There are another couple of points that I want to mention. The phrasing around the results of the logistic regression suggests a misunderstanding of odds ratios.

lines 317 to 320: "For mortality, only five of these features displayed significant Odds Ratios ≥2.9 (p ≤ 0.0124) including septic shock, urban residence, initial treatment failure, vasoactive agent use, and ICU admission (Fig. S4, Data S4). Age was significant (p=0.0004) but displayed an OR of 1.03, 95% CI [1.01, 1.04]."

Crucially, the "but" suggests that age has only a weak effect on the outcome. However, as estimated here, age will have a greater effect than e.g. ICU admission. For a simple explanation, we will return the odds ratios back to log odds estimates by logging the values reported in S4. Since the value for the intercept in the odds scale is reported as 0 and the log of 0 is undefined, we will also assume that the estimated value for the intercept is actually some very small value: 0.0001. So, the log odds of death for a patient who has had an ICU admission, but for whom all other factors are held at their reference values. \beta_{0} + (\beta_{icu} \times 1) = -9.21034 + 1 \times 1 = -8.21034, which on the odds scale is 0.0002718

Turning our attention to the effect of age, the methods do not mention that the age variable was centered or in any other way manipulated. We therefore assume that the reference value for age was 0 years. We note that the median age of the Chinese cohort was 70 years. For a 70 year old patient, and for whom all the other factors are held at their reference values, the log odds of death are: \beta_{0} + (\beta_{age} \times 70) = -9.21034 + (0.02956 * 70) = -7.14114, which on the odds scale is 0.0007918489, i.e., greater odds of death than for the patient with the ICU admission.

There's a further point to make on the discussion of logistic regression in predicting outcomes. Lines 323-326 state: "This discrepancy may reflect the ability of machine learning models to capture non-linear relationships and interactions between predictors that are not represented by the conventional additive linear structure of logistic regression." Logistic regression is perfectly capable of capturing non-linear relationships and interactions, but these do need to be specified in the formulae used.

For example in R, one might use cubic splines to capture the effect of age on an outcome by doing the following: glm(death ~ splines::ns(age, 3), data = klebs, family = binomial)

One might fit an interaction between residence and ICU admission by specifying: glm(death ~ residence * icu_admission, data = klebs, family = binomial)

This is an interesting paper, but I have some thoughts about the epidemiological analysis.

1. This paper has an explicitly causal hypothesis (Introduction, lines 96 & 97: “We hypothesised that canonical virulence factors along with other uncharacterised genomic features contribute to worse patient outcomes and prognoses in a clinical setting.” and Discussion, lines 494-496: “Once infected, patient outcomes are governed by demographic and clinical factors. Simply put, despite substantial research into K. pneumoniae lineage (sequence type, sub-lineage etc.) and virulence determinants, these showed little to no impact on the measured patient outcomes in our study.”), but did not use causal statistical techniques to test the hypothesis. Instead, it applied machine learning to possible predictors, to identify those that performed best at predicting one of eight possible outcomes and then selected the top 15 predictors from the machine learning models on the basis of SHAP values and used those in multivariable logistic regression models and reported odds ratios for each of those identified predictors. Predictive modelling and causal inference may often use the same statistical methods, but require different processes to achieve their intended aims. A causal inference approach would first consider the likely causes of the outcomes and possible steps through which an outcome might be effected. This is commonly achieved through the construction of a directed acyclic graph (DAG), which can be used to identify confounders and mediators. Critical to causal inference is that factors on the causal pathway between the exposure of interest (here infection with a hypervirulent strain of Klebsiella pneumoniae) and the outcome (death or sepsis, supplementary material S4). S4 reports odds ratios for several variables that are likely to be on the causal pathway between infection with a hypervirulent strain and the outcome of death (consciousness, ICU admission, initial treatment failure, sepsis, septic shock, norepinephrine and urea). Inclusion of factors on the causal pathway is likely to result in the underestimate of the effect of the primary exposure of interest (Schisterman, 2009). The same applies to a number of factors for the associations with sepsis (glucose, potassium, C-reactive protein, and others).

2. A further problem with the use of some variables as potential causal factors in outcomes is that their timing relative to the outcome and exposure is not recorded with sufficient precision. For example, glucose is recorded within three days before or after infection with Klebsiella pneumoniae (S2). This means that such factors could be measured prior to the onset of infection and contribute to the acquisition of Klebsiella infection. Adjusting for these factors without accurate timing relative to the onset of disease could weaken any estimation of a causal effect of hypervirulence. Continuing point 2, three factors (ICU admission, oxygen therapy and respiratory rate) are likely to occur as a consequence of sepsis, rather than be a cause of it. While including these factors are likely to be highly predictive, they have poor explanatory performance, i.e. they say little about why the outcome occurred.

3. The analysis considers two outcomes (readmission and reinfection) that are dependent on survival of an initial infection. It is not clear from the text whether this analysis was conducted on the full cohort of 1,310 patients, or on the subset of patients that survived the initial infection.

Confounding factors (those that cause both infection with a hypervirulent K. pneumoniae) and the outcomes of interest (sepsis, death) are likely to include, but not necessarily be limited to: age, sex, comorbidity status, urban status and BMI. Repeating this analysis with a causal inference approach may well result in a different conclusion around the causal effect of hypervirulence factors on patient outcomes.

References Schisterman EF, Cole SR, Platt RW. Overadjustment bias and unnecessary adjustment in epidemiologic studies. Epidemiology. 2009 Jul;20(4):488-95. doi: 10.1097/EDE.0b013e3181a819a1. PMID: 19525685; PMCID: PMC2744485.