Imperial College London

Dr Kris V Parag

Faculty of MedicineSchool of Public Health

MRC- Imperial College Skills Development Research Fellow







Wright Fleming WingSt Mary's Campus





Publication Type

12 results found

Flaxman S, Mishra S, Gandy A, Unwin H, Coupland H, Mellan T, Zhu H, Berah T, Eaton J, Perez Guzman P, Schmit N, Cilloni L, Ainslie K, Baguelin M, Blake I, Boonyasiri A, Boyd O, Cattarino L, Ciavarella C, Cooper L, Cucunuba Perez Z, Cuomo-Dannenburg G, Dighe A, Djaafara A, Dorigatti I, van Elsland S, Fitzjohn R, Fu H, Gaythorpe K, Geidelberg L, Grassly N, Green W, Hallett T, Hamlet A, Hinsley W, Jeffrey B, Jorgensen D, Knock E, Laydon D, Nedjati Gilani G, Nouvellet P, Parag K, Siveroni I, Thompson H, Verity R, Volz E, Walters C, Wang H, Wang Y, Watson O, Winskill P, Xi X, Whittaker C, Walker P, Ghani A, Donnelly C, Riley S, Okell L, Vollmer M, Ferguson N, Bhatt Set al., 2020, Report 13: Estimating the number of infections and the impact of non-pharmaceutical interventions on COVID-19 in 11 European countries

Following the emergence of a novel coronavirus (SARS-CoV-2) and its spread outside of China, Europe is now experiencing large epidemics. In response, many European countries have implemented unprecedented non-pharmaceutical interventions including case isolation, the closure of schools and universities, banning of mass gatherings and/or public events, and most recently, widescale social distancing including local and national lockdowns. In this report, we use a semi-mechanistic Bayesian hierarchical model to attempt to infer the impact of these interventions across 11 European countries. Our methods assume that changes in the reproductive number – a measure of transmission - are an immediate response to these interventions being implemented rather than broader gradual changes in behaviour. Our model estimates these changes by calculating backwards from the deaths observed over time to estimate transmission that occurred several weeks prior, allowing for the time lag between infection and death. One of the key assumptions of the model is that each intervention has the same effect on the reproduction number across countries and over time. This allows us to leverage a greater amount of data across Europe to estimate these effects. It also means that our results are driven strongly by the data from countries with more advanced epidemics, and earlier interventions, such as Italy and Spain. We find that the slowing growth in daily reported deaths in Italy is consistent with a significant impact of interventions implemented several weeks earlier. In Italy, we estimate that the effective reproduction number, Rt, dropped to close to 1 around the time of lockdown (11th March), although with a high level of uncertainty. Overall, we estimate that countries have managed to reduce their reproduction number. Our estimates have wide credible intervals and contain 1 for countries that have implemented all interventions considered in our analysis. This means that the reproducti


Parag K, Du Plessis L, Pybus O, Jointly inferring the dynamics of population size and sampling intensity from molecular sequences, Molecular Biology and Evolution, ISSN: 0737-4038

Estimating past population dynamics from molecular sequences that have been sampled longitudinally through time is an important problem in infectious disease epidemiology, molecular ecology and macroevolution. Popular solutions, such as the skyline and skygrid methods, infer past effective population sizes from the coalescent event times of phylogenies reconstructed from sampled sequences, but assume that sequence sampling times are uninformative about population size changes. Recent work has started to question this assumption by exploring how sampling time information can aid coalescent inference. Here we develop, investigate, and implement a new skyline method, termed the epoch sampling skyline plot (ESP), to jointly estimate the dynamics of population size and sampling rate through time. The ESP is inspired by real-world data collection practices and comprises a flexible model in which the sequence sampling rate is proportional to the population size within an epoch but can change discontinuously between epochs. We show that the ESP is accurate under several realistic sampling protocols and we prove analytically that it can at least double the best precision achievable by standard approaches. We generalise the ESP to incorporate phylogenetic uncertainty in a new Bayesian package (BESP) in BEAST2. We re-examine two well-studied empirical datasets from virus epidemiology and molecular evolution and find that the BESP improves upon previous coalescent estimators and generates new, biologically-useful insights into the sampling protocols underpinning these datasets. Sequence sampling times provide a rich source of information for coalescent inference that will become increasingly important as sequence collection intensifies and becomes more formalised.

Journal article

Parag KV, Donnelly CA, 2019, Optimising Renewal Models for Real-Time Epidemic Prediction and Estimation

<jats:title>Abstract</jats:title><jats:p>The effective reproduction number, <jats:italic>R</jats:italic><jats:sub><jats:italic>t</jats:italic></jats:sub>, is an important prognostic for infectious disease epidemics. Significant changes in <jats:italic>R</jats:italic><jats:sub><jats:italic>t</jats:italic></jats:sub> can forewarn about new transmissions or predict the efficacy of interventions. The renewal model infers <jats:italic>R</jats:italic><jats:sub><jats:italic>t</jats:italic></jats:sub> from incidence data and has been applied to Ebola virus disease and pandemic influenza outbreaks, among others. This model estimates <jats:italic>R</jats:italic><jats:sub><jats:italic>t</jats:italic></jats:sub> using a sliding window of length <jats:italic>k</jats:italic>. While this facilitates real-time detection of statistically significant <jats:italic>R</jats:italic><jats:sub><jats:italic>t</jats:italic></jats:sub> fluctuations, inference is highly <jats:italic>k</jats:italic> -sensitive. Models with too large or small <jats:italic>k</jats:italic> might ignore meaningful changes or over-interpret noise-induced ones. No principled <jats:italic>k</jats:italic> -selection scheme exists. We develop a practical yet rigorous scheme using the accumulated prediction error (APE) metric from information theory. We derive exact incidence prediction distributions and integrate these within an APE framework to identify the <jats:italic>k</jats:italic> best supported by available data. We find that this <jats:italic>k</jats:italic> optimises short-term prediction accuracy and expose how common, heuristic <jats:italic>k</jats:italic> -choices, which seem sensible, could be misleading.</jats:p>

