Description of a new computer wire coding method and its application to evaluate potential control selection bias in the Savitz et al. childhood cancer study

We developed a new computer wire coding method and then applied it to investigate the suggestion that control selection bias might explain the observed association between wire codes and childhood cancer made in the study conducted by Savitz et al. in the Denver area. The computer wire coding method used a geographic information system approach with data on the local distribution electric system and from tax assessor records. Individual residences were represented as a circle scaled to the ground floor area of the residence and centered on the lot centroid. The wire code of the residence was determined from the distance between the circle and the relevant power line, and from the current carrying capacity of that line. Using this method, wire codes were generated for 238 290 residences built before 1986, the time of the Savitz et al. study, in the Denver metropolitan area. We then attempted to reconstruct the 1985 population of hypothetically eligible control children in the Denver metropolitan area by using 1980 census data. Since data were not available to locate the children in each residence within a census block, uniform, Poisson, and negative binomial distributions were used to randomly assign children to residences. To evaluate the likelihood of the wire code distribution of the controls selected by Savitz et al., 100 random trials were conducted for each distribution, matching two controls to each case. The odds ratios between childhood cancer and very high current configuration (VHCC) wire codes were reduced when the assigned controls were used, suggesting control selection bias may have been present. However, control selection bias is unlikely to account for all the reported association between childhood cancer and wire codes in the Savitz et al. study.     

Residential magnetic fields predicted from wiring configurations: I. Exposure model.

A physically based model for residential magnetic fields from electric transmission and distribution wiring was developed to reanalyze the Los Angeles study of childhood leukemia by London et al. For this exposure model, magnetic field measurements were fitted to a function of wire configuration attributes that was derived from a multipole expansion of the Law of Biot and Savart. The model parameters were determined by nonlinear regression techniques, using wiring data, distances, and the geometric mean of the ELF magnetic field magnitude from 24-h bedroom measurements taken at 288 homes during the epidemiologic study. The best fit to the measurement data was obtained with separate models for the two major utilities serving Los Angeles County. This model's predictions produced a correlation of 0.40 with the measured fields, an improvement on the 0.27 correlation obtained with the Wertheimer-Leeper (WL) wire code. For the leukemia risk analysis in a companion paper, the regression model predicts exposures to the 24-h geometric mean of the ELF magnetic fields in Los Angeles homes where only wiring data and distances have been obtained. Since these input parameters for the exposure model usually do not change for many years, the predicted magnetic fields will be stable over long time periods, just like the WL code. If the geometric mean is not the exposure metric associated with cancer, this regression technique could be used to estimate long-term exposures to temporal variability metrics and other characteristics of the ELF magnetic field which may be cancer risk factors.     

Association of residential magnetic fields with contact voltage

The US National Electrical Code's (NEC) requirement to ground a home's electrical service to the residential water line results in a voltage between the water line and earth, V W-E. The voltage may result from ground return current that flows into the earth via the water line or from inductive effects from other sources of magnetic fields, such as transmission lines. This voltage can, in turn, serve as a source for Vbath, the voltage between the water fixtures and conductive drain pipes sunk into the earth beneath a residence. Vbath can be a source of contact current exposure to a child touching a water fixture while bathing. Previous research has suggested that exposure to these currents could be the basis for the association between power-frequency magnetic fields and childhood leukemia. In this study, we assessed the association between measured Vbath and VW-E with the average spot-measured magnetic field, Bavg, in a sample of 191 single-family residences in the Denver metropolitan area. This area was the source of cases and controls for previous studies of electric and magnetic field (EMF) and childhood cancer. The association of both Vbath and VW-E with Bavg had upward trends across magnetic field strata (<0.1 microT (reference); 0.1-<0.3 microT; and > or = 0.3 microT). In addition, VW-E was associated with Vbath. Without further study, these results cannot be applied to multi-dwelling residences or to electrical systems prevalent in other nations. Nonetheless, when combined with the finding that contact current is a far more plausible candidate than the residential magnetic field for mediating biological effects on the basis of comparative dose to bone marrow, these associations indicate that contact current exposure deserves further study.     

