Dynamic Sequential Sampling Plan for Helicowerpa zea (Lepidoptera: Noctuidae) Eggs in Processing Tomatoes: Parasitism and Temporal Patterns

Dynamic Sequential Sampling Plan for Helicowerpa zea (Lepidoptera: Noctuidae) Eggs in Processing Tomatoes: Parasitism and Temporal Patterns MICHAEL P. HOFFMANN, LLOYD T. WILSON,2 FRANK G. ZALOM, AND RICHARD J. HILTON3 Department of Entomology, University of California, Davis, California 95616 Environ. Entomol. 20(4): 1005-1012 (1991) ABSTRACT Commercial fields of processing tomatoes located in the Sacramento Valley of California were monitored for eggs of the tomato fruitworm, Helicoverpa zea (Boddie), over a 5-yr period. In general, egg density remained low until near mid-august. During a narrow window of time, egg density increased rapidly across all fields. The first treatable levels of H. zea eggs were recorded during this period, or later, for all years. These results Letter define when to begin sampling processing tomatoes for eggs of H. zea. Eggs of H. zea were found to have an aggregated spatial pattern in tomato Eields. A dynamic sequential sampling plan was developed which adjusts the economic threshold according to the level of egg parasitism. When compared with the currently recommended sampling plan, sequential sampling required approximately 60% fewer leaves to reach a management decision. KEY WORDS Insecta, Helicoverpa kea, Trichogramma spp., sampling PROCESSING TOMATO (L ycopersicon esculentum Miller) is one of California s major vegetable crops. In 1989, >7,711,000 metric tons were processed (Synder 1989). The tomato fruitworm, Helicoverpa zea (Boddie), is considered one of the most important lepidopterous pests of this crop because the larvae cause direct damage to and contaminate the fruit. The presence of excessive damage, insect parts, or frass can result in part or all of the harvested crop being rejected (Canners League of California 1980). Fields of processing tomatoes located in the San Joaquin and Sacramento Valleys of California that are harvested in early August or later are most likely to have economical infestations of H. zea, Spodoptera exigua (Hubner), or S. praefica (Grote). Fields harvested before this can frequently escape damage entirely (Lange & Bronson 1981). Until recently, relatively little in-depth research concerning the life history and population dynamics of H. zea has been conducted in the San Joaquin or Sacramento Valleys. Valez (1970) developed life tables for H. zea infesting sweet corn in the Sacramento Valley and reported that H. zea pupae enter diapause and successfully overwinter. Lange & Bronson (1981) reported increased blacklight trap catches of H. zea late in the season, but their efforts were limited to a single location in the Sacramento Valley. Recently, Hoffmann et al. (1990a) reported that parasitism of H. zea eggs by Trichogramma Current address: Department of Entomology, Comstock Hall, Cornell University, Ithaca, N.Y. 14853. Current address: Department of Entomology, Texas A&h4 University, College Station, Tex. 77843. Current address: Southern Oregon Esperiment Station, hledford, Oreg. 97502. spp. is an important mortality factor in processing tomatoes, and results from an area-wide trapping program indicate that there are at least two generations of H. zea in the Sacramento Valley and three in the San Joaquin Valley (Hoffmann et al. 1990b). A better understanding of the temporal and spatial patterns of H. zea could make monitoring programs more cost-effective by determining when fields should be sampled and providing the basis for development of more efficient sampling methods. The cost of monitoring can also be reduced (without sacrificing reliability) by sampling a subunit of the plant where the pest is most frequently found (Wilson et al. 1982). The within-plant distribution of N. zea eggs on tomato has been reported by several investigators (Nilakhe & Chalfant 1981, Alvarado-Rodriguez et al. 1982, Zalom et a]. 1983). Zalom et al. (1983) reported the preferred oviposition site of H. zea on processing tomato plants to be leaves below flower clusters. Of all flower clusters on the tomato plant, the first leaf below the highest flower cluster was subsequently determined to be the most frequent site of oviposition, and the number of eggs observed at that location reflects the number on the remainder of the plant (F.G.Z., unpublished data). This information has been used in the development of a practical fixedsize sampling plan for H. zea eggs in processing tomatoes. Associated with this sampling plan is a dynamic treatment threshold that incorporates the level of egg parasitism by Trichogramma spp. (Hoffmann et a]. 1990a). The within-field spatial pattern of H. zea eggs has been reported for several crops and using a 0046-225X/91/1005-1012$02.00/0 0 1991 Entomological Society of America

