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Review

Treatments of Hepatocellular Carcinoma Patients with Hepatitis B Virus Infection: Treat HBV-related HCC

  • There have been major advances recently on the therapeutic approaches of hepatitis B virus (HBV)-related hepatocellular carcinoma (HCC). Surgical treatments are the key curative treatments of HCC, whereas local ablative treatments may also achieve clinical remission in selected cases. Trans-arterial locoregional therapies are regarded as palliative but still lead to improved survival. There have been major breakthroughs in the systemic therapies for HCC. The first marketed targeted therapy, sorafenib, was shown to improve survival in patients with advanced HCC. Studies on other targeted therapies also showed promising results. Suppressing HBV with effective antiviral treatment would also benefit HCC patients by reducing recurrence and improving liver function.

    Citation: Charing Ching-Ning Chong, Grace Lai-Hung Wong. Treatments of Hepatocellular Carcinoma Patients with Hepatitis B Virus Infection: Treat HBV-related HCC[J]. AIMS Medical Science, 2016, 3(1): 162-178. doi: 10.3934/medsci.2016.1.162

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  • There have been major advances recently on the therapeutic approaches of hepatitis B virus (HBV)-related hepatocellular carcinoma (HCC). Surgical treatments are the key curative treatments of HCC, whereas local ablative treatments may also achieve clinical remission in selected cases. Trans-arterial locoregional therapies are regarded as palliative but still lead to improved survival. There have been major breakthroughs in the systemic therapies for HCC. The first marketed targeted therapy, sorafenib, was shown to improve survival in patients with advanced HCC. Studies on other targeted therapies also showed promising results. Suppressing HBV with effective antiviral treatment would also benefit HCC patients by reducing recurrence and improving liver function.


    The COVID-19 pandemic has exerted huge and unprecedented pressure on public health resources globally. Cross-sectional surveys to establish disease prevalence are likely to be financially unsustainable in the long term and rely heavily on continued cooperation from the public [1]. Wastewater monitoring to detect and quantify SARS-CoV-2 viral RNA shed by infected individuals in the population, and to indicate infection prevalence, was adopted relatively early in the course of the pandemic across a number of countries [2,3], expanding to 67 countries by mid-2022 [4]. Although the demographic coverage and utility of wastewater monitoring varies across adopters of this approach, the method is generally less intrusive, relatively unbiased in terms of its demographic and epidemiological coverage, and costs significantly less per capita than clinical testing programmes (e.g. fanxiexian_myfh148 per individual PCR test cf. fanxiexian_myfh300 per wastewater sample representing larger populations [5]). Wastewater surveillance is thus, arguably, an alternative, or at least complementary, approach to clinical testing programmes.

    Wastewater-based epidemiology has been used in some areas of public health for decades [6], but is a relatively novel tool for emerging pathogens. Applications include tracking viral dynamics to monitoring chemical exposures and prescription drug consumption [7,8]. As wastewater sampling for the detection and monitoring of SARS-CoV-2 has been developed and applied at an unprecedented pace, uncertainty remains when interpreting the measured viral RNA signals and their spatiotemporal variation. Variation in the underlying sample, sampling method, and testing, due in part to lack of standardisation, as well as systematic variability in space and time in the measurement environment (e.g. sewersheds), can result in a large degree of noise in the observed signal [9]. Sampling frequency is typically dependent on cost constraints, resulting in sparse and irregularly sampled data. Furthermore, wastewater measurements are typically left-censored if they fall below certain analytical thresholds, such as the limit of detection (LOD), the lowest concentration at which viral RNA is detectable with a given probability (typically 95%); and the limit of quantification (LOQ), the lowest concentration at which viral RNA can be reliably measured with a predefined accuracy. Methods to handle measurements that fall below these limits (e.g. statistical methods, imputation, and scalar or zero replacement) are not standardised and depend on the interpretation of the data (for example, if low values do not impact interpretation they may be omitted from downstream analysis), and information available to the analysts [10,11].

    There are several approaches to infer wastewater concentration from noisy, censored, incomplete time series measurements. One common and straightforward approach for denoising time series is to calculate a moving average (MA). However, MA are sensitive to outliers and missing values. There is ambiguity about the most appropriate window-size, and whether to calculate a weighted or ordinary average. Uncentred MAs also operate with a lag, where larger windows create larger lags, delaying reactivity of surveillance in time-dependent operations. Lastly, an MA estimate can never be smaller than the censoring threshold, which leads to biased estimates.

    State-space methods model observed data as functions of latent, unobserved stochastic processes and can better account for missing data, observational noise, and censoring. Recently, others have proposed state-space methods to infer viral concentrations from wastewater time series. The underlying "true" viral concentration at time $ X_t $ is modelled as a first-order auto-regressive (AR1) process [12,13]. To account for measurement noise and outliers in the observations, measurements $ Y_t $ are assumed to be equal to $ X_t $ plus an independent mean-zero Gaussian observation error. To account for outliers, from time to time $ Y_t $ is assumed to be replaced by an independent Uniformly distributed random variable that is unrelated to $ X_t $. Left-censoring is accounted for by capping $ Y_t $ at the (known) limit of quantification. Using a Kalman Filter and numerical approximations, the state variable $ X_t $ is inferred from observation data $ Y_t $ to produce a smoothed estimate of viral concentration, with outliers removed, that can extend below the known limit of quantification [12].

    In this paper, we propose and test a simpler, more realistic, and more flexible state-space model. Our latent variable is modelled by a first order random walk (RW1) instead of an AR1 process, which reduces the number of model parameters. Instead of randomly replacing observations by a random number, our model generates outliers by assuming observation errors from a heavy-tailed t-distribution. This has the benefit that observations classified as "outliers" can still be informative about viral concentrations.

    Our model is implemented in the Stan modelling language [14], which allows for fast Bayesian inference and straightforward extensions of the model.

    Untreated influent samples were collected from sewage treatment plant sites across England at a frequency of four days a week by the Environmental Monitoring for Health Protection (EMHP) programme, led by the UKHSA. The sampling strategy provides coverage of approximately 40 million people across England. Samples were analysed for SARS-CoV-2 RNA by quantifying the number of copies of the nucleocapsid gene (N1) using RT-qPCR. Concentrations under the limit of detection were assigned a value of -4, to be handled during the data processing pipeline depending on the use case. Only sites sampled 30 times or more (around seven weeks' worth of data) were included; median sample count across sites was 145, ranging from 31 to 323.

    Extraneous sources of flow, such as heavy rainfall, snow melt, or groundwater ingress into sewers, may dilute wastewater and impact estimates of SARS-CoV-2 RNA concentration. Studies have indicated that the effect of dilution in most cases are minor, but in periods of high dilution events, normalisation is critical [15]. The normalisation approach applied by the English wastewater surveillance programme mitigates this by adjusting measured SARS-CoV-2 concentrations to consider flow. The model is based on the assumption that flow $ F_t $ at time $ t $ is not directly observable. Instead, information about flow is obtained by observing the correlation of concentrations $ \rho_{ti} $ of different markers $ i $ (orthophosphate and ammonia nitrogen). The model assumes:

    $ logFtNormal(0,λ2) $ (2.1)
    $ logxtiNormal(μi,σ2i) $ (2.2)
    $ logρti=logxtilogFt $ (2.3)

    where λ2 is the flow variance, xti is the load of marker $ i $ at time $ t $, μi and σ2i are the mean and variance of the load of marker $ i $ (all in log space). logFt is fixed at 0 to identify the model. Using multiple markers jointly to estimate flow variability can improve the accuracy of estimates [9,16].