Study of high- and low-current-configuration homes from the 1988 Denver Childhood Cancer Study

An epidemiological study conducted by Savitz et al. reported that residential wire codes were more strongly associated with childhood cancer than were measured magnetic fields, a peculiar result because wire codes were originally developed to be a surrogate for residential magnetic fields. The primary purpose of the study reported here, known as the Back to Denver (BTD) study, was to obtain data to help in the interpretation of the original results of Savitz et al. The BTD study included 81 homes that had been occupied by case and control subjects of Savitz et al., stratified by wire code as follows: 18 high current configuration (HCC) case homes; 20 HCC control homes; 20 low current configuration (LCC) case homes; and 23 LCC control homes. Analysis of new data acquired in these homes led to the following previously unpublished conclusions. The home-averaged (i.e., mean of fields measured in subjects' bedrooms, family/living rooms, and rooms where meals normally eaten) spot 60 Hz, 180 Hz, and harmonic (i.e., 60-420 Hz) magnetic fields were associated with wire codes. The 180 Hz and harmonic components, but not the 60 Hz component, were associated with case/control status. Measured static magnetic fields were only weakly correlated (rapproximately 0.2) between rooms in homes. The BTD data provide little support for, but are too sparse to definitively test, the 1995 resonance hypothesis proposed by Bowman et al. Case and control homes had similar concentrations of copper in their tap water. Copper concentration was not associated with wire codes nor with the level of electric current carried by a home's water pipe. These results of the BTD study suggest that future case/control studies investigating power frequency magnetic fields might wish to include measurements of 180 Hz or harmonic magnetic fields in order to examine their associations (if any) with disease status.     

Extremely low frequency magnetic fields in residences in Germany. Distribution of measurements, comparison of two methods for assessing exposure, and predictors for the occurrence of magnetic fields above background level

We examined the results of 1,835 magnetic field measurements in German residences conducted between November 1997 and September 1999. The measurements were part of an epidemiological study on the relationship between magnetic fields and childhood leukemia. We performed a fixed-location measurement of the magnetic field at 50 Hz and 16 2/3 Hz (frequency of the German railway system) over 24 h in the child’s bedroom in the residence of each study participant. In addition, we conducted a second 24 h-measurement in the living room at 50 Hz, and spot measurements while walking through all rooms of the respective dwelling. Median 50 Hz magnetic fields above 0.2 μT were found to be infrequent in Germany (only 1.4% of all residences). Fields produced by high-voltage power lines (123–420 kV) were lower than expected: the median magnetic field was above 0.2 μT in only 8 (32.0%) of 25 residences located 50 m or closer to a high-voltage power line indicating that power lines in Germany are usually run well below the maximum power load. We found that magnetic fields were correlated with the type of residence and higher magnetic fields were measured in apartment buildings. There was also some evidence for a positive correlation between magnetic fields and traffic density and an inverse association between magnetic fields and family net income. The 24 h-magnetic field measurements correlated well with the spot measurements (r>0.7). However, when dichotomized with a cut-off point of 0.2 μT, there was only a poor agreement between the two measurement methods. A loss of the strength of the association after categorization was also observed when comparing the arithmetic mean and median of the same 24 h-measurement. In summary, these analyses give a valuable overview of magnetic field distributions in German residences. Received: 31 January 2000 / Accepted: 25 July 2000     

The relationship between residential magnetic fields and contact voltage: a pooled analysis

