free the atmosphere, away from the influences of the earth's surface. From all of these measurements will come an understanding of the processes that control hydroxyl and determine the oxidizing capacity of the atmospherC.
REFERENCES
I . G.
2. S. M.
et a/.. J. Geophys. Res. 92. 1977
H. Mount and F. L Eisele. Scbce256. 1187 (1992).
3. G. H.Mount. J. Gm&s. Res. 97.2427 (1992). 4. F. E i and D. J. T * m M. 9295 (lW1). 5 J. A Logan. M. J. Prather. S. C. Wdsy. M. 6. . Mdlroy. ibid 86. 7210 (1981); D. Pemec e d., t J. Atmos. m. 185 (1987). 5. 6. M. Trainer e e/.. J. Geophys. Res. 92. 11,879 f (1987). 7. c. M. e & . w. 18.441(1990). t. m, 8. A M. Thompson. Science256. 1157 (1992).
~h t t i~n 2448 (m ~ $ DC.$1986). distinct frominthose forw generation are ~ ~ ~ Washington, ~ inference or~ public policy &new, legal ~h & setting ~ w o
The statistical criteria used in scientific
'
The Continuing Case of the : - Florida Dentist :
Temple F. Smith and Michael S. Waterman
Applications of DNA fingerprinting or typing are becoming increasingly common and diverse. A suspect can be convicted or set free on the basis of a "fingerprint" of DNA found at a crime scene. In a recent dramatic case, the Nazi war criminal Josef Mengele of the notorious Auschwitz concentration camp was declared to have been dead for more than a decade on the basis of a DNA fingetprint match between a set of Bradlian bones and a sample from his living son. Ti is an example of the use of DNA hs fingerprintingto establish relationship, in this case by paternity testing. General applications of DNA fingerprinting in pediatric practice range from paternal identification through genetic disease diagnoses to child abuse verification (I). In this issue of scimrc Ou et al. (2) present an analysis of the viral DNAs associated with the alleged human immunodeficiency virus type 1 (HIV-1)infection of a number of patients by their Florida dentist. These uses of molecular data raise a multitude o important issues, both scienf tific and ethical. There are also major unresolved issues as to the levels of statistical and scientific reliability appropriate for deciding public policy or for use in our judicial system. In 1989 Lander (3) argued that new experimental standards must be defined for DNA data use in judicial cases but did not directly address the statistical issues. A recent report of the National Academy of Sciences Panel on DNA and Forensic Science, h d e d by V c o McKusick of Johns itr Hopkins Hospital (4), addresses these and related issues. These questions must be addressed by the scientific community bel F Smith ts at the Blomdecular Engineering Research center. Boston University. Boston. MA 022t 5 M S Waterman IS a! the Department of Mathemallcs. Unversity of Scutbm Calflomia. Los Angeles. CA
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cause science is and will continue to be used to formulate public policy and to form judicial decisions. Quite often scientific data and conclusions are used by those unfamiliar with its limitations. The majority of comparative DNA sequence studies have as their conclusion the generation of scientific inferences. It is ideal if such inferences are supportad by overwhelming statistical evidence. However, under the assumption o eventual experf imental testing of these inferences, those supported by evidence o even marginal f statistical significance can be quite valuable, particularly when deciding which experiment to d o r m next among the m r a yid possible experiments. In other situations, statistics play an important but less welldefined role. For example, in the public policy arena, estimates of statistical signifie cance are Md into riskcost-benefit analyses, cost-effectiveness studies, and policy analyses. Here the links between science, statistics. and conclusions can become very obscure. In these areas, there is not always f a guarantee o timely rejection of incorrect inferences as a result of experimentation nor is there an accepted criterion for statistical significance. The Statistical significance used by the public and many agencies to recommend life-style changes often is not extremely strong, particularty as it may relate to cancer. One should recall that the great statistician and biologist R. A. Fisher never accepted even the evidence linking smoking and lung cancer; the public certainty has come from evidence accumulated since Fisher's death. However, the analyses of HW-I transmission have provided sufficient statistical evidence for most nations to spend considerable money on research, to recommend the wide use of condoms, and to support the use of gloves by all medical personnel.
