senpei. When you spell Senpai wrong. Did you seriously spell Senpai wrong? Senpai will never notice you now. I love Senpei, wait I just. vanguard; advance-guard point; advance detachment. Related Kanji. 尖, be pointed, sharp, taper, displeased, angry, edgy. 兵, soldier, private, troops, army.
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senpei. I study transmission dynamics of infectious diseases. Within this broad topic, I develop mathematical models and computational tools to advance surveillance.
Dr. Sen Pei studies transmission dynamics of infectious disease. He works on mathematical modeling, statistical inference and real-time forecast of seasonal. Translations in context of "Senpei" in Spanish-English from Reverso Context: Hyoroku, Senpei, el jefe quiere verlos.
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Senpei Tang's 8 research works with 64 citations and reads, including: Study on boron and fluorine-doped C3N4 as a solid activator for cyclohexane. samantha-chan · senpei. +4 more. A Happy Girl and A Mysterious Girl? ✓ by Isy_weirdo. #2. A Happy Girl and A Mysterious Girl by ł'M Д ŲЙłĊØЯЙ. senpei View Senpei Kodama's US census record to find family members, occupation details & more. Access is free so discover Senpei Kodama's story today. Sen Pei. Sen_Pei. Academicicon-GoogleScholar · Envelope. Associate Research Scientist. Education. Affiliations. Environmental Health Sciences, Mailman.
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The dynamics of a class of one-dimensional chaotic maps · Sen Pei. Beihang University, School of Mathematics and System Sciences, Beijing, P. R. China. High quality Senpei gifts and merchandise. Inspired designs on t-shirts, posters, stickers, home decor, and more by independent artists and designers from. senpei Want to discover art related to senpei? Check out amazing senpei artwork on DeviantArt. Get inspired by our community of talented artists. A special range of Toundo's Niwaka Senpei featuring Hakata Gion Yamakasa's official character “Oisa” is on sale at the Tourism Promotional. paris chanel memphis senpei. When you spell Senpai wrong. Did you seriously spell Senpai wrong? Senpai will never notice you now. I love Senpei, wait I just.
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Dr. Sen Pei studies transmission dynamics of infectious disease. Within this broad topic, he develops mathematical models and computational. Senpai and Kohai
For a realistic scenario, disease-related model parameters may differ from person to person. The parameter ranges are enlarged slightly to cover the values reported in these works. To infer epidemiological parameters in an agent-based model, we adapt an iterated filtering IF algorithm Ionides et al.
IF can be used to infer the maximum likelihood estimates MLEs of parameters in epidemic models and has been successfully applied to infectious diseases such as cholera King et al. Here, we adapt IF for agent-based models, leveraging an equation-free approach Kevrekidis et al. In applying the IF, we perform multiple iterations using an efficient Bayesian filtering algorithm — the Ensemble Adjustment Kalman Filter EAKF Anderson, , which has been widely used in infectious disease forecast and inference Shaman and Karspeck, ; Yang et al.
Details of the IF implementation can be found in Materials and methods. Before applying the inference system to real-world data, we first need to validate its effectiveness. For the real-world data the inference targets are unobserved, so instead we test the inference system using model-generated synthetic outbreaks for which we know the exact values of the parameter. Although actual MRSA transmission dynamics cannot be fully described by the simplified agent-based model, performing synthetic tests provides validation that the inference system works if the transmission process generally follows the model-specified dynamics.
To generate synthetic outbreak observations, we used the agent-based model to simulate weekly incidence during a one-year period 52 weeks , and then imposed noise to produce the observations used in inference See details in Appendix 1. The blue horizontal lines mark the target values used to generate the outbreak. The orange boxes show the distribution of posterior parameters ensemble members after each iteration. As a result of the stochastic nature of model dynamics and initialization of the inference algorithm, different runs of the IF algorithm usually return slightly different MLEs.