    In our model, the (unobserved) viral concentration signal $ X_t $ is modelled as a first-order random walk (RW1) process

    $ Xt=Xt1+σϵt $ (2.4)

    where $ \epsilon_t \sim N(0, 1) $ is an independent and identically distributed normal random variable for $ t = 2, ..., n $. The measured concentrations $ Y^*_t $ are modelled by adding independent measurement noise to $ X_t $:

    $ Yt=Xt+τϵt $ (2.5)

    where the independent measurement error $ \epsilon'_{t} \sim t_{\nu} $ has a Student t-distribution with $ \nu $ degrees of freedom. The actually observed, censored data, are modelled by truncating $ Y^*_t $ at the known censoring threshold $ \ell_t $:

    $ Yt=max(Yt,t) $ (2.6)

    As samples are taken only four times a week, the vector of measurements $ {\bf{Y}} $ contains data observed at a subset $ \mathcal{T} $ of all $ n $ available time points. We infer the viral concentration $ X_t $ from $ {\bf{Y}} $ by Bayesian inference [17], i.e. by calculating the posterior distributions of the latent state $ X_1, \dots, X_n $ and hyperparameters $ \sigma $, $ \tau $ and $ \nu $, conditional on $ {\bf{Y}} $. The posterior distribution is given by:

    $ p(X1,,Xn,σ,τ,ν|Y)[tTp(Yt|Xt,τ,ν)]×p(X1,,Xn|σ)×p(τ)p(σ)p(ν) $ (2.7)

    The first line on the right hand side of Eq 2.7 is determined by the distribution of independent measurement errors, and left-censoring, of the $ Y_t $. The second term is determined by the RW1 time series model for the $ X_t $. The distributions $ p(\tau) $, $ p(\sigma) $, and $ p(\nu) $ in the last line are prior hyperparameter distributions: we specify uninformative uniform prior distributions for $ \tau > 0 $ and $ \sigma > 0 $, and a left-truncated Normal prior for $ \nu $, with prior expectation 3, prior variance 1, and truncated at 2. The parameters of the truncated Normal prior for $ \nu $ were selected by simulation and based on subjective judgements about the likely magnitude of measurement errors. The (multiplicative) proportionality constant in Eq 2.7 is inferred by Markov-Chain Monte-Carlo (MCMC) using the Stan software [14].

    The hyperparameters $ \tau $ and $ \nu $ of the measurement process can be interpreted as measurement error variance (larger $ \tau $'s correspond to noisier measurements), and the tendency to generate outliers (smaller $ \nu $'s generate greater deviations from measured viral concentrations). Posterior estimates of these parameters are thus interesting for diagnostic purposes, e.g. to identify anomalous sites.

    The DLM was implemented in the open-source programming language Stan [14], which provides efficient sampling of probabilistic models via MCMC and other inference algorithms. Code specifying the model is provided in Supplementary Information Figure S17. MCMC convergence statistics for the fit examples shown in Figure 1 can also be found in the SI (Figure S4S8, Tables S1S4).

    Figure 1.  Observed concentrations of SARS-CoV-2 N1 gc/L ($ \log_{10} $ transformed, orange points) plotted over time at four sites in England, along with corresponding fit of the proposed dynamic linear model (orange line). The shaded orange area around the lines represents the 99.9% credible intervals for the estimated underlying state $ X $, with observed $ \log_{10} $(N1 gc/L) values outside of these intervals classified as outliers to $ X $. Plots a and c are examples of sites with large fitted $ \tau $ parameter values (measurement noise, scale parameter in t-distribution). Plots b and d are sites with small fitted $ \nu $ parameter values (probability of outliers, degrees of freedom in t-distribution). a Site name: Burton-on-Trent, $ \nu $: mean = 5.26, sd = 1.4, $ \hat{r} $ = 1.00, $ \tau $: mean = 1.25, sd = 0.24, $ \hat{r} $ = 1.00. Date range: 21/02/2021 - 30/03/2022. b Site name: Lincoln, $ \nu $: mean = 2.25, sd = 0.28, $ \hat{r} $ = 1.00, $ \tau $: mean = 0.422, sd = 0.04, $ \hat{r} $ = 1.00. Date range: 15/07/2020 - 30/03/2022. c Site name: Alfreton, $ \nu $: mean = 5.91, sd = 1.43, $ \hat{r} $ = 1.00. $ \tau $: mean = 1.36, sd = 0.16, $ \hat{r} $ = 1.00. Date range: 22/02/2021 - 28/03/2022. d Site name: London Beckton, $ \nu $: mean = 2.28, sd = 0.27, $ \hat{r} $ = 1.00, $ \tau $: mean = 0.29, sd = 0.03, $ \hat{r} $ = 1.00. Date range: 08/07/2020 - 30/03/2022.

    10-fold cross-validation was performed on the data across the 286 sites that had at least 30 samples. For each iteration:

    ● Raw SARS-CoV-2 N1 gc/L (with no normalisation for flow) was used with a $ \log_{10} $ transformation.

    ● Data were randomly split (90%/10%) into training and test sets

    ● Pre-existing missing values (days when samples were expected but were not collected) were included in the training set but not in the test set.

    ● The censoring threshold was set to a single value $ \log_{10} {\rm{(133.0 \ gc/L)}} $ for simplicity. In reality the limit of quantification will vary across samples.

    ● Fit DLM, KS and MA models to training data (details below)

    ● generate estimates (MA) and posterior samples (DLM, KS) of $ Y_{\text{pred, }}{t} $ at times $ t $ that were left out during training

    $ Y_{\text{test, }}{t} $ (the left-out observation data) are then compared to $ Y_{\text{pred, }}{t} $ inferred with the three methods, via mean squared error (MSE) and interval coverage.

    $ Y_{\text{pred, }}{t} $ for the DLM were generated by using Stan to sample from the joint posterior distribution of $ X_1, \dots, X_n $ and hyperparameters $ \sigma $, $ \nu $, $ \tau $, inferred from the training data. We then inferred posterior predictive samples $ Y_{\text{pred, }}{t} $ at times $ t $ left out during training by adding t-distributed measurement errors to posterior samples of $ X_t $, and applying censoring if the sampled observation was below the censoring threshold.

    $ Y_{\text{pred, }}{t} $ for KS was generated by taking the fitted parameters $ \tau $, $ p_{\text{outlier}} $, $ \mu_{\text{X-test}} $, $ \sigma_{\text{X-test}} $. To get a posterior distribution on $ X_t $ 4000 samples were generated from a normal distribution with

    $ XtNormal(μX-test,σX-test) $ (2.8)

    To get $ O_t $ 4000 samples were generated from a binomial with

    $ OtBinomial(1,poutlier) $ (2.9)

    To get uncensored observations $ Y_{\text{outliers}} $ 4000 samples were taken from a uniform distribution

    $ a=min(Ytrain)2SDY $ (2.10)
    $ b=max(Ytrain)+2SDY $ (2.11)
    $ Youtliers, tUnif(a,b) $ (2.12)

    To get $ Y_{\text{pred, }}{t} $ $ X_t $ is passed to a Normal distribution with scale $ \tau $

    $ Ypred, tNormal(Xt,τ) $ (2.13)

    Simulating outliers in $ Y_{\text{pred}} $ was done by

    $ Ypred, t={Yout, t,if Ot=1.Ypred, t,otherwise. $ (2.14)

    Finally, $ Y_{\text{pred, }}{t} $ is censored at some limit $ l $

    $ Ypred, t=max(Ypred, t,l) $ (2.15)

    We then further validated model performance by testing how well it is able to predict 10 samples (2.5 weeks) ahead. We refit the model on all samples for all sites minus the final 10 samples, and then predict the left-out samples.

    Analyses were performed using ${\textsf{R}}$ statistical software (Version 4.1.3) to establish whether the DLM is more likely to observe data variability - characterised by $ \nu $ and $ \tau $ outputs - at sites that show greater concentrations of SARS-CoV-2 RNA in wastewater. For this purpose we regressed the median gene copies per litre (gc/L) obtained over all time ($ \log_{10} $ transformed) against mean $ \nu $ or $ \tau $, controlling for the standard deviation of $ \nu $ and $ \tau $, respectively. We obtained the residuals from these linear regression models to identify sites where the $ \nu $ and $ \tau $ outputs from the model vary in excess of what is accountable to median gc/L and the posterior standard deviation of $ \nu $ or $ \tau $. Residuals for both models were then mapped to the Lower Layer Super Output Area (LSOA) for a given site using the Simple Features (sf) package in ${\textsf{R}}$ [18] (Figure 4).

