Estimating average regression effect under non-proportional hazards

A Novel Stratified Analysis Method for Testing and Estimating Overall Treatment Effects on Time-To-Event Outcomes Using Average Hazard With Survival Weight

Given the limitations of using the Cox hazard ratio to summarize the magnitude of the treatment effect, alternative measures that do not have these limitations are gaining attention. One of the recently proposed alternative methods uses the average hazard with survival weight (AH). This population quantity can be interpreted as the average intensity of the event occurrence in a given time window that does not involve study-specific censoring. Inference procedures for the ratio of AH and difference in AH have already been proposed in simple randomized controlled trial settings to compare two groups. However, methods with stratification factors have not been well discussed, although stratified analysis is often used in practice to adjust for confounding factors and increase the power to detect a between-group difference. The conventional stratified analysis or meta-analysis approach, which integrates stratum-specific treatment effects using an optimal weight, directly applies to the ratio of AH and difference in AH. However, this conventional approach has significant limitations similar to the Cochran-Mantel-Haenszel method for a binary outcome and the stratified Cox procedure for a time-to-event outcome. To address this, we propose a new stratified analysis method for AH using standardization. With the proposed method, one can summarize the between-group treatment effect in both absolute difference and relative terms, adjusting for stratification factors. This can be a valuable alternative to the traditional stratified Cox procedure to estimate and report the magnitude of the treatment effect on time-to-event outcomes using hazard.

A Comparison of Statistical Methods for Time-To-Event Analyses in Randomized Controlled Trials Under Non-Proportional Hazards

While well-established methods for time-to-event data are available when the proportional hazards assumption holds, there is no consensus on the best inferential approach under non-proportional hazards (NPH). However, a wide range of parametric and non-parametric methods for testing and estimation in this scenario have been proposed. To provide recommendations on the statistical analysis of clinical trials where non-proportional hazards are expected, we conducted a simulation study under different scenarios of non-proportional hazards, including delayed onset of treatment effect, crossing hazard curves, subgroups with different treatment effects, and changing hazards after disease progression. We assessed type I error rate control, power, and confidence interval coverage, where applicable, for a wide range of methods, including weighted log-rank tests, the MaxCombo test, summary measures such as the restricted mean survival time (RMST), average hazard ratios, and milestone survival probabilities, as well as accelerated failure time regression models. We found a trade-off between interpretability and power when choosing an analysis strategy under NPH scenarios. While analysis methods based on weighted logrank tests typically were favorable in terms of power, they do not provide an easily interpretable treatment effect estimate. Also, depending on the weight function, they test a narrow null hypothesis of equal hazard functions, and rejection of this null hypothesis may not allow for a direct conclusion of treatment benefit in terms of the survival function. In contrast, non-parametric procedures based on well-interpretable measures like the RMST difference had lower power in most scenarios. Model-based methods based on specific survival distributions had larger power; however, often gave biased estimates and lower than nominal confidence interval coverage. The application of the studied methods is illustrated in a case study with reconstructed data from a phase III oncologic trial.

Non-collapsibility and built-in selection bias of period-specific and conventional hazard ratio in randomized controlled trials

BACKGROUND

The hazard ratio of the Cox proportional hazards model is widely used in randomized controlled trials to assess treatment effects. However, two properties of the hazard ratio including the non-collapsibility and built-in selection bias need to be further investigated.

METHODS

We conduct simulations to differentiate the non-collapsibility effect and built-in selection bias from the difference between the marginal and the conditional hazard ratio. Meanwhile, we explore the performance of the Cox model with inverse probability of treatment weighting for covariate adjustment when estimating the marginal hazard ratio. The built-in selection bias is further assessed in the period-specific hazard ratio.