In its implementation, the performance of the inference system depends on the sensitivity of the observations to each parameter. In the agent-based model used here, observed incidence is less sensitive to C 0 due to the long period of colonization. As a consequence, estimates of C 0 do not always exactly match the actual target and are here biased low.
Nevertheless, this slight underestimation does not significantly affect the inferred dynamics. To demonstrate this insensitivity, we ran simulations using the inferred mean parameters and obtained distributions of weekly incidence from the stochastic agent-based model. The distributions of weekly incidence blue boxes are compared with the observed cases red crosses in Figure 2B. We also evaluated the agreement between the observed and simulated incidences in Figure 2B Figure 2—figure supplement 1 ; Analysis details are explained in Appendix 1.
The inferred dynamics fit the observed incidence well. The Matlab code for synthetic test on an example network is uploaded as an additional file. Whiskers mark the inferred values within the range [Q Dots are outliers. Horizontal blue lines indicate the inference targets used in generating the synthetic outbreak. B—C Distributions of weekly incidence B and colonization C generated from realizations of simulations using the inferred parameters are shown by the blue boxes.
The red crosses represent the synthetic observations used during the inference B and actual colonization in the outbreak C. D—E Inference of the transmitted and imported infections.
Blue boxes are distributions generated from simulations, and red crosses are the actual values in the synthetic outbreak. We repeated the above analysis for the colonized population Figure 2C and found that the numbers of unobserved colonized patients can also be well estimated by the inference system. Moreover, the inference system can distinguish the number of infections transmitted in hospital and imported from outside the study hospitals Figure 2D—E.
More tests for alternate synthetic outbreaks and different observation frequencies were performed and are presented in Figure 2—figure supplements 2 — 5. Because the UK EMRSA transmission parameters are unlikely to remain constant over the entire 6-year outbreak cycle, we inferred model parameters year by year 52 weeks. Beginning with the first year, we ran the IF inference sequentially through each year.
Between 2 consecutive years, the inferred results from the previous year were used to initialize the inference system in the next see Figure 3—figure supplement 1. All parameter values increased in the first 3 or 4 years, and then gradually decreased thereafter. B Observed incidence every 4 weeks red crosses and corresponding distributions generated from simulated outbreaks using the inferred mean parameters blue boxes and whiskers.
C Distribution of the number of infected wards obtained from simulations. The vertical red dash line indicates , the observed number of infected wards. D Distributions of the number of infections per ward from simulations blue boxes and whiskers. Red diamonds are the observed probabilities. E Inferred distributions of infections transmitted in hospital turquoise area and imported from outside the study hospitals pink area. The dark areas mark the IQR; light areas show values within the range [Q The data set includes: 1 distributions of inferred parameters in Figure 3A ; 2 distributions of inferred incidence and actual observation in the real-world outbreak in Figure 3B ; 3 distribution of the number of infected wards obtained from inference in Figure 3C ; 4 observed and inferred distributions of the number of infections per ward in Figure 3D ; 5 distributions of inferred nosocomial transmitted and imported cases in Figure 3E.
The inferred parameters can be plugged back into the model to run simulations and obtain information addressing our questions of interest see Video 1 for an example. For instance, we performed model simulations using the inferred mean parameter values, and generated distributions of incidence from the stochastic agent-based model. These distributions are compared to observations in Figure 3B. All observations fall within the whisker range of Tukey boxplots see more analyses in Figure 3—figure supplement 2.
To further explore whether some of the key observed statistics can be reproduced using the inferred parameters, we display the distribution of the number of infected wards in Figure 3C. The observed number lies at the peak of the simulated distribution vertical dash line.
The spatial distribution of infections among different wards can be characterized by the distribution of wards with a certain number of infections in an outbreak. In Figure 3D , we compare this distribution obtained from simulations with what we observed in the data red diamonds : the observed distribution agrees well with the simulated distributions. This close matching indicates that the model structure and inferred parameters can reliably reproduce the observed outbreak pattern in both space and time see also Figure 3—figure supplement 2.
