# Estimating patient-to-patient bacterial transmission likelihood based on antimicrobial resistance profile similarity and rarity

Florian Peron, Guillaume Perrin, Melanie Colomb-Cotinat, Jean-François Gorse, Jean-Philippe Rasigade

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Florian Peron, Guillaume Perrin, Melanie Colomb-Cotinat, Jean-François Gorse, Jean-Philippe Rasigade. Estimating patient-to-patient bacterial transmission likelihood based on antimicrobial resistance profile similarity and rarity. 2026. hal-05484019

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Estimating patient-to-patient bacterial transmission likelihood
based on antimicrobial resistance profile similarity and rarity

Florian PERON<sup>1,2,3</sup>, Guillaume PERRIN<sup>3</sup>, Melanie COLOMB-COTINAT<sup>1,2</sup>,
Jean-François GORSE<sup>3</sup>, Jean-Philippe RASIGADE<sup>1,2</sup>

¹ Centre International de Recherche en Infectiologie, INSERM U1111-CNRS UMR5308-ENS Lyon-
Université de Lyon, Lyon, France

² Institut des Agents Infectieux, Hospices Civils de Lyon, Lyon, France

³ bioMerieux, Marcy-l’Etoile, France

Corresponding author: Jean-Philippe Rasigade, jean-philippe.rasigade@univ-lyon1.fr

Alternate corresponding author: Florian Peron, florian.peron@biomerieux.com

Abstract

Healthcare-associated bacterial outbreaks are difficult to detect with routine phenotypic
data, and incidence-based alerts generate false alarms. We present a method to estimate how
close two patient isolates are in a transmission chain using antimicrobial resistance profiles. The
pairwise transmission proximity (PTR) score combines two ideas: isolates are considered closer
when their resistance profiles are more similar, and when that shared profile is uncommon in the
sampled population. Practically, this is implemented by counting how many other isolates fall
within the same phenotypic distance of each isolate and using these counts to rank pairs; the
score is used as a relative proximity measure rather than a calibrated probability. Phenotypic
distance is computed from minimum inhibitory concentrations (MICs) as the average absolute
difference across drugs, or from binary susceptible/resistant profiles as an equivalent scaled
mismatch count. We simulate pathogen divergence, resistance evolution, and patient-to-patient
transmissions on evolutionary trees while varying transmission and mutation rates and the
number of resistance traits. In closed-population simulations with complete sampling, the PTR
ranking tracks time since common ancestry and provides useful discrimination for identifying
inter-patient transmission events and for distinguishing inter- from intra-patient pairs, with
better performance at moderate rates and larger resistance panels. The method is intended as
a high-coverage screening signal to prioritize epidemiologic review or confirmatory genomics;
calibration and clinical utility require external validation.

**Keywords:** phylodynamics, transmission inference, antimicrobial resistance, outbreak detection, phenotypic profiling, hospital epidemiology, statistical genetics

# 1 Introduction

Healthcare-associated infections (HAIs) are a significant public health concern worldwide [1, 2, 3]. Infection prevention and control (IPC) teams play a central role in limiting HAIs, but outbreak surveillance in most hospitals remains largely manual and often targets pathogens with specific resistance patterns (typically multidrug-resistant organisms) or high-risk units such as intensive care. Comprehensive, system-wide surveillance is therefore impractical in routine settings [4].

To broaden surveillance, automated outbreak detection methods have been developed [5]. Traditional approaches apply statistical process control or model-based baselines to detect increases in
case counts; such methods are implemented in systems such as CLAR at Charite hospital in Berlin [6]. More recently, scan statistics have gained prominence with tools such as SaTScan [7, 8, 9]. These incidence-based methods can generate substantial false alarms because increases in counts do not necessarily imply epidemiological linkage; fluctuations in patient volume or practice changes can trigger signals without true transmission clusters.

Molecular methods are the gold standard to confirm or refute clonality. Routine whole-genome sequencing (WGS) could reduce false alarms, but WGS is not yet available in all hospitals, and cost and turnaround-time constraints limit routine implementation in clinical microbiology laboratories [10, 11].