RESULTS

The conditional hazard ratio is a biased estimate of the marginal effect due to the non-collapsibility property. In contrast, the hazard ratio estimated from the inverse probability of treatment weighting Cox model provides an unbiased estimate of the true marginal hazard ratio. The built-in selection bias only manifests in the period-specific hazard ratios even when the proportional hazards assumption is satisfied. The Cox model with inverse probability of treatment weighting can be used to account for confounding bias and provide an unbiased effect under the randomized controlled trials setting when the parameter of interest is the marginal effect.

CONCLUSIONS

We propose that the period-specific hazard ratios should always be avoided due to the profound effects of built-in selection bias.

Causal interpretation of the hazard ratio in randomized clinical trials

BACKGROUND

Although the hazard ratio has no straightforward causal interpretation, clinical trialists commonly use it as a measure of treatment effect.

METHODS

We review the definition and examples of causal estimands. We discuss the causal interpretation of the hazard ratio from a two-arm randomized clinical trial, and the implications of proportional hazards assumptions in the context of potential outcomes. We illustrate the application of these concepts in a synthetic model and in a model of the time-varying effects of COVID-19 vaccination.

RESULTS

We define causal estimands as having either an individual-level or population-level interpretation. Difference-in-expectation estimands are both individual-level and population-level estimands, whereas without strong untestable assumptions the causal rate ratio and hazard ratio have only population-level interpretations. We caution users against making an incorrect individual-level interpretation, emphasizing that in general a hazard ratio does not on average change each individual's hazard by a factor. We discuss a potentially valid interpretation of the constant hazard ratio as a population-level causal effect under the proportional hazards assumption.

CONCLUSION

We conclude that the population-level hazard ratio remains a useful estimand, but one must interpret it with appropriate attention to the underlying causal model. This is especially important for interpreting hazard ratios over time.

Adiposity and mortality among intensive care patients with COVID-19 and non-COVID-19 respiratory conditions: a cross-context comparison study in the UK

BACKGROUND

Adiposity shows opposing associations with mortality within COVID-19 versus non-COVID-19 respiratory conditions. We assessed the likely causality of adiposity for mortality among intensive care patients with COVID-19 versus non-COVID-19 by examining the consistency of associations across temporal and geographical contexts where biases vary.

METHODS

We used data from 297 intensive care units (ICUs) in England, Wales, and Northern Ireland (Intensive Care National Audit and Research Centre Case Mix Programme). We examined associations of body mass index (BMI) with 30-day mortality, overall and by date and region of ICU admission, among patients admitted with COVID-19 (N = 34,701; February 2020-August 2021) and non-COVID-19 respiratory conditions (N = 25,205; February 2018-August 2019).

RESULTS

Compared with non-COVID-19 patients, COVID-19 patients were younger, less often of a white ethnic group, and more often with extreme obesity. COVID-19 patients had fewer comorbidities but higher mortality. Socio-demographic and comorbidity factors and their associations with BMI and mortality varied more by date than region of ICU admission. Among COVID-19 patients, higher BMI was associated with excess mortality (hazard ratio (HR) per standard deviation (SD) = 1.05; 95% CI = 1.03-1.07). This was evident only for extreme obesity and only during February-April 2020 (HR = 1.52, 95% CI = 1.30-1.77 vs. recommended weight); this weakened thereafter. Among non-COVID-19 patients, higher BMI was associated with lower mortality (HR per SD = 0.83; 95% CI = 0.81-0.86), seen across all overweight/obesity groups and across dates and regions, albeit with a magnitude that varied over time.

CONCLUSIONS

Obesity is associated with higher mortality among COVID-19 patients, but lower mortality among non-COVID-19 respiratory patients. These associations appear vulnerable to confounding/selection bias in both patient groups, questioning the existence or stability of causal effects.

Patient and Operative Risk Factors for Osteoarthritis After Primary Anterior Cruciate Ligament Reconstruction: A Cohort Study of 41,976 Patients

BACKGROUND

The reported incidence of posttraumatic knee osteoarthritis (PTOA) after primary anterior cruciate ligament reconstruction (ACLR) varies considerably. Further, there are gaps in identifying which patients are at risk for PTOA after ACLR and whether there are modifiable factors.

