
==== Front
Am J Respir Crit Care Med
Am J Respir Crit Care Med
ajrccm
American Journal of Respiratory and Critical Care Medicine
1073-449X
1535-4970
American Thoracic Society

202406-1233LE
10.1164/rccm.202406-1233LE
Correspondence
Reply to Cohen et al. and to Lee
Trevisi Letizia 1
Brooks Meredith B. 2
Murray Megan B. 1 3 4
Huang Chuan-Chin 1 3 4
1 Department of Global Health and Social Medicine, Harvard Medical School, Boston, Massachusetts;
2 Department of Global Health, School of Public Health, Boston University, Boston, Massachusetts;
3 Division of Global Health Equity, Brigham and Women’s Hospital, Boston, Massachusetts; and
4 Center for Communicable Disease Dynamics, Department of Epidemiology, Harvard T.H. Chan School of Public Health, Boston, Massachusetts
Correspondence and requests for reprints should be addressed to Chuan-Chin Huang, Sc.D., Department of Global Health and Social Medicine, Harvard Medical School, 641 Huntington Avenue, Boston, MA 02115. Email: chuan-chin_huang@hms.harvard.edu.
17 7 2024
15 9 2024
17 7 2024
210 6 850852
Copyright © 2024 by the American Thoracic Society
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ This article is open access and distributed under the terms of the Creative Commons Attribution Non-Commercial No Derivatives License 4.0. For commercial usage and reprints, please e-mail Diane Gern (dgern@thoracic.org).

National Institutes of Health and the National Institute of Allergy and Infectious Diseases U19AI142793 K01AI151083 The William F. Milton Fund
==== Body
pmcFrom the Authors:

We thank Dr. Lee and Dr. Cohen and colleagues for their comments on our recent article (1).

In our study, we used a SNP distance of three or less as the cutoff to determine direct-transmission patient pairs. This cutoff was chosen on the basis of two household-based studies, which revealed that more than 90% of the index-contact pairs with confirmed one-step transmission relationships had SNP differences of three or less (1, 2). Our previous work showed that most pairs with SNP differences of three or less in our study did not have obvious epidemiological relationships (nonoutbreak setting), as more than 90% of them had spatial distances greater than a 5-minute car drive (3). Therefore, we assume that any patient with tuberculosis (TB) is at risk of being considered a recipient of all potential transmitters who received diagnoses of TB within 60 days before the patient’s own diagnosis. For example, we consider two truly direct-transmission pairs, A → B and A → C, as two independent data points, assuming that A encounters B and C in different geographical regions.

In our study, all defined direct-transmission and non–direct-transmission pairs are patient-pair data. However, the outcome measure (being a direct-transmission pair or not) is a “between pairs” variable, meaning that it differs from pair to pair but not within a pair (4). This allows us to use a logistic regression model for patient-pair data (4).

The repeated use of the same patients in multiple direct-transmission pairs was a minor concern in our study. We applied a parallel approach to Dr. Warren’s work—a cutoff of 40 SNP distance—to patients with TB in our study and identified 16 close genetic clusters with size N ≥ 20. For a cluster with N individuals, assuming a source patient and that all individuals were infected by someone from this cluster, the true number of direct-transmission pairs in a cluster of N is N − 1, as a patient can be infected only once, except for the “source case.” For each genetic cluster, we compared the number of defined direct-transmission pairs (NDT) with two measures: all potential pairs, [N × (N − 1)]/2, and cluster size N. The two comparisons gave us an idea of the extent of the repeated use of the same patient in multiple direct-transmission pairs. We found that the ratio of NDT to [N × (N − 1)]/2 had a median of 1.5% (ranging from 0.1% to 11%); NDT was ≤N in 27 clusters and ≤2N in 32 clusters.