Automated phenotypic cluster detection using routine laboratory data is well established, including approaches that combine antibiogram data with scan statistics [8, 18]. These methods primarily detect increases in incidence over time or space. In contrast, our approach provides a pairwise transmission proximity (PTR) score based on similarity and rarity of resistance profiles, offering a complementary, rank-based view of relatedness at the isolate level.

We describe a methodological approach that estimates the genotypic divergence of two isolates from phenotypic data, typically antimicrobial resistance profiles. Our method generates a PTR score that combines similarity and rarity of resistance profiles for a pair of isolates. Under a simplified model of unresolved local branching, the score equals the chance that two isolates are the closest possible relatives in the local tree; outside that model it is used as a relative, rank-based proximity score rather than a calibrated probability. Using simulations, we show that under certain conditions the metric correlates with divergence time, enabling its use as a proxy for molecular typing in the context of epidemic outbreak detection.

# 2 Methods

## 2.1 Estimating transmission proximity in a closed population

Given a collection of pathogen isolates taken from a population of patients, we are interested in evaluating whether two patients are close in a transmission chain. We formalize this proximity using a model-based cherry probability under a simplifying null model, and use it as the PTR score in empirical settings. Immediate descent from the most recent common ancestor (a cherry) is a necessary condition for direct transmission under a simplified divergence-transmission model. Isolates obtained from biological samples are collected for each patient.

To evaluate this transmission proximity, we assume a closed population of patients. This implies that all transmissions occurred within the population and that all patients were sampled at least once. Under this assumption, one patient is at the source of infection and infects one or more other patients, who then infect others until all patients in the population are infected. The transmission chain can be viewed as a graph where nodes represent patients and edges represent transmission events. The topology of this graph is unknown (Figure 1).

The probability that two sampled isolates form a cherry is strongly linked to the time to the most recent common ancestor (TMRCA) of the isolates sampled from these patients. Under the phylodynamic assumption that each divergence event coincides with a transmission event, which is relevant when the transmission rate is higher than the evolution rate, the TMRCA provides an estimate of the size of the transmission chain. Thus, when considering the clades of isolates from two patients, the older the divergence of the two clades, the longer the transmission chain and the less likely it is that these two patients are adjacent in the chain.

In other words, the transmission graph is closely related to the phylogenetic tree of isolates, where transmission events correspond to edges in the transmission graph and branches in the
phylogenetic tree (Figure 1). Therefore, the more transmission or divergence events that occurred in the ancestry of two isolates, the less likely it is that the two isolates are immediate descendants of their MRCA.

**Assumptions.** We assume (i) a closed population with all patients sampled at least once, (ii) divergence events coincide with transmission events, (iii) tip labels within unresolved local clades are exchangeable, and (iv) the local branching below $A_X$ and $A_Y$ is resolved uniformly at random. These assumptions allow interpreting the PTR score as a cherry probability under the random-resolution model, not as a calibrated probability in the true, fully resolved phylogeny.

<figure><img src="image_2.png" /><figcaption>Figure 1: Correspondence between a transmission graph and a phylogenetic tree. On the left, transmission graph for four patients (A). Direct transmissions are represented by arrows. On the right, example phylogeny based on the transmission graph. Nodes (or leaves) represent isolates sampled from patients and branches correspond to transmission events. This reconstruction is based on the hypothesis that the dark blue patient was infected before the light blue patient.</figcaption></figure>

We use the following notation. Suppose we have reconstructed the phylogenetic tree of all isolates. Let $T$ be the set of nodes in the tree. Let $XY$ be the MRCA of $X$ and $Y$. Let $A_X$ be the oldest ancestor of $X$ but not of $Y$. Let $A_Y$ be the oldest ancestor of $Y$ but not of $X$. Let

$$C_X = A_X \cup \text{Descendants}(A_X)$$

be the largest clade in $T$ containing $X$ but not $XY$, and

$$C_Y = A_Y \cup \text{Descendants}(A_Y)$$

be the largest clade in $T$ containing $Y$ but not $XY$.

