
545 F.Supp. 306 (1982)
Floyd COOK, Plaintiff,
v.
UNITED STATES of America, Defendant.
Esther J. JOLLIFF, Plaintiff,
v.
UNITED STATES of America, Defendant.
Lupe R. PULIDO and Donato Pulido, Plaintiffs,
v.
UNITED STATES of America, Defendant.
No. C-78-2041-WWS, C-78-2769-WWS, C-80-1882-WWS.
United States District Court, N. D. California.
August 5, 1982.
John Echeverria, Walkup, Downing, Shelby, Bastian, Melodia & Kelly & O'Reilly, San Francisco, Cal., for Lupe R. Pulido.
Michael E. Myers, San Francisco, Cal., for Esther J. Jolliff.
Stanley F. Leal, Kelly, Leal & Olimpia, Sunnyvale, Cal., for Floyd Cook.
Kimberly Reiley, Deborah Seymour, Asst. U. S. Attys., San Francisco, Cal., for defendant.

MEMORANDUM OF OPINION, FINDINGS OF FACT AND CONCLUSIONS OF LAW
SCHWARZER, District Judge.
These three actions were brought under the Swine Flu Act (former 42 U.S.C. *307 § 247b(j) (Supp. III 1979)) and the Federal Tort Claims Act (28 U.S.C. §§ 1346 et seq.). Plaintiffs seek damages from the federal government for injuries due to Guillain-Barre Syndrome (GBS), a rare neurological disorder which plaintiffs contend was caused by their swine flu vaccinations under the federally sponsored swine flu immunization program of 1976. This opinion sets out the Court's findings of fact and conclusions of law following a consolidated trial in these cases limited to the issue of proximate cause.

Introduction
As a result of multidistrict pretrial proceedings, the government has stipulated to liability in GBS cases with an onset of ten weeks or less after vaccination. This time period was selected on the basis of a strong statistical correlation between swine flu vaccination and an increase in GBS cases that was discovered by the federal Center for Disease Control (CDC) in the course of its surveillance of neurological complications of vaccine during the swine flu program in 1976.
The three plaintiffs presently before the Court each suffered onset of GBS more than ten weeks, i.e., from twelve and a half to thirteen and a half weeks, following vaccination. The etiology of GBS is not well understood and not readily demonstrated by clinical or laboratory evidence, particularly after such a latency period. Hence, plaintiffs' joint offer of proof, submitted pursuant to an order of this Court, relied on statistical correlation to establish causation, interpreting the CDC data differently than did the doctors who worked with CDC, in order to show a connection between vaccination and GBS having an onset fourteen or eighteen weeks following vaccination. The extended period of probable causation would then cover the latency periods experienced by each of these plaintiffs.
As the case for causation in these actions turns on the interpretation of the CDC statistical data, the Court held an evidentiary hearing on the issue of causation, receiving legal memoranda, narrative statements and testimony from plaintiffs' expert witnesses, Dr. Bear and Dr. Goldfield, and from defendant's expert, Dr. Mack. In addition, the Court reviewed exhibits and relevant portions of documents from the multidistrict pretrial proceedings. The following constitutes the Court's findings of fact and conclusions of law after considering the evidence and the arguments of counsel.