    Figure 4.  Exploratory analysis of fitted site parameter $ \nu $ (degrees of freedom). a Local Layer Super Output Area (LSOA) map of the posterior mean of $ \nu $. Smaller values of $ \nu $ indicate heavier tails in the t-distribution and thus a stronger probability of outliers at a given site. b Scatterplot showing the relationship between the posterior mean of $ \nu $, median flow-normalised viral RNA concentration $ {\rm{log}}_{10} {\rm{(N1 \ gc/L)}} $, and the posterior standard deviation of $ \nu $. c LSOA map of residuals from multivariable linear regression fit (posterior mean of $ \nu \sim \ {\mathrm{median}}(\log_{10} {\rm{(N1 \ gc/L)) + SD}}_{\nu} $). Values closer to 0 indicate that observed variance in $ \nu $ is better explained by a linear combination of the posterior standard deviation of $ \nu $ and median $ {\rm{log}}_{10} {\rm{(N1 \ gc/L)}} $, while larger residuals indicate there are likely other factors driving the propensity of outliers. The approach may be useful to highlight sites or geographical areas with abnormal results. Six sites with the largest residuals are shown.

    To test the output of the DLM, we first simulated data by generating a random walk with variance parameter $ \sigma^2 $ to model the underlying state, which was then sampled with measurement error parameters $ \tau $ and $ \nu $. Exact values are provided in the code. Any values below a predefined limit $ l $ are set to the value of $ l $. These synthetic data were then fit with the DLM. Supplementary Figure S1 shows that the underlying state $ X $-true is tracked rather well by the $ X $-smoothed estimate and lies within the inferred credible intervals, demonstrating that the model can reliably recover the underlying state from noisy observations in a synthetic dataset.

    We fit the DLM to data from 286 sewage treatment works across England, restricted to sites with greater than 30 samples present. Each site is sampled four times a week. Figure 1 shows a range of fitted sites selected, based upon their estimated parameters $ \tau $ and $ \nu $, to illustrate model behaviour at the extreme ends of the spectrum, i.e. low $ \nu $ and low $ \tau $ (Figures 1b and 1d) or high $ \nu $ and high $ \tau $ (Figures 1a and 1c). Sites with high parameter values typically show low levels of SARS-CoV-2 (N1 gene gc/L, the target used to approximate viral concentration in the sample) recovery and more frequent censoring. More censoring leads to more estimation uncertainty (wider credible intervals) as less information is available to constrain viral concentration estimates. Conversely, sites with low parameter values generally correspond to high levels of SARS-CoV-2 recovery and less censoring, therefore providing more information and tighter credible intervals. Supplementary Figure S2 shows a strong positive correlation between $ \nu $ and $ \tau $, and Figures 4b and 4b show a strong negative correlation between $ \nu $ and $ \tau $ in relation to the site's median viral RNA concentration $ (\log_{10} {\rm{(N1 \ gc/L)}}) $, respectively. We note that our model seems to produce realistic estimates of viral concentration during long periods of censoring, and on days where observations are missing entirely.

    Model performance was assessed by comparing the MSE produced by the DLM, KS and a seven-day centered MA over 10 folds of cross-validation (see Methods). The MA represents a simple way to remove noise from data, and is used here as a benchmark for comparison. All three models generated comparable MSE per site (Figure 2). However, the DLM and KS can estimate viral concentrations below the censoring threshold and, therefore, provide additional information on value for applications, such as case prevalence estimation (see Applications section). In addition both the DLM and KS provide useful parameters for quantifying uncertainty and outliers within the data (DLM: $ \sigma $/$ \tau $/$ \nu $, KS: $ \sigma $/$ \tau $/$ p_{\text{outlier}} $). This is particularly useful to identify sites generating unexpected data. So, while an MA scores equally well in terms of the MSE, the smoothing methods still confer additional advantages. A boxplot of the pairwise MSE differences, shown in Supplementary Figure S6, shows that the differences are not consistently better or worse for the DLM when compared to the KS or MA models.

    Figure 2.  10-fold cross-validation: comparison between a DLM, KS and seven-day centered MA. 286 sites with at least 30 samples were used. See methods for further details on k-fold CV methodology. a Boxplots of MSE, with dots representing each site used in the CV. b Calibration plot showing coverage of different intervals for both the DLM and KS (moving averages do not generate intervals of the predictive distribution). Each point represents mean coverage frequency for all 286 sites for that interval width; error bars show two times the standard error of the mean.

    As MSE assesses the accuracy of a single point estimate of the predictive distribution, it cannot inform on the reliability of the whole model distribution. In Figure 2, the coverage frequency of prediction intervals was used to characterise the reliability of the predictive distribution. Coverage frequency assesses how well the fitted model represents the variability of the data by analysing to what extent the observations could pass as a random sample from the predictive distribution. If observations and samples from the predictive distribution are statistically indistinguishable, we should expect a 90$ % $ chance that the observation is included in a 90% prediction interval derived from the predictive distribution. See Methods for information on calculating coverage. Figure 2b shows mean coverage frequencies across all sites. For nominal interval widths between 0.8 and 0.95, the KS coverage frequencies lie above the dashed line indicating that the model intervals are slightly wider than the true interval and are thus slightly under-confident. For the DLM, the coverage is too wide below nominal values of 90% and appears more reliable between 0.90 and 0.95 than KS. Both models appear over-confident at nominal values above 95%. For additional information on the distributions coverage values see Figures S4 and S5.

    Cross-validation was also performed for forward prediction by removing the last 10 samples and predicting them with either the DLM or KS. Figures S9 and S10 show that both the DLM and KS perform equally well at forecasting up to 10 days of samples.

    The DLM performed equally as well as the KS in cross-validation, but with greater parsimony: we removed the Bernoulli outlier functionality, and autoregressive and offset parameters ($ \eta $ and $ \delta $), to specify a simpler model. By providing full Bayesian posterior information, the DLM offers more information on the distributions of all the parameters in the model, thereby facilitating greater quantification of model uncertainty. Furthermore, the Stan framework offers flexibility for modification of the underlying state model (e.g. AR(2) random walk) or the addition of autoregressive parameters, if desired. The MCMC inference algorithm provided in Stan also allowed the model to be estimated more than 10x faster than the Kalman Smoother: the mean runtime of the DLM for each fold in 10-fold cross-validation of 10 sites was 14 seconds compared to 155 seconds with the KS, although with known parameters the prediction speed by the KS is much improved. Results of the test are provided in Supplementary Table S5, however in both cases the run times are small enough that we believe the difference is of little practical significance. The speed difference that is of more practical relevance (although difficult to quantify) is that our model was written in a general purpose modelling framework and so is easier to maintain, modify and adapt than the handcrafted R code of the Kalman Smoother. On the other hand, only the Kalman Smoother is able to quantify the probability of a given sample being an outlier and, therefore, this model will be more desirable for specific use cases. The DLM can only inform on whether a given sample lies outside of a predefined interval of the estimated underlying state, as shown in Figure 1.

    Work by multiple groups has shown that SARS-CoV-2 gc/l concentrations in wastewater measurements can track case prevalence ('positivity rate', the percentage of people who have tested positive for COVID-19 on a polymerase chain reaction (PCR) test at a point in time) [19,20,21]. In England, the latter has been measured by the Office for National Statistics' Coronavirus (COVID-19) Infection Survey (CIS), a randomised household survey that provides an estimate of disease prevalence at sub-regional, regional and national levels [22]. Therefore, smoothed estimates of $ \log_{10} {\rm{(N1\; gc/L)}} $ from a DLM or KS can be compared with flow-normalised raw estimates to establish which correlates more strongly with $ \log_{10} {\rm{(CIS\; prevalence}} %) $ over time. Figure 3 compares correlations of CIS with (i) flow-normalised $ \log_{10} {\rm{(N1 \ gc/L)}} $, (ii) flow-normalised $ \log_{10} {\rm{(N1 \ gc/L)}} $ with a 7-day centered MA, and (iii) flow normalised $ \log_{10} {\rm{(N1 \ gc/L)}} $ smoothed estimate of $ X $ for all nine English regions between 1st September 2020 and 1st March 2022. This time range includes a period in which wastewater RNA concentration rates decoupled from clinical measures of disease prevalence, of which the cause is unknown [23]. It is worth noting that this relationship is likely not deterministic, i.e. they are not equivalent and are subject to their own spatiotemporal variation and uncertainty that would manifest in significant changes in the ratio of the measures. Such observations have not been limited to England, and the cause is likely to have multiple factors, both epidemiological (i.e., changes in viral shedding distribution as circulating virus variants emerge and evolve) and metrological (e.g., degree of clinical testing coverage can be demographically biased; laboratory sensitivity can vary significantly with virus concentration method employed for wastewater analysis) [24,25,26].