1006 ENVIRONMENTAL ENTOMOLOGY Vol. 20, no. 3 variety of dispersion indices (Nilakhe et al. 1982, Wilson & Room 1982, Terry et al. 1989). The objective of most of these investigations was to develop the basis for a sampling technique for H. zeu eggs. Sequential sampling has the advantage of being less time-consuming than sampling a fixed number of units, especially when pest densities are well below or above the economic threshold. In cotton, sequential sampling techniques for several insect species has resulted in >76% savings in time over conventional sampling (Sterling 1975). The objectives of the research reported here were to better define the late-season spatial and temporal pattern of H. zea eggs in processing tomatoes in the Sacramento Valley and to develop a dynamic sequential sampling plan that would adjust the economic threshold according to the level of egg parasitism. Materials and Methods Commercial fields of processing tomatoe2 located in the Sacramento Valley were monitored for eggs of H. zeu in 1983-1986 and 1989 as part of various research and demonstration projects. Fields were generally sampled weekly, starting in midto late July; sampling continued until just before harvest. In 1983, four fields located in three different counties were monitored by examining the leaves located immediately below all flower clusters on 18-30 plants per field. The primary purpose of this study was to determine if certain flower clusters on the tomato plant were preferred sites for oviposition by female H. zea (F.G.Z., unpublished data). The early season sample size of 30 plants per field had to be reduced to 18 because of the increased time required to sample plants in full bloom. In 1984, H. zea egg data were obtained from 31 fields distributed throughout the southern Sacramento Valley. These fields were monitored as part of a project that demonstrated the Integrated Pzst Management (IPM) program for processing tomatoes (Zalom et al. 1990). Each field was monitored by pest control advisors, using an early version of the H. zea egg sampling protocol (Brendler et al. 1985). At each field visit, the advisors sampled at least 30 tomato leaves for white H. zea eggs. In 1985 and 1986, 16 fields were sampled as described by Hoffmann et al. (1990a). Up to 540 leaves were examined at each field observation, and the number of white (unparasitized or parasitized, but not yet black) and black (parasitized) H. zea eggs was recorded. White eggs included those in the brown ring and black head stage. Parasitism was confirmed by holding field-collected eggs in the laboratory and observing if a larva or parasitoid(s) emerged. In 1989, 10 fields were monitored and 200 leaves were sampled randomly at each field observation and examined for eggs. These fields were monitored to validate the treatment threshold that incorporates mortality due to Trichogramma spp. The first leaf below the highest flower cluster on the tomato plant was the sample unit in all years except 1983. Cultural practices \vithin fields were typical of the Sacramento Valley. Pest control varied among fields, but many fields after 1983 were managed nccording to the University of California IPM protocol for processing tomatoes. On average, fields were treated with an insecticide less than one time per season for control of lepidopteran pests, and these applications \vere generally made late in the season. To determine when the late-season increase in H. zea egg density occurred and whether there were similarities among fields and years in the tiniing of this event, we examined the seasonal patterns in egg density during all years. We selected the first date during the season on which the number of eggs per day (number of eggs observed divided by number of days since last observation) at least doubled from the previous observation to be the starting point of late-season oviposition activity (i.e., the date on which egg densities started to increase rapidly). Because egg densities increased rapidly, a doubling in egg density appeared to be a reasonable measure of change. Some fields were not included because the number of eggs per day ne\ er doubled or very few or no eggs were recorded. Analysis of variance (ANOVA) was used to determine if the mean dates on which the number of eggs per day first doubled were significantly different among years (Abacus Concepts, 1986). This statistical package also was used for the regression analyses reported herein. Because there were many fields sampled in 1984, and because of the considerable variability in egg abundance among fields, we converted egg records per date