On the interpretation of the hazard ratio in Cox regression

Differential gene expression analysis pipelines and bioinformatic tools for the identification of specific biomarkers: A review

In recent years, the role of bioinformatics and computational biology together with omics techniques and transcriptomics has gained tremendous importance in biomedicine and healthcare, particularly for the identification of biomarkers for precision medicine and drug discovery. Differential gene expression (DGE) analysis is one of the most used techniques for RNA-sequencing (RNA-seq) data analysis. This tool, which is typically used in various RNA-seq data processing applications, allows the identification of differentially expressed genes across two or more sample sets. Functional enrichment analyses can then be performed to annotate and contextualize the resulting gene lists. These studies provide valuable information about disease-causing biological processes and can help in identifying molecular targets for novel therapies. This review focuses on differential gene expression (DGE) analysis pipelines and bioinformatic techniques commonly used to identify specific biomarkers and discuss the advantages and disadvantages of these techniques.

Excess mortality among people in homelessness with substance use disorders: a Swedish cohort study

BACKGROUND

People in homelessness have an increased risk of substance use disorders (SUDs) and poor health outcomes. This cohort study aimed to investigate the association between homelessness and mortality in people with SUDs, adjusting for age, sex, narcotic use, intravenous drug use and inpatient care for SUDs.

METHODS

Data from the Swedish National Addiction Care Quality Register in the Stockholm region were used to analyse mortality risk in people with SUDs (n=8397), including 637 in homelessness, 1135 in precarious housing and 6625 in stable housing, at baseline. HRs and CIs were calculated using Cox regression.

RESULTS

Mortality was increased for people in homelessness (HR 2.30; 95% CI 1.70 to 3.12) and precarious housing (HR 1.23; 95% CI 0.86 to 1.75) compared with those in stable housing. The association between homelessness and mortality decreased (HR 1.27; 95% CI 0.91 to 1.78) after adjusting for narcotic use (HR 1.28; 95% CI 1.00 to 1.63), intravenous drug use (HR 1.98; 95% CI 1.52 to 2.58) and inpatient care for SUDs (HR 1.96; 95% CI 1.57 to 2.45). Standardised mortality ratios (SMRs) showed that mortality among people in homelessness with SUDs was 13.6 times higher than the general population (SMR=13.6; 95% CI 10.2 to 17.9), and 3.7 times higher in people in stable housing with SUDs (SMR=3.7; 95% CI 3.2 to 4.1).

CONCLUSION

Homelessness increased mortality, but the risk decreased after adjusting for narcotic use, intravenous drug use and inpatient care for SUDs. Interventions are needed to reduce excess mortality among people in homelessness with SUDs.

Lactate in breast cancer cells is associated with evasion of hypoxia-induced cell cycle arrest and adverse patient outcome

Tumor hypoxia is a common microenvironmental factor in breast cancers, resulting in stabilization of Hypoxia-Inducible Factor 1 (HIF-1), the master regulator of hypoxic response in cells. Metabolic adaptation by HIF-1 results in inhibition of citric acid cycle, causing accumulation of lactate in large concentrations in hypoxic cancers. Lactate can therefore serve as a secondary microenvironmental factor influencing cellular response to hypoxia. Presence of lactate can alter the hypoxic response of breast cancers in many ways, sometimes in opposite manners. Lactate stabilizes HIF-1 in oxidative condition, as well as destabilizes HIF-1 in hypoxia, increases cellular acidification, and mitigates HIF-1-driven inhibition of cellular respiration. We therefore tested the effect of lactate in MDA-MB-231 under hypoxia, finding that lactate can activate pathways associated with DNA replication, and cell cycling, as well as tissue morphogenesis associated with invasive processes. Using a bioengineered nano-patterned stromal invasion assay, we also confirmed that high lactate and induced HIF-1α gene overexpression can synergistically promote MDA-MB-231 dissemination and stromal trespass. Furthermore, using The Cancer Genome Atlas, we also surprisingly found that lactate in hypoxia promotes gene expression signatures prognosticating low survival in breast cancer patients. Our work documents that lactate accumulation contributes to increased heterogeneity in breast cancer gene expression promoting cancer growth and reducing patient survival.