    Figure 3.  A bar chart showing the correlation against Coronavirus (COVID-19) infection survey (CIS) for: $ X $ – smoothed estimate DLM; sites in a give region are smoothed using the Dynamic Linear Model and then aggregated with a mean average; $ X $ – smoothed estimate KS; sites in a give region are smoothed using the Kalman Smoother and then aggregated with a mean average; $ Y $ – Observed $ \log_{10} {\rm{(N1 \ gc/L)}} $ with a 7-day centered moving average; sites are aggregated with a mean average and then the rolling average applied; and $ Y $ – Observed $ \log_{10} {\rm{(N1 \ gc/L)}} $; sites aggregated with a mean average and no additional transformation is applied. DLM and KS smoothed estimates improve the correlation of wastewater measurements against CIS in every region in England. All data used in this analysis were flow normalised prior to any additional manipulation, see methods for more information on flow normalisation.

    Smoothed wastewater concentration rates using a DLM or KS correlate more strongly with CIS positivity rate than raw or averaged rates (Figure 3). The enhanced correlation performance of the DLM and KS is likely due to both models' ability to generate data from below the censoring limit. This assertion is supported by the comparison between the smoothed estimates improvement in correlations verses the averaged $ \log_{10} {\rm{(N1 \ gc/L)}} $, which according to the MSE cross-validation should perform equally well. The key difference being that the DLM and KS infer values below the censored limit, thus we attribute at least part of the increase in correlation to this aspect of the models. Figure S9 provides a time series comparison of $ \log_{10} {\rm{(CIS\; prevalence}} %) $, $ \log_{10} {\rm{(N1 \ gc/L)}} $, and smoothed estimates. Smoothed estimates show a specific advantage over raw $ \log_{10} {\rm{(N1 \ gc/L)}} $ during times of low case prevalence. Using a simple sensitivity analysis to exclude the period in which wastewater concentration rates diverged from case rates to train the models, we find the same results (Figures S10–S11). DLM-smoothed rates therefore better complement CIS data, providing additional useful information for public health decision makers.

    The DLM provides two useful parameters for a given site: the extent to which outliers are observed ($ \nu $), with smaller values indicating greater frequency and size of outlier values, and the amount of measurement noise at a given site ($ \tau $), with larger values indicating noisier measurements. Figure 4a shows the geographical distribution of $ \nu $ values for fitted sites mapped to each Lower Layer Super Output Area (LSOA) in England. There is some evidence of localised behaviour, with areas of large $ \nu $ in the North and East, and low values found in the West and London regions. However, interpretation of this map is challenging as $ \nu $ is strongly related to $ {\mathrm{median}}(\log_{10} {\rm{(N1 \ gc/L)}}) $ and the quality of fit, quantified here as the posterior standard deviation of $ \nu $ ($ SD_{\nu} $ (Figure 4b). To account for these relationships and draw more insight from the $ \nu $ parameter we performed a multivariable linear regression analysis where $ {\mathrm{median}}(\log_{10} {\rm{(N1 \ gc/L)}}) $ was regressed onto the mean of the posterior of $ \nu $, controlling for the standard deviation of the posterior of $ \nu $ (see Methods). Figure 4c plots the absolute values of the regression model residuals (see Figure S12 for distribution of residuals); sites with the highest absolute residuals (i.e., the most variance not explained by either $ {\mathrm{median}}(\log_{10} {\rm{(N1 \ gc/L)}}) $ or quality of fit) are clustered in the North West. We repeat this analysis for $ \tau $ in Figure S3; again sites with the largest absolute residuals are concentrated in the North West, with additional large residuals seen in the South and East of England. Observed non-linearity is potentially attributable to high levels of censorship at low levels of $ {\mathrm{median}}(\log_{10} {\rm{(N1 \ gc/L)}}) $. Future analyses should explore this suggestion, potentially with a censored regression model.

    Further examples of sites with high and low parameter values are provided in Figures S13–S16.

    We show that use of a Bayesian Dynamic Linear Model is a viable method for smoothing left-censored wastewater SARS-CoV-2 measurement data. Handling outliers through a t-distribution, rather than through an independent Bernoulli distribution, as applied in a previously published Kalman Smoother [12], is likely to more directly relate to the underlying state to be recovered. While the DLM and KS perform equivalently with mean squared error under cross-validation, the proposed DLM is more parsimonious (fewer model parameters), has a faster computational time, and is implemented in a more flexible modelling framework, allowing for easier modifications. Additionally, the DLM produces two site-specific parameters, $ \nu $ and $ \tau $, which are able to highlight sites with variable performance. This can be useful when assessing sampling strategies applied at scale (e.g. national or regional surveillance). Sites identified as providing inconsistent, noisy, or low information data may be removed from multi-site monitoring campaigns, for example.

    The smoothed data, using our method, more closely correlate with regional infection survey data (CIS) than untransformed raw measurements. Wastewater data, smoothed in this fashion, are therefore more robust, capable of better complementing traditional surveillance, and providing additional confidence and utility for public health decision making.

    Nevertheless, our approach has some limitations. The limit of censorship was set to a single value during cross-validation $ \log_{10}({\rm{133.0 \ gc/L)}} $, for simplicity. In reality this limit can vary across samples. From September 2021 SARS-CoV-2 RNA measurements from English wastewater diverged from reported clinical data where it had been previously tracking it. The reason why has still not been established but is potentially attributable to differential shedding rates between variants. Our sensitivity analyses reported in the Supplementary material found this does not impact the performance of our model.

    The United Kingdom Government (Department of Health and Social Care) funded the sampling, testing, and data analysis of wastewater in England. Obépine funded the work of Marie Courbariaux and provided the R code of the modified Kalman Smoother and support to use it.

    The authors declare no conflicting interests in this paper.

