INTRODUCTION
In the early 1950s, large-scale national surveys identified endemic areas of schistosomiasis japonica in 12 southern provinces in the Yangtze River basin of China, and estimated infection of 11·6 million humans and 1·2 million domestic animals, predominantly bovines (Chen and Feng, Reference Chen and Feng1999; Li et al. Reference Li, Zhao, Ellis and McManus2005). In 2004, the results of the third nationwide cluster sampling survey demonstrated remaining endemic areas in the lake areas of Hunan, Hubei, Jiangxi, Anhui, Jiangsu provinces, and the two mountainous provinces of Yunnan and Sichuan. The estimated prevalence rates were 4·2%, 3·8%, 3·1%, 2·2%, 0·3%, 1·7% and 0·9%, respectively (Engels et al. Reference Engels, Wang and Palmer2005; Zhao et al. Reference Zhao, Zhao, Jiang, Chen, Wang and Yuan2005; Zhou et al. Reference Zhou, Wang, Chen, Wu, Jiang, Chen, Zheng and Utzinger2005; Zheng, Reference Zheng2005; Zhou et al. Reference Zhou, Guo, Wu, Jiang, Zheng, Dang, Wang, Xu, Zhu, Wu, Li, Xu, Chen, Wang, Zhu, Qiu, Dong, Zhao, Zhang, Zhao, Xia, Wang, Zhang, Lin, Chen and Hao2007). In mountainous areas, mostly in Yunnan and Sichuan, the complexity of environment and retarded socio-economic status make the disease control rather difficult (Zhang and Wong, Reference Zhang and Wong2003; Cao et al. Reference Cao, Zhu, Bao and Zheng2004; Yang et al. Reference Yang, Yang, Duan, Yang and Li2004).
Immunodiagnostic techniques have a high sensitivity and are easy to perform, thus they are commonly used as an epidemiological tool for screening in endemic areas (Utzinger et al. Reference Utzinger, Zhou, Chen and Bergquist2005; Zhou et al. Reference Zhou, Wang, Chen, Wu, Jiang, Chen, Zheng and Utzinger2005). Indirect haemagglutination assay (IHA) as a widely used general immunoassay is based on an indicator system consisting of sheep red blood cells coated with antigen. It was first used for diagnosis of schistosomiasis japonica in China by Tao in 1958 (Li et al. Reference Li, Ross, Li, He, Luo and McManus1997; Zhu, Reference Zhu2005). After being developed as a simple and rapid test in the mid-1970s, it has been used mostly for community screening (Wu, Reference Wu2005b; Zhao et al. Reference Zhao, Zhao, Jiang, Chen, Wang and Yuan2005).
Since individual sample testing in low prevalence areas incurs a high cost per case detected, an inexpensive alternative strategy, pooled sample testing (PST), has been proposed for disease screening in low prevalence areas. The general PST approach for identifying individually infected humans or animals is initially to test pools of samples, and then to retest individual samples only from positive pools, thus avoiding testing the majority of individual negative samples (Greiner and Gardner, Reference Greiner and Gardner2000; Muñoz-Zanzi et al. Reference Muñoz-Zanzi, Johnson, Thurmond and Hietala2000, Reference Muñoz-Zanzi, Thurmond, Hietala and Johnson2006). Use of a pooling strategy with the assay will reduce the number of tests and provide substantial cost reduction for screening. The PST principle has been applied to a wide variety of disease screening in animals and humans (Cahoon-Young et al. Reference Cahoon-Young, Chandler, Livermore, Gaudino and Benjamin1989; Raboud et al. Reference Raboud, Major, Sherlock and O'Shaughnessy1996; Kacena et al. Reference Kacena, Quinn, Howell, Madico, Quinn and Gaydos1998; Muñoz-Zanzi et al. Reference Muñoz-Zanzi, Johnson, Thurmond and Hietala2000; Wells et al. Reference Wells, Godden, Lindeman and Collins2003; Jordan, Reference Jordan2005; Calafat et al. Reference Calafat, Kuklenyik, Caudill, Reidy and Needham2006; Singer et al. Reference Singer, Cooke, Maddox, Isaacson and Wallace2006; Rovira et al. Reference Rovira, Cano and Muñoz-Zanzi2008). Sensitivity of PST varies from disease to disease and a suitable pool size needs to be investigated for each situation. So far, there has been no standard guideline for PST in schistosomiasis screening. This study aimed to document the optimum pool size for PST for screening Schistosoma japonicum infection in Yunnan, China. The specific objective was to compute sensitivity of various pool sizes with various prevalences. The first part was based on laboratory experiments of testing IHA in sera pooled from a positive subject with various negative subjects with different dilution. The second part used results from the first part to predict sensitivity of various pool size based on simulated populations with various prevalence.
