A new method to estimate factors associated with tuberculosis transmission using whole genome sequencing and other additional metadata

Abstract

Background:

Understanding tuberculosis (TB) transmission dynamics is necessary to interrupt disease spread. We developed a model to estimate adjusted odds ratios (ORs) for factors associated with genetic relatedness, as proxy for transmission.

Methods:

We build upon an existing iterative model that modifies genetically linked tuberculosis case data to better represent true transmission links. We incorporate bootstrapped logistic regression to calculate adjusted ORs with confidence intervals that account for correlation from individuals present across multiple transmission pairs. We assess model performance with simulation studies and apply the method to cohort data from Lima, Peru.

Results:

Iterative algorithm estimates resembled those from logistic regression but had larger confidence intervals, reflecting the data correlation adjustment. Transmission pairs where at least one member was >34 years had decreased transmission odds. Pairs with at least one incarcerated or male member had increased adjusted transmission odds.

Conclusions:

We produce adjusted ORs accounting for the correlation of pairwise genetic relatedness data. These ORs are an accurate proxy for the association between covariates and transmission and further our understanding of factors associated with tuberculosis transmission.

1. INTRODUCTION

Tuberculosis (TB) is the leading cause of death from a single infectious agent globally, infecting and killing millions annually despite global efforts to combat TB.¹ Challenges in interrupting TB transmission include disease burden heterogeneity ^{2, 3} and slow disease progression, such that transmission events are often unobservable and difficult to trace.⁴ In this data-limited setting, modeling can serve as a tool to help infer disease dynamics. Understanding TB transmission dynamics and risk factors is important for informing targeted interventions to reduce the spread of, and ultimately eliminate, TB.

Multiple studies estimate transmission risk factors using various methods.^{5, 6, 7, 8} Most rely on genetic differences between the infecting Mycobacterium tuberculosis (M.tb), which cannot definitively determine transmission⁹ and/or modeling phylogenetic trees, which requires strong assumptions^{10, 11, 12, 13} A recent study by Trevisi et al.¹⁴ used multivariable logistic regression on pairs of people with TB to estimate odds ratios (ORs) of factors associated with TB transmission, as defined by single nucleotide polymorphisms (SNP) distances between the infecting M.tb obtained from whole genome sequencing (WGS). However, concerns were raised that not accounting for correlation present in the pairwise genetic data used in the analysis resulted in artificially small standard errors and that a single SNP cutoff cannot determine transmission.^{15, 16}

In response, we build upon previous work¹⁷ (henceforth “mlTransEpi”) to redo the analysis presented in Trevisi et al.¹⁴ mlTransEpi is an iterative framework to calculate transmission probabilities between two individuals in a TB outbreak and univariate (unadjusted) ORs of the association between covariates and genetic relatedness (as defined by SNP distances between the infecting M.tb), which we showed to be adequate proxies for the association between covariates and transmission.¹⁷ We expand mlTransEpi to calculate adjusted ORs using a bootstrapped logistic regression, which provides standard errors robust to correlation.¹⁸ Adjusted ORs are important because TB exhibits significant disease burden heterogeneity and many known risk factors impact transmission rates across demographics.^{19, 20} Understanding how these risk factors work together in an adjusted model, as Trevisi et al. did,¹⁴ is necessary for accurate transmission risk estimation. A strength of mlTransEpi is that it does not require the strong assumptions or high computational costs necessary in generating phylogenetic trees.⁹

This paper extends the mlTransEpi framework to estimate adjusted ORs of associations between covariates and genetic relatedness, serving as a transmission proxy, and use it to re-estimate the ORs produced in Trevisi et al.¹⁴ We calculate adjusted ORs via a bootstrapped logistic regression model nested within mlTransEpi’s iterative model, which modifies the pairwise genetic relatedness data to more closely resemble transmission data and accounts for correlation present from the pairwise data structure. We show via simulation studies that these adjusted ORs capture the covariate-transmission associations. This methodological extension is necessary to rigorously quantify the extent to which putative risk factors actually drive TB transmission, while accounting for the associations inherent amongst the risk factors.