    Figure S1.  Fit of the proposed dynamic linear model on synthetic data (see Methods in the main text for a description of how these data were generated). In blue is the underlying true process ($ X $ - True), in a real-world situation $ X $ would be latent and unobservable. $ X $ is sampled giving observed values shown in purple ($ Y $ – Observed values), some of which are censored at some limit l (green crosses). The fit of the dynamic linear model is shown in orange with the bold line being the mean of the posterior of the estimated $ X $ ($ X $ – smoothed estimate) and light orange is the 95$ % $ Bayesian credible interval of the posterior of estimated $ X $. Note at time step n $ > $ 150 the model is predicting $ X $ for 14 time steps forward, which is why the credible intervals expand over this period.
    Figure S2.  Posterior means and standard deviations (and the relationships between them) of fitted site parameters $ \nu $ and $ \tau $.
    Figure S3.  Exploratory analysis of fitted site parameter $ \tau $ (measurement noise). a Local Layer Super Output Area (LSOA) map of the posterior mean of $ \tau $. Larger values of $ \tau $ indicate a wider t-distribution and thus more measurement noise at a given site. b Scatterplot showing the relationship between the posterior mean of $ \tau $, median flow-normalised viral RNA concentration $ log_{10} {\rm{(N1 \ gc/L)}} $, and the posterior standard deviation of $ \tau $. c LSOA map of residuals from multivariable linear regression fit (posterior mean of $ \tau \sim \ {\mathrm{median}}(\log_{10} {\rm{(N1 \ gc/L)) + SD}}_{\tau} $). Values closer to 0 indicate that observed variance in $ \tau $ is better explained by a linear combination of the posterior standard deviation of $ \tau $ and median $ log_{10} {\rm{(N1 \ gc/L)}} $, while larger residuals indicate there are likely other factors driving the fitted $ \tau $ parameter.
    Figure S4.  Mean proportion of coverage for the dynamic linear model versus the Kalman smoother at eight different intervals (0.50 to 0.93). The dashed line is the expected proportion of coverage at this interval. Boxplot medians above and below this line indicate overestimation and underestimation of the uncertainty respectively. Both models consistently overestimate; their coverage proportions for each interval do not differ significantly.
    Figure S5.  Mean proportion of coverage for the dynamic linear model versus the Kalman smoother at two different intervals (0.95 and 0.99). The dashed line is the expected proportion of coverage at this interval. Boxplot medians above and below this line indicate overestimation and underestimation of the uncertainty respectively. The DLM more closely matches the expected value at a lower interval of 0.95, although their confidence intervals overlap.
    Figure S6.  Pairwise differences in mean squared error (MSE) between Kalman Smoother and DLM (blue) and between simple moving average and DLM (orange). Although the median MSE is positive in both cases representing slight superiority of the DLM, this should not be considered significant.
    Figure S7.  Predictions over a period of growth: 15th June 2021 to 4th July 2021. 20-sample forward prediction cross-validation on all sites with more than 30 samples for 74 sites. Each site is a point. The dynamic linear model (left) produces a lower MSE in 10-fold cross-validation than the Kalman smoother, although the confidence intervals of the two models overlap.
    Figure S8.  Predictions over a stable period of high wastewater concentrations: 1st January 2021 to 20th January 2021. 20-sample forward prediction cross-validation on 268 sites with more than 30 samples and data available until 20th January 2021. Each site is a point. The Kalman smoother (right) produces a slightly smaller lower MSE in 10-fold cross-validation than the dynamic linear model, although the confidence intervals of the two models overlap.
    Figure S9.  Regional time-series plot of smoothed estimate of wastewater concentration (gc/L) (red) and case prevalence established via the Coronavirus (COVID-19) Infection Survey (green). Raw log-10 N1 gc/L over time is provided in blue. These time series plots cover the period in which wastewater concentrations diverged from case rates in September 2021 onwards.
    Figure S10.  To assess the sensitivity of the model to the divergent period beyond 19th September 2021 the model was refit to exclude the period where wastewater concentrations diverged from case rates in this period (253 sites).
    Figure S11.  Region-level correlations of raw (orange), averaged (pink) and DLM-smoothed (purple) wastewater concentration data with Coronavirus (COVID-19) Infection Survey (CIS) data. In all regions, to varying degrees, smoothing time series data via the proposed DLM improves correlations between wastewater and CIS data. Note that this chart shows, and the smoothing model is trained on, data up until 17th September 2021, before the period where wastewater concentration trends stopped tracking case prevalence.
    Figure S12.  Histograms showing the distribution of residuals for $ \nu $ and $ \tau $ from multivariable linear regression.
    Figure S13.  Example of a site with high $ \nu $ and high $ \tau $: Burton upon Trent. The blue lines, Effective Sample Size (ESS, upper) and $ \hat{r} $ (lower) correspond to the secondary Y-axes on the right. ESS and $ \hat{r} $ are efficiency and convergence diagnostic statistics for Markov Chains.
    Figure S14.  Example of a site with low $ \nu $ and low $ \tau $: Lincoln. The blue lines correspond to the secondary Y-axes on the right.
    Figure S15.  Example of a site with high $ \nu $ and high $ \tau $: Alfreton. The blue lines correspond to the secondary Y-axes on the right.
    Figure S16.  Example of a site with low $ \nu $ and low $ \tau $: Beckton. The blue lines correspond to the secondary Y-axes on the right.
    Figure S17.  Stan model code specifying the proposed dynamic linear model.
    Table S1.  MCMC convergence statistics for Burton upon Trent. SD: Standard Deviation, HDI: Highest Density Interval, MCSE: Markov Chain Standard Error, ESS: Effective Sample Size.
    Mean SD HDI 3% HDI 97% MCSE Mean MCSE SD ESS Bulk ESS tail $ \hat{r} $
    $ \sigma $ 0.394 0.155 0.150 0.677 0.023 0.016 42.0 154.0 1.08
    $ \tau $ 1.251 0.241 0.851 1.731 0.011 0.008 523.0 906.0 1.00
    $ \nu $ 5.260 1.397 2.667 7.737 0.022 0.015 3687.0 2701.0 1.00

     | Show Table
    DownLoad: CSV
    Table S2.  MCMC convergence statistics for Lincoln. SD: Standard Deviation, HDI: Highest Density Interval, MCSE: Markov Chain Standard Error, ESS: Effective Sample Size.
    Mean SD HDI 3% HDI 97% MCSE Mean MCSE SD ESS Bulk ESS tail $ \hat{r} $
    $ \sigma $ 0.189 0.027 0.140 0.240 0.002 0.001 206.0 447.0 1.01
    $ \tau $ 0.422 0.039 0.356 0.502 0.001 0.001 2849.0 3718.0 1.00
    $ \nu $ 2.254 0.276 2.000 2.737 0.005 0.003 3155.0 2741.0 1.00

     | Show Table
    DownLoad: CSV
    Table S3.  MCMC convergence statistics for Alfreton. SD: Standard Deviation, HDI: Highest Density Interval, MCSE: Markov Chain Standard Error, ESS: Effective Sample Size.
    Mean SD HDI 3% HDI 97% MCSE Mean MCSE SD ESS Bulk ESS tail $ \hat{r} $
    $ \sigma $ 0.242 0.097 0.057 0.409 0.014 0.010 44.0 22.0 1.13
    $ \tau $ 1.355 0.159 1.064 1.650 0.005 0.003 1046.0 2012.0 1.00
    $ \nu $ 5.911 1.43v0 3.477 8.745 0.025 0.017 3157.0 2205.0 1.00

     | Show Table
    DownLoad: CSV
    Table S4.  MCMC convergence statistics for London Beckton. SD: Standard Deviation, HDI: Highest Density Interval, MCSE: Markov Chain Standard Error, ESS: Effective Sample Size.
    Mean SD HDI 3% HDI 97% MCSE Mean MCSE SD ESS Bulk ESS tail $ \hat{r} $
    $ \sigma $ 0.153 0.024 0.110 0.198 0.002 0.001 193.0 358.0 1.01
    $ \tau $ 0.288 0.026 0.237 0.333 0.001 0.000 1569.0 3334.0 1.00
    $ \nu $ 2.283 0.273 2.000 2.758 0.005 0.003 2761.0 2587.0 1.00

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    DownLoad: CSV
    Table S5.  Mean run times in seconds for model estimation of each fold in a 10-fold cross-validation. N Train: mean number of train datapoints. Tests were performed on Amazon AWS Sagemaker ml.t2.2xlarge notebook instance.
    Site Code N Train Mean DLM run time Mean KS run time
    UKENAN_AW_TP000004 199 14.8 169.9
    UKENAN_AW_TP000012 203 10.7 135.8
    UKENAN_AW_TP000015 203 16.1 174.1
    UKENAN_AW_TP000016 206 13.5 166.6
    UKENAN_AW_TP000023 202 16.4 155.3
    UKENAN_AW_TP000026 192 11.2 131.4
    UKENAN_AW_TP000028 203 18.7 184
    UKENAN_AW_TP000029 202 15.1 160.2
    UKENAN_AW_TP000037 205 14.8 126.6
    UKENAN_AW_TP000041 201 12.4 149.4
    mean 201.6 14.37 155.33