The built-in selection bias of hazard ratios formalized using structural causal models

It is known that the hazard ratio lacks a useful causal interpretation. Even for data from a randomized controlled trial, the hazard ratio suffers from so-called built-in selection bias as, over time, the individuals at risk among the exposed and unexposed are no longer exchangeable. In this paper, we formalize how the expectation of the observed hazard ratio evolves and deviates from the causal effect of interest in the presence of heterogeneity of the hazard rate of unexposed individuals (frailty) and heterogeneity in effect (individual modification). For the case of effect heterogeneity, we define the causal hazard ratio. We show that the expected observed hazard ratio equals the ratio of expectations of the latent variables (frailty and modifier) conditionally on survival in the world with and without exposure, respectively. Examples with gamma, inverse Gaussian and compound Poisson distributed frailty and categorical (harming, beneficial or neutral) distributed effect modifiers are presented for illustration. This set of examples shows that an observed hazard ratio with a particular value can arise for all values of the causal hazard ratio. Therefore, the hazard ratio cannot be used as a measure of the causal effect without making untestable assumptions, stressing the importance of using more appropriate estimands, such as contrasts of the survival probabilities.

Overweight in childhood and consumer purchases in a Danish cohort

BACKGROUND

Prevention and management of childhood overweight involves the entire family. We aimed to investigate purchase patterns in households with at least one member with overweight in childhood by describing expenditure on different food groups.

METHODS

This Danish register-based cohort study included households where at least one member donated receipts concerning consumers purchases in 2019-2021 and at least one member had their Body mass index (BMI) measured in childhood within ten years prior to first purchase. A probability index model was used to evaluate differences in proportion expenditure spent on specific food groups.

RESULTS

We identified 737 households that included a member who had a BMI measurement in childhood, 220 with overweight and 517 with underweight or normal weight (reference households). Adjusting for education, income, family type, and urbanization, households with a member who had a BMI classified as overweight in childhood had statistically significant higher probability of spending a larger proportion of expenditure on ready meals 56.29% (95% CI: 51.70;60.78) and sugary drinks 55.98% (95% CI: 51.63;60.23). Conversely, they had a statistically significant lower probability of spending a larger proportion expenditure on vegetables 38.44% (95% CI: 34.09;42.99), compared to the reference households.

CONCLUSION

Households with a member with BMI classified as overweight in childhood spent more on unhealthy foods and less on vegetables, compared to the reference households. This study highlights the need for household/family-oriented nutrition education and intervention.

How hazardous are hazard ratios? An empirical investigation of individual patient data from 27 large randomized clinical trials

The use of hazard ratios as the standard treatment effect estimators for randomized trials with time-to-event outcomes has been the subject of repeated criticisms in recent years, e.g., for its non-collapsibility or with respect to (causal) interpretation. Another important issue is the built-in selection bias, which arises when the treatment is effective and when there are unobserved or not included prognostic factors that influence time-to-event. In these cases, the hazard ratio has even been termed "hazardous" because it is estimated from groups that increasingly differ in their (unobserved or omitted) baseline characteristics, yielding biased treatment estimates. We therefore adapt the Landmarking approach to assess the effect of ignoring a gradually increasing proportion of early events on the estimated hazard ratio. We propose an extension called "Dynamic Landmarking". This approach is based on successive deletion of observations, refitting Cox models and balance checking of omitted but observed prognostic factors, to obtain a visualization that can indicate built-in selection bias. In a small proof-of-concept simulation, we show that our approach is valid under the given assumptions. We further use "Dynamic Landmarking" to assess the suspected selection bias in the individual patient data sets of 27 large randomized clinical trials (RCTs). Surprisingly, we find no empirical evidence of selection bias in these RCTs and thus conclude that the supposed bias of the hazard ratio is of little practical relevance in most cases. This is mainly due to treatment effects in RCTs being small and the patient populations being homogeneous, e.g., due to inclusion and exclusion criteria.

A comparison of different methods to adjust survival curves for confounders

Treatment specific survival curves are an important tool to illustrate the treatment effect in studies with time-to-event outcomes. In non-randomized studies, unadjusted estimates can lead to biased depictions due to confounding. Multiple methods to adjust survival curves for confounders exist. However, it is currently unclear which method is the most appropriate in which situation. Our goal is to compare forms of inverse probability of treatment weighting, the G-Formula, propensity score matching, empirical likelihood estimation and augmented estimators as well as their pseudo-values based counterparts in different scenarios with a focus on their bias and goodness-of-fit. We provide a short review of all methods and illustrate their usage by contrasting the survival of smokers and non-smokers, using data from the German Epidemiological Trial on Ankle-Brachial-Index. Subsequently, we compare the methods using a Monte-Carlo simulation. We consider scenarios in which correctly or incorrectly specified models for describing the treatment assignment and the time-to-event outcome are used with varying sample sizes. The bias and goodness-of-fit is determined by taking the entire survival curve into account. When used properly, all methods showed no systematic bias in medium to large samples. Cox regression based methods, however, showed systematic bias in small samples. The goodness-of-fit varied greatly between different methods and scenarios. Methods utilizing an outcome model were more efficient than other techniques, while augmented estimators using an additional treatment assignment model were unbiased when either model was correct with a goodness-of-fit comparable to other methods. These "doubly-robust" methods have important advantages in every considered scenario.