2. METHODS

2.1. Naïve Bayes Transmission Method Odds Ratios

To understand TB transmission dynamics, ideally we would estimate the OR for transmission and covariates (OR^T). However, this is unfeasible as transmission events are typically unobservable. As a proxy, we can estimate the OR describing the association between genetic relatedness and covariates (OR^G). We expect OR^G to be similar but not identical to OR^T, as genetic relatedness does not necessarily imply direct transmission.

In mlTransEpi, we improved upon estimates of OR^G through an iterative estimation procedure that modifies the dataset of genetic links to better resemble the dataset of true (unobserved) transmission links, and then used this dataset to produce new estimates that we will refer to as OR^M.¹⁷ Figure 1 shows the relationship between OR^T, OR^G, and OR^M and the iterative procedure is shown in Figure 2 and detailed in Supplementary Materials Section S1 and elsewhere.^{17, 21} Using genetic relatedness to inform probable transmission links as in OR^G may result in one case having probable links with multiple infectors, despite there only being one true infector. The iterative procedure corrects for this in OR^M by randomly choosing one true infector in each iteration amongst all possible infectors (based on SNP distances) and designating all other possible infectors as non-transmission links. Multiple iterations ensure each possible infector is considered. OR^M estimates are averaged across all iterations, with variances pooled using Rubin’s rules,²² to achieve a final estimate.

Figure 1.

Diagram of the relationships of the odds ratios described and calculated in this paper. The unadjusted association between covariates and transmission, which is usually unobserved, is represented as OR^T and the relationship between covariates and observed genetic relatedness assess by single nucleotide polymorphisms (SNP) distances (as a proxy for transmission) is represented as OR^G. OR^M refers to the odds ratio between covariates and genetic links modified through the iterative algorithm. We also generate non-bootstrapped adjusted associations between covariates links modified through the iterative algorithm via logistic regression (${\text{OR}}_{\mathrm{A}}^{\mathrm{M}\prime }$), and bootstrapped adjusted logistic regression odds ratios (to account for correlation) within the iterative using modified links (${\text{OR}}_{\mathrm{A}}^{\mathrm{M}}$).

Figure 2.

Diagram of the iterative process to generate odds ratios.

2.2. Adjusted Odds Ratios

We extend mlTransEpi to calculate adjusted ORs that account for the correlation induced by using a pairwise dataset through (1) using the dataset modified to better resemble true transmission links such that only one true infector exists for each infectee and (2) bootstrapping the adjusted OR to calculate non-parametric errors that are robust to correlation.¹⁸ We will refer to this estimate as ${\text{OR}}_{\mathrm{A}}^{\mathrm{M}}$. Note all ORs described in Section 2.1 are unadjusted. Figure 2 shows the relationship between ${\text{OR}}_{\mathrm{A}}^{\mathrm{M}}$, ${\text{OR}}^{\mathrm{T}}$, ${\text{OR}}^{\mathrm{G}}$, and ${\text{OR}}^{\mathrm{M}}$.

For a model run with $m$ iterations and $n$ within-iteration folds, the iterative estimation procedure results in $m\ast n$ estimates of each ${\text{OR}}_{\mathrm{A}}^{\mathrm{M}}$, for each of which we estimate and pool 100 bootstrap samples. Further bootstrap details are presented in Supplementary Materials Section 2. The final estimate of is calculated by averaging ${\text{OR}}_{\mathrm{A}}^{\mathrm{M}}$ across all iterations; standard errors are pooled using Rubin’s rules.²²

2.3. Simulation study

We simulate 500 outbreaks using R v4.4.0 informed by TB epidemiology. ^{17, 21} For each outbreak we simulate six categorical pairwise covariates ($Z_i,i=1,\dots ,6$) using the transmission tree structure, such all covariates are associated with transmission, and simulate covariates $Z_1$ and $Z_5$ to be correlated. Simulation structure is described in detail Supplementary Materials Section 3.

We run each outbreak through mlTransEpi with 10 iterations and 10 within-iteration folds. Pairs with <4 SNP differences are considered probable transmission links; pairs with >12 SNP differences are probable non-links. Pairs with 4-12 SNP differences are considered indeterminate and excluded from the training dataset. For each outbreak, we calculate OR^T, OR^G, OR^M, ${\text{OR}}_{\mathrm{A}}^{\mathrm{M}}$, and an adjusted OR from logistic regression without bootstrapping (${\text{OR}}_{\mathrm{A}}^{{\mathrm{M}}^{\prime }}$) for each outbreak. ${\text{OR}}_{\mathrm{A}}^{{\mathrm{M}}^{\prime }}$ does not account for correlation, so its standard errors are expected to be underestimates (i.e. smaller than those of ${\text{OR}}_{\mathrm{A}}^{\mathrm{M}}$). Figure 2 shows how ${\text{OR}}_{\mathrm{A}}^{{\mathrm{M}}^{\prime }}$ relates to other ORs.