     | Show Table
    DownLoad: CSV
    Table S6.  Date ranges for all wastewater treatment sites used in study. Showing site code, minimum date (date min), maximum date (date max), site reporting name.
    ww_site_code date_min date_max site_reporting_name
    UKENNE_YW_TP000095 06/07/2020 30/03/2022 Hull
    UKENTH_TWU_TP000054 08/07/2020 30/03/2022 London (Deepham)
    UKENSW_SWS_TP000058 08/07/2020 27/03/2022 Plymouth
    UKENTH_TWU_TP000010 08/07/2020 25/03/2022 Aylesbury
    UKENTH_TWU_TP000013 08/07/2020 30/03/2022 Basingstoke
    UKENTH_TWU_TP000014 08/07/2020 30/03/2022 London (Beckton)
    UKENTH_TWU_TP000015 08/07/2020 30/03/2022 London (Beddington)
    UKENSW_SWS_TP000031 08/07/2020 30/03/2022 St Ives and Penzance
    UKENNW_UU_TP000076 08/07/2020 30/03/2022 Lancaster
    UKENTH_TWU_TP000084 08/07/2020 30/03/2022 London (Hogsmill Valley)
    UKENMI_ST_TP000222 08/07/2020 30/03/2022 Leicester
    UKENNW_UU_TP000012 08/07/2020 30/03/2022 Barrow-in-Furness
    UKENTH_TWU_TP000125 08/07/2020 30/03/2022 London (Riverside)
    UKENSO_SW_TP000030 08/07/2020 30/03/2022 Maidstone and Aylesford
    UKENSO_SW_TP000025 08/07/2020 30/03/2022 Chatham
    UKENNW_UU_TP000110 08/07/2020 24/03/2022 Liverpool (Sandon)
    UKENMI_ST_TP000156 08/07/2020 30/03/2022 Birmingham (Minworth)
    UKENNW_UU_TP000095 08/07/2020 30/03/2022 Wirral
    UKENSO_SW_TP000011 08/07/2020 30/03/2022 New Forest
    UKENSO_SW_TP000001 08/07/2020 30/03/2022 Southampton
    UKENNE_NU_TP000055 15/07/2020 30/03/2022 Washington
    UKENMI_ST_TP000020 15/07/2020 30/03/2022 Barston
    UKENMI_ST_TP000074 15/07/2020 30/03/2022 Derby
    UKENNW_UU_TP000078 15/07/2020 30/03/2022 Leigh
    UKENAN_AW_TP000200 15/07/2020 30/03/2022 Norwich
    UKENAN_AW_TP000210 15/07/2020 30/03/2022 Peterborough
    UKENMI_ST_TP000163 15/07/2020 30/03/2022 Nottingham
    UKENSW_WXW_TP000004 15/07/2020 30/03/2022 Bristol
    UKENNE_NU_TP000030 15/07/2020 30/03/2022 Horden
    UKENNE_YW_TP000082 15/07/2020 30/03/2022 Bradford
    UKENAN_AW_TP000161 15/07/2020 30/03/2022 Lincoln
    UKENMI_ST_TP000068 15/07/2020 25/03/2022 Coventry
    UKENSW_WXW_TP000092 15/07/2020 30/03/2022 Trowbridge
    UKENTH_TWU_TP000113 15/07/2020 30/03/2022 London (Mogden)
    UKENTH_TWU_TP000103 15/07/2020 30/03/2022 Luton
    UKENNW_UU_TP000019 15/07/2020 30/03/2022 Bolton
    UKENAN_AW_TP000063 15/07/2020 30/03/2022 Colchester
    UKENNE_YW_TP000098 15/07/2020 30/03/2022 Leeds
    UKENNE_YW_TP000107 15/07/2020 30/03/2022 Dewsbury
    UKENNW_UU_TP000011 01/10/2020 30/03/2022 Barnoldswick
    UKENNE_YW_TP000119 08/02/2021 30/03/2022 Doncaster (Sandall)
    UKENNE_NU_TP000012 10/02/2021 30/03/2022 Middlesbrough
    UKENNE_NU_TP000031 10/02/2021 30/03/2022 Newcastle
    UKENNE_NU_TP000003 10/02/2021 30/03/2022 Newton Aycliffe
    UKENNE_NU_TP000051 10/02/2021 30/03/2022 Darlington
    UKENNE_YW_TP000057 15/02/2021 30/03/2022 Sheffield (Blackburn Meadows)
    UKENNE_NU_TP000019 17/02/2021 18/02/2022 Consett
    UKENNE_YW_TP000094 17/02/2021 30/03/2022 Huddersfield
    UKENTH_TWU_TP000139 17/02/2021 30/03/2022 Swindon
    UKENNW_UU_TP000097 17/02/2021 30/03/2022 Northwich
    UKENTH_TWU_TP000133 17/02/2021 28/03/2022 Slough
    UKENTH_TWU_TP000126 17/02/2021 30/03/2022 Harlow
    UKENTH_TWU_TP000122 17/02/2021 25/03/2022 Reading
    UKENNE_NU_TP000020 17/02/2021 30/03/2022 Cramlington
    UKENNE_NU_TP000054 17/02/2021 21/02/2022 Bishop Auckland
    UKENTH_TWU_TP000102 17/02/2021 30/03/2022 London (Long Reach)
    UKENNE_NU_TP000009 17/02/2021 30/03/2022 Billingham
    UKENMI_ST_TP000050 19/02/2021 30/03/2022 Checkley
    UKENNE_YW_TP000029 19/02/2021 30/03/2022 York
    UKENNE_YW_TP000063 20/02/2021 30/03/2022 Wakefield
    UKENNW_UU_TP000026 20/02/2021 30/03/2022 Bury
    UKENNW_UU_TP000070 20/02/2021 30/03/2022 Kendal
    UKENMI_ST_TP000099 21/02/2021 30/03/2022 Gloucester
    UKENMI_ST_TP000100 21/02/2021 29/03/2022 Walsall
    UKENMI_ST_TP000130 21/02/2021 30/03/2022 Leek
    UKENMI_ST_TP000137 21/02/2021 30/03/2022 Loughborough
    UKENMI_ST_TP000184 21/02/2021 25/03/2022 Telford
    UKENNW_UU_TP000100 21/02/2021 30/03/2022 Penrith
    UKENNW_UU_TP000050 21/02/2021 30/03/2022 Fleetwood
    UKENMI_ST_TP000152 21/02/2021 30/03/2022 Melton Mowbray
    UKENMI_ST_TP000242 21/02/2021 30/03/2022 Worksop
    UKENMI_ST_TP000207 21/02/2021 30/03/2022 Stoke-on-Trent
    UKENMI_ST_TP000180 21/02/2021 30/03/2022 Stourbridge and Halesowen
    UKENMI_ST_TP000164 21/02/2021 30/03/2022 Nuneaton
    UKENNW_UU_TP000116 21/02/2021 30/03/2022 Stockport
    UKENMI_ST_TP000036 22/02/2021 23/03/2022 Brancote
    UKENNW_UU_TP000139 22/02/2021 30/03/2022 Workington
    UKENMI_ST_TP000241 22/02/2021 30/03/2022 Worcester
    UKENTH_TWU_TP000033 23/02/2021 30/03/2022 Camberley
    UKENSW_SWS_TP000050 24/02/2021 30/03/2022 Newquay
    UKENSW_SWS_TP000064 24/02/2021 30/03/2022 Sidmouth
    UKENSO_SW_TP000096 24/02/2021 30/03/2022 Hailsham
    UKENMI_ST_TP000062 24/02/2021 30/03/2022 Birmingham (Coleshill)
    UKENTH_TWU_TP000050 24/02/2021 30/03/2022 Crawley
    UKENSO_SW_TP000091 24/02/2021 30/03/2022 Bexhill
    UKENTH_TWU_TP000159 24/02/2021 30/03/2022 Oxford
    UKENSO_SW_TP000084 24/02/2021 30/03/2022 Scaynes Hill
    UKENSO_SW_TP000083 24/02/2021 30/03/2022 Worthing
    UKENSO_SW_TP000090 24/02/2021 30/03/2022 Littlehampton and Bognor
    UKENSO_SW_TP000020 24/02/2021 30/03/2022 Tonbridge
    UKENSO_SW_TP000082 24/02/2021 30/03/2022 Lewes
    UKENSO_SW_TP000081 24/02/2021 30/03/2022 Burgess Hill