In addition to generating a good model fit, the inference system also discriminates the burdens of nosocomial transmission and infection importation. Nosocomial and imported infections are distinguished by the location of MRSA colonization: if patients acquire MRSA in hospital, they are classified as nosocomial transmission cases; otherwise they are imported cases.
Figure 3E compares the distributions of both types of infections generated from simulations: a substantial number of infections are inferred as importations. In clinical practice, the number of days between hospital admission and infection is usually used to distinguish hospital-acquired from community-acquired infections, typically with 48 hr used as the threshold.
We performed this classification and compared the findings with our inference result. As shown in Figure 3—figure supplement 3 , the number of imported and nosocomial cases obtained from inference generally matches the classification result using days from admission to infection.
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We visualize a single realization of the agent-based model during a one-year period. The grey nodes represent susceptible people, green nodes represent colonized individuals, and red nodes highlight infected patients. The contact network changes from day to day. Our findings indicate that, at its onset, during the first year of the outbreak, UK EMRSA gradually invaded the hospital system from the community. Only sporadic nosocomial transmission occurred.
Concurrently, both the infection and colonization importation rates, I 0 and C 0 , also experienced growth. This simultaneous rise may have been caused by household transmission initiated by asymptomatically colonized patients discharged from hospitals. After this growth phase, both transmission and importation rates were suppressed.
However, if control measures in hospital were to be relaxed, the colonized patients might spark another outbreak due to the lengthy colonization period, which highlights the need for asymptomatic colonization control in order to effect MRSA elimination Cooper et al. Asymptomatic colonization is a major issue hindering the control and elimination of MRSA in hospitals Cooper et al. Screening can identify colonized patients and evaluate the general colonization burden; however, it is an inefficient and costly measure that wastes resources that otherwise could be used to solve more urgent problems.
As shown above, given the heterogeneity of contact among patients, levels of exposure to the hazard of colonization differ substantially. As a result, more efficient intervention strategies can be designed that leverage this individual-level heterogeneity. In Figure 4A , we display the inferred distribution of colonized patients in the Swedish hospitals over time.
Colonized patient numbers peak in the middle of the record and decline thereafter. To determine who and where these high-risk individuals reside within the network, we can use the agent-based model to quantify colonization risk at the individual level.
The complex spatiotemporal interaction patterns within the network give rise to a small number of patients with a disproportionately high risk of colonization. To examine how these individuals distribute among hospitals, we visualize the colonization probability in Figure 4C. High-risk patients tend to appear in densely connected clusters. A Inferred distributions of colonized patients through time. The red line is the power-law fitting. The probability is color-coded in a logarithmic scale.
Node size reflects the number of connections. Cost-effective interventions can be practiced by the targeted screen and decolonization of identified high-risk patients. In order to evaluate the effectiveness of such interventions, we performed a retrospective control experiment. Specifically, we used the inferred parameters in Figure 3A to run the model for 6 years to reproduce the outbreak. Every 4 weeks, we used currently available information as would be available in real time to estimate patient colonization probabilities see details in Materials and methods.
The colonization probabilities estimated in real time are highly correlated with the results obtained using information from the whole course of the epidemic, shown in Figure 4C. During the model integration, every 4 weeks, we selected patients with an estimated colonization probability higher than a certain threshold for screening.
If positive, these inpatients were decolonized. The findings show that the proposed intervention strategy can avert considerable numbers of colonization and infection Figure 5A—B.
Decreasing the decolonization threshold leads to a larger screened population as shown in the inset of Figure 5B , and thus reduces colonization and infection further. However, the marginal benefit becomes negligible below a certain threshold value, as the remaining colonized and infected patients are possibly caused by importation, which cannot be directly controlled by inpatient intervention.
The decolonization success rate also plays an important role, as indicated by the increased colonization and infection for the lower success rate. The cumulative cases of colonization A and infection B after decolonizing patients with a hazard of colonization higher than a specified decolonization threshold.