PURPOSE

To (1) determine the incidence of PTOA in a primary ACLR cohort and (2) identify patient and perioperative factors associated with the development of PTOA after primary ACLR.

STUDY DESIGN

Cohort study; Level of evidence, 3.

METHODS

Data from the Kaiser Permanente ACLR Registry were used to conduct a cohort study. Patients who had undergone primary ACLR without a previous diagnosis of osteoarthritis were identified (2009-2020). The crude incidence of PTOA was calculated using the Aalen-Johansen estimator with a multistate model. The association of patient and operative factors with the development of PTOA after primary ACLR was modeled as a time to event using multistate Cox proportional hazards regression. Models stratified by age (<22 and ≥22 years) were also conducted because of the effect modification of age.

RESULTS

The study sample included 41,976 cases of primary ACLR. The incidence of PTOA was 1.7%, 5.1%, and 13.6% at 2, 5, and 10 year follow-ups, respectively. Risk factors for PTOA that were consistently identified in the overall cohort and age-stratified groups included a body mass index ≥30 versus <30 and an allograft or quadriceps tendon autograft versus a hamstring tendon autograft. Patients presenting with knee pain after ACLR were further identified when considering postoperative factors. Other risk factors for PTOA in the overall cohort included age ≥22 versus <22 years, bone-patellar tendon-bone autograft versus hamstring tendon autograft, hypertension, cartilage injury, meniscal injury, revision after primary ACLR with concomitant meniscal/cartilage surgery, multiligament injury, other activity at the time of injury compared with sport, and tibial tunnel drilling technique rather than the anteromedial portal.

CONCLUSION

Knee pain after ACLR may be an early sign of PTOA. Surgeons should consider the adverse associations of a higher body mass index and an allograft or quadriceps tendon autograft with the development of PTOA, as these were factors identified with a higher risk, regardless of a patient's age at the time of primary ACLR.

Methods for non-proportional hazards in clinical trials: A systematic review

For the analysis of time-to-event data, frequently used methods such as the log-rank test or the Cox proportional hazards model are based on the proportional hazards assumption, which is often debatable. Although a wide range of parametric and non-parametric methods for non-proportional hazards has been proposed, there is no consensus on the best approaches. To close this gap, we conducted a systematic literature search to identify statistical methods and software appropriate under non-proportional hazard. Our literature search identified 907 abstracts, out of which we included 211 articles, mostly methodological ones. Review articles and applications were less frequently identified. The articles discuss effect measures, effect estimation and regression approaches, hypothesis tests, and sample size calculation approaches, which are often tailored to specific non-proportional hazard situations. Using a unified notation, we provide an overview of methods available. Furthermore, we derive some guidance from the identified articles.

Win Statistics in Observational Cancer Research: Integrating Clinical and Quality-of-Life Outcomes