SCIENCE
precedents o for civil or uiminal coum. r Legal situations require the hrghesr statistical significance to generate a verdict beyond a reasonable doubt! The obvious potential forensic utility of various molecular techniques could be lost if their early judical use i inconclusive o improper. The s r concern here is not academic as exemplified by Ou et al. (2) in which statistical analyses of the aUeg4 HIV-1 infection of patients by their dentist were used to conclude that, for at least five of hi patients, the dentist w s the most likely source o the infection. a f The work can influence pending insurance cases and public health policies and has already been involved in a Florida court process. The court delayed certain actions hi until the publication decision of ti journal and until all o the data were made f public (5)Not only were the authors likely to be quoted or called by the court, but the reviewers were under some additional pressure. A News & Comment piece (5) even appeared before the review process was complete. This was due, in part, t the fact o that some of the data in the proent analysis had been used in an evlki preliminary study (6) and that an d y copy of Ouir d. (2) had beenobtained through the& F of Information A t In Iddidon, there was c. some delay in d i n g aMilaMc the entire data set to all parties conccmcd. Thus, it is c l d y possible for data, a manuscript, and even the review process to become entangled in the legal process. When there is potential for legal implica150I
. VOL
8knyrffy 0 01strhUoM o lwckdd. .bnikrlty bof mothusnd Intnt..The intermother histogram i of the lluckme similaritiesbes . tweenallpairsofvadantS,eachpaircomposed of one variant from two different mothers. The mother-infant histogram is o the nucleotide f similarities between pairs of variants. each pair from a mother and her M infant. The sequences were obtained from the Genl3ank database. *ere Wdinsky and m-workers have deposcted 12 isolates from mother 1, 19 f r o m mother 2. and 23 from mother 3.along with 21 isolates for the infant of mother 1. 13 for that of mother 2. and 27 for that of mother 3
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tions or major public policy. the scientist has a responsibiliol to decide, in advance, what statistical criteria are most appropriate. The fingerprint utilized in Ou et al. (2) was based on the C2-V3 domain of the HIV-1 envelope gene. Under the hypothesis that the dentist has infected a patient, viral sequences of this highly variable region that are isolated from the patient should be much closer to viral sequences from the dentist than to a sequence from a randomly chosen HIV-1-positive person. However, analysis of the relationships HIV-1 among sequences is more complicated than in situations such as paternity. testing. In the more common appIications of DNA typirpth4 loci remain fixed for the lifetime of ab individual, but HIV-1 is evolving so rapidly that each individual is host to a population of HIV-1 variants. In particular this holds for the C2-V3 domain. There is a large difference between tracing the history of a singlecopy gene and tracing the histories of viral variants each evolving in an individual member of the infected population. Furthermore. each variant could have different tissue and transmission
behaviors (7). A relevant study of the C2-V3 region has been published by Wolinsky et d. (8).
They studied cases of known transmission from infected women to their unborn children for three mother-infant pairs when the i f n s were 2 to 4 months old. Up to 27 nat variants were isolated from one of these patients. Unexpectedly, in two o the three f pairs a proviral form infrequent in the mother was dominant in the infant. In addition, the infant's viral sequences were less variable than were their mother's. H s itograms of the distribution of mother and infant nucleotide sequence similarities, based on data deposited in GenBank, are shown in the figure. There is a small positive overlap between these distributions, suggesting that mothers and infants (where the pattern of transmission is incontrovertible) had m e sequences that were just as different from each other as if they had been taken from the unrelated mothers. Motherinfant transmission is one example of HIV-1 transmission modes, but these data illustrate some of the difficulties that arise in studies of the transmission of this virus. O et d. (2) have data from the dentist, u from seven patients infected with HIV-1, and from 35 local controls (LO). Two of these patients were identified as having high-risk behavior and thus were not considered as valid tests of 'the dentist's virus being their infectious source. Additional epidemiological data would have been of interest, such as the randomness of the LC sample including their randomness of times since infection. Time since infection is an
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important variable, since HIV-1 evolves so rapidly. There is an additional factor that adds difficulty in evaluating the data. For analysis, DNA was first amplified by the polymerase chain reaction (PCR). For the dentist, the patients, and some LCs, this DNA was then cloned into M13 and sequences were obtained from individual clones. Five to 12 cloned sequences were obtained from each patient. Direct PCR sequencing without first cloning was used to determine sequences for all LCs. Direct PCR sequencing is a sampling method that at best generates a sequence composed of the most prevalent base at each position and at worst generates only the sequence of ains one of the more prevalent viral v r a t . The task of using this molecular data to test the hypothesis that the five non-highrisk patients contacted HN-1 from the dentist is statistical in nature. The Wilcoxon rank-sum test was used by Ou et d. (2) and has the following form. We have two samples of numerical values X,X2 * X, and YIY2 Ym and wish to test if the * X (patient) distribution coincides with the Y (LC) distribution. The X samples and the Y samples are pooled and the 5 30 values are ranked, smallest to largest. The Wilcoxon rank-sum statistic S is the sum of the ranks corresponding to the X sample. The hypothesis of identical X and Y distribution is rejected if S is too small or too large. With the molecular data at hand, the ideal test would be to use one dentist DNA to compare with one DNA from each of the 5 patients and the 30 LO and reject the hypothesis if S is too small. There were at least two DNAs cloned from the dentist f and varying numbers o cloned patient DNAs. These unequal sample sizes were handled by using the average distances between the dentist DNAs and those of the patients and LCs. Since average3 with different samples sizes have dderent distributions, there is a problem with using the Wilcoxon statistic with averaged X and Y. s s Another problem is the distinction between the cloned sequences and the direct sequences, which again starts us off with different X and Ys. The authors turned to s bootstrappingto get around these problems. Bootstrapping is a statistical procedure that resamples the origins data with replacement, obtaining statistical replic...