For clarity, we summarize notation used in this section:

<table><thead><tr><th>Symbol</th><th>Definition</th></tr></thead><tbody><tr><td><i>T</i></td><td>Set of nodes in the phylogenetic tree</td></tr><tr><td><i>X</i>, <i>Y</i></td><td>Isolates sampled from two patients</td></tr><tr><td><i>XY</i></td><td>Most recent common ancestor (MRCA) of <i>X</i> and <i>Y</i></td></tr><tr><td><i>A</i><sub><i>X</i></sub></td><td>Oldest ancestor of <i>X</i> that is not an ancestor of <i>Y</i></td></tr><tr><td><i>A</i><sub><i>Y</i></sub></td><td>Oldest ancestor of <i>Y</i> that is not an ancestor of <i>X</i></td></tr><tr><td><i>C</i><sub><i>X</i></sub></td><td>Largest clade containing <i>X</i> but not <i>XY</i></td></tr><tr><td><i>C</i><sub><i>Y</i></sub></td><td>Largest clade containing <i>Y</i> but not <i>XY</i></td></tr><tr><td><i>t</i><sub><i>XY</i></sub></td><td>TMRCA between <i>X</i> and <i>Y</i></td></tr><tr><td><i>d</i><sub><i>XY</i></sub></td><td>Observable dissimilarity between <i>X</i> and <i>Y</i></td></tr><tr><td><i>n</i><sub><i>X</i></sub>, <i>n</i><sub><i>Y</i></sub></td><td>Neighborhood counts within radius <i>d</i><sub><i>XY</i></sub></td></tr></tbody></table>
Under the hypothesis of a closed population, if the two sampled isolates form a cherry, then Patient($A_X$) = Patient($X$) and Patient($A_Y$) = Patient($Y$). In other words, for $X$ and $Y$ to be immediate descendants of their MRCA, both patients must have been part of the last transmission event in their common ancestry. These notations are reported in Figure 2.

After defining $A_X$, $A_Y$, and their respective clades, suppose the topology in $C_X$ is unknown and $A_X$ is a multifurcating node with $N_X = |\text{Descendants}(A_X)|$ children (where $|\cdot|$ denotes set cardinality). The same applies to $A_Y$, defining $N_Y$.

Then the probability $P(\text{Patient}(A_X) = \text{Patient}(X)) = 1/N_X$, and similarly $P(\text{Patient}(A_Y) = \text{Patient}(Y)) = 1/N_Y$. This is obtained by assuming that every descendant of $A_X$ has equal probability of being Patient($A_X$). Under independence, the probability that $X$ and $Y$ are immediate descendants of their MRCA is $1/(N_X N_Y)$. These are simplifying assumptions that yield a tractable, rank-based PTR score rather than a mechanistic transmission model.

Let the TMRCA between isolates $X$ and $Y$ be $t_{XY}$. Intuitively, the MRCA between all isolates in $C_X$ is more recent than $XY$. Thus,

$$N_X = |\{Z | t_{ZX} < t_{XY}\}|$$

that is, the number of isolates descending from $A_X$ but not $A_Y$ equals the number of isolates whose TMRCA with $X$ is smaller than with $Y$. By definition, $X$ is included in this count, so $N_X \ge 1$ (and similarly for $N_Y$).

We assume that, although TMRCAs are unobservable, there exists an observable dissimilarity between pairs of isolates that increases with their TMRCA and that a metric function $d_{XY}$ can be defined as a non-decreasing function of the TMRCA $t_{XY}$. Since it is possible to observe no divergence between recently diverged isolates, this relation is not strictly monotonic. Therefore, for all $X, Y, Z \in \mathcal{I}$,

$$t_{XY} < t_{XZ} \Rightarrow d_{XY} \le d_{XZ}.$$

Based on the assumption that $d_{XY}$ is a non-decreasing function of $t_{XY}$, we obtain an approximation of the null-model cherry probability between two isolates as $1/(n_X n_Y)$. This assumption is a modeling convenience rather than a biological guarantee: resistance phenotypes can change rapidly under selection, converge through parallel evolution, or be altered by horizontal gene transfer. We therefore treat $d_{XY}$ as a noisy proxy for divergence time and interpret PTR as a ranking statistic rather than a strict mapping to evolutionary time. The neighborhood counts are defined as

$$n_X = |\{Z \neq X | d_{XZ} \le d_{XY}\}|, \quad n_Y = |\{Z \neq Y | d_{YZ} \le d_{XY}\}|.$$