    UKENSO_SW_TP000021 24/02/2021 30/03/2022 Tunbridge Wells
    UKENNW_UU_TP000124 25/02/2021 28/03/2022 Warrington
    UKENSW_WXW_TP000023 26/02/2021 30/03/2022 Chippenham
    UKENSO_SW_TP000016 26/02/2021 30/03/2022 Isle of Wight
    UKENNW_UU_TP000047 26/02/2021 30/03/2022 Ellesmere Port
    UKENSW_SWS_TP000010 26/02/2021 30/03/2022 Camborne
    UKENMI_ST_TP000120 26/02/2021 30/03/2022 Kidderminster
    UKENSW_WXW_TP000005 26/02/2021 30/03/2022 Bath
    UKENSW_WXW_TP000100 26/02/2021 30/03/2022 Weston-super-Mare
    UKENSW_WXW_TP000044 28/02/2021 30/03/2022 Clevedon and Nailsea
    UKENMI_ST_TP000167 01/03/2021 30/03/2022 Oswestry
    UKENTH_TWU_TP000154 02/03/2021 30/03/2022 Witney
    UKENMI_ST_TP000091 03/03/2021 30/03/2022 Evesham
    UKENTH_TWU_TP000012 03/03/2021 25/03/2022 Banbury
    UKENMI_ST_TP000178 03/03/2021 28/03/2022 Retford
    UKENMI_ST_TP000139 03/03/2021 30/03/2022 Ludlow
    UKENMI_ST_TP000147 03/03/2021 30/03/2022 Market Drayton
    UKENMI_ST_TP000186 03/03/2021 28/03/2022 Scunthorpe
    UKENMI_ST_TP000017 03/03/2021 30/03/2022 Malvern
    UKENMI_ST_TP000256 03/03/2021 30/03/2022 Cheltenham
    UKENTH_TWU_TP000021 05/03/2021 30/03/2022 Radlett
    UKENTH_TWU_TP000116 05/03/2021 30/03/2022 Newbury
    UKENAN_AW_TP000004 08/03/2021 30/03/2022 Anwick
    UKENAN_AW_TP000254 08/03/2021 30/03/2022 Sudbury
    UKENAN_AW_TP000293 08/03/2021 30/03/2022 Wisbech
    UKENAN_AW_TP000116 08/03/2021 30/03/2022 Grimsby
    UKENAN_AW_TP000261 08/03/2021 30/03/2022 Thetford
    UKENAN_AW_TP000286 08/03/2021 30/03/2022 Daventry
    UKENAN_AW_TP000051 08/03/2021 30/03/2022 Chalton
    UKENAN_AW_TP000041 08/03/2021 30/03/2022 Buckingham
    UKENAN_AW_TP000028 08/03/2021 30/03/2022 Brackley
    UKENAN_AW_TP000107 08/03/2021 30/03/2022 Northampton
    UKENAN_AW_TP000055 08/03/2021 30/03/2022 Chelmsford
    UKENAN_AW_TP000067 08/03/2021 30/03/2022 Corby
    UKENAN_AW_TP000069 08/03/2021 30/03/2022 Milton Keynes
    UKENAN_AW_TP000037 08/03/2021 30/03/2022 Wellingborough
    UKENAN_AW_TP000023 08/03/2021 30/03/2022 Boston
    UKENAN_AW_TP000026 08/03/2021 30/03/2022 Bourne
    UKENAN_AW_TP000078 08/03/2021 30/03/2022 Diss
    UKENAN_AW_TP000082 08/03/2021 30/03/2022 Downham Market
    UKENAN_AW_TP000096 08/03/2021 30/03/2022 Felixstowe
    UKENAN_AW_TP000106 08/03/2021 30/03/2022 Grantham
    UKENAN_AW_TP000016 08/03/2021 30/03/2022 Bedford
    UKENAN_AW_TP000015 08/03/2021 30/03/2022 Beccles
    UKENAN_AW_TP000012 08/03/2021 30/03/2022 Barton-upon-Humber
    UKENAN_AW_TP000077 08/03/2021 30/03/2022 Breckland
    UKENAN_AW_TP000029 08/03/2021 27/03/2022 Braintree
    UKENTH_TWU_TP000123 10/03/2021 30/03/2022 Reigate
    UKENAN_AW_TP000237 10/03/2021 30/03/2022 Soham
    UKENSW_WXW_TP000086 10/03/2021 30/03/2022 Taunton
    UKENAN_AW_TP000194 10/03/2021 30/03/2022 Newmarket
    UKENAN_AW_TP000047 10/03/2021 30/03/2022 Bury St. Edmunds
    UKENSW_WXW_TP000096 10/03/2021 30/03/2022 Wellington
    UKENSW_WXW_TP000057 10/03/2021 30/03/2022 Minehead
    UKENSW_WXW_TP000077 10/03/2021 30/03/2022 Shepton Mallet
    UKENAN_AW_TP000224 10/03/2021 30/03/2022 Saffron Walden
    UKENAN_AW_TP000222 10/03/2021 30/03/2022 Royston
    UKENTH_TWU_TP000019 12/03/2021 30/03/2022 Bicester
    UKENAN_AW_TP000060 15/03/2021 30/03/2022 Shefford
    UKENAN_AW_TP000154 15/03/2021 30/03/2022 Kings Lynn
    UKENNE_YW_TP000076 15/03/2021 30/03/2022 Driffield
    UKENNE_YW_TP000112 15/03/2021 30/03/2022 Chesterfield
    UKENNE_YW_TP000026 15/03/2021 30/03/2022 Malton
    UKENSW_SWS_TP000045 22/02/2021 30/03/2022 Liskeard
    UKENSW_SWS_TP000051 22/02/2021 30/03/2022 Newton Abbot
    UKENMI_ST_TP000233 22/02/2021 30/03/2022 Wigston
    UKENSW_SWS_TP000056 22/02/2021 30/03/2022 Plymouth (Camels Head)
    UKENSW_SWS_TP000055 22/02/2021 30/03/2022 Par
    UKENSW_SWS_TP000059 22/02/2021 30/03/2022 Plympton
    UKENNW_UU_TP000129 22/02/2021 30/03/2022 Whaley Bridge
    UKENSW_SWS_TP000074 22/02/2021 30/03/2022 Tiverton
    UKENMI_ST_TP000003 22/02/2021 28/03/2022 Alfreton
    UKENSW_SWS_TP000075 22/02/2021 30/03/2022 Torquay
    UKENMI_ST_TP000018 22/02/2021 30/03/2022 Wolverhampton
    UKENAN_AW_TP000148 08/03/2021 30/03/2022 Jaywick
    UKENAN_AW_TP000160 08/03/2021 30/03/2022 Letchworth
    UKENAN_AW_TP000169 08/03/2021 30/03/2022 Louth
    UKENAN_AW_TP000170 08/03/2021 30/03/2022 Lowestoft
    UKENAN_AW_TP000172 08/03/2021 30/03/2022 Mablethorpe
    UKENAN_AW_TP000176 08/03/2021 30/03/2022 March
    UKENAN_AW_TP000177 08/03/2021 30/03/2022 Market Harborough
    UKENAN_AW_TP000308 08/03/2021 30/03/2022 Tilbury
    UKENAN_AW_TP000307 08/03/2021 30/03/2022 Southend-on-Sea
    UKENAN_AW_TP000201 08/03/2021 30/03/2022 Oakham
    UKENAN_AW_TP000303 08/03/2021 30/03/2022 Basildon
    UKENAN_AW_TP000296 08/03/2021 30/03/2022 Witham
    UKENAN_AW_TP000242 08/03/2021 30/03/2022 Spalding
    UKENAN_AW_TP000248 08/03/2021 30/03/2022 Stamford
    UKENAN_AW_TP000253 08/03/2021 30/03/2022 Stowmarket
    UKENNE_YW_TP000061 15/03/2021 30/03/2022 Bridlington
    UKENNE_YW_TP000131 15/03/2021 30/03/2022 Pontefract
    UKENNE_YW_TP000102 17/03/2021 30/03/2022 Barnsley
    UKENNE_YW_TP000096 17/03/2021 30/03/2022 Keighley
    UKENNE_YW_TP000133 17/03/2021 30/03/2022 Doncaster (Thorne)
    UKENMI_ST_TP000208 19/03/2021 30/03/2022 Stroud
    UKENNW_UU_TP000133 21/03/2021 30/03/2022 Wigan
    UKENNW_UU_TP000103 21/03/2021 30/03/2022 Rochdale
    UKENNW_UU_TP000067 21/03/2021 30/03/2022 Hyde
    UKENNW_UU_TP000037 21/03/2021 25/03/2022 Congleton