Distributions were obtained from realizations of the retrospective control experiment. The inset in A reports the Pearson correlation coefficient between colonization probability estimated in real time and that obtained using information from the whole course of the epidemic. The inset in B shows the number of screened patients as a function of the decolonization threshold. C—D Comparison of the inference-based intervention with heuristic control measures informed by number of contacts, length of stay and contact tracing.
The data set includes: 1 distributions of colonization for each decolonization threshold in Figure 5A ; 2 distributions of infection for each decolonization threshold in Figure 5B ; 3 colonization number for each control strategy in Figure 5C ; 4 infection number for each control strategy in Figure 5D.
The advantage of the proposed inference-based intervention can be better appreciated by examining its additional benefit over other heuristic control measures. Here, we compare the performance of the inference-based intervention with three alternative screening strategies informed by patient number of contacts, length of stay and contact tracing.
For the former two, at each month, we ranked patients by their current total number of contacts i. For contact tracing, upon each observation of infection, we tracked patients who stayed in the same ward with an infected individual within a certain time window prior to the infection, and screened those possibly colonized patients in hospitals.
Tracing time windows ranging from 1 day to 14 days were tested. The number of screened patients does not increase significantly with tracing times longer than 14 days. Note that, screening and decolonization are performed only within hospitals. If patients listed for screening have already discharged before the diagnosis of infection, they are screened upon their next re-admission. In Figure 5C—D , the average numbers of colonized and infected patients are compared based on the number of screened patients.
Heuristic control measures relying on the number of contacts, length of stay and contact tracing all limit MRSA transmission; however, a substantial additional reduction in both colonization and infection can be achieved through inference-based intervention.
On average, inference-based screening of approximately 0. The colonization probability obtained from inference quantifies individual systemic risk given the general situation of transmission, regardless of the specific location of undetected colonization.
In contrast, screening based on contact tracing identifies colonized individuals related to observed infections; however, with an unknown amount of imported colonization, this approach may overlook a considerable number of colonized patients, who can sustain subsequent transmission. As a result, the inference-based intervention can identify and treat the pivotal individuals, or superspreaders Pei and Makse, ; Pei et al.
This preventive approach is more effective than contact tracing in the presence of frequent importation, as it disrupts probable transmission pathways. In real-world hospital settings, the proposed inference-based intervention could be implemented and evaluated in real time: it only requires hospitalization records and ward information. In this work, we have developed an agent-based model-inference framework that can estimate nosocomial MRSA transmission dynamics in the presence of importation.
Further, we have shown that these inferred dynamics can be used to quantify patient colonization risk and guide more effective interventions. The transmission dynamics generated using the agent-based model are intrinsically stochastic, that is, the observed record of UK EMRSA infections is just one realization among an ensemble of all possible outcomes of an underlying highly stochastic process.
In order to evaluate the general risk of MRSA transmission, key epidemiological parameters were inferred from the single observed realization. Previous studies have developed methods to infer transmission risk factors and reconstruct transmission paths using individual-level infection data for diseases such as H1N1 and MERS-CoV Cauchemez et al.
The data assimilation scheme we developed here enables estimation of epidemiological parameters and key transmission information using aggregated incidence data. As demonstrated in the retrospective control experiment, assessment of individual colonization risk using aggregated data can be quite useful for preventing future MRSA transmission, especially when stealth importations are frequent. In this study, we omitted representation of heterogeneity across different wards.
This simplification is valid for the study Swedish hospitals, as we observed no infection clusters and the model reproduced key statistics of observations well. However, in other settings, clustering analysis and ward information may be necessary before the application of the inference system. Should certain wards suffer a much higher rate of infection, a separate suite of parameters can be defined and inferred for these wards, using priors that better represent this more intense transmission.
We also only considered transmission among patients staying in the same ward. In the future, more contact information such as healthcare workers shared by a group of patients could be incorporated into the contact network. In addition, as the community defined in the model may include non-sampled hospitals, inferred community risk may have been overestimated as it also included contributions from those healthcare facilities outside the network.