to proportions of the seasonal total for each field. For every week, proportions were averaged across fields located in each of four areas of the Sacramento Valley. From north to south, these areas included seven fields in Colusa County and eight fields each at a latitude similar to that of the communities of Robbins, Woodland, and Davis. The distance (north to south) encompassing these fields was approximately 95 km. Because the data are presented as proportions, the dates ivhen egg densities first doubled were not calculated, and no comparable statistic was calculated. To determine if the sequential sampling plan (Table I), developed using the 1985-1986 data, would be more cost-effective (require fewer samples) than the fixed sample size of 30 or 60 leaves, we compared the sample size (number of leave%) required to reach a management decision for each sampling plan. To make the comparison, \\e used subsets (30 leaf samples) of data and considered each subset to be equivalent to a whole-field sample. All dates on which fields were sampled between the last week of July and the first insecticide application or harvest were used. During these two years, fields Lvere divided into 18 areas (3 x 6 grid) and from each area, 30 leaves were sampled and

August 1991 HOFFMANN ET AL.: SEQUENTIAL SAMPLING PLAN FOR Helicoverpa tea 1007 Table 1. Sequential sompiing plan for H. tea eggs in processing tometoes at different ratios of black/white eggs c- - Ratio of black/white eggs Leaves 0.0-0.4" > 0.04-0.08 > 0.08-0.15 > 0.15-0.30 >0.30 sampled No treat Treat treat No Trent treat No Treat treat No Treat tet Treat 10 0 5 1 6 2 7 2 8 3 9 20 1 6 3 9 11 5 12 6 14 30 2 8 5 12 4 15 8 17 11 19 40 4 10 7 15 9 18 12 21 14 24 50 5 11 9 18 12 22 15 2.5 18 29 60 63 13 11 20 15 25 18 29 22 34 50 15 13 23 18 29 22 34 26 39 80 8 16 15 26 20 32 '"" 25 38 30 44 90 9 18 15 28 23 36 28 42 34 49 100 11 20 20 31 26 39 32 46 38 53 0 Range of ratios of l)lack/white eggs for decision columns. Values in columns are numbers of white eggs. See text for further (qplanation of how to use decision columns (lines). examined for eggs of H. zea (Hoffmann et al. 1990a). For each date, the number of eggs recorded from each of the four centermost areas of fields was used. The selection of these four areas was somewhat arbitrary, but if there was an edge effect, these areas would least likely be affected. Because the maximum sample size for the fixed sample size plan was 60, this same maximum was used for sequential sampling when the two methods were compared. Depending on the proximity to the economic threshold, each set of four areas resulted in up to four decisions (treat or not to treat). For example, four decisions could be made if each sampling plan required 30 or fewer leaves to reach a decision. Fewer decisions were made if >30 leaves were needed because additional leaves were required from a second area. Results and Discussion Temporal Distribution and Initiation of Sampling. Hoffmann et al. (1990a) previously presented seasonal oviposition trends of H. zea for the years of 1983, 1985, and 1986. These data are presented here in a cumulative manner, along with 1984 and 1989 data, to depict the time period when egg density begins to increase rapidly (Fig. 1-3). In 1983, 1985, 1986, and 1989, the mean day-ofyear (tsem, n) on which the number of eggs per day first doubled was 223.8 (9.2, 4), 223.4 (3.0, 8), 230.5 (2,4,8), and 225.7 (2,1,7), respectively. These means were not significantly different (F = 0.90; df = 3, 23; P = 0.46). The calendar date equivalents for these days of the year are 12, 11, 19, and 14 August. Although nine fields are depicted for 1989 (Fig. 2), two fields were not used for this comparison because the increase in egg density per day never doubled. The 1984 data, which are presented as mean proportion of seasonal total, also show that in late season, egg densities rapidly increase starting during the second week of August (Fig. 3). The results from all years indicate that a rapid increase in egg density occurs about the same time and within a narrow window of time each year. If fields had been sampled more frequently in these studies, the window in time might have been more closely defined. Roltsch & Mayse (1984) also reported similar field-to-field temporal patterns of H. zea egg density in tomatoes in Arkansas. The reason for the variability in egg density among fields and rapid increase in egg density late in the season in processing tomatoes is not known. Processing tomatoes are grown in a matrix of several other potential host crops for H. zea in the Sacramento Valley, including a substantial amount of field corn. It is possible that the proximity to corn or the phenology of corn or other