    UKENSW_WXW_TP000074 24/03/2021 30/03/2022 Salisbury
    UKENSW_WXW_TP000018 24/03/2021 30/03/2022 Chard
    UKENSO_SW_TP000107 24/03/2021 30/03/2022 Chichester
    UKENSO_SW_TP000002 24/03/2021 30/03/2022 Lymington and New Milton
    UKENSO_SW_TP000004 24/03/2021 30/03/2022 Portsmouth and Havant
    UKENSO_SW_TP000006 24/03/2021 30/03/2022 Andover
    UKENSO_SW_TP000033 24/03/2021 30/03/2022 Canterbury
    UKENSO_SW_TP000032 24/03/2021 30/03/2022 Sittingbourne
    UKENSO_SW_TP000008 24/03/2021 30/03/2022 Fareham and Gosport
    UKENSO_SW_TP000026 24/03/2021 30/03/2022 Ashford
    UKENSO_SW_TP000013 24/03/2021 30/03/2022 Eastleigh
    UKENNW_UU_TP000027 24/03/2021 30/03/2022 Carlisle
    UKENSW_WXW_TP000085 24/03/2021 30/03/2022 Blandford Forum
    UKENNW_UU_TP000062 26/03/2021 27/03/2022 Maghull
    UKENNW_UU_TP000018 26/03/2021 30/03/2022 Blackburn
    UKENTH_TWU_TP000039 26/03/2021 14/03/2022 Chesham
    UKENSW_WXW_TP000111 26/03/2021 30/03/2022 Yeovil
    UKENTH_TWU_TP000047 26/03/2021 30/03/2022 Cirencester
    UKENTH_TWU_TP000055 26/03/2021 30/03/2022 Didcot
    UKENTH_TWU_TP000073 26/03/2021 28/03/2022 Guildford
    UKENNW_UU_TP000024 26/03/2021 30/03/2022 Burnley
    UKENMI_ST_TP000141 29/03/2021 30/03/2022 Lydney
    UKENTH_TWU_TP000004 31/03/2021 28/03/2022 Alton
    UKENTH_TWU_TP000106 31/03/2021 30/03/2022 St Albans
    UKENTH_TWU_TP000023 31/03/2021 21/03/2022 Bordon
    UKENSW_WXW_TP000012 07/04/2021 30/03/2022 Bridport
    UKENMI_ST_TP000060 07/04/2021 30/03/2022 Telford South
    UKENSW_WXW_TP000038 07/04/2021 30/03/2022 Bournemouth (Central)
    UKENSO_SW_TP000027 07/04/2021 30/03/2022 Hythe
    UKENSW_WXW_TP000084 07/04/2021 30/03/2022 Swanage
    UKENSO_SW_TP000028 07/04/2021 30/03/2022 Dover and Folkestone
    UKENMI_ST_TP000143 09/04/2021 30/03/2022 Mansfield
    UKENSO_SW_TP000022 05/05/2021 30/03/2022 "Ramsgate, Sandwich and Deal"
    UKENNE_NU_TP000046 21/05/2021 30/03/2022 Hartlepool
    UKENSW_SWS_TP000067 26/05/2021 30/03/2022 Menagwins
    UKENSW_SWS_TP000033 26/05/2021 30/03/2022 Helston
    UKENSW_SWS_TP000005 26/05/2021 30/03/2022 Bodmin Sc.Well
    UKENTH_TWU_TP000155 04/06/2021 25/03/2022 Woking
    UKENAN_AW_TP000071 09/06/2021 30/03/2022 Cromer
    UKENAN_AW_TP000280 09/06/2021 30/03/2022 Wells-next-the-Sea
    UKENAN_AW_TP000247 09/06/2021 30/03/2022 Stalham
    UKENAN_AW_TP000219 09/06/2021 30/03/2022 Reepham
    UKENAN_AW_TP000128 09/06/2021 30/03/2022 Hunstanton
    UKENAN_AW_TP000191 11/06/2021 30/03/2022 Needham Market
    UKENNE_NU_TP000028 21/06/2021 30/03/2022 Sunderland
    UKENNW_UU_TP000113 30/07/2021 30/03/2022 Skelmersdale
    UKENNW_UU_TP000104 04/08/2021 27/03/2022 Rossendale
    UKENNW_UU_TP000032 13/08/2021 30/03/2022 Chorley
    UKENNW_UU_TP000034 16/08/2021 30/03/2022 Clitheroe
    UKENNE_YW_TP000039 18/08/2021 30/03/2022 Scarborough
    UKENNW_UU_TP000068 20/08/2021 30/03/2022 Hyndburn
    UKENSW_SWS_TP000016 13/10/2021 30/03/2022 Bideford
    UKENSW_SWS_TP000073 13/10/2021 30/03/2022 Tavistock
    UKENNE_NU_TP000004 05/11/2021 30/03/2022 Durham (Barkers Haugh)
    UKENNE_NU_TP000048 05/11/2021 30/03/2022 Houghton-le-Spring
    UKENNE_NU_TP000007 17/11/2021 30/03/2022 Durham (Belmont)
    UKENNE_NU_TP000039 28/11/2021 30/03/2022 MARSKE REDCAR
    UKENNW_UU_TP000017 20/12/2021 30/03/2022 Birkenhead
    UKENNW_UU_TP000023 20/12/2021 30/03/2022 Bromborough
    UKENNW_UU_TP000066 22/12/2021 30/03/2022 Huyton and Prescot
    UKENAN_AW_TP000056 05/01/2022 30/03/2022 Clacton-on-Sea and Holland-on-Sea
    UKENAN_AW_TP000306 05/01/2022 30/03/2022 Basildon (Vange)
    UKENAN_AW_TP000289 05/01/2022 30/03/2022 Wickford
    UKENAN_AW_TP000221 05/01/2022 30/03/2022 Rochford
    UKENAN_AW_TP000305 05/01/2022 30/03/2022 Canvey Island
    UKENAN_AW_TP000052 05/01/2022 30/03/2022 Ipswich (Chantry)
    UKENAN_AW_TP000084 09/01/2022 30/03/2022 Dunstable
    UKENNE_YW_TP000126 10/01/2022 30/03/2022 Hemsworth and South Elmsall
    UKENNE_YW_TP000054 10/01/2022 30/03/2022 Rotherham
    UKENNE_YW_TP000075 10/01/2022 30/03/2022 Bingley
    UKENNE_YW_TP000137 12/01/2022 30/03/2022 Castleford
    UKENNE_YW_TP000073 14/01/2022 30/03/2022 Mexborough and Conisbrough
    UKENAN_AW_TP000115 08/03/2021 30/03/2022 Great Yarmouth
    UKENAN_AW_TP000127 08/03/2021 30/03/2022 Haverhill
    UKENAN_AW_TP000139 08/03/2021 30/03/2022 Huntingdon
    UKENAN_AW_TP000143 08/03/2021 30/03/2022 Ingoldmells
    UKENAN_AW_TP000144 08/03/2021 30/03/2022 Ipswich
    UKENNW_UU_TP000102 21/02/2021 30/03/2022 Preston
    UKENMI_ST_TP000056 21/02/2021 30/03/2022 Burton on Trent
    UKENMI_ST_TP000225 22/02/2021 30/03/2022 Warwick
    UKENSW_SWS_TP000002 22/02/2021 30/03/2022 Barnstaple
    UKENMI_ST_TP000199 22/02/2021 28/03/2022 Spernal
    UKENSW_SWS_TP000022 22/02/2021 30/03/2022 Ernesettle and Saltash
    UKENSW_SWS_TP000024 22/02/2021 30/03/2022 Exmouth
    UKENMI_ST_TP000182 22/02/2021 28/03/2022 Rugby
    UKENNE_YW_TP000141 15/03/2021 30/03/2022 Sheffield (Woodhouse Mill)
    UKENNE_YW_TP000008 15/03/2021 30/03/2022 Colburn
    UKENNE_YW_TP000015 15/03/2021 30/03/2022 Harrogate North
    UKENNE_YW_TP000030 15/03/2021 30/03/2022 Northallerton
    UKENNE_YW_TP000056 15/03/2021 30/03/2022 Beverley
    UKENAN_AW_TP000050 15/07/2020 30/03/2022 Cambridge
    UKENTH_TWU_TP000100 15/07/2020 30/03/2022 Wycombe
    UKENSW_WXW_TP000101 15/07/2020 30/03/2022 Weymouth
    UKENTH_TWU_TP000052 15/07/2020 30/03/2022 London (Crossness)

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