It has been suggested that residential exposure to contact currents may be more directly associated with the potential for an increased risk of leukemia in childhood than magnetic fields. Contact current exposure occurs when a child contacts a bathtub's water fixtures, which are usually contiguous with a residence's electrical ground, and when the drainpipe is conductive. The Northern California Childhood Leukemia Study (NCCLS) is the only epidemiological study known to address whether contact current may confound the reported association between residential magnetic fields and childhood leukemia. The study contributed contact voltage and magnetic-field data for over 500 residences of leukemia cases and control children. We combined these data with the results of previous measurement studies of contact voltage in other communities to conduct an analysis of the relationship of magnetic fields with contact voltage for a total sample of 702 residences. The Spearman correlation of magnetic field with contact voltage was 0.29 (Spearman, P < 0.0001). Magnetic-field and contact voltage data were both divided into tertiles, with an upper magnetic-field cutpoint of 0.3 μT suggested by values used in epidemiological results and an upper contact voltage cutpoint of 60 mV based on dosimetric considerations. Expressed as an exposure odds ratios (EOR), we report an association of contact voltage with magnetic fields of 15.1 (95% CI 3.6-61) as well as a statistically significant positive trend across magnetic-field strata (EOR of 4.2 per stratum with 95% CI 2.4-7.4). The associations appear to be large enough to support the possibility that contact current could be responsible for the association of childhood leukemia with magnetic fields.     

Use of wiring configuration and wiring codes for estimating externally generated electric and magnetic fields

The relative locations and characteristics of the distribution lines feeding 434 residences in the Denver metropolitan area were recorded and classified according to the Wertheimer-Leeper code (WL code) as a part of an epidemiological study of the incidence of childhood cancer. The WL code was found to place the mean values of the fields in rank order. However, the standard deviations were approximately the same size as the means. Theoretical calculations indicate that a significant fraction of the low-power magnetic fields can be generated by the distribution lines, especially in the cases where the distribution lines are within 50 feet of the residence. Thus, the wiring code was shown to be a useful method for making a first-order approximation to predict long-term, low-level magnetic fields in residences.     

Ambient 60-Hz magnetic flux density in an urban neighborhood

A residential neighborhood in Buffalo, NY, was surveyed with a magnetic field meter to evaluate whether or not spot measurements are reliable predictors of the 60-Hz fields at street corners and residences. The results of repeated measurements over 7 days at 33 street corners in this neighborhood indicate that day-to-day variation in power line magnetic fields is negligible (intraclass correlation coefficient = 0.94). Multivariate linear regression analysis of the data indicates that transmission lines and thick, three-phase primary wires near the field measurement site are strong predictors and account for the majority of the ambient magnetic field variance between locations (multiple correlation coefficient squared = 0.60; F ratio = 22.2, P less than .001). Magnetic fields measured at the front sidewalk were highly correlated with fields at the front doorsteps of 45 homes in this neighborhood (gamma = 0.81). These results suggest that ambient power line magnetic field levels at urban residences can be reliably characterized on a one-time site inspection using a hand-held magnetic field meter and a simple wiring classification system.     

Rate of occurrence of transient magnetic field events in U.S. residences

Recent interest in the transient magnetic field events produced by electrical switching events in residential and occupational environments has been kindled by the possibility that these fields may explain observed associations between childhood cancer and wire codes. This paper reports the results of a study in which the rate of occurrence of magnetic field events with 2-200 kHz frequency content were measured over 24 h or longer periods in 156 U.S. residences. A dual-channel meter was developed for the study that, during 20 s contiguous intervals of time, counted the number of events with peak 2-200 kHz magnetic fields exceeding thresholds of 3. 3 nT and 33 nT. Transient activity exhibited a distinct diurnal rhythm similar to that followed by power frequency magnetic fields in residences. Homes that were electrically grounded to a conductive water system that extended into the street and beyond, had higher levels of 33 nT channel transient activity. Homes located in rural surroundings had less 33 nT transient activity than homes in suburban/urban areas. Finally, while transient activity was perhaps somewhat elevated in homes with OLCC, OHCC, and VHCC wire codes relative to homes with underground (UG) and VLCC codes, the elevation was the smallest in VHCC and the largest in OLCC homes. This result does not provide much support for the hypothesis that transient magnetic fields are the underlying exposure that explains the associations, observed in several epidemiologic studies, between childhood cancer and residence in homes with VHCC, but not OLCC and OHCC, wire codes.     