Should more data e. Our model-inference framework provides a foundational platform for flexible simulation and inference of antibiotic resistant pathogens. However, in the future, it could be used to provide actionable information for disease control in less developed settings where MRSA is endemic. In a highly interconnected area, transmission of antibiotic resistant pathogens from endemic regions to epidemic-free hospitals is more likely.
This risk calls for containment measures in the general population and collaborative control efforts among multiple healthcare facilities Smith et al. The dataset contains admission and discharge records of , distinct patients from 66 hospitals clinics, wards in Stockholm County, Sweden Jarynowski and Liljeros, ; Rocha et al.
The exact dates and ward types are confidential for the protection of patient privacy. In total, 2,, admission records were collected. The hospitalization dataset is quite comprehensive as the patients constitute over one third of the total 2. Diagnosis was performed on patients with symptomatic infections as well as asymptomatic patients in contact with positive cases. Here, we focus on this specific strain. Although the dataset spans over days nearly 10 years , we limit our study to a 6-year week period with reported UK EMRSA incidence.
We infer system epidemiological parameters using an iterated filtering IF algorithm Ionides et al. This algorithm has been coupled with ODE models and used to infer latent variables associated with the transmission of cholera King et al. The IF framework is designed as follows: an ensemble of system states, which represent the distribution of parameters, are repeatedly adjusted using filtering techniques in a series of iterations, during which the variance of the parameters is gradually tuned down.
In the process, the distribution of parameters is iteratively optimized per observations and narrowed down to values that achieve maximum likelihood. This approach is based on an analytical proof that guarantees its convergence under mild assumptions Ionides et al. In its original implementation, the data assimilation method used in IF is sequential Monte Carlo, or particle filtering Arulampalam et al. Here, due to the high computational cost of the agent-based model, we use a different efficient data assimilation algorithm - the Ensemble Adjustment Kalman Filter EAKF Anderson, Unlike particle filtering, which requires a large ensemble size usually of the order O 10 4 or higher Snyder et al.
Originally developed for use in weather prediction, the EAKF assumes a Gaussian distribution of both the prior and likelihood, and adjusts the prior distribution to a posterior using Bayes rule in a deterministic way such that the first two moments mean and variance of an observed variable are adjusted while higher moments remain unchanged during the update Anderson, In epidemiological studies, the EAKF has been widely used for parameter inference and forecast of infectious diseases Shaman and Karspeck, ; Yang et al.
The initial prior ranges for these parameters are reported in Table 1. Should more specific information about these parameters become available, it may be possible in the future to better constrain the model with their incorporation into the system. In practice, the discount factor a can range between 0.
We stop the IF algorithm once the estimates of the ensemble mean stabilize. The number of iterations required for this convergence was determined by inspecting the evolution of posterior parameter distributions, as in Figure 2A. Note that once the ensemble mean stabilizes, increasing the iteration time will not affect the MLE, although it can lead to a further narrowing of the ensemble distribution.
For deterministic ODE models, Ionides et al. Here, for a highly stochastic system, evaluating the Fisher information numerically is challenging. As a result, we took another approach by running multiple realizations of the IF algorithm. In different runs, the MLEs are slightly different due to stochasticity in the agent-based model and in the initialization of the inference algorithm.
Results from synthetic tests indicate that this approach is effective in calculating MLEs and quantifying their uncertainties. ABC-based methods employ numerical simulations to approximate the likelihood function, in which the simulated samples are compared with the observed data.
In a typical ABC rejection algorithm, large numbers of parameters are sampled from the prior distribution. For each set of parameters, the distance between simulated samples generated using the parameters and observed data is calculated. Parameters resulting in a distance larger than a certain tolerance are rejected, and the retained parameters form the posterior distribution.