alternate host crops for H. zea (or both) may account for the observed variability among fields. Corn may also be the source of adult H. zea that rapidly infest fields late in the season. Field corn in the Sacramento Valley is frequently heavily infested with H. zea (Hoffmann, M. P., L. T. Wilson, F. G. Zaloin, unpublished data). The timing of economical infestations of H. zea also reflects the late-season increase in egg density. During 1984, 1985, 1986, and 1989, treatable levels (four or more eggs per 30-leaf sample) were recorded 31 times. The average date on which the threshold was reached was about 21 August (SEM & 1.4) (range, 9 August-4 September). The current IPM protocol for processing tomatoes suggests that sampling for eggs of H. zea and fruit damage caused by lepidopterous pests should begin at 722 degree-days (DD) (lower threshold of 10 C) after planting. This is based on the fact that fruit damaged by H. zea or other lepidopterous pests that occurs within 5-6 wk of harvest can still be present at harvest and thereby jeopardize crop quality. Fruit damaged before this should decay and fall from the plant before harvest (Zalom et al. 1986). Early damage is generally light and considered to have minimal effect on yield. Initiating sampling at 722 DD from planting does not adequately consider that only the late-planted fields (harvested mid-august or later) are the most likely

1008 ENVIRONMENTAL ENTOMOLOGY Vol. 20, no. 4 0.5 I 0.6 I 0.4 0.3 0.2 0.1 0.0 1 1986 0.8 0.6 0.4 0.2 0.0 t lgs5 0.3 1 0.08 0.06 July August Sept. Fig. 1. Cumulative H. tea eggs per leaf in several fields of processing tomatoes monitored in 1983 and 1985. Each line represents a different field. Arrow indicates mean date on which the number of eggs per day doubled for the first time. to incur damage. Wilson et al. (1983) developed a sequential sampling technique that takes into account the seasonal variation in fruit damage due to H. zea and Spodoptem spp.; i.e., the economic threshold becomes morkconservative as the season progresses. Because egg densities do not start to increase rapidly until near mid- August and treatable densities of eggs do not occur until mid-august or later, intensive sampling for eggs before the first week of August may not be necessary. However, to be conservative, sampling should be started the last week of July. This does not, however, preclude 0.04 0.02 0.00 Fig. 2. Cumulative H. tea eggs per leaf in several fields of processing tomatoes monitored in 1986 and 1989. Each line represents a different field. Arrow indicates mean date on which the number of eggs per day doubled for the first time. sampling for other pests for which the seasonal activity is not as well understood. Approximately 17% (6,300 ha) of the processing tomato crop grown in the Sacramento Valley is harvested before the last week of July (California Processing Tomato Advisory Board, personal communication). Consequently, this portion of the crop would not have to be monitored for H. zea infestations. Monitoring

I -- c - August 1991 HOFFMANN ET AL.: SEQUENTIAL SAMPLING PLAN FOR Hellcoverpa zea 1009 of the remaining fields would begin at the recommended 722 DD from planting. It is likely that the patterns of egg density observed in the Sacramento Valley may also occur in the San Joaquin Valley because patterns in captures of male H. zea in pheromone traps are similar in both areas (Hoffmann et al. 1990b). However, until the seasonal patterns of H. zeu egg density is investigated in other areas, the results presented here are applicable only to the Sacramento Valley. Like pheromone trap catch patterns of H. zea males, these data indicate that the seasonal pattern of egg density is similar across widely dispersed fields in the Sacramento Valley and suggests that there is potential for regional management of H. zea, at least as it relates to initiating sampling. Sequential Sampling and Spatial Pattern. The University of California IPM protocol for processing tomatoes designates four unparasitized H. zea eggs per 30 tomato leaves as the treatment threshold (Brendler et al. 1990). Infestations at this level will result in fruit damage below the 2% maximum set by industry (Canners League of California 1980). This threshold assumes a larval mortality rate of about 97% and that each surviving larva will damage three fruit (unpublished data). Apparently most mortality to larvae is due to abiotic factors and factors associated with the tomato plant. The assumption that this larval mortality rate is constant across space and time could lead to treatment decision errors. However, the threshold is apparently conservative and to date has been satisfactory in commercial use (Zalom et al. 1990). The sample