Journal article

Parag KV, 2019, On signalling and estimation limits for molecular birth-processes, Journal of Theoretical Biology, Vol: 480, Pages: 262-273, ISSN: 0022-5193

Understanding and uncovering the mechanisms or motifs that molecular networks employ to regulate noise is a key problem in cell biology. As it is often difficult to obtain direct and detailed insight into these mechanisms, many studies instead focus on assessing the best precision attainable on the signalling pathways that compose these networks. Molecules signal one another over such pathways to solve noise regulating estimation and control problems. Quantifying the maximum precision of these solutions delimits what is achievable and allows hypotheses about underlying motifs to be tested without requiring detailed biological knowledge. The pathway capacity, which defines the maximum rate of transmitting information along it, is a widely used proxy for precision. Here it is shown, for estimation problems involving elementary yet biologically relevant birth-process networks, that capacity can be surprisingly misleading. A time-optimal signalling motif, called birth-following, is derived and proven to better the precision expected from the capacity, provided the maximum signalling rate constraint is large and the mean one above a certain threshold. When the maximum constraint is relaxed, perfect estimation is predicted by the capacity. However, the true achievable precision is found highly variable and sensitive to the mean constraint. Since the same capacity can map to different combinations of rate constraints, it can only equivocally measure precision. Deciphering the rate constraints on a signalling pathway may therefore be more important than computing its capacity.

Journal article

Parag KV, Pybus OG, 2019, Robust Design for Coalescent Model Inference, SYSTEMATIC BIOLOGY, Vol: 68, Pages: 730-743, ISSN: 1063-5157

Journal article

Parag KV, Donnelly CA, 2019, Adaptive Estimation for Epidemic Renewal and Phylogenetic Skyline Models

<jats:title>Abstract</jats:title><jats:p>Estimating temporal changes in a target population from phylogenetic or count data is an important problem in ecology and epidemiology. Reliable estimates can provide key insights into the climatic and biological drivers influencing the diversity or structure of that population and evidence hypotheses concerning its future growth or decline. In infectious disease applications, the individuals infected across an epidemic form the target population. The renewal model estimates the effective reproduction number, <jats:italic>R</jats:italic>, of the epidemic from counts of its observed cases. The skyline model infers the effective population size, <jats:italic>N</jats:italic>, underlying a phylogeny of sequences sampled from that epidemic. Practically, <jats:italic>R</jats:italic> measures ongoing epidemic growth while <jats:italic>N</jats:italic> informs on historical caseload. While both models solve distinct problems, the reliability of their estimates depends on <jats:italic>p</jats:italic>-dimensional piecewise-constant functions. If <jats:italic>p</jats:italic> is misspecified, the model might underfit significant changes or overfit noise and promote a spurious understanding of the epidemic, which might misguide intervention policies or misinform forecasts. Surprisingly, no transparent yet principled approach for optimising <jats:italic>p</jats:italic> exists. Usually, <jats:italic>p</jats:italic> is heuristically set, or obscurely controlled via complex algorithms. We present a computable and interpretable <jats:italic>p</jats:italic>-selection method based on the minimum description length (MDL) formalism of information theory. Unlike many standard model selection techniques, MDL accounts for the additional statistical complexity induced by how parameters interact. As a result, our method optimises

Journal article

Hill SC, Hansen R, Watson S, Coward V, Russell C, Cooper J, Essen S, Everest H, Parag K, Fiddaman S, Reid S, Lewis N, Brookes SM, Smith AL, Sheldon B, Perrins CM, Brown IH, Pybus OGet al., 2019, Comparative micro-epidemiology of pathogenic avian influenza virus outbreaks in a wild bird population, PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY B-BIOLOGICAL SCIENCES, Vol: 374, ISSN: 0962-8436

Journal article

Parag K, Pybus OG, 2018, Exact Bayesian inference for phylogenetic birth-death models, BIOINFORMATICS, Vol: 34, Pages: 3638-3645, ISSN: 1367-4803

Journal article

Parag KV, Vinnicombe G, 2017, Point process analysis of noise in early invertebrate vision, PLOS COMPUTATIONAL BIOLOGY, Vol: 13

Journal article

Parag KV, Pybus OG, 2017, Optimal point process filtering and estimation of the coalescent process, JOURNAL OF THEORETICAL BIOLOGY, Vol: 421, Pages: 153-167, ISSN: 0022-5193

Journal article

Parag K, Vinnicombe G, Event triggered signalling codecs for molecular estimation, 52nd IEEE Conference on Decision and Control

Conference paper

Parag K, Vinnicombe G, Single event molecular signalling for estimation and control, 2013 European Control Conference (ECC)

Conference paper

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