We calculate the mean absolute percentage error (MAPE) and mean squared error (MSE) with respect to OR^T (${\text{OR}}_{\mathrm{A}}^{\mathrm{T}}$, an adjusted OR describing the association between covariates and transmission) for OR^G and OR^M (${\text{OR}}_{\mathrm{A}}^{\mathrm{M}}$ and ${\text{OR}}_{\mathrm{A}}^{{\mathrm{M}}^{\prime }}$). We calculate confidence interval (CI) coverage as the percentage of time that OR^T (${\text{OR}}_{\mathrm{A}}^{\mathrm{T}}$) is within the CI of OR^G and OR^M (${\text{OR}}_{\mathrm{A}}^{\mathrm{M}}$ and ${\text{OR}}_{\mathrm{A}}^{{\mathrm{M}}^{\prime }}$), and the CI width for all estimates.

We perform sensitivity analyses on simulation assumptions. We examine using multiple lower SNP distance lower thresholds, scale parameters of the gamma distributions describing the generation interval and sampling distribution, and reproductive numbers. We also vary the proportion of the outbreak sampled and the time allowed between potential infectors and infectees. For each setting, we estimate and compare values of OR^T, OR^M, ${\text{OR}}_{\mathrm{A}}^{\mathrm{T}}$, and ${\text{OR}}_{\mathrm{A}}^{\mathrm{M}}$.

Functions to calculate OR^M and ${\text{OR}}_{\mathrm{A}}^{\mathrm{M}}$ are implemented in the R package nbTransmission.²¹

2.4. Data application

The original study by Trevisi et al. identified factors associated with TB transmission in a large prospective cohort in Lima, Peru.¹⁴ The data consist of individuals aged 16 or older with pulmonary TB diagnosed at a participating health center.²³ Trevisi et al. assigned pairs as direct transmission (<4 SNP differences) or non-transmission (>=4 SNP differences). They created pairwise covariates and used logistic regression to calculate OR based on SNP-defined transmission,¹⁴ assuming pair independence.²⁴

We apply mlTransEpi to data from Trevisi et al.¹⁴ with 60 iterations and 10 within-iteration folds. We used 60 iterations to ensure each of the up to 32 potential infectors per individual had ample opportunity to be selected as the 'true' infector. Pairs with <4 SNP differences are probable links, >12 SNP differences are probable non-links, and 4-12 SNP differences are indeterminate. We considered pairs where an infector was observed more than 60 days before an infectee, as in Trevisi et al.¹⁴ Pairwise covariates were created as described in the original paper. We consider people public transit users if they use it ≥4 times/week. A socioeconomic status (SES) score, created via principal component analysis, was dichotomized into low (first tercile) and not low (second/third terciles). Smokers and drinkers consumed ≥1 cigarette or alcoholic drink/day, respectively. Univariate OR (OR^M) were calculated for all variables described in Table 1.

Table 1.

Cohort pair-level demographic and clinical characteristics, n (%) stratified by single nucleotide polymorphisms (SNP) differences