A robust hazard ratio for general modeling of survival-times

Hazard ratios (HR) associated with the well-known proportional hazard Cox regression models are routinely used for measuring the impact of one factor of interest on a time-to-event outcome. However, if the underlying real model does not fit with the theoretical requirements, the interpretation of those HRs is not clear. We propose a new index, gHR, which generalizes the HR beyond the underlying survival model. We consider the case in which the study factor is a binary variable and we are interested in both the unadjusted and adjusted effect of this factor on a time-to-event variable, potentially, observed in a right-censored scenario. We propose non-parametric estimations for unadjusted gHR and semi-parametric regression-induced techniques for the adjusted case. The behavior of those estimators is studied in both large and finite sample situations. Monte Carlo simulations reveal that both estimators provide good approximations of their respective inferential targets. Data from the Health and Lifestyle Study are used for studying the relationship of the tobacco use and the age of death and illustrate the practical application of the proposed technique. gHR is a promising index which can help facilitate better understanding of the association of one study factor on a time-dependent outcome.

Standardised survival probabilities: a useful and informative tool for reporting regression models for survival data

BACKGROUND

When interested in studying the effect of a treatment (or other exposure) on a time-to-event outcome, the most popular approach is to estimate survival probabilities using the Kaplan-Meier estimator. In the presence of confounding, regression models are fitted, and results are often summarised as hazard ratios. However, despite their broad use, hazard ratios are frequently misinterpreted as relative risks instead of relative rates.

METHODS

We discuss measures for summarising the analysis from a regression model that overcome some of the limitations associated with hazard ratios. Such measures are the standardised survival probabilities for treated and untreated: survival probabilities if everyone in the population received treatment and if everyone did not. The difference between treatment arms can be calculated to provide a measure for the treatment effect.

RESULTS

Using publicly available data on breast cancer, we demonstrated the usefulness of standardised survival probabilities for comparing the experience between treated and untreated after adjusting for confounding. We also showed that additional important research questions can be addressed by standardising among subgroups of the total population.

DISCUSSION

Standardised survival probabilities are a useful way to report the treatment effect while adjusting for confounding and have an informative interpretation in terms of risk.

Food purchases in households with and without diabetes based on consumer purchase data

OBJECTIVES

Dietary recommendations for individuals with diabetes are easy to provide, but adherence is difficult to monitor. The objective of this study was to investigate whether there was a difference in grocery purchases between households with and without diabetes.

STUDY DESIGN

Cohort study.

METHODS

Consumer purchase data in 2019 was collected from 6662 households donating their supermarket receipts via a receipt collecting service. Of these households, 718 included at least one individual with diabetes. The monetary percentages spent on specific food groups were used to characterize households using all purchases in 2019. A probability index model was used to compare households with diabetes to households without diabetes.

RESULTS

We included 405,264 shopping trips in 2019 attributed to 6662 households. Both households with and without diabetes spent the highest monetary percentage on sweets (with diabetes: 9.3%, without diabetes: 8.8%), with no statistically significant difference detected. However, compared to households without diabetes, households with diabetes had a significantly higher probability of spending a higher monetary percentage on butter, oil and dressings; non-sugary drinks; processed red meat and ready meals as well as a significantly lower probability of spending a higher monetary percentage on accessory compounds; alcoholic beverages; eggs; grains; rice and pasta, and raw vegetables.

CONCLUSIONS

Households with diabetes spent a relatively higher monetary value on several unhealthy foods and less on several healthy groceries compared to households without diabetes. There is a need for more diabetes self-management education focused on including more healthy dietary choices in their household grocery purchases.