The possible role of contact current in cancer risk associated with residential magnetic fields

Residential electrical wiring safety practices in the US result in the possibility of a small voltage (up to a few tenths of a volt) on appliance surfaces with respect to water pipes or other grounded surfaces. This "open circuit voltage" (V(OC)) will cause "contact current" to flow in a person who touches the appliance and completes an electrical circuit to ground. This paper presents data suggesting that contact current due to V(OC) is an exposure that may explain the reported associations of residential magnetic fields with childhood leukemia. Our analysis is based on a computer model of a 40 house (single-unit, detached dwelling) neighborhood with electrical service that is representative of US grounding practices. The analysis was motivated by recent research suggesting that the physical location of power lines in the backyard, in contrast to the street, may be relevant to a relationship of power lines with childhood leukemia. In the model, the highest magnetic field levels and V(OC)s were both associated with backyard lines, and the highest V(OC)s were also associated with long ground paths in the residence. Across the entire neighborhood, magnetic field exposure was highly correlated with V(OC) (r = 0.93). Dosimetric modeling indicates that, compared to a very high residential level of a uniform horizontal magnetic field (10 mu T) or a vertical electric field (100 V/m), a modest level of contact current (approximately 18 mu A) leads to considerably greater induced electric fields (> 1 mV/m) averaged across tissue, such as bone marrow and heart. The correlation of V(OC) with magnetic fields in the model, combined with the dose estimates, lead us to conclude that V(OC) is a potentially important exposure with respect to childhood leukemia risks associated with residential magnetic fields. These findings, nonetheless, may not apply to residential service used in several European countries or to the Scandinavian studies concerned with populations exposed to magnetic fields from overhead transmission lines.     

Development of a protocol for assessing time-weighted-average exposures of young children to power-frequency magnetic fields

A study was carried out in 1990 to guide the development of a protocol for assessing residential exposures of children to time-weighted-average (TWA) power-frequency magnetic fields. The principal goal of this dosimetry study was to determine whether area (i.e., spot and/or 24 h) measurements of power-frequency magnetic fields in the residences and in the schools and daycare centers of 29 children (4 months through 8 years of age) could be used to predict their measured personal 24-h exposures. TWA personal exposures, measured with AMEX-3D meters worn by subjects, were approximately log-normally distributed with both residential and nonresidential geometric means of 0.10 μT (1.0 mG). Between-subjects variability in residential personal exposure levels (geometric standard deviation of 2.4) was substantially greater than that observed for nonresidential personal exposure levels (1.4). The correlation between log-transformed residential and total personal exposure levels was 0.97. Time-weighted averages of the magnetic fields measured in children's bedrooms, family rooms, living rooms, and kitchens were highly correlated with residential personal exposure levels (r = 0.90). In general, magnetic field levels measured in schools and daycare centers attended by subjects were smaller and less variable than measured residential fields and were only weakly correlated with measured nonresidential personal exposures. The final measurement protocol, which will be used in a large US study examining the relationship between childhood leukemia and exposure to magnetic fields, contains the following elements: normal- and low-power spot magnetic field measurements in bedrooms occupied by subjects during the 5 years prior to the date of diagnosis for cases or the corresponding date for controls; spot measurements under normal and low power-usage conditions at the centers of the kitchen and the family room; 24-h magnetic-field recordings near subjects' beds; and wire coding using the Wertheimer-Leeper method. © 1994 Wiley-Liss, Inc.

1 This article is a US Government work and, as such, is in the public domain in the United States of America.

     

Residential magnetic fields predicted from wiring configurations: II. Relationships To childhood leukemia.