Variable	Level	Total pairs (n =3,078,413)	Pairs with SNP Differences < 4 (n = 2,481)	Pairs with SNP Differences > 12 (n = 3,069,784)
Age (years)	>34 → >34	719,262 (23.36)	445 (17.94)	717,424 (23.37)
	>34 → ≤ 34	684,504 (22.24)	510 (20.56)	682,754 (22.24)
	≤ 34 → >34	1,295,056 (42.07)	1,345 (54.21)	1,290,844 (42.05)
	≤ 34 → ≤ 34	465,730 (15.13)	268 (10.8)	464,830 (15.14)
Sex	F → F	734,742 (23.87)	523 (21.08)	732,934 (23.88)
	F → M	729,298 (23.69)	574 (23.14)	727,331 (23.69)
	M → F	1,148,643 (37.31)	1,116 (44.98)	1,144,689 (37.29)
	M → M	2,111,652 (68.6)	1,494 (60.22)	2,106,210 (68.61)
Work outside the home	No → No	292,440 (9.5)	298 (12.01)	291,545 (9.5)
	No → Yes	216,035 (7.02)	228 (9.19)	215,330 (7.01)
	Yes → No	262,829 (8.54)	264 (10.64)	261,930 (8.53)
	Yes → Yes	195,457 (6.35)	197 (7.94)	194,769 (6.34)
Public transit use	Heavy → Light	709,513 (23.05)	586 (23.62)	707,571 (23.05)
	Light → Heavy	736,082 (23.91)	573 (23.1)	733,940 (23.91)
	Light → Light	435,319 (14.14)	305 (12.29)	434,083 (14.14)
Socioeconomic status	Low → Low	646,099 (20.99)	523 (21.08)	644,222 (20.99)
	Low → Not low	750,293 (24.37)	644 (25.96)	748,142 (24.37)
	Not low → Low	778,751 (25.3)	617 (24.87)	776,572 (25.3)
	Not low → Not low	903,270 (29.34)	697 (28.09)	900,848 (29.35)
Spent at least one night in prison	No → No	335,815 (10.91)	323 (13.02)	334,670 (10.9)
	No → Yes	722,637 (23.47)	541 (21.81)	720,580 (23.47)
	Yes → No	639,944 (20.79)	510 (20.56)	638,055 (20.79)
	Yes → Yes	1,380,017 (44.83)	1,107 (44.62)	1,376,479 (44.84)
Smoking status	Nonsmoker → Nonsmoker	2,797,980 (90.89)	1,806 (72.79)	2,791,097 (90.92)
	Nonsmoker → Smoker	135,689 (4.41)	255 (10.28)	134,945 (4.4)
	Smoker → Nonsmoker	138,115 (4.49)	343 (13.83)	137,258 (4.47)
	Smoker → Smoker	6,629 (0.22)	77 (3.1)	6,484 (0.21)
Drinking status	Nondrinker → Nondrinker	2,922,026 (94.92)	2,295 (92.5)	2,914,019 (94.93)
	Nondrinker → Drinker	75,012 (2.44)	63 (2.54)	74,758 (2.44)
	Drinker → Nondrinker	79,375 (2.58)	114 (4.59)	79,024 (2.57)
	Drinker → Drinker	2,000 (0.06)	9 (0.36)	1,983 (0.06)
HIV status	Negative → Negative	985,536 (32.01)	572 (23.06)	983,460 (32.04)
	Negative → Positive	699,378 (22.72)	520 (20.96)	697,400 (22.72)
	Positive → Negative	813,718 (26.43)	727 (29.3)	811,375 (26.43)
	Positive → Positive	579,781 (18.83)	662 (26.68)	577,549 (18.81)
Diabetes	No → No	2,866,811 (93.13)	2,320 (93.51)	2,858,745 (93.13)
	No → Yes	98,291 (3.19)	69 (2.78)	98,032 (3.19)
	Yes → Everyone else	109,590 (3.56)	86 (3.47)	109,299 (3.56)
Cavity	No → Everyone else	3,721 (0.12)	6 (0.24)	3,708 (0.12)
	Yes → Everyone else	2,743,900 (89.13)	2,290 (92.3)	2,735,969 (89.13)
Cough	No → Everyone else	162,351 (5.27)	90 (3.63)	161,967 (5.28)
	Yes → Everyone else	172,162 (5.59)	101 (4.07)	171,848 (5.6)
Prior TB history	No → Everyone else	2,211,442 (71.84)	1,742 (70.21)	2,205,274 (71.84)
	Yes → Everyone else	866,971 (28.16)	739 (29.79)	864,510 (28.16)
Smear	Negative → Everyone else	1,520,228 (49.38)	1,265 (50.99)	1,516,201 (49.39)
	Positive → Everyone else	1,558,185 (50.62)	1,216 (49.01)	1,553,583 (50.61)

Due to the size of the dataset (>3 million pairs), a full bootstrap within the iterative framework is computationally intensive. Instead, we sample all transmission pairs (SNP distances < 4; n = 2,481) and 100,000 non-transmission pairs (SNP distances > 12; n = 3,069,784) with replacement for 100 bootstrap replicates. We assess via sensitivity analysis within a single logistic regression that OR estimates and standard errors from samples of this size were consistent with OR estimates and standard errors from a traditional bootstrap after an adequate sample size was reached (Supplemental Materials Figure S2).