A. The CDC Data Base

Anticipating the possibility of vaccine-linked illnesses when the government initiated the massive swine flue immunization program of 1976, CDC established a surveillance program to collect reports of post-vaccinal complications from all state public health authorities. Shortly after the immunization began under the program on October 1, 1976, reports arrived of scattered post-vaccinal cases of GBS. Relatively little was known at the time concerning the background incidence of GBS in the general population, but the disease was sufficiently rare that the reports were cause for alarm. CDC notified neurologists as well as health departments throughout the country to report any new cases of GBS, whether or not post-vaccinal, in order for CDC to assess the risk posed by the immunization program. For a period of time, then, reports of GBS were actively solicited in a climate of large-scale publicity and concern over imminent public health dangers  conditions that resulted in the most thorough nationwide study of GBS ever undertaken.
As a result of the increasing reports of GBS in recently vaccinated patients, the government declared a moratorium on swine flu inoculations on December 16, 1976, just over eleven weeks after the immunization program began. The immunization program was not resumed. CDC continued to solicit GBS reports from the states until January 31, 1977. Thus, for a period of nearly eighteen weeks, CDC had data on the incidence of GBS in both the vaccinated and unvaccinated populations of the nation.
Dr. Schonberger and his colleagues, who had participated in the surveillance program, *308 produced a 1977 study from the CDC data of October 1, 1976, to January 31, 1977. Schonberger, et al., Guillain-Barre Syndrome Following Vaccination in the National Influenza Immunization Program, United States, 1976-1977, 110 American J. Epidemiology No. 2 (1979) (M.D.L. # 121). Schonberger calculated estimated GBS attack rate ratios by comparing the number of GBS cases reported among vaccinated persons to the size of the vaccinated portion of the population, and the number of unvaccinated GBS cases in the same eighteen-week period to the size of the unvaccinated population of the United States. The vaccinated cases were organized according to the period of latency between vaccination and the onset of the acute symptoms of motor weakness which characterize GBS. In this way, Schonberger could compare the frequency of GBS cases among vaccinees in their third week after vaccination, for example (expressed as a proportion of the vaccinated population at that time), against the background attack rate of GBS among the unvaccinated population (again expressed as a proportion  the number of GBS cases per million persons per week).
Schonberger relied essentially on the characterization of cases as GBS in the state health departments' reports to CDC, as well as on their data concerning the dates of vaccination and onset and their figures for total vaccinees by week. Census figures were used for the general population, subtracting the numbers of persons already vaccinated. The chief adjustment Schonberger made to this raw CDC data was to exclude all case reports (and the corresponding vaccination and population figures) from four states whose reporting was considered to be unreliable, and from eight more states after the week ending December 18, 1976. Reports to the CDC after the December 16 moratorium was announced fell off generally  presumably because there was no longer the concern to collect sufficient data to determine if the immunization program should be continued  but Schonberger apparently considered the decline in reporting data particularly serious or troublesome in these eight additional states which he excluded from his study.
After excluding case reports from the suspect states, Schonberger calculated an estimated GBS attack rate in the unvaccinated population at .22 cases per million persons per week. Among vaccinees, however, the attack rate was over 1 case per million per week in the first week after vaccination, rising to over 2.5 cases per million in the second week of latency, peaking at nearly 3.5 in the third week, and dropping back to just over 1 case per million in the fourth week. The Schonberger curve trails off with minor variations toward the plateau after that. Thus, Schonberger's figures show a greatly increased risk of GBS among vaccines that diminishes after the third week following vaccination. The dispute between the parties in the present actions is how soon the attack rate in the vaccinated population drops below the point where the relative risk is not sufficiently large to assure the Court that a given GBS case was more likely than not caused by swine flu vaccination rather than by some other event.
The government stipulation of liability extends to ten-week latency periods because, according to Dr. Schonberger's figures, the attack rate among vaccinees drops below twice that of non-vaccinees shortly before the tenth week. Whenever the relative risk to vaccinated persons is greater than two times the risk to unvaccinated persons, there is a greater than 50% chance that a given GBS case among vaccinees of that latency period is attributable to vaccination, thus sustaining plaintiff's burden of proof on causation.[1]
*309 Plaintiffs' theory is that Dr. Schonberger erred in categorizing some of the cases of GBS reported to CDC, erred in estimating the size of the vaccinated population, and did not make satisfactory adjustments to correct for the under-reporting of GBS cases, particularly after December 18, the week in which the moratorium on immunization was announced. Plaintiffs' two experts use different methods of interpreting the CDC data and correcting for reporting errors, but both conclude that the data demonstrate the probability of a causal connection between swine flu vaccination and GBS where the period between the shot and the onset of symptoms is as long as those of the plaintiffs, or even longer.