Case-control data on childhood leukemia in Los Angeles County were reanalyzed with residential magnetic fields predicted from the wiring configurations of nearby transmission and distribution lines. As described in a companion paper, the 24-h means of the magnetic field's magnitude in subjects' homes were predicted by a physically based regression model that had been fitted to 24-h measurements and wiring data. In addition, magnetic field exposures were adjusted for the most likely form of exposure assessment errors: classic errors for the 24-h measurements and Berkson errors for the predictions from wire configurations. Although the measured fields had no association with childhood leukemia (P for trend=.88), the risks were significant for predicted magnetic fields above 1.25 mG (odds ratio=2.00, 95% confidence interval=1.03-3.89), and a significant dose-response was seen (P for trend=.02). When exposures were determined by a combination of predictions and measurements that corrects for errors, the odds ratio (odd ratio=2.19, 95% confidence interval=1.12-4.31) and the trend (p =.007) showed somewhat greater significance. These findings support the hypothesis that magnetic fields from electrical lines are causally related to childhood leukemia but that this association has been inconsistent among epidemiologic studies due to different types of exposure assessment error. In these data, the leukemia risks from a child's residential magnetic field exposure appears to be better assessed by wire configurations than by 24-h area measurements. However, the predicted fields only partially account for the effect of the Wertheimer-Leeper wire code in a multivariate analysis and do not completely explain why these wire codes have been so often associated with childhood leukemia. The most plausible explanation for our findings is that the causal factor is another magnetic field exposure metric correlated to both wire code and the field's time-averaged magnitude.     

The determinants of Canadian children's personal exposures to magnetic fields

Study of the health effects of magnetic fields often depends on identifying determinants and hence indicators of personal exposure. This study identified determinants of children's exposure to magnetic fields and constructed a prediction model for them. For 632 children participating in a case-control study of childhood leukemia, we made direct measures of exposure over 48 h using a portable device, together with observations on candidate determinants. A child's age and sex, the proportion of time spent in the home, and their parents' education or income were very weak predictors of (logged) mean 48 h magnetic field (R(2) < 1%). More important were province (R(2) = 8.0%) and type of residence (R(2) = 11.3%). Low temperatures at the time of measurement were associated with high fields (about 20% increase for each 10 degrees C below 14, R(2) = 4.9%). Several visible attributes of wiring around residences predicted exposure, mostly captured in the Wertheimer-Leeper wire code (R(2) = 13.5%). Stationary 24 h measurement in the bedroom (R(2) = 63.3%) and spot measurements outside the house (R(2) = 40.7%) predicted personal exposures best. Adding other minor predictors increased only slightly variance explained by 24 h stationary (R(2) = 66.2%) and spot (R(2) = 46.8%) measurements. Without spot or stationary measurements, the best model was much less powerful (R(2) = 29.0%). We conclude that spot measurements outside the residence provide a moderately effective basis for estimating exposure for children living there, but do not perform as well as 24 h stationary measurements in the child's bedroom. Although several other easily-observed variables were associated with personal exposure, they were weak determinants, either individually or in combination.     

Residential magnetic and electric fields

A magnetic flux density (MFD) and electric-field (E-field) data-acquisition system was built for characterizing extremely low-frequency fields in residences. Every 2 min during 24-h periods, MFD and E-field measurements were made in 43 homes in King, Pierce, and Snohomish counties of Washington State. The total electrical energy used in each residence during the 24-h measurement period was also recorded, and maps were drawn to scale of the distribution wiring within 43 m (140 ft) of these homes. Finally, on a separate date, field measurements were made in each home during an epidemiological interview. The results of this study can be summarized as follows: 1) 24-h-average MFD measured at two separate points in the family room were correlated, as were a 24-h-average bedroom measurement and the mean of the two family-room measurements. 2) The 24-h-average family-room MFD and E-field measurements were uncorrelated. 3) The 24-h-average total harmonic distortions of family-room MFD and E-fields were less than about 24% and 7%, respectively. 4) Residential MFD exhibited a definite 24-h (diurnal) cycle. 5) The 24-h-average and interviewer-measured MFD were correlated. 6) Residential 24-h-average MFD were correlated with the wiring code developed by Wertheimer and Leeper. 7) An improved prediction of 24-h-average residential MFD was obtained using the total number of service drops, the distance to neighboring transmission lines, and the number of primary phase conductors.     