ABC methods can fully explore the likelihood landscape in parameter space. However, it requires large numbers of simulations, which may be prohibitive for the large-scale agent-based models considered here. In addition, a good choice of the tolerance in the rejection algorithm is needed. The IF algorithm, instead, is applicable to computationally expensive agent-based models, but may become trapped in the local optimum of the posterior distribution.
In practice, this problem can be alleviated by exploring a larger prior parameter space and setting a slower quenching speed, that is, a smaller discount factor a. The actual parameters used to generate the synthetic outbreaks are also reported. Results are obtained from independent realizations of the IF algorithm. To guarantee a fair comparison between the inference-based intervention and other heuristic strategies, we estimated the colonization probability using only real-time information available before control measures are effected.
For instance, to estimate the colonization probability at the fifth month in the third year, we first infer the model parameters for the first 2 years, where we have data from the whole year, and then use the partial observation in the remaining 5 months to infer the model parameters for the third year. The inferred parameters are then used to generate synthetic outbreaks from the beginning, and the current colonization probability for each individual is calculated from these simulations.
In the inset of Figure 5A , we show that the colonization probability estimated in real time is highly correlated with that obtained using information from the entire outbreak record.
In practice, every 4 weeks, the estimated colonization probability and the decolonization list were updated. The inference-based intervention only uses information available at the time control measures are effected. As a consequence, it is a practical method that can be implemented in real time. We performed an analysis of the admission and discharge traffic in the study hospitals.
In the hospitals, the inpatient population changed on a daily basis. This is possibly due to reduced patient traffic during weekends. We next examined the total number of patients in the study hospitals. As shown in Figure 1—figure supplement 2B , the in-hospital patient number fluctuates between and Patient numbers exhibit a periodic behavior at an annual time-scale, as well as at finer weekly time-scale.
We also present the number of new patients with respect to the patients present the previous day in the hospitals each day in Figure 1—figure supplement 2B. The number of new patients is relatively small compared with the total patients. The distribution of patient time in hospital follows a power-law shape with a heavy tail see Figure 1—figure supplement 2C.
Such heterogeneity leads to high spatiotemporal contact network complexity. In fact, the contact time between all pairs of patients follows a similar power-law distribution, as shown in the upper inset of Figure 1—figure supplement 2C. The readmission time, that is, individual patient time between discharge and next admission, is a key parameter in MRSA transmission models. The lower inset of Figure 1—figure supplement 2C indicates that this readmission time is also quite heterogeneous, spanning from several days to up to a few years.
Next we examined the topological features of the weekly aggregated contact network in Figure 1—figure supplement 2D , which shows the number of patients in the giant connected component GCC and the entire contact network.
While most patients belong to the GCC, there also exist many fragmented small connected components CCs. The total number of CCs in the contact network is also presented in Figure 1—figure supplement 2D. About CCs coexist in the network each week, but the size of small CCs is usually below , as shown in the inset of Figure 1—figure supplement 2D. Connections between different CCs change over time due to the transfer and readmission of patients.
These patient movements connect healthcare facilities that would otherwise be isolated in the network and are responsible for long-range transmission across multiple hospitals. Given the large heterogeneity in the network structure and contact time, a traditional compartmental model using ordinary differential equations ODE may not adequately capture actual transmission dynamics.
Therefore, in this study we adopt an individual-level agent-based model. Instead of using a parsimonious ordinary differential equation model, we employ an agent-based model to account for the spatiotemporal complexity of the underlying contact patterns. In particular, agent-based models can be used to simulate epidemic spread using an Equation-Free approach Kevrekidis et al. The transmission process evolves following microscopic update rules defined at the individual-level, and macroscopic states are aggregated from the total simulated population.
The Equation-Free approach has been widely used for multi-scale modeling in applied mathematics and statistical physics. It consists of three basic elements: 1 , lift, which transforms macroscopic observations through lifting to one or more consistent microscopic realizations; 2 , evolve, which uses the microscopic simulator to evolve these realizations for a given time; and 3 , restrict, which aggregates the evolved microscopic realizations to obtain the macroscopic observation.