We call this model-based probability under the random-resolution assumption the pairwise transmission proximity (PTR) score. It is not a calibrated probability in the true, fully resolved phylogeny, and is used here as a rank-based proximity score. We also call the quantity $n_X n_Y$ the neighborhood metric (or N-metric). Indeed, $n_X$ and $n_Y$ can be seen as the number of isolates in the neighborhoods of $X$ and $Y$, each neighborhood being defined as a sphere of radius $d_{XY}$. We exclude each focal isolate from its own neighborhood; using $\le$ includes ties, so pairs at the same distance as $d_{XY}$ are included in the neighborhood. By construction, $1 \le n_X \le |T|-1$ (and similarly for $n_Y$). The N-metric is thus defined between 1 and $(|T|-1)^2$. In this framework, rarity refers to scarcity of similar profiles in the sampled population and is operationalized by small neighborhood counts $n_X$ and $n_Y$.

To interpret $1/(n_X n_Y)$ as a probability, we make an explicit local random-resolution assumption. Suppose the topology below $A_X$ and $A_Y$ is unresolved and that tip labels within each clade are
exchangeable. If the local branching is resolved uniformly at random, then the probability that X (respectively Y ) is the immediate descendant of A$_{X}$ (respectively A$_{Y}$ ) is 1 /N$_{X}$ (respectively 1 /N$_{Y}$ ). Under independence, the probability that X and Y are the two tips immediately descending from their MRCA (i.e., a cherry) is 1 / ( N$_{X}$N$_{Y}$ ). This probabilistic interpretation is limited to the random-resolution null model; outside that model, PTR is used as a rank-based proximity score rather than a calibrated probability in the true, fully resolved phylogeny. Direct transmission adjacency is the operational target but is not directly observable in the simulated phylogeny without an explicit transmission graph; we therefore use cherry probability as a tractable proxy under the null model and evaluate performance against host-transition labels as a surrogate outcome.

<figure><img src="image_3.png" /><figcaption>Figure 2: Representation of a phylogenetic tree and the clades C$_{X}$ and C$_{Y}$ . Isolates X and Y are represented by blue and green dots. Their MRCA, XY , is represented by the yellow dot. The clade C$_{X}$ is the blue subtree and clade C$_{Y}$ is the green subtree. A cherry corresponds to the case where X and Y are the two immediate descendants of XY .</figcaption></figure>

2.2 Phenotypic dissimilarity

In our application with resistance profiles as the characteristics of interest, phenotypic dissimilarity between two isolates is calculated as an average absolute difference between the minimum inhibitory concentrations of the tested drugs.

Given two isolates X and Y , we define their respective resistance profiles as the vectors x = { x$_{i}$ } and y = { y$_{i}$ } , where x$_{i}$ is the log2 MIC of drug i for isolate X . We assume that X and Y share at least one common antibiotic for which the MIC is measured (non-missing). The average absolute difference is defined as

$$
d_{Em}(x, y) = \frac{\sum_{j} d_{j}(x, y)}{\sum_{j} \delta_{j}(x, y)}
$$

where d$_{j}$ ( x, y ) = √ ( x$_{j}$ − y$_{j}$ ) 2 = | x$_{j}$ − y$_{j}$ | is the absolute difference between the j th elements of vectors x and y if x$_{j}$ and y$_{j}$ are non-missing; otherwise d$_{j}$ ( x, y ) = 0. The denominator is defined by

$$
\delta_j(x, y) = \begin{cases} 1 & \text{if } x_j \text{ and } y_j \text{ are non-missing} \\ 0 & \text{if } x_j \text{ and/or } y_j \text{ are missing} \end{cases}
$$
and represents the number of non-missing pairs of values in the distance computation. This
distance can be interpreted as the mean absolute difference across all non-missing pairs of test
results; for binary R/S profiles it is proportional to the Hamming distance.

Because the distance averages only observed drug pairs, systematic missingness (e.g., different
testing panels) can bias distances downward; we therefore interpret $d_{Em}$ as a pragmatic similarity
score rather than a fully standardized metric.

Because resistance phenotypes can be shaped by non-vertical processes, phenotypic distance
may not monotonically track genetic divergence; this limitation motivates interpreting PTR as a
relative proximity score.

In the following simulations, only R/S results are generated and the antibiograms are binary
vectors, but the same method is applied.