MATERIALS AND METHODS
Study setting
In a routine survey in 2007 conducted by the Section of Schistosomiasis Control and Prevention in Dali, a mountainous area of Yunnan, China, and the average seroprevalence rate was reported to be 4·7% (the Section of Schistosomiasis Control and Prevention in Dali, 2007). To find enough samples, the highest prevalence township of Shuanglang, where 201 sero-positive subjects and 1446 sero-negative subjects were identified, was selected. In this study, 31 positive and 24 negative individuals were re-approached for voluntary venous blood. The protocol received prior approval from the Ethics Committee of the Faculty of Medicine, Prince of Songkla University, and the subjects all gave their informed consent.
Specimen collection
An amount of 1·5 ml and 4·0 ml of venous blood was drawn from positive and negative subjects, respectively. After being centrifuged, serum specimens were stored at −20°C and the laboratory test described below was done within 2 weeks.
Laboratory test
Materials
IHA kits used in this study were purchased from Anhui Anji Pharmaceutical Science and Technology Co., Ltd in Anhui province, China, which is the official company of the Institute of Schistosomiasis Control and Prevention of Anhui http://www.ahzwgk.gov.cn/xxgkweb/apply.aspx?unit=OA810 (in Chinese). The kit is widely used in studies and the local routine surveys in China (Chen et al. Reference Chen, Wen, Zhang, Lu, Yu, Ding, Shen, Wang, Zhang, Chen, Ye, Zhou and Zhou2005; Xu et al. Reference Xu, Chen, Feng, Wang, Wu, Chen, Wang, Zhou and Zheng2007). It is based on freeze-dried soluble egg antigen (SEA) of Schistosoma japonicum and detects overall antibody to SEA in human sera. The sensitivity and specificity of IHA kits for individual tests at the dilution of 1:10 are stated to be 94% and 97%, respectively. The laboratory work was carried out at the Parasitology Department laboratory of Kunming Medical University in Yunnan, China.
All positive and negative serum specimens were individually confirmed by IHA according to the protocols of the manufacturer of the IHA kits at the same laboratory before the pooling process described below. All positive subjects had a titre over 1:20 and all negative subjects had a titre below 1:05.
Pooling test
Both the positive and the negative serum samples were divided into 2 groups at random. The first group comprised sera of 15 positive individuals and 12 negative individuals. The other came from 16 positive and 12 negative subjects. Each positive sample was mixed with each of the 12 negative sera in the same set, with 6 pooling ratios, namely 1:1, 1:2, 1:3, 1:4, 1:9 and 1:14, or pool sizes of 2, 3, 4, 5, 10 and 15, respectively. These mixed sera were then subjected to the IHA test at the dilution titres of 1:05, 1:10, 1:20 and 1:40. A titre of 1:10 or above with diluting liquid was considered as the cut-off point recommended by the manufacturer. Therefore, the final number of tests for all combinations of pool ratios and dilutions was (15 positive×12 negative+16 positive×12 negative)=372. As each pool had 4 dilution titres, the final number of preparations being tested was 1448.
Statistical analysis
From the laboratory experiments, each of the 1448 preparations had 1 positive subject serum. The probability to have a positive test of pool-titre combination is one component of sensitivity. These numbers needed further multiplication with 94%, which is the reported sensitivity of the test by the company.
The sensitivity for each pool size containing 1 positive subject was estimated from the product between the sensitivity given by the company (the sensitivity for pool size of 1) and the probability of getting a positive result from each combination of sera from various pool sizes and dilution. These sensitivities of PST and their 95% CI obtained from computation using exact method were broken down by pool size and dilution titre. A generalised linear model (glm) was chosen from various polynomial regressions below, predicting having a positive test for various pool ratios which gave the best fit to the data set.