Background: Quality-of-life metrics are increasingly important for oncological patients alongside traditional endpoints like mortality and disease progression. Statistical tools such as Win Ratio, Win Odds, and Net Benefit prioritize clinically significant outcomes using composite endpoints. In randomized trials, Win Statistics provide fair comparisons between treatment and control groups. However, their use in observational studies is complicated by confounding variables. Propensity score (PS) matching mitigates confounding variables but may reduce the sample size, affecting the power of win statistics analyses. Alternatively, PS matching can stratify samples, preserving the sample size. This study aims to assess the long-term impact of these methods on decision making, particularly in colorectal cancer patients. Methods: A motivating example involves a cohort of patients from the ReSARCh observational study (2016-2021) with locally advanced adenocarcinoma of the rectum, situated up to 12 cm from the anal verge. These patients underwent either a watch-and-wait approach (WW) or trans-anal local excision (LE). Win statistics compared the effects of WW and LE on a composite outcome (overall survival, recurrence, presence of ostomy, and rectum excision). For matched win statistics, we used robust inference techniques proposed by Matsouaka et al. (2022), and for stratified win statistics, we applied the method proposed by Dong et al. (2018). A simulation study assessed the coverage probability of matched and stratified win statistics in balanced and unbalanced groups, calculating how often the confidence intervals included the true values of WR, NB, and WO across 1000 simulations. Results: The results suggest a better efficacy of the LE approach when considering efficacy outcomes alone (WR: 0.47 (0.01 to 1.14); NB: -0.16 (-0.34 to 0.02); and WO: 0.73 (0.5 to 1.05)). However, when QoL outcomes are included in the analyses, the estimates are closer to 1 (WR: 0.87 (0.06 to 2.06); WO: 0.93 (0.61 to 1.4)) and to 0 (NB: -0.04 (-0.25 to 0.17)), indicating a negative impact of the treatment effect of LE regarding the presence of ostomy and the excision of the rectum. Moreover, based on the simulation study, our findings underscore the superior performance of matched compared to stratified win statistics in terms of coverage probability (matched WR: 97% vs. stratified WR: 33.3% in a high-imbalance setting; matched WR: 98% vs. stratified WR: 34.4% in a medium-imbalance setting; and matched WR: 99.2% vs. stratified WR: 37.4% in a low-imbalance setting). Conclusions: In conclusion, our study sheds light on the interpretation of the results of win statistics in terms of statistical significance, providing insights into the application of pairwise comparison in observational settings, promoting its use to improve outcomes for cancer patients.

Sample size calculation for mixture model based on geometric average hazard ratio and its applications to nonproportional hazard

With the advent of cancer immunotherapy, some special features including delayed treatment effect, cure rate, diminishing treatment effect and crossing survival are often observed in survival analysis. They violate the proportional hazard model assumption and pose a unique challenge for the conventional trial design and analysis strategies. Many methods like cure rate model have been developed based on mixture model to incorporate some of these features. In this work, we extend the mixture model to deal with multiple non-proportional patterns and develop its geometric average hazard ratio (gAHR) to quantify the treatment effect. We further derive a sample size and power formula based on the non-centrality parameter of the log-rank test and conduct a thorough analysis of the impact of each parameter on performance. Simulation studies showed a clear advantage of our new method over the proportional hazard based calculation across different non-proportional hazard scenarios. Moreover, the mixture modeling of two real trials demonstrates how to use the prior information on the survival distribution among patients with different biomarker and early efficacy results in practice. By comparison with a simulation-based design, the new method provided a more efficient way to compute the power and sample size with high accuracy of estimation. Overall, both theoretical derivation and empirical studies demonstrate the promise of the proposed method in powering future innovative trial designs.

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.

Regression models for average hazard

Limitations of using the traditional Cox's hazard ratio for summarizing the magnitude of the treatment effect on time-to-event outcomes have been widely discussed, and alternative measures that do not have such limitations are gaining attention. One of the alternative methods recently proposed, in a simple 2-sample comparison setting, uses the average hazard with survival weight (AH), which can be interpreted as the general censoring-free person-time incidence rate on a given time window. In this paper, we propose a new regression analysis approach for the AH with a truncation time τ. We investigate 3 versions of AH regression analysis, assuming (1) independent censoring, (2) group-specific censoring, and (3) covariate-dependent censoring. The proposed AH regression methods are closely related to robust Poisson regression. While the new approach needs to require a truncation time τ explicitly, it can be more robust than Poisson regression in the presence of censoring. With the AH regression approach, one can summarize the between-group treatment difference in both absolute difference and relative terms, adjusting for covariates that are associated with the outcome. This property will increase the likelihood that the treatment effect magnitude is correctly interpreted. The AH regression approach can be a useful alternative to the traditional Cox's hazard ratio approach for estimating and reporting the magnitude of the treatment effect on time-to-event outcomes.