B. Dr. Bear's Testimony

Dr. Bear, an economist with statistical expertise, obtained copies of the case report summaries from CDC which had formed the basis for Dr. Schonberger's article. He and his colleagues eliminated cases of persons under the age of eighteen, as Dr. Schonberger had done (because so few non-adults were vaccinated that statistical comparisons would be meaningless). He also classified some of the cases differently than Dr. Schonberger had, noting, for example, that some cases treated as unvaccinated had actually occurred after vaccination. In addition, he included more cases than did Dr. Schonberger by counting reports from the half-weeks preceding December 19 and February 1, and by using data from all fifty states for the entire surveillance period, rather than excluding some states for unreliable reporting as Dr. Schonberger had done.
Because of the relatively small number of GBS cases, particularly in the longer latency intervals, these adjustments to the data base have significant consequences. CDC collected about 500 GBS case reports each from the vaccinated and unvaccinated populations during the eighteen weeks of surveillance. A little over a hundred vaccinated GBS cases were reported after December 18; only nine of them of twelve-week latency or longer (by Dr. Bear's count). But the chief reason for the dramatic difference between Dr. Bear's and Dr. Schonberger's statistical analyses of the CDC data is not these adjustments but Dr. Bear's manipulation of the data to correct for underreporting of GBS cases after December 18.
The fact of underreporting is not disputed, but its magnitude is. Dr. Schonberger had noted the sharp decline in case reports after December 16, when the decision to discontinue the immunization program lessened the incentive to collect information on the vaccine's side effects. Dr. Bear's thesis is that the effect of underreporting after the week ending December 18 was especially significant for the late-onset vaccinated GBS cases, primarily because most would necessarily have occurred in the period after December 18 if they arose during the surveillance period at all.
Dr. Bear demonstrated the degree of underreporting after December 18 by four tests. First, the raw attack rate among all vaccinees dropped from double-digit to single-digit figures between the twelfth and thirteenth calendar weeks of the surveillance  from about 1.7 cases per million to about .6 per million  after remaining in double digits through the first twelve weeks of the program. Second, the weekly attack rates in the unvaccinated population immediately declined to about half their previous levels, yet there was no reason to suppose that half as many cases of GBS were occurring in the general population. Third, Dr. Bear calculated the attack rates for various onset intervals (periods of latency) among vaccinees, and found large differences depending on whether pre-December 18 reports or post-December 18 reports were used to calculate the rates. Finally, Dr. Bear compared Dr. Schonberger's estimated *310 attack rates (which were averaged from the states that he relied on over the entire period of surveillance) to the numbers of vaccinees in each calendar week. The Schonberger averages consistently underestimated the observed cases in the first twelve weeks, before December 18, and overestimated the observed cases in the six weeks after December 18. As the reporting was clearly more complete in the earlier period, this is another sign that the average attack rates computed by Dr. Schonberger were too low. These trends were similar when the calculations were based either on the states Dr. Schonberger used or on all fifty states.
Dr. Bear attempted to correct for the underreporting in the later (post-December 18) period, essentially by measuring the decline in the rate of reporting of vaccinated cases of one to twelve weeks' latency between the two periods, weighting the reporting rates derived from each period according to the size of the population sample it was based on,[2] and producing an estimated attack rate for each onset interval that was most likely to predict the cases that were actually reported in a given week. He employed a sequence of mathematical formulae that simultaneously estimated the "reporting factor" (the chance that an actual GBS case would be reported) for the later period and the attack rate for vaccinees at various onset intervals. The formulae applied information about the reporting factor (the difference between weighted pre- and post-December 18 rates) to raise the estimated attack rates proportionately with the observed decline in reporting in the weeks after December 18, added the predicted but unreported cases, and simultaneously corrected the reporting factor as the attack rate was increased, indicating that yet more cases had gone unreported. The reciprocal corrections were made successively until they yielded only trivial refinements of the figures.
The result of this method is an estimated post-December 18 reporting factor of about 38% in all vaccinated cases (compared to a 47% reporting factor for unvaccinated cases after December 18). That is, Dr. Bear estimated that only about 38% of the actual GBS cases among vaccinees that occurred after December 18 were reported to CDC. He increased the estimated attack rates for each onset interval accordingly, using the formulae briefly described above. The attack rates were refigured for each onset interval of one to twelve weeks, and for the average of onset intervals of from thirteen to eighteen weeks (averaged because so few cases of such an interval would occur that the attack rate for each week within that *311 period would vary greatly according to which cases happened to have been reported). Using the unvaccinated reporting rate for the post-December 18 period, he recalculated the baseline rate among the unvaccinated population as about .24 per million persons (compared to Dr. Schonberger's estimated baseline of .22 per million). The adjusted attack rate for the vaccinated population at thirteen to eighteen weeks following vaccination came to about .79 cases per million  a relative risk over the unvaccinated population of approximately 3.3, well above the relative risk of two which marks the 50% likelihood that a vaccinated case was caused by the inoculation. This would mean that about 70% of all GBS cases occurring among vaccinated persons thirteen to eighteen weeks after vaccination are attributable to the vaccine. The relative risk is even higher using data only from the states Dr. Schonberger used.
Because the surveillance program ended in the eighteenth week, Dr. Bear could not plot the return of his attack rate curve to the baseline, but he found that it remained more than twice the rate of the unvaccinated population at least through the end of the eighteenth week following immunization, long enough to establish the probability that plaintiffs' GBS cases were caused by the vaccine.