Early pregnancy loss and exposure to 50-Hz magnetic fields

The possibility of an association of early pregnancy loss (EPL) with residential exposure to ELF magnetic fields was investigated in a case-control study. Eighty-nine cases and 102 controls were obtained from the data of an earlier study aimed at investigating the occurrence of EPL in a group of women attempting to get pregnant. Magnetic-field exposure was characterized by measurements in residences. Strong magnetic fields were measured more often in case than in control residences. In an analysis based on fields measured at the front door, a cutoff score of 0.5 A/m (0.63 μT) resulted in an odds ratio of 5.1 (95% confidence interval 1.0–25). The results should be interpreted cautiously due to the small number of highly exposed subjects and other limitations of the data. © 1993 Wiley-Liss. Inc.     

Interference of programmed electromagnetic stimulation with pacemakers and automatic implantable cardioverter defibrillators

A commercially available magnetic therapy system, designed for clinical application as well as for private use without medical supervision, was examined with respect to its potential for causing electromagnetic interference with implantable pacemakers (PMs) and automatic implantable cardioverter defibrillators (AICDs). A sample of 15 PMs and 5 AICDs were experimentally investigated. Each of the implants was realistically positioned in a homogeneous, electrically passive torso phantom and exposed to the magnetic fields of the system's applicators (whole body mat, cushion, and bar applicator). The detection thresholds of the implants were programmed to maximum sensitivity and both unipolar as well as bipolar electrode configurations were considered. The evaluation of possible interferences was derived from the internal event storages and pacing statistics recorded by the implants during exposure. Any "heart activity" recorded by the implants during exposure was interpreted as a potential interference, because the implant obviously misinterpreted the external interference signal as a physiological signal. Only cases without any recorded "heart activity" and with nominal pacing rates (as expected from the program parameter settings) of the implants were rated as "interference-free." Exposure to the whole body mat (peak magnetic induction up to 265 microT) did not show an influence on PMs and AICD in any case. The cushion applicator at the highest field intensity (peak magnetic induction up to 360 microT) led to atrial sensing defects in four PM models with unipolar electrode configuration. Under bipolar electrode configuration no disturbances occurred. The bar applicator led to sensing problems and consecutively reduced pacing rates in all tested PM models under unipolar electrode configuration and maximum field intensity (peak magnetic induction up to 980 microT). Bipolar electrode configuration resolved the problem. The investigated AICDs did not show malfunctions under any investigated condition. In conclusion, the examined PEMF therapy system did not interfere with the investigated implantable cardiac devices with bipolar electrode configuration. However, unipolar electrode configuration in pacemakers seems to be potentially hazardous during application of the examined PEMF therapy system.     

Measuring temporal variability in residential magnetic field exposures

Considerable interest has developed during the past ten years regarding the hypothesis that living organisms may respond to temporal variability in ELF magnetic fields to which they are exposed. Consequently, methods to measure various aspects of temporal variability are of interest. In this paper, five measures of temporal variability were examined: Arithmetic means (D(mean)) and rms values (D(rms)) of the first differences (i.e., absolute value of the difference between consecutive measurements) of magnetic field recordings; "standardized" forms of D(rms), denoted RCMS, obtained by dividing D(rms) by the standard deviations of the magnetic field data; and mean (F(mean)) and rms (F(rms)) values of fractional first differences. Theoretical investigations showed that D(mean) and D(rms) are virtually unaffected by long-term systematic trends (changes) in exposure. These measures thus provide rather specific measures of short-term temporal variability. This was also true to a lesser extent for F(mean) and F(rms). In contrast, the RCMS metric was affected by both short-term and long-term exposure variabilities. The metrics were also investigated using a data set consisting of twice-repeated two-calendar-day recordings of bedroom magnetic fields and personal exposures of 203 women residing in the western portion of Washington State. The predominant source of short-term temporal variability in magnetic field exposures arose from the movement of subjects through spatially varying magnetic fields. Spearman correlations between TWA bedroom magnetic fields or TWA personal exposures and five measures of temporal variability were relatively low. Weak to moderate levels of correlation were observed between temporal variability measured during two different sessions separated in time by 3 or 6 months. We conclude that first difference and fractional difference metrics provide specific and fairly independent measures of short-term temporal variability. The RCMS metric does not provide an easily interpreted measure of short-term or long-term temporal variability. This last result raises uncertainties about the interpretation of published studies that use the RCMS metric.     

