猪瘟病毒栏内和栏间传播:一种通过传播实验估算基本复制比的新方法（下）
Within- and between-pen transmission of Classical Swine Fever Virus: a new method to estimate the basic reproduction ratio from transmission experiments - Part 2
作者 Authors:
D. KLINKENBERG1, J. DE BREE1, H. LAEVENS2 and M. C. M. DE JONG1
1荷兰动物科学与健康研究所，定量兽医传染病学
1Institute for animal science and health, quantitative veterinary epidemiology, The Netherlands
2比利时根特大学兽医学院兽医流行病学组，生殖、生育和畜群健康系
2Department of reproduction, obstetrics and herd health, veterinary epidemiology unit, school of veterinary medicine, Ghent University, Belgium
结果 RESULTS
用于估计传播参数βw 和 βb的最大似然估计方法，对断奶猪产生的点估计分别为8.52和0.656，对育肥猪产生的点估计分别为1.85 和0.402。
The maximum likelihood estimation method used to estimate transmission parameters βw and βb produced point estimates of 8.52 and 0.656 for weaner pigs and 1.85 and 0.402 for slaughter pigs, respectively.
采用三种方法确定了βw 的95%置信区间。基于似然比的构建方法，分别获得断奶猪和育肥猪的βw区间为(4.77-14.1) 和(0.704—3.63)。采用log方法，测定了区间分别为(4. 78-14. 1) 和 (0. 709-3. 79)，似然方差法产生的区间为(4. 98-14. 6)和 (0. 817-4. 18)。因为构造方法没有基于渐近特征假定具体的分布，因此我们认为该方法估计的置信区间最为精确。log方法，它比数值方法要快得多，表现很好，而方差方法导致可能性略向上转移区间。然而，我们决定使用最后提到的方法做进一步计算，因为所获得的协方差矩阵和方差可以用来估计的协方差矩阵。
Three methods were used to determine 95% confidence intervals for βw. With the construction method based on the likelihood ratio , the intervals for βw obtained were (4.77-14.1) and (0.704—3.63) for weaner pigs and slaughter pigs, respectively. With the log method the intervals were (4. 78-14. 1) and (0. 709-3. 79), respectively, and the likelihood variance method produced intervals of (4. 98-14. 6) and (0. 817-4. 18). Because the construction method does not assume specific distributions based on asymptotic features, we believe that the estimated confidence intervals from this method would be the most precise. The log method, which is much faster than the numerical method, performed quite well, while the likelihood variance method resulted in slightly upwards shifted intervals. However, we decided to use this last-mentioned method for further calculations, because the obtained covariance matrices for together with the variances for can be used to estimate covariance matrices for .
log协方差矩阵M可以被计算为:
The covariance matrices M of log thus calculated were:
为了比较估计断奶猪和育肥猪的logs, 计算这两者的区别(log)，连同相应的协方差矩阵， Mweaner + Mslaughter。这种差异的95%置信区间在图1中显示这个区域没有越过这条线log=0，因此断奶猪和育肥猪的logs有显著差异。然而，logs的情况并非如此。断奶猪的估计恢复参数的log2. 47，方差为0. 0231，育肥猪为2. 13，方差为 0. 0433
To compare the estimated logs of weaner and slaughter pigs, the difference of the two was calculated (log), together with the accompanying covariance matrix, Mweaner + Mslaughter. The 95% confidence area of this difference in Figure 1 shows that this area does not cross the line log=0 and therefore the logs of weaner and slaughter pigs differ significantly. This is not the case for the logs. Estimation of recovery parameter resulted in a log for weaner pigs of 2. 47 with variance 0. 0231 and for slaughter pigs of 2. 13 with variance 0. 0433.