We first calculate adjusted OR using the same variables included in Trevisi et al.’s multivariable model¹⁴ to directly compare mlTransEpi estimates (${\text{OR}}_{\mathrm{A}}^{\mathrm{M}}$) the logistic regression estimates (OR_A). They included in their adjusted model variables which had univariate odds ratios (from standard logistic regression) with p-value ≥ 0.1.

We then perform model selection using unadjusted ORs from mlTransEpi. Covariates with at least one OR^M p-value ≤ 0.1 were included in a multivariable model for ${\text{OR}}_{\mathrm{A}}^{\mathrm{M}}$. This strategy is similar to the selection process in Trevisi et al. with the exception that they employed backward elimination for variables with p < 0.1.¹⁴ We were unable to adopt this approach due to the high computational demands of our iterative bootstrap framework with a dataset of this size. This second analysis included all pairs where the potential infector was observed prior to the potential infectee.

3. RESULTS

3.1. Simulation study

Results from the simulation study are shown in Figure 3. Recall that covariates $Z_1$ and $Z_5$were simulated to be correlated. In the unadjusted analyses describing the association between covariates and transmission (OR^T), all covariates except $Z_3$ are strongly associated with transmission. After adjusting, both $Z_1$ and $Z_5$ become much closer to the null. OR^M and ${\text{OR}}_{\mathrm{A}}^{\mathrm{M}}$, the unadjusted and adjusted iteratively modified OR describing the association between transmission and covariates, follow similar trends but are all biased towards the null compared to OR^T and ${\text{OR}}_{\mathrm{A}}^{\mathrm{T}}$, respectively. Results show the same patterns across varying the reproductive number and scale parameters of the generation interval and sampling distribution (Supplemental Materials Figure S3). As the SNP distance threshold increases, all estimates move slightly closer to the null (Supplemental Materials Figure S4).

Figure 3.

Mean estimated odds ratios from 500 simulated outbreaks describing the unadjusted association between covariates and transmission (OR^T), adjusted association between covariates and transmission (${\text{OR}}_{\mathrm{A}}^{\mathrm{T}}$), unadjusted odds ratios describing the association between covariates and iteratively modified close genetic relatedness (OR^M), and adjusted bootstrapped odds ratios describing the association between covariates and iteratively modified close genetic relatedness (${\text{OR}}_{\mathrm{A}}^{\mathrm{M}}$). Covariates Z1 and Z5 are simulated to be correlated. We are interested in obtaining OR^T and ${\text{OR}}_{\mathrm{A}}^{\mathrm{T}}$ but these quantities are not measurable so we estimate OR^M and ${\text{OR}}_{\mathrm{A}}^{\mathrm{M}}$ as a proxy.

MSE and MAPE are lower for ${\text{OR}}_{\mathrm{A}}^{\mathrm{M}}$, and ${\text{OR}}_{\mathrm{A}}^{{\mathrm{M}}^{\prime }}$ compared to OR^M, indicating that they more closely capture ${\text{OR}}_{\mathrm{A}}^{\mathrm{T}}$ than OR^M captures OR^T (Supplemental Materials Figure S5).

3.2. Data application

Covariates stratified by probable links (SNP distance < 4) and non-links (SNP distance > 12) are shown in Table 1.

Adjusted ORs from the iterative method (${\text{OR}}_{\mathrm{A}}^{\mathrm{M}}$) and original paper (OR_A) are presented in Figure 4. This figure includes all covariates included in Trevisi et al.’s adjusted analysis.¹⁴ Point estimates from both models are similar but estimates from the iterative model are often closer to the null. Transmission pairs with the infector ≤34 years old and the infectee > 34 years old have significantly lower ${\text{OR}}_{\mathrm{A}}^{\mathrm{M}}$ compared to pairs with both the infector and infectee ≤34 years old. Transmission pairs with a male infector and female infectee and both infector and infectee being smokers no longer have significantly increased ${\text{OR}}_{\mathrm{A}}^{\mathrm{M}}$ compared to pairs with female infectors and infectees and non-smoking infectors and infectees, respectively.