C. Dr. Goldfield's Testimony

Dr. Goldfield, an epidemiologist, took a much simpler approach to the problem of estimating relative risk among the vaccinated population thirteen or fourteen weeks after vaccination. Dr. Goldfield used reports from all fifty states and, after examining the computer case summaries from CDC upon which Dr. Schonberger relied, reclassified many of the GBS cases. Six cases counted as unimmunized he found had actually been immunized, for example, and he included some cases with uncertain incubation periods (where he knew the range of possible periods) that Dr. Schonberger had excluded. In addition, using figures reported in Dr. Langmuir's study that purportedly came from CDC, Dr. Goldfield estimated the total number of vaccinees at a figure four million persons lower than Dr. Schonberger had, also using figures purportedly from CDC.
Because he found that the decline in reporting after December 18 amounted to about 50% in both the vaccinated and unvaccinated cases, Dr. Goldfield rejected the theory that there was a differential effect of underreporting after that time and simply compared the relative risk for each period separately. That is, he compared the baseline rate among the unvaccinated, based on pre-December 18 reports, with the attack rate among vaccinees with onsets of from one to twelve weeks latency, also based only on pre-December 18 reports. He then compared the lower baseline rate computed from post-December data alone with the attack rate among vaccinees with onsets of from one to eighteen weeks, using only post-December 18 reports. Finally, he averaged the results for each onset interval.
By this method, Dr. Goldfield calculated a relative risk for vaccinees in their thirteenth week after vaccination of 3.99 (based on five vaccinated cases); and for vaccinees in their fourteenth to sixteenth weeks of 2.84 on the average (there were no reported cases with fourteen-, sixteen-, seventeen-, or eighteen-week onsets, but the four cases of fifteen-week onsets were averaged over the fourteenth to sixteenth weeks). The average for eleven to sixteen latent weeks was 3.7, or a nearly 75% chance of vaccine causation. Hence, Dr. Goldfield concluded that plaintiffs' thirteen- or fourteen-week GBS onsets were more probably than not caused by vaccination.

D. Dr. Mack's Testimony

The government's expert, Dr. Mack, also an epidemiologist, responded to plaintiffs' theories of causation. From the point of view of an epidemiologist, he considered three factors in determining causation: (1) the degree of relative risk, measured by statistical likelihood; (2) alternate explanations for a statistical correlation, such as bias or confounding with other causes or associations; (3) the biological credibility of the purported association.