Warren and colleagues defined a genetic cluster of 99 patients with TB in the Republic of Moldova (5). In our study’s one large cluster with N = 175, we found that among 15,225 potential pairs, only 1.6% were defined as direct-transmission pairs. In panel 2 in Figure 1 of Warren and colleagues’ work, they showed that an extremely small proportion of pairs had a probability of >0.1 (6). We presume that these pairs with transmission probability of >0.1 are those with extremely short genetic distances. Therefore, despite differences in our methods (frequentist vs. Bayesian), both likely rely on the concept that patient pairs with very short genetic distances have an increased likelihood of being true direct-transmission pairs. We would like to note that although we provided descriptive statistics for our data together with an approach for defining closely related genetic clusters, our method can be applied to all patients with TB without prespecifying any genetic clusters or cluster sizes.

Figure 1. SEs of β values by the sample size of control pairs.

We agree that when several patients have a very small pairwise genetic distance, the outcome measure of some pairs may therefore be conditional on other pairs. However, we consider that this type of bias is attributable more to the misclassification of the outcome measure than to the independence of outcome measure. For two true direct-transmission events A → B and A → C, it is correct that the outcome definition of B–C is constrained by A–B and A–C. Therefore, the B → C pair, which is not a true direct-transmission pair, is likely to be misclassified as such, introducing a misclassification of the outcome measure. Accounting for nonindependence of outcome measure (e.g., a random effect) in a regression model might mitigate the bias introduced by the misclassification of the outcome measure (B → C) by giving it reduced weight in the model but could also affect other truly independent outcome measures (A → C and B → C). In one of the sensitivity analyses of our work, we showed that the effect size of most point estimates increased, suggesting the introduced bias of misclassification drove our findings toward a null value (1).

Regarding the issue of independent and identical distribution, using the same dataset from our study, we first showed that the SE of β values for all covariates remained almost unchanged once the sample size of control pairs exceeded approximately 10,000 (Figure 1). We then compared the P values of the naive logistic regression model with the permutation-based P values and found that the P values of the naive logistic regression model were usually similar to or larger than the permutation-based P values. This finding suggests that the repeated use of individual-level data in many pairs does not create any correlation and therefore did not violate the assumption of independent and identical distribution.

Additional material related to this response is available at https://shorturl.at/osOAJ.

Supported by the National Institutes of Health and the National Institute of Allergy and Infectious Diseases grants U19AI142793 (Beat-TB), K01AI151083, and The William F. Milton Fund.

Author Contributions: L.T. and C.-C.H. and drafted the response. C.-C.H., L.T., M.B.B., and M.B.M. edited and approved the final version.

Originally Published in Press as DOI: 10.1164/rccm.202406-1233LE on July 17, 2024

Author disclosures are available with the text of this letter at www.atsjournals.org.
==== Refs
References

1. Trevisi L Brooks MB Becerra MC Calderón RI Contreras CC Galea JT et al. Who transmits tuberculosis to whom: a cross-sectional analysis of a cohort study in Lima, Peru Am J Respir Crit Care Med 2024 210 222 233 38416532
2. Colangeli R Gupta A Vinhas SA Chippada Venkata UD Kim S Grady C et al. Mycobacterium tuberculosis progresses through two phases of latent infection in humans Nat Commun 2020 11 4870 32978384
3. Huang CC Trevisi L Becerra MC Calderón RI Contreras CC Jimenez J et al. Spatial scale of tuberculosis transmission in Lima, Peru Proc Natl Acad Sci USA 2022 119 e2207022119 36322726
4. Kenny DA Kashy DA Cook WL Dyadic data analysis New York Guilford 2020
5. Yang C Sobkowiak B Naidu V Codreanu A Ciobanu N Gunasekera KS et al. Phylogeography and transmission of M. tuberculosis in Moldova: a prospective genomic analysis PLoS Med 2022 19 e1003933 35192619
6. Warren JL Chitwood MH Sobkowiak B Colijn C Cohen T Spatial modeling of Mycobacterium tuberculosis transmission with dyadic genetic relatedness data Biometrics 2023 79 3650 3663 36745619