Figure 4.

Estimated adjusted naïve Bayes modified close genetic relatedness odds ratios (${\text{OR}}_{\mathrm{A}}^{\mathrm{M}}$) and odds ratios estimated by a multivariable logistic regression model (OR_A) for the Lima, Peru cohort dataset. Covariates in this model were taken from the adjusted model in Trevisi et al., where variables included in the analysis had univariate odds ratios (from standard logistic regression) with p-value ≥ 0.1. Both estimates are presented with 95% confidence intervals. *The value is out of scale and has not been included or entirely represented.

We redo the analysis from Trevisi et al.¹⁴ using OR^M for model selection. Unadjusted OR^M are presented in Supplemental Materials Table S2. Variables describing age, sex, drinking status, incarceration status, smoking status, prior TB history, socioeconomic status, and time between diagnosis were found to be significant at the 0.1 level and included in the multivariable model (Figure 5). In the multivariable model, transmission pairs consisting of someone > 34 had significantly lower ${\text{OR}}_{\mathrm{A}}^{\mathrm{M}}$ compared to pairs with both individuals being ≤34 (${\text{OR}}_{\mathrm{A}}^{\mathrm{M}}$ (95% CI) ≤ 34 → >34: 0.65, (0.59, 0.71); >34 → ≤ 34: 0.64 (0.55, 0.73); >34 → >34: 0.61 (0.52, 0.7)) (Figure 5). Pairs with individuals both considered drinkers and both males had increased odds of transmission (drinker → drinker 1.14 (1.02, 1.27); M → M 1.42 (1.22, 1.65)) compared to pairs with both individuals considered nondrinkers and females, respectively. All transmission pairs consisting of one individual not in the lowest socioeconomic status (SES) group (bottom 33% of adjusted SES score) had significantly lower ${\text{OR}}_{\mathrm{A}}^{\mathrm{M}}$ compared to pairs with both individuals in the lowest SES group (Low → Not low: 0.65(0.55, 0.78); Not low → Low: 0.74 (0.61, 0.9); Not low → Not low: 0.83 (0.73, 0.95)). Pairs in which the infector had a previous TB diagnosis had 17% increased odds (95% CI (1.02, 1.34)) of being a transmission pair. ${\text{OR}}_{\mathrm{A}}^{\mathrm{M}}$ for time between diagnosis decreased as the time increased (3-6 months: 0.76 (0.65, 0.88); 6-12 months: 0.65 (0.56, 0.75); ${\text{OR}}_{\mathrm{A}}^{\mathrm{M}}$ > 1 year: 0.5 (0.41, 0.62) (reference <3 months)).

Figure 5.

Adjusted naïve Bayes modified close genetic relatedness odds ratios (${\text{OR}}_{\mathrm{A}}^{\mathrm{M}}$) and 95% confidence intervals for covariate contributions from the Lima, Peru cohort dataset. Covariate selection was performed using unadjusted ORs from mlTransEpi; variables included in this analysis had unadjusted naïve Bayes modified close genetic relationship odds ratios with p-value ≥ 0.1. Note that this model includes all pairs in which the infectee was diagnosed any time after the infector. *The value is out of scale and has not been included or entirely represented.

4. DISCUSSION

We describe a method to generate adjusted ORs describing the relationship between pathogen genetic relatedness and pair level covariates using bootstrapping within mlTransEpi.¹⁷ Importantly, this approach accounts for correlation in the data, which has been lacking in other approaches.^{14, 15, 16, 24} We show using data from a cohort study in Lima, Peru that our method estimates similar point estimates compared to logistic regressions but with increased standard errors, reflecting correlation adjustments.

The iterative process accounts for correlation that arises in pathogen genetic relatedness datasets from two factors: (1) a SNP distance-based cut-off can yield multiple potential infectors for one infectee and (2) one infector can appear in multiple potential transmission instances. mlTransEpi corrects for the first source by randomly choosing one ‘true’ infector per infectee per iteration, removing multi-potential-infector correlation. The second is addressed by bootstrapping the logistic regression model within each fold and iteration, as bootstrapped standard errors are robust to correlation.¹⁸

Our findings largely agree with those from the Trevisi et al. analysis.¹⁴ Both show that transmission is more likely in pairs with at least one male.¹⁴ Men are well-documented as over- represented in the TB epidemic,^{2, 19} possibly due to lower rates of care seeking^{25, 26} and/or greater sputum expectoration.²⁷ We also echo the finding that the social risk factors (smoking, drinking, incarceration) increase transmission odds, consistent with other studies.^{28, 29, 30, 31, 32} We no longer show a significant increase in transmission smoker-smoker transmission pairs, although this could be due to the low incidence of such pairs.

