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      豬瘟病毒欄內和欄間傳播:一種通過傳播實驗估算基本復制比的新方法(上)
      時間:2020-11-13 08:02:07 來源:文通網

      豬瘟病毒欄內和欄間傳播:一種通過傳播實驗估算基本復制比的新方法(上)

      來源:豬譯館 2020-11-12 14:26:09| 查看:

        豬瘟病毒欄內和欄間傳播:一種通過傳播實驗估算基本復制比的新方法(上)

        Within- and between-pen transmission of Classical Swine Fever Virus: a new method to estimate the basic reproduction ratio from transmission experiments - Part 1

        1

        作者 Authors:

        D. KLINKENBERG1, J. DE BREE1, H. LAEVENS2 and M. C. M. DE JONG1

        1荷蘭動物科學與健康研究所,定量獸醫傳染病學

        1Institute for animal science and health, quantitative veterinary epidemiology, The Netherlands

        2比利時根特大學獸醫學院獸醫流行病學組,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

        2

        總結 SUMMARY

        本文提出了一種從傳播實驗中估算基本復制比Ro的方法。通過更廣泛地使用先前發表的經典豬瘟病毒實驗數據,我們得到了比原始論文中使用的鞅方法更小的置信區間。

        We present a method to estimate basic reproduction ratio Ro from transmission experiments. By using previously published data of experiments with Classical Swine Fever Virus more extensively, we obtained smaller confidence intervals than the martingale method used in the original papers.

        此外,我們的方法允許同時估算欄內的復制比(ROw)和調整后欄與欄之間的復制比 (R’ob)。對ROw和R 'ob斷奶仔豬的估算值分別為100 (95% CI 54-4-186)和7.77(4-68-12. 9)。

        Moreover, our method allows simultaneous estimation of a reproduction ratio within pens ROw and a modified reproduction ratio between pens R’ob. Resulting estimates of ROw and R’ob weaner pigs were 100 (95% CI 54. 4-186) and 7.77 (4. 68-12. 9), respectively.

        對于育肥豬來說,這兩個數值分別是15. 5 (6. 20-38. 7) 和3. 39 (1. 54-7. 45)。我們認為,由于我們能夠獲得較小的置信區間,因此本文提出的方法更適合在未來的實驗中使用。

        For slaughter pigs they were 15. 5 (6. 20-38. 7) and 3. 39 (1. 54-7. 45), respectively. We believe, because of the smaller confidence intervals we were able to obtain, that the method presented here is better suited for use in future experiments.

        3

        簡介 INTRODUCTION

        豬瘟(CSF)或豬霍亂是一種高度傳染性的豬病[1-3],這種疾病的流行會引起巨大的問題,如動物福利的減少,以及由于出口限制和豬群大規模毀滅而造成的高經濟損失[4],這種疾病是由豬瘟病毒(CS FV)引起的[1-3]。病毒在豬之間的傳播可以通過從傳播實驗中的估算參數來量化,在這些實驗中,欄內的一些豬只接種了病毒,并在隨后跟蹤了傳播進程[5]。

        Classical Swine Fever (CSF) or hog cholera is a highly contagious pig disease [1-3], an epidemic of which can cause huge problems like reduction in animal welfare, and high economic losses as a result of export limitations and mass destruction [4]. The disease is caused by the Classical Swine Fever Virus (CSFV) [1-3]. Transmission of the virus between pigs can be quantified by estimating parameters from transmission experiments, in which a number of pigs within a pen are inoculated with the virus and the transmission process in followed [5].

        病毒傳播的一個重要參數是基本復制比Ro,定義為在無限易感豬群中由一個典型傳染性個體引起的繼發性感染個體的數量。如果Ro小于1,然后平均每一個有傳染性的動物感染的動物少于一個,導致疫情消退。反之,如果Ro大于1,則可能發生重大疫情[6]。

        An important parameter of virus transmission is the basic reproduction ratio Ro, defined as the number of secondary infected individuals caused by one typical infectious individual in an infinite susceptible population. If Ro is smaller than 1, then on average every infectious animal infects less than one other animal causing the outbreak to wane. If on the other hand Ro is greater than 1, major outbreaks can occur [6].