*312 1. Statistical Evidence of Relative Risk

In the case of the swine flu episode, the statistical relation to GBS is so strong for the first five weeks of latency that, considering the systematic elimination of significant bias in that period and the plausibility of a vaccine-induced GBS syndrome, causation is unquestioned. But the fact that a temporal association with GBS is the strongest argument for causality also indicates that at some point that temporal association becomes so attenuated that causation cannot safely be attributed to the vaccine. And because most of the vaccine-linked GBS cases occur soon after vaccination, there will be less and less data for the longer periods of latency, and hence a greater likelihood of bias as an alternate explanation for the apparent association. In order to evaluate the relative risk, then, Dr. Mack examined the quality of the CDC data, attempted to estimate the risk to vaccinated and unvaccinated persons from that data, and then compared these results to other "sources of expectancy"; i.e., other studies casting light on the probable incidence of GBS among the general population and among swine flue vaccinees.
Dr. Mack observed some of the deficiencies in the CDC data from the swine flue episode. GBS was not formerly reported to CDC on a regular basis, and the scientific motivation of doctors to report instances of the disease to state health authorities would be expected to increase as the evidence of a vaccine danger became known and to decrease, especially for unvaccinated cases, after the moratorium removed much of this concern. The states varied greatly in their criteria for soliciting and screening reports; the only restrictions CDC placed upon the reports were that there must be evidence of motor weakness and the state must have treated the case as one of GBS. Dr. Mack agreed that substantial underreporting was likely, especially after the moratorium of December 16, but he disagreed with plaintiffs' estimation that underreporting was likely to be similar for unvaccinated persons and for vaccinated persons in various latency periods. Because of the publicity and the legal liability, he felt vaccinated cases were more likely to be reported in the later period. As the late-onset cases tended to be milder, they were also more readily confused with other neurological disorders which in a person who had been vaccinated might be taken as GBS, so that the possibility that post-December 18 reports among vaccinees included "false positives" was large.
Dr. Mack drew several conclusions about the value of the CDC data as a source for relative risk estimates. He considered that underreporting was likely to be greater among non-vaccinees than among vaccinees, a conclusion shared by Dr. Langmuir, who also studied the CDC data. He agreed with Dr. Goldfield that the estimate Dr. Schonberger used of the total vaccinated population was too high  because of inflated figures from vaccination centers and estimates based on the amount of vaccine shipped to those centers which did not take into account vaccine wastage  but he considered the error slight and much outweighed by the differential underreporting of nonvaccinated GBS cases.
He also concluded that the baseline attack rate employed by Dr. Schonberger, about .22 cases per million per week, was an underestimate. It was based on an average over the period of the surveillance for the incidence of GBS among unvaccinated persons, but that rate varied greatly in the course of the surveillance, despite the fact that there was no evidence of a seasonal change in the rate of GBS in the general population. The reporting of unvaccinated GBS cases was lower both at the beginning and the end of the surveillance period  as might be expected considering how the concern over the side-effects of immunization developed and then diminished. In the weeks of late November and early December, the reports were highest in both vaccinated and unvaccinated populations; these might be expected to be the weeks of fullest reporting. Hence, Dr. Mack preferred to use as a baseline the rate of .31, which *313 was maintained continuously for those few weeks of presumably best reporting.
Dr. Mack found supporting evidence for a baseline rate of at least .31 per million per week in other sources and in the CDC data itself. Dr. Schonberger's figures for vaccinated GBS cases during the surveillance revealed a decline in the attack rate for several latent weeks until a plateau was reached in about the twelfth week after onset. That plateau, at about .34 cases per million, is evidence of the true baseline in the unvaccinated population, as the risk of vaccinated persons would be expected to decline until it leveled out at the baseline rate for the general population. In Michigan, where state authorities cooperated with CDC in an intensive active surveillance during the 1976-77 incident  contacting hospitals, clinics, and neurologists periodically to ascertain new GBS cases  Dr. Breman reported a baseline GBS attack rate of about .37 million in the unvaccinated adult population. In four or five states with higher reporting levels generally during the swine flue incident (probably indicating more thorough reporting), baseline rates over .4 per million were computed. Dr. Kurland reported a baseline rate (adjusted to exclude children) of about .44 per million in the course of a forty-year study conducted by the Mayo Clinic in one Minnesota county before the swine flue episode. Dr. Nelson reported a baseline adult rate of about .31 in a large-scale six-month survey of neurologists by the CDC more recent than the 1976 swine flu episode. A recent study in San Joaquin County, California, produced a rate of .29 cases per million per week (after excluding children). Therefore, Dr. Mack considered a baseline rate of .31 cases per million per week to be a conservative estimate, with .4 probably more nearly accurate.
Using an unvaccinated baseline attack rate of .31, the probability of vaccine-causation declines below 50% after the fifth or sixth week of latency, whether Dr. Schonberger's cases or data from all fifty states are used.
That conclusion is reached, however, without making any adjustment to compensate for underreporting of post-December 18 vaccinated cases. Dr. Mack rejected Dr. Goldfield's method of compensating for underreporting, which used the baseline rate of about .11 drawn only from post-December 18 reports to compute the relative risk for late-onset cases, for which there were only post-December 18 reports. This baseline rate was used by Dr. Goldfield, although concededly lower than the pre-December 18 rate, on the assumption of a decline in reporting of vaccinated cases after December 18 that corresponded to the decline in reporting of unvaccinated cases. Dr. Mack considered that assumption speculative.
Dr. Mack also rejected Dr. Bear's method of adjusting the data to account for presumed underreporting after December 18. Theoretically, Dr. Mack noted, Dr. Bear's method is plausible: if the same factors result in the shrinkage of reports, both of unvaccinated and vaccinated cases and of vaccinated cases of early or late onset, then the data before and after December 18 on the unvaccinated and early-onset cases can be summarized and compared in order to estimate by how much the late-onset vaccinated cases were similarly underreported. Applied to this case, however, the method assumes similar reasons and degrees of underreporting for unvaccinated, vaccinated early-onset, and vaccinated late-onset GBS cases. It also assumes accurate measurement of the data on both sides of the December 18 line. In the instant case, Dr. Mack did not think that these assumptions were justified.
As discussed above, Dr. Mack considered that there were different motives at different times for reporting vaccinated and unvaccinated cases. Evidence of this is the variation in the weekly reports of unvaccinated GBS, which there is no reason to believe is seasonal, even in the weeks before December 18. Also, the surveillance was not uniformly active across the states and over the period of time, which may have *314 exacerbated the differential reporting of vaccinated and unvaccinated cases. Within the pre-December 18 period, different latent periods show different trends in reporting efficiency. Thus, it is not possible to ascertain that the effect of the moratorium was similar on reporting for all vaccinated and unvaccinated cases, or even for all latent periods of vaccinated cases.
Moreover, the accuracy of the data before and after December 18 is questionable, especially for the late-onset cases. There were very few of these; they tended to be milder and so more readily confused with other diseases; and there was greater incentive to report these than other mild neurological cases where a history of vaccination was absent. There were very few latency periods, for that matter, for which a significant number of cases existed both before and after December 18. Therefore, Dr. Mack thought it doubtful that the assumptions underlying a correcting method such as Dr. Bear's could be shown to be true.
A simpler method of correcting for a presumed equivalent decline in reporting would be to extrapolate the curve plotted exclusively from the more reliable pre-December 18 data. Such a curve, depending on the choice of baseline rate, would fall below the 50% probable causation point six to ten weeks after vaccination. An advantage of this extrapolated curve is that it accords with what is known about epidemiological causation generally: a temporally associated event, such as vaccination, is expected to be progressively less associated with disease as time passes, not to level out at a plateau over twice the baseline rate for an indefinite period, as Dr. Bear's adjusted curve does.