Both methods find decreased odds of transmission when the infector is >34. However, mlTransEpi also finds significantly decreased odds of transmission when the infector is ≤34 and the infectee is >34. Younger patients have higher TB rates,^{3, 19, 33} hypothesized to be due to more social contacts and thus greater transmission contribution, though evidence is limited.^{34, 35} Two studies in the Netherlands support younger adults as more likely infectors, showing 67% of source cases from ages 15-34, versus 58% of secondary cases.^{36, 37} However, as these percentages are not population adjusted, they may simply be reflective of the high rates of TB in these populations.

In their response letter, Cohen, Colijn, and Warren¹⁶ suggest using GenePair⁶ to account for correlation in genetic relatedness data. They compare results using GenePair to those using methods from Trevisi et al,¹⁴ and show that estimates that are statistically significant using logistic regression are no longer significant using GenePair. GenePair uses transmission probabilities generated by TransPhylo, a method that infers transmission trees using WGS and observation dates,¹⁰ to generate ORs from a zero-inflated distribution model with individual-level spatially correlated random effect parameters to account for correlation. The model includes a binary component to account for the large proportion of transmission probabilities of 0. Thus, their ORs describe the odds of having non-zero transmission probabilities whereas those generated by logistic regression, and by extension mlTransEpi, describe the odds of transmission (as assessed through genetic relatedness) and given covariates. mlTransEpi also accounts for the pairwise correlation in the genetic data. Furthermore, GenePair relies on transmission probabilities generated by TransPhylo,¹⁰ which require full sequences and sampling dates. These data requirements are not met by our study and remain a significant barrier for many other large-scale studies.

Our method, in comparison, estimates an OR describing the relationship between pathogen genetic relatedness and pair level covariates, a demonstrated proxy for transmission-covariate relationships. We do not assume full transmission network sampling, nor that an infectee’s true infector is in the dataset. Instead, we create possible transmission pairs based on timing, designating potential links and non-links by SNP distances.

We also avoid assuming SNP distance thresholds firmly define links/non-links, as we randomly select one true infector per iteration. Sensitivity analyses show our method is robust to varying SNP distance thresholds (Supplementary Materials Figure S4). That said, future work aims to enhance link selection with additional WGS data and other data such as geographical distances.

In this work, we assume directionality of potential transmission pairs from the time of diagnosis. We know that care seeking delays exist for a myriad of reasons,^{38, 39, 40} as such it is possible that the individual diagnosed second actually infected the first. However, a sensitivity analysis where we allowing ‘negative’ time (infectee diagnosed before infector) showed ORs remained constant despite varying time windows for infector/infectee pair specification, except for low-incidence pairs (e.g., both smokers or incarcerated history) where window changes significantly altered pair instances (Supplemental Materials Figure S6).We also note that our model selection strategy of relying on univariate pre-screening with p-values ≤ 0,1 to maintain consistency with Trevisi et al. presents a limitation, as it may exclude variables that lack strong univariate associations but act as key confounders in a multivariable model. While a backwards selection procedure with confounding checks (such as monitoring for >10% shifts in estimates) would be ideal, it was computationally prohibitive. Because our iterative bootstrap framework requires running logistic regressions 60,000 times (100 bootstraps across 600 iterations) on a dataset of over 2 million pairs, multi-step selection is highly intensive. To mitigate this risk, all candidate variables were selected a priori based on clinical expertise and established roles in TB transmission, balancing computational stability with epidemiological relevance.

We produce adjusted ORs via bootstrapped logistic regression within an iterative algorithm, appropriately accounting for pairwise genetic relatedness data correlation. The extension of this method allows for precise quantification of how specific factors drive transmission in real-world populations. This method is applicable to any disease with WGS to estimate covariate-transmission associations, furthering knowledge of transmission risk factors. Understanding these risk factors is crucial for better transmission control and outbreak prevention.