## 2.3 Closed population simulations

We used simulations of pathogen transmission, evolution, and sampling to examine the performance
of the proposed method. The spread of the pathogen among the population and its evolution were
simulated using Markov models.

In these simulations several performance criteria were assessed:

* The correlation between the N-metric and the TMRCA (time to the most recent common ancestor) for each pair of isolates (inter-patient) was calculated. The correlation was evaluated using the Spearman rank method. The TMRCA corresponds to the time of the last divergence event in the common ancestry of both isolates. The MRCA of two isolates in a phylogenetic tree is represented in Figure 3. For results, see "Correlation between TMRCA and N-metric."

* The area under the ROC curve (AUC) of a classifier using the N-metric to infer inter-patient host transitions. The classifier only used the N-metric of pairs of isolates from different patients, since the goal was to assess transmission adjacency. A true inter-patient transition was defined as the presence of a host-state change between two different patients along the simulated phylogenetic tree; this is a surrogate for adjacency because inter-patient cherries necessarily include a host transition, but host transitions are not sufficient for adjacency. Host transitions in a phylogenetic tree are represented in Figure 4. For results, see "Inter-patient transition identification."

* The area under the ROC curve (AUROC) of a classifier using the N-metric to classify pairs of isolates as coming from the same patient (intra-patient pairs) or from two different patients (inter-patient pairs). For results, see "Inter-patient vs intra-patient classification."

## 2.4 Divergence tree simulation

The first step was to simulate a divergence tree. Along its evolution, a bacterial lineage can split into two different lineages. We call this event a divergence event. Each divergence event can coincide with two possible events: a mutation event, when the pathogen acquires or loses resistance to a drug, and a transmission event, when the pathogen moves from one patient (host) to another. At each divergence event, it is possible to observe one or multiple mutation events and/or a transmission event, or no observable divergence.

We refer to this tree as the true divergence tree that represents the succession of divergence
events in the phylogeny of a pathogen. The evolution of resistance traits as well as host traits along
<figure><img src="image_4.png" /><figcaption>Figure 3: MRCA of two isolates represented on a phylogenetic tree. The ancestors of the two isolates are represented in green and yellow, and their common ancestor is represented in colored lines. The blue dot is the last divergence event in their ancestry, that is, their most recent common ancestor (MRCA).</figcaption></figure>

this tree is then simulated using Markov models. This approach enables simulation of a population of bacterial isolates that have been transmitted in a population of patients and have evolved, in terms of resistance or susceptibility, independently of each other. Assuming all isolates have been sampled from patients at the same time, the tree can be considered an ultrametric tree, which can be simulated using a standard coalescent model. This tree represents the history of divergences in the evolution of a pathogen. To reflect that, in practice, we do not observe the entire diversity of isolates, we sampled a proportion of isolates while enforcing that each patient was represented by at least one isolate.

In our simulations, we generate random coalescent trees with a fixed number of leaves along which we model divergence and evolution of a single pathogen. The R package ape provides functions to generate random trees and, more specifically, coalescent trees (rcoal) [12]. We interpret branch lengths as time units; when reporting rates as events per year, we treat the coalescent time scale as years (i.e., one unit of branch length corresponds to one year).

To generate a coalescent tree with *N* leaves, the algorithm generates *N* − 1 branching times following a coalescent model. Two random tips are selected and their branching time is set to the lower of the branching times generated. Those two tips are aggregated into a new one, corresponding to an interior node of the tree, and the lower branching time is removed from the list of generated branching times. These steps are repeated for all branching times until all tips and nodes have been joined into a tree.

## 2.5 Resistance profile evolution

We consider resistance traits as a set of susceptibility (S) or resistance (R) states to individual drugs. These resistance traits evolve independently and are vertically inherited. Along each branch between divergence events, there is a probability of switching between states. This probability depends on:
<figure><img src="image_5.png" /><figcaption>Figure 4: Identification of host transitions in the phylogenetic tree. On the left-hand side, a phylogenetic tree is represented with the evolution of the host trait (represented by colors). Black arrows represent host transitions (transmission events) and are summarized on the right-hand side of the figure. In this example, patient B infected patients B, C, and D, and patient B infected patient C.</figcaption></figure>

* The state of the trait at the previous divergence event.

* The elapsed time between the two divergence events.

* The transition rates from one state to another.