2. Alternate Explanations for Statistical Association

Even a significant long-term statistical association such as Dr. Bear and Dr. Goldfield assert must, according to Dr. Mack, be tested for other explanations such as sampling bias, as well as for biological credibility. The difference in motivation to report vaccinated and unvaccinated GBS cases, particularly for the longer latency periods and after the moratorium was announced, has been discussed above. This difference, which cannot be measured empirically, would result in a bias toward a higher late-onset rate. More demonstrably, the numbers of late-onset cases are very small. They are not invalid for this reason, as they represent a substantial number of person-weeks among vaccinees, but they are more easily biased by the inclusion of false positives  milder neurological disorders mistaken for the milder symptoms typical of late-onset GBS.
Dr. Mack proposes as a useful control on the possibility of bias in late-onset cases the approach taken by the Nathanson committee. Dr. Nathanson and his colleagues attempted to study the late-onset problem in the swine flu episode by having one neurologist, with a standardized set of diagnostic criteria, examine the CDC case summaries. He excluded cases that appeared not to be GBS, and he also computed separate attack rates for the total GBS cases and for the moderate to severe GBS cases. The latter were considered to be less likely to be unreported or to be confused with other diseases. The Nathanson committee used a very low baseline rate estimate  .19 cases per million (compared with Dr. Schonberger's .22 and Dr. Mack's .31 to .4). Still, they found that the relative risk was less than two after the sixth to eighth week. As this study militated against some of the biases that may have affected the Schonberger study, Dr. Mack considered it further support for his thesis that the late-onset rate was actually quite low and that Dr. Bear's adjustments simply compounded a bias already present in the CDC data.