WhereY=PST result being positive,
X=polynomial vector of x,
x=pool ratio,
β=coefficient of x,
j=1 to n where n gives the best fit.
In simulation, we set the pool size (ps) to vary from 2 to 15. For each pool size, the number of positive subjects contributing to the pool (i) for calculation of sensitivity must be at least 1. So i varied from 1 to ps. The sensitivity of the test in the pool size of ps with i positive subjects or S(i, ps) was predicted from the above regression model.
Pooled sera from ps subjects may have positive: negative ratio varying from 0: ps to ps: 0. The probability of getting a higher pool ratio increases as the prevalence (p) increases. The relationship follows a binomial probability density function of Bin (i, ps, p) or C ips×p i×(1−p)ps−i.
Then, the probability weight function for a pool size ps would be Bin (i, ps, p)/∑ (Bin (i, ps, p)), and the overall sensitivity of PST of pool size ps would be

The prevalence of antigen in the antibody negative sera (P Ag) is not known but assumed to be equal to kp where k is a constant value and k≪1. The neutralizing effect of antigen on antibody is also not known but assumed in the worst case to be strong enough that any presence of antigen would turn the positive test results to negative. The new sensitivity of PST is therefore

where Pr(Ag=0)is the probability of not having any antigen in the pool. This term is equal to 1 when i=ps and Bin (0, ps−i, kp) otherwise. In the simulation we tried different k.
Finally any sensitivity value above 90% was considered as acceptable. Since it remains very close to the original value of 94% sensitivity defined by the manufacturer.
All the above calculation was performed in R-2.7.1 and graph using Epicalc package (Chongsuvivatwong, Reference Chongsuvivatwong2008; R Development Core Team, 2008).
RESULTS
Out of 372 tests for all pool ratios and dilution combinations, the numbers of positive tests are shown in Table 1. When these numbers are divided by the denominator 372, and multiplied by 94% (sensitivity reported by the manufacturer of the IHA kits), the probability (or sensitivity of 1: (ps-1) pooling) and its 95% CI can be summarized in Fig. 1.

Fig. 1 Sensitivity and 95% CI by pool ratio and dilution of PST from an experiment having 1 positive serum.
Table 1. The number of positive results for different pool ratios and dilutions

From Fig. 1, the sensitivity in 1:05 dilution group was distinctively and significantly higher than that of the other 3 dilutions. It decreased with the pool size for all dilutions. The relationship between sensitivity and pool size follows a sigmoid curve. With these findings, we decided to keep only 1:05 titre for further calculation as the other titres had too low sensitivity. Based on the data of 1:05 titre, a generalised linear model was set up to predict the sensitivity of PST having 1 positive subject in pool sizes from 2 to 15.
Among various polynomial regressions, the model best fitting our data set was the one with the maximum power of pool ratio being 1. The coefficients from this model were used to predict the sensitivity s(i, ps) for each combination of i and ps. After weighting by Bin (i, ps, p)/∑ (Bin (i, ps, p)), the sensitivities of the PST are summarised against the prevalence of 1% to 15% in Fig. 2. The vertical and horizontal dotted lines indicated that, to maintain the sensitivity of PST at 90% or above with this range of prevalence, the pool size must not be larger than 6.

Fig. 2. Sensitivity of PST by pool size and prevalence of infection ignoring the effect of antigen.
Involvement of antigen has rather little effect when the disease prevalence is low. The curve for the prevalence of 0·01 was basically not changed. In contrast, the curves of high prevalence were depressed. The degree of decrease in sensitivities of the high prevalence curves is increased when the pool size increases. As all curves are sigmoid and the depression is more substantial in the high prevalence and large pool size, the relative positions of the curves was changed. In the small pool size area, the increasing prevalence results in decreased sensitivity. The reverse is true in the large pool size area. The term k or proportion of antibody negative sera which has antigen has strong effect on the relative position. With k being 1/100, assumed in Fig. 3, the positions are changed very little. The pool size that has a sensitivity value of 90% or above is 6 or smaller. This optimum pool size is reduced to 5 only when k⩾1/25.