size currently recommended for use in processing tomatoes is 30 leaves/2o-ha field (Brendler et al. 1990). If three or more eggs are recorded per 30-leaf sample, an additional sample of 30 leaves is required. Because of the potential savings in time over the existing sampling plan (30 or GO leaf samples per field) for eggs of H. zea, we developed a sequential sampling plan using equation 1 as developed by Wilson (1985). This equation provides an estimate of the sample size required to estimate whether the pest density is above or below its economic threshold. where n is the number of tomato leaves to be sampled, t is the standard normal variate, CY is the probability of treating when it is not necessary and P is the probability of not treating when it is necessary, T, is the threshold expressed as mean white eggs per leaf for the ith level of parasitism (estimated by ratio of black to Xvhite eggs), i? is the mean density of white H. zea eggs per leaf, and a and b are Taylor s coefficients (Taylor 1961). The ratio of black to white eggs is used to estimate what proportion of the white eggs are parasitized but have yet to turn black (Hoffmann et al. 1990a). We selected an CY and 0 rate of 0.3 and 0.15, respectively. This assigns twofold more importance to minimizing the potential loss of revenue by not 1.0 - ~ 0.8-0.6-0.4-0.2-0.0. 1984 H. zea Eggs --. Colusa Co. (7) Robbins (8) Fig. 3. Cumulative mean proportion of total white H. zea eggs observed during 1984 in fields of processing tomatoes located in four regions of the Sacramento Valley. Number of fields is indicated in parentheses. controlling H, zea, when in fact a treatment was required. Because of the large and relatively consistent sample size used in 1985-1986, these data were used to develop a sequential sampling plan. Taylor s a and b coefficients were estimated by regression of log, variance against log, mean (Taylor 1961) for white, black, and white plus black eggs per leaf for the combined 1985 and 1986 data (Fig. 4). The antilog of the intercept estimates the a coefficient and the slope estimates the b coefficient. The regression line slopes and intercepts of the logtransformed white and black eggs were not significantly different (P < 0.05) (Zar 1984). Therefore, the sequential sampling decision lines were based on the combined black and white egg data. Taylor s Coefficients were estimated to be 1.792 and 1.079 for white eggs and 2.112 and 1.113 for black eggs. For the combined data, the coefficients were 1.838 and 1.083, respectively. Table 1 depicts several sets of sequential sampling decision lines. To use the table, the cumulative number of black and white eggs observed per incremental sample of 10 leaves is recorded, and the ratio of black to white eggs is calculated for each increment. Each set of decision lines (columns) is for a different black/white egg ratio (Le,, different threshold). AS

1010 ENVIRONMENTAL ENTOMOLOGY Vol. 20, no. 4 Y white Eggs t ' v y = 0.58315 + 1.0790~ R"2 = 0.980 0- n=83.i -2 - F y = 0.60869 +- 1.0827~ R"2 = 0 n=83-2 - -4 - " -7-6 -6-4 -3-2 -1 0 Log Mean Fig. 4. Log,, mean and log, variance regressions of H. zeu eggs observed in 1985 and 1986. Each point is based on a sample of 500-540 tomato leaves. the ratio increases, so does the threshold. The ratios depicted in this table are equal to thresholds of 0.13-0.23, > 0.23-0.30, > 0.30-0.36, > 0.36-0.43, and >0.43 white eggs per leaf. The decision lines in Table 1 are conservative because each set was calculated using the lowest ratio (threshold) of each range presented. Once the ratio of black/white eggs is determined, the appropriate set of decision lines is selected. If the number of white eggs is equal to or a C less than the number in the "no treat" column, a treatment is not warranted. If the number of eggs equals or exceeds the upper decision line, a treatment is warranted. If the number falls between these decision lines, additional samples are taken until a decision is made or the maximum number of leaves (n = 100) are sampled. If the maximum number of leaves is sampled without a decision being made, the field should be sampled again in 2-3 d. Table 1 can be used in the Sacramento Valley, where egg and larval mortality have been quantified. In other areas, such as the San Joaquin Valley, these mortality factors may differ and may require modification or small-scale testing of the sampling program before full-scale implementation. Use of the black/white egg ratio to estimate rates of parasitism following applications of broad-spectrum insecticides is currently not recommended because the insecticides can cause significant mortality to adult Trichogramma and consequently can reduce levels of parasitism (Hoffmann et al. 