3. Biological Credibility

As previously discussed, Dr. Mack considered the plateau produced by Dr. Bear's adjusted figures to be implausible for a *315 disease agent temporally linked to GBS. Ordinarily, epidemiologists find a fairly well-distributed curve representing the biological minimum and maximum latency periods in which an agent will bring about a disease. A long plateau or second peak usually suggests another disease agent or an associated disease. Thus, an extrapolation of the curve plotted with raw CDC data, returning to the baseline after a few weeks, is more consistent with what is known by epidemiologists generally than is the elevated plateau of indefinite duration postulated by Dr. Bear after making his adjustments for presumed underreporting of late-onset cases.
Further, other agents associated with GBS  such as viral infection or lead poisoning  seem to have latency periods of no more than a few weeks. This fact lends credibility to the curves plotted by Dr. Schonberger, Dr. Nathanson, and Dr. Breman, and makes Dr. Bear's calculations less plausible.

Discussion
The heart of the controversy is graphically portrayed by defendant's Exhibit O, which is attached as Appendix A. It demonstrates that all of the statistical studies based on CDC's data agree that a sharp increase in the incidence of GBS occurred in the second and third week after vaccination, followed by a sharp decline during the next three to four weeks. This increase among vaccinees during the approximately five to six weeks after inoculation is sufficiently dramatic proof of causation to overcome any possible bias, reporting deficiencies, or statistical aberrations.
Equally dramatic is the general leveling off of the incidence rate following the sixth week. The contrast between the statistics for the first six-week period and those for the following weeks, even after adjustments by plaintiffs' experts, brings home emphatically the fundamental difference in the evidence of causation for those two periods.
The evidence offered by plaintiffs to extend the period of causality is characterized by relatively minute samples and consequently minute differences in the relevant data. Taking into account the numerous uncertainties which surround the data relied on and the degree of speculation incorporated into plaintiffs' computations, as shown by Dr. Mack's testimony, the Court is compelled to conclude that plaintiffs have failed to prove by a preponderance of the evidence the existence of a causal relationship after the tenth week following vaccination.
Consideration of a few of the key elements of the statistical case is sufficient to explain the Court's conclusion.

1. The Baseline GBS Attack Rate

Plaintiffs' theory of causation necessarily turns on the selection of a baseline sufficiently low to result in an attack rate for late onset cases of over twice the base rate. Dr. Bear selected a base rate of .24 per million persons per week; Dr. Goldfield used a base rate of .11 to compare against late-onset rates.
The evidence shows that the various studies of the incidence of GBS have produced baseline rates ranging from .19 to .44.[3] Dr. Mack urged adoption of a base rate of .4 and, in any event, of not less than .31.
On the evidence before the Court, a finding of a single true base rate would be wholly arbitrary. There is insufficient evidence to select a particular rate and reject the others. Moreover, none of the base rates purport to be more than estimates. Given the limitations of the available data, *316 the most the Court could do is to find that the evidence reflects a range within which base rates may reasonably be expected to fall.
Given that conclusion plaintiffs' data are insufficient to prove causation, inasmuch as they fail to establish a late onset attack rate in excess of twice the upper limit of the reasonable range.

2. The Adjusted Attack Rates

The second component of plaintiffs' proof is a computed attack rate in the vaccinated population which is more than twice the baseline rate.
Both Dr. Goldfield and Dr. Bear calculated attack rates for late onset cases which rested on certain assumptions concerning the degree of underreporting of GBS cases following the December 18 termination of the vaccination program.
The principal deficiency in these calculations is the assumption that late-onset cases occurred, yet went unreported as often as early-onset or unvaccinated cases did after December 18. Neither Dr. Bear nor Dr. Goldfield show a 50% likelihood of vaccine-causation as late as the thirteenth week without adjusting either the incidence of vaccinated cases or the baseline rate according to that assumption regarding underreporting. The assumption is largely unprovable, and there are indications in the evidence that it is false. Moreover, in order to employ the assumption, plaintiffs' experts must postulate larger numbers of cases from the handful of late-onset cases that were actually observed. The effect of manipulating such small samples is revealed in the jagged peaks and troughs of Dr. Bear's adjusted attack rate curve: it declines steadily from the third to the sixth latent week after vaccination, climbs again in the eighth week, falls to the tenth, climbs in the eleventh and then falls. (Appendix A) In the absence of any biological or clinical data to justify increases in the attack rate for particular late onset periods, these statistical results must be taken to reflect a lack of reliability due to the small samples.
While it is not disputed that a degree of underreporting occurred following December 18, how it affected the reporting of cases, both vaccinated and unvaccinated, remains a matter of speculation. Although Dr. Bear and Dr. Goldfield have made workmanlike attempts to quantify the underreporting, the Court is not persuaded that their results are more probably true than not. Just as in the case of baseline rates, the best anyone could do, given the small sample and the biases and uncertainties of the reporting process,[4] is to arrive at a probable range of estimates. Although none has been offered here, as previously pointed out, the vaccinated attack rates for late onset cases are so close to the range of unvaccinated baseline rates that the statistical evidence does not establish a probability of cause and effect relationship.