Associations of interpersonal trust with juvenile offending/conduct disorder, callous-unemotional traits, and criminal recidivism

Interpersonal trust has been described as a core dimension of cooperative, mutually beneficial interpersonal relationships but it is unclear if it is related to antisocial behaviours in youth. The present study aimed at analysing a subsample of male juveniles who committed serious violent offenses and met criteria of conduct disorder (JO/CD), and a subsample of healthy controls (HC) using a series of trust games (TGs). Twenty-four male JO/CD and 24 age matched male HC performed a series of eight one-shot TGs against different unknown human respectively computer opponents. Mixed model analyses found a non-significant trend that JO/CD invested less points than HC during TGs. In the subsample of JO/CD, the overall investment in TGs was found to be negatively associated with self-reported uncaring behaviours and officially reported general re-offenses. Our findings suggest some indication of an impaired ability of JO/CD to initiate mutually trusting relationships to others that should be addressed in further research. Trust is a promising factor to predict general criminal recidivism and can be a target for treatment of juveniles who committed violent offenses, for example through the building of stable relationships to care givers. This study encourages future studies to investigate the effects of trust-increasing psychosocial interventions.

Associations of Daily Steps and Step Intensity With Incident Diabetes in a Prospective Cohort Study of Older Women: The OPACH Study

OBJECTIVE

The primary aim was to assess associations between total steps per day and incident diabetes, whereas the secondary aim was to assess whether the intensity and/or cadence of steps is associated with incident diabetes.

RESEARCH DESIGN AND METHODS

Women without physician-diagnosed diabetes (n = 4,838; mean [SD] age 78.9 [6.7] years) were followed up to 6.9 years; 395 developed diabetes. Hip-worn ActiGraph GT3X+ accelerometers worn for 1 week enabled measures of total, light-intensity, and moderate- to vigorous-intensity (MV-intensity) steps per day. Using Cox proportional hazards analysis we modeled adjusted change in the hazard rate for incident diabetes associated with total, light-intensity, and MV-intensity steps per day. We further estimated the proportion of the steps-diabetes association mediated by BMI.

RESULTS

On average, participants took 3,729 (SD 2,114) steps/day, of which 1,875 (791) were light-intensity steps and 1,854 ± 1,762 were MV-intensity. More steps per day were associated with a lower hazard rate for incident diabetes. Confounder-adjusted models for a 2,000 steps/day increment yielded hazard ratio (HR) 0.88 (95% CI 0.78-1.00; P = 0.046). After further adjustment for BMI, HR was 0.90 (95% CI 0.80-1.02; P = 0.11). BMI did not significantly mediate the steps-diabetes association (proportion mediated = 17.7% [95% CI -55.0 to 142.0]; P = 0.09]). The relationship between MV-intensity steps per day (HR 0.86 [95% CI 0.74-1.00]; P = 0.04) and incident diabetes was stronger than for light-intensity steps per day (HR 0.97 [95% CI 0.73-1.29]; P = 0.84).

CONCLUSIONS

These findings suggest that for older adults, more steps per day are associated with lower incident diabetes and MV-intensity steps are most strongly associated with a lower hazard of diabetes. This evidence supports that regular stepping is an important risk factor for type 2 diabetes prevention in older adults.

"Translating" All-Cause Mortality Rate Ratios or Hazard Ratios to Age-, Longevity-, and Probability-Based Measures

Epidemiologists commonly use an adjusted hazard ratio or incidence density ratio, or a standardized mortality ratio, to measure a difference in all-cause mortality rates. They seldom translate it into an age-, time-, or probability-based measure that would be easier to communicate and to relate to. Several articles have shown how to translate from a standardized mortality ratio or hazard ratio to a longevity difference, a difference in actuarial ages, or a probability of being outlived. In this paper, we describe the settings where these translations are and are not appropriate and provide some of the heuristics behind the formulae. The tools that yield differences in "effective age" and in longevity are applicable when both 1) the mortality rate ratio (hazard ratio) is constant over age and 2) the rates themselves are log-linear in age. The "probability/odds of being outlived" metric is applicable whenever the first condition holds, and thus it provides no direct information on the magnitude of the effective age/longevity difference.

Survival outcomes for patients with four treatments in stages I-III esophageal squamous cell carcinoma: a SEER analysis

Background

Esophageal cancer (EC) is globally acknowledged as one of the most common malignancies among all gastrointestinal cancers. Furthermore, in Eastern Asia, squamous cell carcinoma is the main pathological type of EC. There are different treatments for esophageal squamous cell carcinoma (ESCC), but there is still a lack of large-sample analysis of prognosis among different treatments, especially for different tumor stages. The analysis of the prognosis of ESCC patients with different treatments may be helpful to choose the treatment methods for different stages ESCC.