Comparison of coupling of humans to electric and magnetic fields with frequencies between 100 Hz and 100 kHz

Recent laboratory and epidemiological results have stimulated interest in the hypothesis that human beings may exhibit biological responses to magnetic and/or electric field transients with frequencies in the range between 100 Hz and 100 kHz. Much can be learned about the response of a system to a transient stimulation by understanding its response to sinusoidal disturbances over the entire frequency range of interest. Thus, the main effort of this paper was to compare the strengths of the electric fields induced in homogeneous ellipsoidal models by uniform 100 Hz through 100 kHz electric and magnetic fields. Over this frequency range, external electric fields of about 25–2000 V/m (depending primarily on the orientation of the body relative to the field) are required to induce electric fields inside models of adults and children that are similar in strength to those induced by an external 1 μT magnetic field. Additional analysis indicates that electric fields induced by uniform external electric and magnetic fields and by the nonuniform electric and magnetic fields produced by idealized point sources will not differ by more than a factor of two until the sources are brought close to the body. Published data on electric and magnetic field transients in residential environments indicate that, for most field orientations, the magnetic component will induce stronger electric fields inside adults and children than the electric component. This conclusion is also true for the currents induced in humans by typical levels of 60 Hz electric and magnetic fields in U.S. residences. Bioelectromagnetics 18:67–76, 1997. © 1997 Wiley-Liss, Inc.     

Study of the implosion of wire arrays at the PF-3 facility

Results of experiments on the compression of tungsten wire arrays by the plasma current sheath (PCS) of the PF-3 facility at currents of up to 2 MA are presented. The efficiency of current transportation to the wire array and switching-over of the discharge current to the array were studied. Information on the penetration of the magnetic field into the wire array obtained using microprobes made it possible to compare the obtained experimental data with the results of magnetic field measurements carried out at other high-power electrophysical devices. The intensity of plasma production from tungsten wires under the action of the plasma focus PCS is estimated. The experimental results are tested against the existing models of wire array implosion with prolonged plasma production.     

Estimating missing data: an iterative regression approach

The problem of missing data is common in all fields of science. Various methods of estimating missing values in a dataset exist, such as deletion of cases, insertion of sample mean, and linear regression. Each approach presents problems inherent in the method itself or in the nature of the pattern of missing data. We report a method that (1) is more general in application and (2) provides better estimates than traditional approaches, such as one-step regression. The model is general in that it may be applied to singular matrices, such as small datasets or those that contain dummy or index variables. The strength of the model is that it builds a regression equation iteratively, using a bootstrap method. The precision of the regressed estimates of a variable increases as regressed estimates of the predictor variables improve. We illustrate this method with a set of measurements of European Upper Paleolithic and Mesolithic human postcranial remains, as well as a set of primate anthropometric data. First, simulation tests using the primate data set involved randomly turning 20% of the values to "missing". In each case, the first iteration produced significantly better estimates than other estimating techniques. Second, we applied our method to the incomplete set of human postcranial measurements. MISDAT estimates always perform better than replacement of missing data by means and better than classical multiple regression. As with classical multiple regression, MISDAT performs when squared multiple correlation values approach the reliability of the measurement to be estimated, e.g., above about 0. 8.