Conclusion
For the reasons stated, judgment will be entered for defendant, the parties to bear their own costs.
IT IS SO ORDERED.


*317 APPENDIX A

NOTES
[1]  This fact is readily illustrated by a hypothetical example. Suppose the relative risk for vaccines nine weeks after vaccination is two  i.e., that they are twice as likely to experience onset of GBS after that interval as are persons in the unvaccinated population during the calendar week. If fifty GBS cases occur among a million unvaccinated persons that week, then a hundred cases would be expected among a million nine-week vaccinees. Of that hundred, fifty would have been expected without vaccination, while the other fifty are explained only by the event of vaccination. Thus, the likelihood that a given nine-week vaccinated case of GBS is attributable to vaccination is 50%.

Similarly, if the relative risk of GBS to nine-week vaccinees is four, then 75% of all nine-week vaccinees are vaccine-linked. Once the relative risk rises above two, it becomes more probable than not that a given case was caused by the vaccine.
[2]  The raw difference between the attack rates based on pre- and post-December 18 report figures would not be an accurate measure of reporting deficiencies after December 18. Instead, the attack rate derived from each of the two sets of reports is weighted according to the size of the population sample from which it was derived, because a larger sample renders greater accuracy. Thus, the attack rate among vaccinees whose onset occurred one week after inoculation is different depending on whether pre-December 18 reports or post-December 18 reports are used to compute the rate. But the data from the former period represent the experience of eleven weeks of vaccinees, while only one week's vaccinees could be included in the post-December 18 figures for one-week onset, because vaccination ceased after the week ending December 18. In estimating the attack rate for one-week vaccinees, then, the pre-December 18 data is weighted much more heavily to compute the rate against which the reporting deficiencies of the later period will be measured. Conversely, the sample size for vaccinees who contracted GBS eleven weeks after vaccination is very small in the pre-December 18 period, as only vaccinees inoculated in the first week of the swine flu program could be observed in their eleventh latent week before December 18, while the sample after December 18 includes most of the vaccinees in the program. The rate computed for eleven-week onsets is therefore based more heavily on post-December 18 reports. Since eleven-week onsets are the latest that can be measured in the pre-December 18 period, Dr. Bear took the weighted average of these attack rates for onset intervals of one to eleven weeks and compared them with the attack rates computed from post-December 18 data alone for onsets of from one to eleven weeks. This comparison yielded an average implied reporting factor for the later period  the percentage of actual cases after December 18 which were likely to be reported, based on the experience with cases of one to eleven weeks latency which were measured in both periods.
[3]  The following seven studies computed these attack rates (per million persons per week):



Nathanson (total)               .19
Schonberger (CDC data)          .22
Bear (adjusted CDC data)        .24
Hugg (San Joaquin County)       .29
Nelson                          .31
Breman (Michigan)               .37
Kurland (Olmsted County)        .44

[4]  Dr. Mack observes that the size of the vaccinated GBS results through the first five or six weeks of latency renders insignificant the likely sources of bias, but that these become more critical in discussing the late-onset cases, which are relatively rare. If vaccinated cases at those longer onset intervals are more likely to be reported than unvaccinated cases  perhaps because of the publicity and interest surrounding the swine flu incident and the question of government liability  then there is an increasing bias in the post-December 18 figures. Similarly, where fewer unvaccinated cases are being reported, the cases of other diseases that are confounded with GBS disproportionately affect the relative risk estimates. Neither of these factors can be empirically measured, but their possibility weakens the reliability of the statistics drawn from the later weeks of surveillance, especially in Dr. Bear's study, which multiplied those figures in order to establish probable causation.