估计的log导致这些向量和协方差矩阵为：
Estimation of log resulted in these vectors and covariance matrices:
这意味着断奶猪组的Row 和 R’ob分别为100 (CI 54.4-186) 和 7.77 (CI 4.68-12.9)，育肥猪的Row 和 R’ob分别为15.5 (CI 6.20-38.7) 和 3.39 (CI 1.54-7.45)。通过计算差值和伴随的协方差矩阵来检验logweaner与logslaughter是否不同，然后绘制95%置信区间(图2)。它表明置信区间没有越过logRow, =0这条线，但是越过了log R’ob = 0这条线。因此，结论是使断奶猪和育肥猪之间Row存在差异，但R’ob没有。
This means that the estimated Row and R’ob for weaner pigs were 100 (CI 54.4-186) and 7.77 (CI 4.68-12.9), and for slaughter pigs 15.5 (CI 6.20-38.7) and 3.39 (CI 1.54-7.45), respectively. Testing whether logweaner differs from logslaughter has been done by calculating the difference and accompanying covariance matrix, and subsequently plotting the 95% confidence area (Fig. 2).It illustrates that the confidence area does not cross the line logRow, =0, but does cross the line log R’ob = 0. Therefore, the conclusion is that Row differs between weaner and slaughter pigs, but R’ob does not.
图2.的95%置信区间为阴影区面积
讨论 DISCUSSION
本文提出的大最似然法得到Row的置信区间比鞅法小得多[7, 8]。这可能是由于更广泛地使用了数据，将病毒传播过程划分为已知数量的新病例和易感性和传染性猪只的间隔。
The maximum likelihood method presented in this paper resulted in a much smaller confidence interval of Row than the martingale method [7, 8]. This was probably due to the more extensive use of the data, by dividing the virus transmission process into intervals with known numbers of new cases and susceptible and infectious pigs.
此外，最大似然法使用所有大栏的数据，而鞅方法只使用中间 (最初被感染的) 大栏的数据。我们相信，本文提出的方法更适合用于未来实验的数据分析。
Also, the maximum likelihood method uses data from all the pens, in contrast with the martingale method, which only uses the data of the middle (the primarily infected) pen. We are convinced that the method presented here is more suitable to be used in data analysis of future experiments.
三种不同的方法被用来计算置信区间，基于似然比�，log方法和可能性方差法的构造方法。构造方法不是基于渐近特征(即许多数据点)，在这个意义上是一种可靠的方法。
Three different methods were used to calculate confidence intervals for : a construction method based on the likelihood ratio, the log method, and the likelihood variance method. The construction method is not based on asymptotic features (i.e. many data points), and is in this sense a reliable method.
然而，它的缺点是计算时间很长，不可能同时为两个参数( and建立一个置信区间，它是不可能使用结果来为Ro构造区间。其他两个方法都是基于渐近特性的—21og和似然函数本身，这两种方法都很快。
However, its disadvantages were that the calculation time was long, it was impossible to construct a confidence area for two parameters ( and simultaneously, and it was not possible to use the results to construct intervals for Ro. The other two methods are based on asymptotic features of the —21og and of the likelihood function itself. Both of these methods are fast.
log方法的优势在于它采用似然比，就像这个构造方法，结果非常相似。可能性方差方法的优势，然而，是它允许同时派生和的自信区间，估计方差可以用来获取log的方差估计。这就是为什么这个可能性方差方法被用于 和 log方差估计。
The advantage of the log method is that it uses the likelihood ratio, just like the construction method, and that the results are very similar. The advantage of the likelihood variance method, however, is that it allows derivation of confidence areas for and simultaneously and that the estimated variances can be used to obtain variances of the log estimates. That is why this likelihood variance method is used to estimate variances for and log as well.
采用本文提出的最大似然法，断奶仔猪和育肥猪的Row 和 均显著大于1。这个结论不能从鞅估算中得出，但是由于两个实验(所有动物均被感染)的大规模爆发和病毒引起CSF流行的能力，这个结论是可以预料的。
With the maximum likelihood method presented in this paper, the Row and appeared to be significantly greater than 1 for both weaner and slaughter pigs. This conclusion could not be made from the martingale estimation, but was expected because of the large outbreak in both experiments (all animals infected) and the ability of the virus to cause CSF epidemics.