        1998年和1999年,Laevens等人用CSFV做了兩個傳播實驗;一個用斷奶豬,另一個實驗用育肥豬[7,8]。在這兩個實驗中,有3個相鄰的大欄,每個大欄中有15只斷奶豬或6只育肥豬。在中間的大欄中一只豬接種了CSFV,每2天采集所有豬的血樣檢測病毒血癥。根據這些測量結果,當一頭豬是病毒血癥的,就假設這頭豬是有傳染性的,從而重建了每頭豬的感染周期。隨后Ro采用鞅估算方法,基于隨機SIR模型進行估算[5,9]。

        In 1998 and 1999 Laevens et al. did two transmission experiments with CSFV; one with weaner pigs and the other with slaughter pigs [7, 8]. In both experiments there were 3 adjacent pens with either 15 weaner pigs or 6 slaughter pigs in each pen. In the middle pen one pig was inoculated with CSFV and every 2 days blood samples of all the pigs were taken to measure viraemia. From these measurements the infectious period of every pig was reconstructed by assuming that a pig is infectious when it is viraemic. Subsequently Ro was estimated using the martingale estimation method, based on the stochastic SIR model [5, 9].



       

        注:將病毒傳播過程劃分為2天時間段,按大欄分層。時間從接種疫苗那天開始。S為區間開始時易感動物的數量;I為受感染動物的數目;C是新病例數,N是動物總數,其中0·5是某一類別2天中只出現1天的動物。

        Division of the virus transmission process in 2-day time periods, stratified by pen. Time starts at day of inoculation. S is the number of susceptible animals at the start of the interval; I is the number of infectious animals; C is the number of new cases and N is the total number of animals, where 0·5 is an animal present for only 1 of 2 days in a certain category.

        該模型通過描述易感(S)和傳染性(I)動物數量的變化和動物總數(N)來描述病毒在一組動物中的傳播。在該模型中,假設易感動物的感染和感染動物的恢復是由速率為βSI/N和α I的泊松過程產生的,其中β和α分別是傳播和恢復參數。

        This model describes transmission of a virus in a group of animals by describing the change in the numbers of susceptible (S) and infectious (I) animals in terms of these numbers and the total number of animals (N). In the model, infection of susceptible animals and recovery of infectious animals are assumed to be generated by a Poisson process with rates βSI/N and αI, where β and α are the transmission and recovery parameter, respectively.

        Ro是根據實驗中最終感染的動物數量來估算的,此時沒有易感動物或無傳染性動物存在。如果相關,使用最后一個易感動物被感染時剩余的感染期分數之和。Laevens等僅使用中間大欄的數據來估算Ro,因為在其它大欄中,傳播并不僅僅是由同一大欄內的傳染性動物引起的[7,8]。

        The Ro is estimated from the number of animals ultimately infected during the experiment, when no susceptible or no infectious animals remain. The sum of the fractions of infectious periods remaining when the last susceptible animal is infected is used if relevant. Laevens et al. [7, 8] used only the data of the middle pen to estimate Ro because in the other pens transmission was not solely caused by infectious animals in the same pen.

        斷奶豬和育肥豬分別得到的估算數據是(s.e. 109, i.e. 95% CI -132-295)和13. 7 (s.e. 13. 7, i.e. 95% CI -13. 2-40. 6) 。這意味著,盡管感染過程發生得非常快,所有動物都被感染了,但估算的Ros并不顯著大于1。由于數據的某些方面并沒有被用于估算(三個大欄內所有動物的感染時間和感染周期),因此,盡可能多地利用數據信息,尋找另一種估算方法是值得的。期望這會得到更小的置信空間。

        The estimates obtained were (s.e. 109, i.e. 95% CI -132-295) and 13. 7 (s.e. 13. 7, i.e. 95% CI —13. 2-40. 6) for weaner and slaughter pigs, respectively. This meant that despite the fact that the infection process took place very quickly and all animals were infected, the estimated Ros were not significantly greater than 1. Since some aspects of the data were not used for the estimation (infection times and infectious periods of all animals known for all three pens), searching for an alternative estimation method would be worthwhile, using as much information from the data as possible. Hopefully this will lead to a smaller confidence interval.

