosophy has more to do with language, which is important for, uhm you know abstract reasoning.

Allen notes that men and women have similar IQs. She doesn't seem to know that this is a methodological a priori. The tests were designed so that males and females have similar scores, obviously because females scored higher before they rejiggered the tests.

Allen has shown that at least one woman is dumb. Unless, of course, the Author's true name is Allen Charlotte.

update: Welcome Economists' Viewers. I also want to add that Allen was blatantly (and as far as I can tell extremely successfully) Fukayaming. Thus to excoriate the column is to fall into Charlottes web.

update II: Charlotte Allen did stimulate Hilzoy to write something which, in my ignorant opinion, might be brilliant.

Second, [genre] romance novels ... are not "books", as that word is normally used. They are either tools for relaxation or the female equivalent of porn. They should therefore be compared not to War and Peace, but to either Ultimate Sudoku or the Hustler centerfold. Personally, I think they come out fine in either comparison, but that's probably because I'm just a dumb woman.

[snip]

as I read the WaPo piece, the part about romance novels was meant to imply that women's taste in fiction runs to romance novels, which (according to Charlotte Allen) don't stack up well against fiction generally. My point was that that is not the relevant comparison. If you want to make some sort of stupid generalization about women, then it matters what the male analog of a romance novel is. If, for instance, many women read genre romances for some of the same reasons that lead many men to read/watch/look at porn, then it would be silly to draw any conclusion at all about men and women from a comparison of romance novels to novels generally. It's not the right comparison. I stand by this point.

Note: this does not imply, and I did not mean it to imply, anything about the quality of genre romances. I honestly think not just that most of them stack up pretty well against your average Hustler centerfold, which isn't hard, but that some of them are quite good.

[snip]

Genre romance novels are, in my experience, written according to very serious constraints. There are plot constraints, characterization constraints, all kinds of constraints.

[snip]

I do not think badly of a particular genre romance because the author should not have made the hero so strong, noble, and self-contained, or because its heroine should not be so completely ignorant of her own charms, or because some complication prevents the hero and heroine from recognizing their attraction to one another until they are forced into close proximity by some unexpected turn of events. Those are the rules. And I assess a genre romance novel not by its quality as a work of creation ex nihilo, but as a novel written according to those rules.

That sounds brilliant, but I wouldn't know, as I have never opened a genre romance novel or Ultimate Sudoku for that matter (the reader is free to infer the obvious from my 2 out of 3 denial).

update III As confessed above, I have never read a genre romance novel, but I understand the appeal of reading Novels in which not just anything can happen. I enjoy re-reading novels. Reading an original novel for the first time requires mental effort -- one must acculturate oneself and get to know the characters. Reading good novels stretches our minds and makes them more flexible. This is not what I am after when I am tired (of feeling lazy). Re-reading a novel, I recognize the familiar pattern (comforting) and am pleased by the details which I had semi-forgotten. I have looked a novel which I have never read and thought "no I'm too tired" and picked up a novel which I have read for an easy relaxing reading experience.

Italian Lesson for an Anonymous TPM commenter

Someone (who did not sign his post) wrote "what Benito Mussolini called corporatism, a collusion between business interests and government at the highest levels. " The phrase following the comma incorrectly defines what Benito Mussolini called corporativismo. In Italian "corporazione" means guild. The Italian word for a corporation is a "società." Mussonilini proposed a state in which the people would be represented indirectly via "corporazione." Whatever these might be they certainly weren't corporations, firms, businesses or any such thing.

The innumerable references to the "corporate state" made by leftists in the late 60s and early 70s (and someone in 2008) were based on a gross mistranslation. It is similar to the mistranslation of "canali" that is "channels" as "canals" which is responsible for so much bad science and bad to excellent science fiction about the canals of Mars (if you don't think any of the science fiction was excellent you must not know who Leigh Bracket is)

Orwell Remembered ?

I will attempt to list one percent of one percent of the cases in which Orwell is quoted in current political discussions.

I think Julian Sanchez doesn't quite remember "Politics and the English Language." He asked if "In the tank" is a dead metaphor. my twitty comment follows:

And what is the etymology of "dead metaphor" ?

I think, when you check here

you will find that you meant to write "dying metaphor." That is, I believe the phrases come from "Politics and the English Language," where "in the tank" would be denounced as a metaphor without an associated image which has not yet reverted to being like an ordinary word (now that I'm being a parody of nit-picking I should underline my absurdity by noting that Orwell seems to have miscounted the number of words in "Iron resolution."

DYING METAPHORS. A newly invented metaphor assists thought by evoking a visual image, while on the other hand a metaphor which is technically ‘dead’ (e. g. iron resolution) has in effect reverted to being an ordinary word and can generally be used without loss of vividness. But in between these two classes there is a huge dump of worn-out metaphors which have lost all evocative power and are merely used because they save people the trouble of inventing phrases for themselves.

While we're on Orwell I consider Sanchez's list of tanks. How often did Orwell write about each of them ?

"In the [fish] tank" as in "like a domesticated pet"?
I'm not sure Orwell ever did. Could he have written 1984 without using "like a fish tank" as a metaphor ? Quite possible. Could anyone else have done so ? Less likely.


"In the [Abrams] tank" as in "going to battle for"?
Well wouldn't be an Abrams. Can't think of an example in all of his war commentary.

"In the [gas] tank" as in "acting as fuel for"?
hmm about petrol rationing. No memory.

"In the [drunk] tank" as in "besotted with"?
He wrote an early essay about his experience in which he pretended to be drunk and was forcibly taken to a drunk tank. Don't recall what he called it.

"In the [septic] tank" as in "prepared to get dirty on behalf of"?

Ah yesss. Twice at least. He shifts from a review of another book to review "No Orchids for Miss Blandish" writing IIRC "and now for a header into the cess pool."

And also once wrote IIRC "sawing sawing the branch we were sitting on, but when it gave way (much sooner than anyone excpected) it seems that there had been some confusion. Below instead of a bed of roses there was a cess pool full of barbed wire."