Methods

A total of 3,346 patients with pathological ESCC between 1976 and 2016 were derived from the Surveillance, Epidemiology, and End Results (SEER) database. All clinical factors associated with prognosis were collected and analyzed to achieve the difference of prognosis among different treatments in ESCC patients, such as ages, sex, race, tumor grade, anatomic location and so on. Kaplan-Meier and Cox proportional hazard analysis were used to compare survival of different treatments in ESCC patients with stage I–III.

Results

The overall survival (OS) in all ESCC patients who had received surgery and surgery plus radiation therapy or/and chemotherapy are superior than that had not received any treatments and radiation therapy or/and chemotherapy. The OS in ESCC patients with stage I who had received surgery and surgery plus radiation therapy or/and chemotherapy are superior than that had not received any treatments and radiation therapy or/and chemotherapy. The OS in ESCC patients with stage II/III who had received surgery and surgery plus radiation therapy or/and chemotherapy are superior than that in other groups. Age, race and grade as an independent predictive factor for survival (P<0.05). A nomogram model was constructed to show surgery group had better 1-, 3- and 5-year OS than radiation therapy or/and chemotherapy group (OS: 78.5% vs. 59.2%, 37.9% vs. 18.4%, 16.9% vs. 6.1%).

Conclusions

Surgery is still the first choice for all ESCC patients with stage I–III. Radiotherapy and chemotherapy could improve the survival rate in ESCC patients with stage II–III who have received surgery.

Delayed treatment effects, treatment switching and heterogeneous patient populations: How to design and analyze RCTs in oncology

In the analysis of survival times, the logrank test and the Cox model have been established as key tools, which do not require specific distributional assumptions. Under the assumption of proportional hazards, they are efficient and their results can be interpreted unambiguously. However, delayed treatment effects, disease progression, treatment switchers or the presence of subgroups with differential treatment effects may challenge the assumption of proportional hazards. In practice, weighted logrank tests emphasizing either early, intermediate or late event times via an appropriate weighting function may be used to accommodate for an expected pattern of non‐proportionality. We model these sources of non‐proportional hazards via a mixture of survival functions with piecewise constant hazard. The model is then applied to study the power of unweighted and weighted log‐rank tests, as well as maximum tests allowing different time dependent weights. Simulation results suggest a robust performance of maximum tests across different scenarios, with little loss in power compared to the most powerful among the considered weighting schemes and huge power gain compared to unfavorable weights. The actual sources of non‐proportional hazards are not obvious from resulting populationwise survival functions, highlighting the importance of detailed simulations in the planning phase of a trial when assuming non‐proportional hazards.We provide the required tools in a software package, allowing to model data generating processes under complex non‐proportional hazard scenarios, to simulate data from these models and to perform the weighted logrank tests.

Late Adiposity Rebound and the Probability of Developing and Reversing Childhood Obesity

OBJECTIVE

To evaluate the associations between late adiposity rebound (at or after 7.0 years of age) and the probability of developing and reversing obesity during elementary school years.

STUDY DESIGN

Using nationally representative cohorts from Early Childhood Longitudinal Studies, Kindergarten Class of 1998-1999 and 2010-2011, weighted extended Cox hazard models were used to assess the probability of developing and reversing obesity (cut-offs for extended models were 6 and 12 months after kindergarten entry, respectively). Measurements used in the study were collected 6 times between kindergarten and fifth grade (Early Childhood Longitudinal Studies, Kindergarten Class of 1998-1999) and 8 times between kindergarten through fourth grade (Early Childhood Longitudinal Studies, Kindergarten Class of 2010-2011).

RESULTS

Among children with obesity at kindergarten entry, within 6 months, the risk of developing obesity was 73% and 76% lower for boys with late adiposity rebound than their classmates without late adiposity rebound (hazard ratio 0.27 and 0.24). Six months after entering kindergarten, similar association was observed for both boys and girls. Among children without obesity at kindergarten entry, within 12 months, the probability of reversing obesity was 52% and 54% higher for boys with late adiposity rebound than their peers without late adiposity rebound (hazard ratio 1.52 and 1.54). Twelve months after entering kindergarten, the probability of reversing obesity among both sexes with late adiposity rebound was 6-8 times that among children without late adiposity rebound.

CONCLUSIONS

Late adiposity rebound was significantly associated with a decreased risk of developing obesity and an increased probability of reversing obesity among kindergarteners.