        為了得到一個較小置信區間的 Ro 估算,我們分別估算了感染性參數β和恢復性參數α,這兩個參數用來計算 (Ro =β/α)。 對于β的估算根據已知的感染個案數目(C)、易受感染動物數目(S)及感染動物數目(I),把感染過程劃分為不同的時間間隔。 這些(S, I, C)的集合被用來構造一個概率函數,我們最大化為β得到一個最大概率估算。對α進行估算,以感染周期的長度擬合一個廣義線性模型。

        In an attempt to obtain an Ro estimate with a smaller confidence interval, we did separate estimations of β, the infectivity parameter, and α, the recovery parameter, which are used to calculate Ro (Ro =β/α). For β estimation, the infection process was partitioned into intervals with known numbers of infection cases (C) and susceptible (S) and infectious (I) animals. These sets of (S, I, C) were used to construct a likelihood function, which we maximized to get a maximum likelihood estimator for β. For α estimation, the lengths of the infectious periods were used to fit a generalized linear model.

        4

        材料和方法 MATERIALS AND METHODS

        我們使用了laevens 等人在傳播實驗中獲得的數據(詳情請見[7,8])。在兩個實驗中,有3個相鄰的大欄,豬的數量相等: 一個實驗中有15頭斷奶仔豬,另一個實驗中有6頭育肥豬。在中間的大欄中一只豬接種了CSFV,每2天采集所有豬的血樣檢測病毒血癥。當一頭豬是病毒血癥的,就假設這頭豬是有傳染性的,從而重建了每頭豬的感染周期。

        We used the data obtained in the transmission experiments of Laevens et al. (for more detail see [7, 8]). In both experiments there were 3 adjacent pens with equal numbers of pigs: 15 weaner pigs in one experiment and 6 slaughter pigs in the other. One of the pigs in the middle pen was inoculated with CSFV and every 2 days blood samples were taken from all animals, which were tested for viraemia. From these data the infectious period of each pig was reconstructed, assuming that the animal is infectious when it is viraemic.

        通過假設的潛伏期為6天(已感染但還沒有傳染性),我們能夠在三個欄中重建整個病毒傳播過程[2]。這些重建使我們能夠估計參數,使用以下隨機SIR模型[6],包括大欄內和大欄間傳播:

        比率 (S →S -1) = (βwIw/Nw+βbIb/Nb)S (1)

        比率 (I→I -l) =αI.                     (2)

        By assuming a latent period of 6 days (infected but not yet infectious) [2], we were able to reconstruct the entire virus transmission process in the three pens. These reconstructions enabled us to estimate the parameters, by using the following stochastic SIR model [6], incorporating both within- and between- pen transmission:

        rate (S →S -1) = (βwIw/Nw+βbIb/Nb)S (1)

        rate(I→I -l) =αI.                     (2)

        在這個模型中,βw是大欄內傳播參數,定義為在一個完全易感的群體中,在同一大欄中,每只典型的傳染性動物每天新感染的預期數量。同樣地,βb是大欄間傳播參數,定義為是在完全易感群體中,每個典型傳染性動物每天在其他大欄中預期的新感染數量。

        In this model, βw is the within-pen transmission parameter defined as the expected number of new infections in the same pen per day per typical infectious animal in a fully susceptible population. Likewise, βb is the between-pen transmission parameter defined as the expected number of new infections in other pens per day per typical infectious animal in a fully susceptible population.

        參數α代表每只感染動物的恢復率。由于有兩個傳輸參數 βw 和βb,我們還區分了大欄內復制比ROw和大欄間復制比ROb。ROw定義為在同一個大欄內一個典型的傳染性動物引起的預期繼發感染的動物數量。ROb定義為由一種典型的傳染性大欄引起的預期繼發感染大欄數,考慮到一個大欄被感染,則欄內至少有一頭豬被感染。ROw和ROb的估算可以計算如下:

        The parameter α represents the recovery rate per infectious animal. Because there are two transmission parameters βw and βb,we also make a distinction between a within-pen reproduction ratio ROw and a between-pen reproduction ratio ROb. ROw is defined as the expected number of secondary infected animals caused by one typical infectious animal in the same pen. ROb is defined as the expected number of secondary infected pens caused by one typical infectious pen, considering a pen as infected when at least one pig is infected. Estimates for ROw and ROb can be calculated as follows:


       

        在這個等式中,E(Itot)是一個大欄內最終被感染的動物的預估數量。如果ROw是已知的,那么E(Itot)在我們的模型假設條件下容易確定[10],但本文不做進一步探討。R’ob是指由一種典型的傳染性動物引起的繼發感染大欄數量的預估數量。R’ob獨立于E(Itot),是本文即將估計的參數。為了便于計數,我們引入了向量 = (βw, βb),log= (logβw, logβb),  =( ROw, R’ob),和log = (log ROw,log R’ob)。因為感染和恢復是相互獨立的過程,是通過分別估計和計算得出的。