1990a). However, it is unlikely that a second insecticide application would be required before harvest. In the absence of black eggs in field samples, the first set of decision lines (ratio, 0.0-0.04) should be used, or if time permits, eggs can be held and observed for parasitism. The between-leaf distributions of white, black, and white plus black eggs combined were found to be aggregated (S2/f > 1). In each case, the slope of the regression line was significantly (P < 0.01) greater than 1, indicating an aggregated distribution. Respective t values and sample size (n) for each regression analysis were as follows: white eggs, 42.5, 83; black eggs, 29.4, 34; and black and white eggs combined, 51.5, 83. Nilakhe et al. (1982)also found the between-leaf distribution of H. zea eggs to be aggregated in tomatoes. Savings Using Sequential Sampling. A total of 276 decisions was compared using the fixed and sequential sampling technique (Table 2). Fewer samples were required to reach a decision using the sequential plan in 97.8% of the comparisons. On a single date, a maximum sample of 60 leaves was taken with the sequential sample without a decision being made. Overall, 62.2% fewer leaves needed to be sampled to reach a management decision using the sequential sampling plan versus the currently recommended egg sampling procedure. Both plans incorporate egg mortality from Trichogramma spp. The number of decisions to treat were nearly identical for both sampling plans. These results indicate that sequential sampling can substantially reduce the number of samples required to make a treatment decision. It shouldbbe noted, however, that the reduction in the number of leaves sampled is not necessarily directly reflected in time saved because the sampler must still walk the entire field to take the fruit damage sample (Brendler et al. 1990). An additional study to evaluate acceptance of the sequential sampling

~~ August 1991 HOFFMANN ET AL.: SEQUENTIAL SAMPLING PLAN FOR Helicoverpa zea 1011 Table 2. Comparison of the sample size (number of leaves) required to reach a management decision using the sequential sampling plan versi~s the currently recommended sample of 30 or 60 leaves Year na Mean sample size ( +SE:M)h No of treat decisions Fived Sequential Fixed Sequential lndecisionc 1985 110 35 73 (1 13) 13 45 (I 29) 8 8 1 1986 166 34 52 (0 84) 13 07 (0 71) 10 9 0 Overall 276 35 00 (0 67) 13 22 (0 53) 18 17 1 I Number of decisions made (treat + no treat). 1 h4eans within years and overall mean significantly different (t test, P < 0.01). Applies to sequential only; marimum of GO leaves sampled without a decision being made. technique for H. zea eggs by potential users would also be useful. The use of the sequential sampling plan coupled with quantification of the temporal pattern of H. zea egg density in processing tomatoes has the potential to improve the efficiency of monitoring this important pest. Although the processing tomato IPM program is widely adopted or adapted in the Sacramento Valley (Grieshop et al. 1988), further improvements in its efficiency should provide the impetus for additional adoption. Acknowledgment The authors thank L. E. Ehler and two anonymous reviewers for their critical review of an earlier draft of this manuscript and R. Hanna for valuable discussion related to sequential sampling. \Ye also thank the various growers for allowing us to sample their fields and C. M eakle), E. Chin, L. Hesler. and G. Routh for assisting with data collection. This research was supported in part by the University of California Statewide IPM Program. References Cited Abacus Concepts. 1986. StatView 512+. Abacus Concepts, Inc., Calabasas, Calif. 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1012 ENVIRONMENTAL ENTOMOLOGY Vol. 20, no. 4 Wilson, L. T., F. G. Zalom, R. Smith & M. P. Hoffmann. 1983. Monitoring for fruit damage in processing tomatoes: use of a dynamic sequential sampling plan. Environ. Entomol. 12: 835-839. Zalom, F. G., L. T. Wilson & R. Smith. 1983. Oviposition patterns by several lepidopterous pests on processing tomatoes in California. Environ. Entomol. 12: 1133-1137. Zalom, F. G., L. T. Wilson & M. P. HoiTmann. 1986. Impact of feeding by tomato fruitworm, Heliothis zea (Boddie) (Lepidoptera: Noctuidae), and beet armyworm, Spodoptera exigua (Hubner)(Lepidoptera: Noctuidae). on processing tomato fruit quality. J, Econ. Entomol. 79: 822-826. Zalom, F. G., C. V. Weakley, M. P. Hoffman, L. T. Wilson, J. 1. Grieshop & G. Miyao. 1990. hlonitoring tomato fruitworm eggs in processing tomatoes. Calif. Agric. 44(5): 12-15. Zar, J. H. 1984. Biostatistical analysis. Prentice-Hall, Englewood Cliffs, N.J. Received for publication 21 June 1990; accepted 11 klarch 1991. t