* A global mutation rate that we call the evolution rate.

We model these transition probabilities using generalized time-reversible (GTR) Markov models [13]. These models are continuous-time, depend only on the current state, and are time-reversible.

We model the evolution of K independent resistance traits, each representing a drug tested in the resistance profile. For each trait, the GTR model is parameterized as follows:

* The equilibrium frequencies $\pi = (\pi_S, \pi_R)$ for each state (R or S).

* The instantaneous rate matrix of the form

$$Q = \begin{pmatrix} * & \alpha\pi_R \\ \alpha\pi_S & * \end{pmatrix}$$

where rows sum to 0, which allows us to omit the diagonal terms.

In addition, a global mutation rate $\mu$ acts as a time-scaling parameter controlling the mutation rates of all traits.

At each divergence event, the transition probability matrix is given by

$$P_{\text{trait}}(t) = \begin{pmatrix} P_{SS}(t) & P_{SR}(t) \\ P_{RS}(t) & P_{RR}(t) \end{pmatrix} = e^{\mu tQ}.$$

Here, $P_{RS}(t)$ is the probability for trait $i$ to go from state $R$ to state $S$ during an elapsed time $t$ between two divergence events. The R package phangorn provides functions to simulate the evolution of a sequence along a divergence tree based on the model described above [14].
## 2.6 Host transmission modelling

Transmission of the pathogen from patient to patient is modelled as an additional categorical trait taking as many possible values as there are potential hosts. The host trait evolves along the divergence tree like the resistance traits. When the host of the bacteria changes, it indicates a bacterial transmission between the former and the new host. Therefore, to model transmission we first define the population in which the pathogen evolves. We denote $(H_1, H_2, \dots, H_n)$ the potential hosts. This represents the at-risk population that can be infected by the pathogen.

Using the same Markov models as for resistance evolution, we model the evolution of the host trait. At each divergence event, the probability for the pathogen to have changed its host depends on:

* The host of the pathogen at the previous divergence event.

* The elapsed time between the two divergence events.

* The transition rates from one patient to another.

* The global transmission rate, acting as a time-scale factor like the global mutation rate of resistance traits.

The GTR model for pathogen transmission is parameterized as follows:

* The equilibrium frequencies $\pi_{\text{host}} = (\pi_{H_1}, \pi_{H_2}, \dots, \pi_{H_n})$.

* The instantaneous rate matrix $Q_{\text{host}} = (Q_{ij})$, where $Q_{ij}$ is the transition rate from patient $H_i$ to patient $H_j$.

* The global transmission rate $\mu_{\text{host}}$. The higher the rate, the faster transmissions occur.

At each divergence event, the transition probability matrix is given by

$$P_{\text{host}}(t) = (P_{ij}(t)) = e^{Q_{\text{host}}\mu_{\text{host}}t}$$

where $P_{ij}(t)$ is the probability for the pathogen to move from patient $H_i$ to patient $H_j$ during an elapsed time $t$ between two divergence events.

## 2.7 Simulation parameters

In each simulation, a tree with $N_{\text{isolates}}$ leaves was generated. We then sampled a proportion $p_{\text{sampled}}$ of isolates using a stratified scheme that ensured each patient contributed at least one isolate. We modelled the independent evolution of $K$ identical resistance traits. All traits had the same transition matrix $Q_{\text{res}}$, evolution rate $\mu_{\text{res}}$, and equilibrium frequencies $\pi_{\text{res}}$. The host trait used an instantaneous rate matrix $Q_{\text{host}}$, evolution rate $\mu_{\text{host}}$, and equilibrium frequencies $\pi_{\text{host}}$. All patients had the same probability of being infected by any patient, thus all instantaneous rates in $Q_{\text{host}}$ were set equal.