        In this equation, E(Itot)is the expected number of animals ultimately infected within one pen. E(Itot) can under our model assumptions easily be determined if ROw is known [10], but will not be further discussed in this paper. R’ob is the expected number of secondary infected pens caused by one typical infectious animal. R’ob, being independent of E(Itot), is the parameter that will be estimated in this paper. For notational convenience, we have introduced the vectors  = (βw, βb),log= (logβw, logβb),  =( ROw, R’ob),and log = (log ROw,log R’ob). Because infection and recovery are independent processes,  was calculated from separate estimations of  and .

        為了估計傳播參數,,將感染過程分為兩天的時間間隔,即兩次隨后抽樣之間的時間間隔。對于每一間隔,間隔開始時易感豬只的數量(S),具有傳染性豬只的數目(I)以及新增病例(C)的數目已確定(表1)。 在每個時間間隔 k 中,易感動物逃脫恒定感染率(βw Iwk /Nwk+βbIbk/Nbk)的概率,按照泊松分布,是e-(βw Iwk /Nwk+βbIbk/Nbk)。 因此,根據二項分布,在同一大欄Ck病例的概率是,Sk易感豬和ik具有傳染性的豬只比例(Ik/ Nk) ,jk為其它大欄中具有傳染性的豬只比例:


       

        用所有時間間隔的概率組成對數似然函數,可以寫成:


       

        在此過程中,log中忽略未計,因為它沒有作用。使這個函數最大化,得到了對βw和βb的最大似然估計。

        In order to estimate transmission parameters, the infection process has been divided into time intervals of two days, the intervals between two subsequent samplings. For each interval, the number of susceptible pigs at the start of the interval (S), the number of infectious pigs (I) and the number of new cases (C) was determined (Table 1). In each time interval k, the probability of a susceptible animal escaping infection from the constant rate (βw Iwk /Nwk+βbIbk/Nbk)  is, according to the Poisson distribution, e-(βw Iwk /Nwk+βbIbk/Nbk).Therefore, the probability of getting Ck cases, with Sk susceptibles and ik as the fraction of infectious pigs (Ik/ Nk) in the same pen and jk as the fraction of infectious pigs in the other pens is, according to the binomial distribution:


       

        The probabilities for all time intervals have been used to make up the log-likelihood function, which may be written as:


       

        where log has been omitted because it plays no role. Maximising this function results in maximum likelihood estimators for βw and βb.

        采用三種方法推導出了βw的置信區間。比較幾個特性(如數學背景,實用價值),然后決定哪些方法應該用于βb和ROw 以及 R’ob的區間估計。第一個方法,我們稱之為構建方法,是基于似然比和等價的測試并且構建的置信區間。這里使用的檢驗是從以下觀察得出的:檢驗一個值(Ho: βw = βo)與另一個值βw (HA: βw =β’< βo )的似然比是每個C的單調遞減函數。

        Three methods were used to derive confidence intervals for βw. After comparing several features (e.g. mathematical background, practical value), a decision was made as to which method should be used for interval estimation of βb,ROw and R’ob .The first method, which we shall refer to as the construction method, is based on the likelihood ratio and on the equivalence of testing and construction of a confidence interval. The test used here is derived from the observation that the likelihood ratio for testing one value of (Ho: βw = βo) against another value of βw (HA: βw =β’< βo ) is a monotonic and decreasing function of each C.


       

        它允許我們用C本身的概率函數為C構造一個臨界區域,而不需要調用任何近似似然比的概率分布。詳情請參閱附錄。用這種方法可以構造兩個βs (βw or βb)中的一個的置信區間,將另一個作為常數作為其估計。遺憾的是,這種計算幾乎是非常耗時的,如何構造參數向量的置信區間或者如何確定Ro的置信區間是不清楚的。第二種方法是Neyman 和 Pearson (參考文獻[11])所描述的似然比()檢驗,它依賴于—21og 的漸近卡方分布,在我們的案例中是1自由度。

        It allowed us to construct a critical region for the C by using the probability function of C itself,without invoking any approximate probability distribution of the likelihood ratio. For details, see the appendix. With this method confidence intervals can be constructed for one of the two βs (βw or βb) treating the other as a constant as its estimate. Unfortunately, the computation is almost prohibitively time-consuming, and just how to construct a confidence area for the parameter vector or how to determine confidence intervals for Ro is not clear. The second method is the likelihood ratio () test as described by Neyman and Pearson (reference in [11]), which relies on the asymptotic chi-square distribution of —21og with, in our case, 1 degree of freedom.