Fig. 3. Sensitivity of PST by pool size and prevalence of infection assuming that 100th of the negative sera has antigen that completely converts test results to negative.
DISCUSSION
From our data set with only 1 positive subject per pool and the dilution titre of 1:05, the sensitivity of pool size of up to 6 was quite satisfactory (above 90%). The sensitivity of PST is also not much affected by the variation of the prevalence when the pool size is not greater than 6.
In tests for other infectious diseases, the optimum pool size of PST can be different. In a PST study in HIV, it was reported that the optimal sizes of 5-10 were appropriate for screening human HIV antibody-positive specimens with commercial EIA and WB; sensitivity was 98·9% and 100%, respectively (Soroka et al. Reference Soroka, Granade, Phillips and Parekh2003). In testing for hepatitis B virus (HBV), hepatitis C virus (HCV), and HIV in other reports also confirmed that using a pool of 5~6 would give reasonable sensitivity (García et al. Reference García, Taylor, Ruano, Pavon, Ayerdis, Luftig and Visona1998; Sarov et al. Reference Sarov, Novack, Beer, Safi, Soliman, Pliskin, Litvak, Yaari and Shinar2007; Westreich et al. Reference Westreich, Hudgens, Fiscus and Pilcher2008; Novack et al. Reference Novack, Sarov, Goldman-Levi, Yahalom, Safi, Soliman, Orgel, Yaari, Galai, Pliskin and Shinar2008). This level of pool size is similar to the PST for schistosomiasis japonica screening in our model where the sensitivity of the original test changed only slightly when the prevalence was in the range reported by a previous study was taken into account (Muñoz-Zanzi et al. Reference Muñoz-Zanzi, Thurmond, Hietala and Johnson2006).
It has been mentioned that in various diseases the presence of antigen without antibody in those who have negative tests may neutralise the positivity in a pool containing positive samples (Raboud et al. Reference Raboud, Major, Sherlock and O'Shaughnessy1996; Fernández et al. Reference Fernández, Rodrigo, García, Riestra and Blanco2006). The probability of antibody being neutralised would depend on the strength and concentration of the antigen and the prevalence of antigen in the investigated population. Schistosoma antigen in serum was shown to be uncommon and the titre is usually weak. The longest detectable period after exposure was shorter than 15 weeks (Van et al. Reference Van, Polderman, Visser, Verwey and Deelder1997). As the duration of the presence of antigen is much shorter than that of antibody, the prevalence of antigen would also be proportionally much smaller than the prevalence of antibody. From our simulation, even in the worst case assumption that any presence of antigen would give a false negative result to the PST, the effect of antigen could be ignored if the prevalence of antibody is below 0·01. In Dali, the sitting of Yunnan, the latest (2003) reported prevalence of infection was 2·2% and the infection intensity was 1·07 egg per gram of feces, which was low. It is therefore unlikely that the antigen will interfere with the sensitivity of PST (Polman et al. Reference Polman, Stelma, Gryseels, Van Dam, Talla, Niang, Van and Deelder1995; Zhao et al. Reference Zhao, Zhao, Jiang, Chen, Wang and Yuan2005).
Since the 1970's, the IHA technique has remained the most practical screening test due to its high sensitivity (93~100%) (Zhu, Reference Zhu2005). Serum reactivity develops relatively rapidly. For example, domestic rabbits after infection with Schistosoma japonicum showed a positive reaction of IHA during the 15th-30th days. This sero-positive result is earlier than the presence of the parasite ova in stool (Wu, Reference Wu2005a). The feasible pool size of 5~6 reported in this study is limited by the sensitivity of IHA. In the future, if a more convenient, sensitive and specific test is available at reasonable cost, this recommended pool size could be increased.
One factor that may determine the appropriate pool size apart from sensitivity of the individual test and the prevalence of disease is the level of titre of the positive subjects. If the antibody titre is high, the pool ratio may be increased. Unfortunately, we could not find any previous report on the distribution of the subjects with positive titre in our study population. Further studies in a real situation using PST are needed to elucidate this phenomenon. Our conclusion, however, was based on a real data set from the endemic area of Dali, Yunnan. Therefore, the results may indicate the applicability of PST in a similar but wider population in China where the total costs of the individual test are too high.
Our data were limited to the experiment with 31 positive and 24 negative subjects and the theoretical projection of the sensitivity based on a mathematical model, which took into account the interaction between the positive and the negative specimens when put into the same container. The numbers of positive and negative serum samples used in this study were relatively small. It is necessary to check the current results in real field work before the strategy could be launched on a large scale. In low prevalence populations and with a pool size not greater than 6, however, our results should be reasonable.
The study was a part of the thesis of X. M. Jia to fulfill the requirement for a Ph.D. degree in the Epidemiology Unit at Prince of Songkla University. We thank the Section of Schistosomiasis Control and Prevention in Dali, Yunnan, China for providing the serum specimens and facilitating the fieldwork.