In the MRSA transmission model, some quantities, for example colonization importation, infection importation, and weekly incidence, are macroscopic values aggregated from the individual-level states. In model simulation, we first need to lift these macroscopic quantities to consistent microscopic realizations. To do this, we maintained multiple realizations ensemble members of individual-level states.
This lifting procedure was performed for all realizations and produced an ensemble of possible microscopic states. The model estimate of the observed state, that is 4 week incidence, was obtained by aggregating the total number of new infections across the entire population in the study hospitals.
This multi-scale method enables system-level analysis directly from microscopic simulations, which bypasses the need to derive macroscopic evolution equations. To represent the state-space distribution, the EAKF maintains an ensemble of system state vectors acting as samples from the distribution. In particular, the EAKF assumes that both the prior distribution and likelihood are Gaussian, and thus can be fully characterized by their first two moments, that is mean and covariance.
For observed state variables, the posterior of the i t h ensemble member is updated through. Unobserved variables and parameters are updated through their covariability with the observed variable, which can be computed directly from the ensemble. In particular, the i t h ensemble member of unobserved variable or parameter x i is updated by.
In the EAKF, variables and parameters are updated deterministically so that the higher moments of the prior distribution are preserved in the posterior. To generate synthetic outbreak observations, we used the agent-based model to simulate weekly incidence during a one-year period 52 weeks , and then imposed noise to produce the observations used in inference.
In reality, because we have only one data point at each observation time point, the variance of observed incidence is unknown. As such, we have to use a heuristic OEV in the inference algorithm. In each iteration, the covariance matrix was contracted by a factor of a 2 equivalent to a reduction of the standard deviation by a factor of a.
Figure 2 presents the synthetic situation where nosocomial transmission accounts for the majority of incidence see Figure 2D—E. To evaluate the goodness of fit for incidence number in Figure 2B , we performed the following statistical analysis. As the agent-based model is a highly stochastic system, the observed incidence in Figure 2B is only one possible outcome of the actual dynamics, whereas in our analysis, the stochasticity of incidence number needs to be considered.
To this end, we compared several summary statistics quantifying the goodness of fit in Figure 2B with their distributions calculated from synthetic outbreaks surrogate data generated from the inferred dynamics. We first considered the log likelihood of observations. In particular, we generated synthetic outbreaks using the inferred parameters, and approximated the distribution of incidence number at each week.
Then we calculated the log likelihood for the observed incidence in each synthetic outbreak, and estimated its distribution using these log likelihood values computed from the surrogate data. In Figure 2—figure supplement 1A , we compared the log likelihood computed from Figure 2B vertical red line with this distribution blue bars and calculated the 2-sided p-value. The p-value is well above zero, indicating that, in terms of log likelihood, our inferred dynamics span and thus agree well with the observed incidence.
In other words, the observed incidence in Figure 2B is a typical outcome from our inferred dynamics. The same analysis was also applied to root-mean-square error RMSE , coefficient of determination R 2 and Pearson correlation coefficient Figure 2—figure supplement 1B—D. The RMSE, R 2 and Pearson correlation coefficient were calculated using the incidence time series in each synthetic outbreak and the mean incidence time series averaged over simulations.
For the opposite situation in which nosocomial transmission is less than importation, we performed the same test. The distributions of posterior parameters after each iteration blue boxes shown in Figure 2—figure supplement 2A are gradually adjusted to their targets red horizontal lines.
Additionally, weekly incidence, colonized population, and nosocomial and imported infections can be generally reproduced with the inferred parameters see Figure 2—figure supplement 2B—E. The goodness of fit in Figure 2—figure supplement 2B is analyzed in Figure 2—figure supplement 3. We finally tested the effect of observation frequency.
In the actual diagnostic data from the Swedish hospitals, weekly incidence is very low. To account for the large uncertainty in weekly observation, we instead use 4 week incidence.
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View all. Teresa K. Saulo D. Assistant Professor, Columbia University.