        該方法通過求解方程—21og = 3. 84計算95% 置信區間,對于兩個βs (βw 或βb)中的一個,將另一個作為常數作為其估計。這是一個比第一個快得多的方法,盡管如此,它在同時置信區間的構造上也存在同樣的困難。第三種方法是基于最大似然估計的漸近(多元)正態分布[12]。估計量的假設是由log估計值 (而不是), 同時也是一個ML-估計值,是漸近正態分布因為非現實(負的)的βw 和 βb不能發生。結果如下協方差矩陣M:

        This method calculates 95% confidence limits by solving the equation —21og = 3. 84 for one of the two βs (βw or βb) treating the other as a constant as its estimate. This is a much faster method than the first one; nonetheless it suffers from the same construction difficulties with regard to simultaneous confidence intervals. The third method is based on the asymptotic (multivariate) normal distribution of a maximum likelihood estimator [12]. The assumption is made that the estimator of log (instead of ),being also a ML-estimator, is asymptotically normally distributed because then non-realistic (negative) values of βw and βb cannot occur. This results in the following covariance matrix M:


       

        該方法計算速度快,因為它提供了一個估計的協方差矩陣,它顯然使log和 log※。

        This method is computationally fast and, since it provides an estimate of the covariance matrix, it obviously enables construction of confidence areas for logand log.※

        ※注:如果只估計了一個傳輸參數,這種似然方差方法實際上與響應變量C的廣義線性模型相同,二項分布的指數S,一個互補的對數-對數鏈接函數,以及log(I/N)作為偏移量。因為在這種情況下,我們想同時估計兩個傳播參數,是不可能使用這個GLM。

        ※Note that, if only one transmission parameter is estimated, this likelihood variance method is in fact the same as a generalized linear model with response variate C, binomially distributed with index S, and a complementary log-log LINK function, and log(I/N) as offset. Because in this case we want to estimate two transmission parameters simultaneously, it is not possible to use this GLM.

        恢復/死亡率參數使用廣義線性模型估計了審查生存分析(Aitken 等人[13])。在這個模型中,每個動物可以觀察到兩個解釋變量Tk 和yk。第一個變量,Tk是觀察到的傳染期長度。第二個變量yk是一個審查變量,如果Tk是真實存活時間,yk是1,而如果真實存活時間大于Tk, yk是0。似然函數如下:

        The recovery/death rate parameter has been estimated using a generalized linear model for survival analysis with censoring, as described by Aitken et al. [13]. In this model for each animal two explanatory variables Tk and yk can be observed. The first one, Tk  is the observed length of the infectious period. The second one, yk, is a censoring variable: yk is 1 if Tk is the true survival time, whereas yk is 0 if the true survival time is greater than Tk. The likelihood function reads as follows:


       

        這個可能性的核心是一樣的,是一組n觀察值yk各有一個獨立的泊松分布與平均值 (見[13])。用Genstat進行分析[14],使用RSURVIVAL程序,即yk表示響應變量,log為偏移量,模型配備了一個對數連接功能和泊松分布。結果是一個估計的對數和它的估計方差的估值。 以下運算給出log的估計:

        The kernel of this likelihood is the same as it would be with a set of n observations yk each having an independent Poisson distribution with mean (see [13]). The analysis was performed in Genstat  [14], using the RSURVIVAL procedure, where yk denotes the response variate, loghe offset, and the model is fitted with a log LINK function and a Poisson distribution. The output is an estimate of log and its estimated variance. The estimator of log is given by:

        log = log- log.                       (9)

        推導log的置信區間是通過添加log 和 log協方差矩陣得到的:

        Derivation of a confidence area for log is done by adding the covariance matrices for log and log:


       

        估計斷奶豬和育肥豬的logs和var(log)s被用來構造一個置信區間差異的兩個logs,并評估是否Row 和R’ob使斷奶豬和育肥豬之間有明顯的差異。

        The estimated logs and var(log)s for weaner and slaughter pigs were used to construct a confidence area for the difference of the two logs, and to assess whether Row or R’ob  differ significantly between weaner and slaughter pigs.

        未完待續

        To be continued…

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