一个更令人惊讶的结果是两个年龄组之间的显著差异：断奶猪的Row比育肥猪的Row大。这可能是由于几个原因，应根据并无不同这一事实来判断。首先，仔猪对感染的抵抗力可能较低(易感性较高)。第二，仔猪的体积越小，可能导致动物群体内的病毒浓度越高，因此病毒排泄率也就越高(传染性越强)。第三，最有可能的原因是断奶仔猪之间可能会有更密集的接触，因为前面提到的两点也会导致较高的。然而，也有可能是确实不同，但在这些实验中没有观察到这一点。
A more surprising result was the significant difference between the two age groups: the Row of weaner pigs is larger than the Row of slaughter pigs. This can be due to several causes, which should be judged by the fact that the do not differ. First, the resistance to infection in younger pigs could be lower (higher susceptibility). Second, the smaller volume of younger pigs could be responsible for a higher virus concentration in the animals and consequently a higher virus excretion (higher infectiousness). Third, weaner pigs might have more intensive contacts with each other, which is the most probable cause, because the first two mentioned would also result in higher However, it is also possible that the do differ, but that this was not observed in these experiments.
从流行病学的角度来看，两组之间的差异可能是重要的，因为病毒在低日龄猪群的单元内(母猪群中断奶猪)的传播要比在高日龄猪群的单元内（育肥猪群）中传播要快。因此，重要的是要知道这种差异是否存在于其他猪瘟病毒毒株之间。如果差异主要是由于更密集的接触，这是意料之中的。
From an epidemiological point of view, the difference between the groups can be important because virus transmission in units with younger pigs (weaner pigs in a sow herd) will be quicker than in units with older pigs (in a finishing herd). Therefore it is important to know whether this difference exists with other CSF strains as well. If the difference is mainly due to more intensive animal contacts, this is to be expected.
致谢 ACKNOWLEDGEMENT
作者感谢位于荷兰乌得勒支的STW(技术基金会)的财政支持。
The authors thank STW (Technology Foundation), Utrecht, The Netherlands, for financial support.
附录 APPENDIX
本文提出了一种构造传播参数置信区间(CI)的数值方法。为了使推导更有序，这里只显示了一个传播参数，就类似于只有大栏内传播。当其他参数保持不变时，如文本中的示例所示，推导是类似的。只有一个参数的对数似然方程类似于(6)：
Here a numerical method is derived to construct confidence intervals (CI) for the transmission parameters . To keep the derivation more orderly, it is shown here for only one transmission parameter , as if there were only within-pen transmission. When the other parameter is kept constant, as in the examples in the text, the derivation is similar. The log-likelihood equation with one parameter is, analogous to (6):
现在, 考虑到测试等价性和CI构造, 建议做一个测试: Ho:= 对 HA:=。然后，让 趋向 ,一个测试将获得测试反对任何。这个检验可以用来构造置信区间的上限。对于下限也采用类似的程序。
Now, with the equivalence of testing and CI construction in mind, a test is suggested of Ho:= against HA:=. Then, letting tend to a test will be obtained to test against any . This test can be used to construct an upper limit of a confidence interval. A similar procedure is followed for the lower limit.
这个测试， ɸ基于似然比 () [15]：
The test, ɸ is based on the likelihood ratio () [15]:
d是由(ɸ)=0.05 (95% CI)决定的。当ɸ= 1 Ho被否定且ɸ= 0时Ho不被否定。在(16)中, log：
where d is determined by (ɸ)=0.05 (for a 95% CI). Ho is rejected when ɸ =1 and Ho is not rejected when ɸ = 0. In (16), log is:
其中
Where
观察到log在每个Cjk中都是单调递减的：
Observed that log is monotonically decreasing in every Cjk:
这是真实的，因为
是一个单调递增函数。
which is true since is a monotonic and increasing function of.
因此log可以为来构造一个测试。该测试是为任何上限)所构造，让趋向 ()，结果是：
Hence, log can be used to construct a test for . The test is constructed for any (upper limit) by letting tend to (), which results in:
它决定了上限形式的测试(因为其他所有因素独立于)：
which determines the form of the test for the upper limit (since all other factors are independent of ):
为此案 (下限)，推导是一样的, 除了式(20)中的不等式符号被调换了。
For the case (lower limit), the derivation is the same, except for the inequality signs in formula (20), which are switched.
测试是用于迭代搜索的是适于：
The test is used for an iterative search of that for which holds:
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