Parameter values used in the simulations are shown in Table 1 and Table 2.
<table><caption>Table 1: Simulation default parameters.</caption><thead><tr><th>Symbol</th><th>Value</th><th>Units</th><th>Description</th></tr></thead><tbody><tr><td>N<sub>sim</sub></td><td>30</td><td>-</td><td>Number of simulations</td></tr><tr><td>N<sub>isolates</sub></td><td>10,000</td><td>isolates</td><td>Number of isolates generated in the simulation</td></tr><tr><td>p<sub>sampled</sub></td><td>0.01</td><td>-</td><td>Proportion of isolates sampled after enforcing ≥ 1 isolate per patient</td></tr><tr><td>π<sub>res</sub></td><td>(0.8, 0.2)</td><td>-</td><td>Equilibrium frequencies of R/S status (S, R)</td></tr><tr><td>N<sub>patients</sub></td><td>100</td><td>patients</td><td>Number of patients in the population</td></tr><tr><td>π<sub>host</sub></td><td>1/100</td><td>-</td><td>Equilibrium frequencies for each patient</td></tr></tbody></table>

<table><caption>Table 2: Parameter ranges tested in the simulations.</caption><thead><tr><th>Symbol</th><th>Range</th><th>Step</th><th>Units</th><th>Description</th></tr></thead><tbody><tr><td>μ<sub>res</sub></td><td>[2<sup>-6</sup>, 2<sup>2</sup>]</td><td>log2</td><td>events per year</td><td>Evolution rate of the resistance trait</td></tr><tr><td>μ<sub>host</sub></td><td>[2<sup>-4</sup>, 2<sup>4</sup>]</td><td>log2</td><td>events per year</td><td>Evolution rate of the host trait</td></tr><tr><td>K</td><td>[12, 24, 48]</td><td>-</td><td>traits</td><td>Number of resistance traits</td></tr></tbody></table>

# 3 Results

We report results using the N-metric. Because PTR is defined as $1/(n_X n_Y)$, it is a monotonic transformation of the N-metric and yields the same rank ordering of pairs. Accordingly, results below evaluate ranking performance and do not imply calibrated probabilities. Our operational target is transmission adjacency, which is difficult to observe directly; we therefore use cherries as a tractable proxy under the random-resolution model and evaluate performance against host-transition labels as a practical surrogate for adjacency.

## 3.1 Correlation between TMRCA and N-metric

Figure 5 shows the evolution of the Spearman rank correlation between TMRCA and N-metric as a function of the resistance-trait evolution rate. The correlation was not affected by the transmission rate because it is computed between the N-metric (based on resistance profiles) and the TMRCA. The mean correlation shows an optimum for mid-to-low antimicrobial susceptibility testing (AST) mutation rates (between $2^{-4}$ and $2^{-3}$ events per year). For higher mutation rates, the correlation rapidly decreases. Increasing $K$, the number of tested antibiotics per isolate, increased the correlation.

## 3.2 Inter-patient transition identification

Figure 6 shows the mean AUC of a classifier using the N-metric to identify inter-patient host transitions based on bacterial isolates, as a practical surrogate for adjacency in the transmission chain. We focus on host transitions because direct transmission adjacency is not directly observable in the simulated phylogeny, and enumerating true cherries across patients is not the operational goal. For all sizes of resistance profile, performance decreased for high values of transmission and/or mutation rates. An optimal AUC appeared for moderate values of mutation and transmission rates. The optimal value increased with $K$, the size of the resistance profile.
## 3.3 Inter-patient vs intra-patient classification

Figure 7 shows the mean AUC of a classifier using the N-metric to classify pairs as intra- or inter-patient. The N-metric shows relatively good performance except for high mutation rates and low transmission rates. Performance increased with the number of drugs in the resistance profile.

# 4 Discussion

We present a method to estimate transmission proximity between two patients in a closed population. The method can be applied using resistance profile data and yields a novel metric, the N-metric. Using simulations of pathogen evolution, we show that the N-metric correlates with the TMRCA between two bacterial isolates and that this correlation increases with the resolution of the data (number of antibiotics tested). We anticipate that the correlation would further increase when using full resistance profiles with MIC values rather than R/S status, as used in the simulations.

This theoretical model is intended as a methodological framework for quantifying transmission proximity from routine resistance profiles. Interpretation of the PTR score is anchored to the cherry probability under the random-resolution null model, and in empirical settings PTR is used as a rank-based measure rather than a calibrated probability. The AUC results reported here quantify performance for identifying inter-patient host transitions as a pragmatic proxy for adjacency and do not, on their own, establish direct transmission. Practical utility and operational impact are not evaluated in this study.

The domain of application of the method resides in settings where the transmission rate is higher than the evolution rate but still moderate. Some hospital settings may satisfy these conditions, but the relationship between transmission and evolution varies substantially by pathogen, ward, and epidemiologic context. Therefore, expected performance should not be assumed a priori and should be assessed empirically for each organism and setting. However, the derivation assumes that divergence events coincide with transmission events and that phenotypic dissimilarity is broadly ordered with divergence time. This assumption can be violated by within-host diversity, mixed infection, or weak transmission bottlenecks, which may decouple phylogenetic divergence from transmission timing [15, 16, 17]. The PTR score should therefore be interpreted as a proximity signal in contexts where within-host diversity is limited, bottlenecks are strong, and sampling is dense.

Phenotypic convergence, mobile genetic elements, and rapid selection can produce similar resistance profiles among distantly related isolates, while within-host evolution can generate divergent profiles over short timescales. These effects can break the monotonicity between resistance-based distance and TMRCA, and thus reduce the interpretability of PTR as a proxy for genetic relatedness.

The derivation also assumes exchangeable descendants within clades and independence between the two focal clades. Heterogeneous contact structures, superspreading, or uneven sampling could violate these assumptions, affecting calibration and interpretability. We therefore present PTR as a rank-based proximity score under a simplifying null model rather than a detailed mechanistic transmission model or a calibrated probability.

While these theoretical simulations provide valuable insights into the behavior of the metric under controlled conditions, their predictive value for clinical surveillance can only be ascertained through validation against actual clinical data. The clinical microbiology laboratory is a crucial source of real-world data, offering an opportunity to assess accuracy and operational performance. Such validation is outside the scope of this methodological study.
Resistance profiles are an imperfect surrogate for genomic relatedness and can yield false positives and false negatives when used to infer transmission links [19, 20]. We therefore position the N-metric as a high-coverage screening tool: its imprecision is balanced by its ability to be computed uniformly for essentially all isolates with available resistance profiles, enabling consistent system-wide surveillance. In practice, we envisage this score as a triage signal that prioritizes clusters or pairs for epidemiological review or confirmatory whole-genome sequencing rather than as a definitive measure of relatedness. Accordingly, PTR is most appropriate as a screening signal rather than a definitive indicator of phylogenetic proximity.

To establish the reliability and suitability of any novel methodology, it is necessary to undertake a thorough comparative analysis against existing gold standards. For detecting transmission clusters within healthcare settings, the gold standards typically involve the expertise of infection control and prevention teams, as well as whole-genome sequencing. By comparing outcomes of the proposed method with results obtained using these well-established approaches, we may determine its effectiveness, sensitivity, and specificity. Such evaluation would also clarify strengths and limitations in accurately identifying clusters of infection cases.

# 5 Conclusion

This study establishes a robust methodological framework and provides a detailed simulation-based characterization of the proposed approach. These results suggest that the approach could estimate patient-to-patient transmission likelihood from routinely collected microbiology data. With rigorous validation against clinical datasets and comparison with established gold standards, the accuracy, reliability, and effectiveness of this approach can be assessed. By providing timely, probabilistic signals ahead of genomic confirmation, this approach may support infection prevention strategies and facilitate earlier control measures to limit outbreak expansion.

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<figure><img src="image_6.png" /><figcaption>Figure 5: Spearman rank correlation between N-metric and TMRCA of pairs of isolates. The mean correlation between N-metric and TMRCA is represented by the red dots for various *K* and *μ*<sub>res</sub>. The complete distribution is represented by a boxplot and violin plot for each parameter. Results summarize *n* = 30 simulations.</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>Figure 6: Mean AUROC for the detection of inter-patient host transitions. Each panel represents a different number of resistance traits simulated. The mutation rate and transmission rate are represented on the x and y axes, respectively. Only pairs of isolates from two different patients are considered. The mean AUC for classification of pairs as host-transition-linked or not for 30 simulations is represented by tile colors. The parameter grid follows the ranges in Table 2 with log2 steps.</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>Figure 7: Mean AUROC for classification as intra- or inter-patient pairs. Each panel represents a different number of resistance traits simulated. The mutation rate and transmission rate are represented on the x and y axes, respectively. The mean AUC for classification of pairs as intra- or inter-patient for 30 simulations is represented by tile colors. The parameter grid follows the ranges in Table 2 with log2 steps.</figcaption></figure>