Dealing With Nonproportional Hazards in Coronary Revascularisation Studies

The Cox proportional hazards model is one of the most popular statistical tools to model time to event outcomes without the need for specifying the hazards or survival time distributions. The Cox model requires that the ratio of the hazards of the occurrence of the outcome for any 2 individuals remains constant during the entire follow-up. Studies comparing coronary revascularisation strategies, however, might be prone to violations of proportionality by the crossing of the hazard functions over time. Early increases in the risk of cardiovascular outcomes are commonly observed when comparing coronary artery bypass grafting vs percutaneous coronary intervention, whereas decreased risk might be observed later during the follow-up. The same is valid for comparisons between invasive vs conservative coronary revascularisation strategies. In these situations, the statistical power of the Cox model is reduced, and hazard ratios might not be an informative summary measure of treatment effect. In this article, we discuss methods to identify and account for nonproportionality. We illustrate the use of these methods in a case study based on reconstructed data from a coronary revascularisation clinical trial. And finally, we review the cardiovascular literature to estimate how the proportionality assumption has been reported in coronary revascularisation studies recently.

Cox (1972): recollections and reflections

I present some personal memories and thoughts on Cox's 1972 paper "Regression Models and Life-Tables".

Ratio and difference of average hazard with survival weight: New measures to quantify survival benefit of new therapy

The hazard ratio (HR) has been the most popular measure to quantify the magnitude of treatment effect on time-to-event outcomes in clinical research. However, the traditional Cox's HR approach has several drawbacks. One major issue is that there is no clear interpretation when the proportional hazards (PH) assumption does not hold, because the estimated HR is affected by study-specific censoring time distribution in non-PH cases. Another major issue is that the lack of a group-specific absolute hazard value in each group obscures the clinical significance of the magnitude of the treatment effect. Given these, we propose average hazard with survival weight (AH-SW) as a summary metric of event time distribution and will use difference in AH-SW (DAH-SW) or ratio of AH-SW (RAH-SW) to quantify the treatment effect magnitude. The AH-SW is interpreted as a person-time incidence rate that does not depend on random censoring. It is defined as the ratio of cumulative incidence probability and restricted mean survival time (RMST), which can be estimated non-parametrically. Numerical studies demonstrate that DAH-SW and RAH-SW offer almost identical power to Cox's HR-based tests under PH scenarios and can be more powerful for delayed-difference patterns often seen in immunotherapy trials. Like median and RMST differences, the proposed approach is a good model-free alternative to the HR-based approach for evaluating the treatment effect magnitude. Such a model-free measure will increase the likelihood that results from clinical studies are correctly interpreted and generalized to future populations.

Psychiatric visits during the postpartum year in women with eating disorders who continue or discontinue antidepressant treatment in pregnancy

OBJECTIVE

To determine the association between continued antidepressant use in pregnancy and postpartum psychiatric visits for eating (ED) or mood/anxiety disorders in women with preexisting ED.

METHOD

Using Danish health registry data (1998-2015), we identified 3529 pregnancies in women with ED prepregnancy: (i) 564 with continued antidepressant use before and during pregnancy; (ii) 778 with discontinued antidepressants before pregnancy; (iii) 2137 unexposed. Outpatient and inpatient postpartum visits for an ED or a mood/anxiety disorder constituted the outcome measures. We estimated hazard ratios (HRs) and 95% confidence intervals (CI) using Cox regression with inverse probability of treatment weighting, and performed stratified analyses by antidepressant prescription filling in the first 3 months postpartum.

RESULTS

The weighted cumulative incidence for an ED visit at end of follow-up was 4.5% (continued) and 4.8% (discontinued). We found no association between continued antidepressant and postpartum ED visit, relative to discontinued (HR: 0.89, 95% CI: 0.52-1.52). The HR for postpartum mood/anxiety disorder visit was 1.27 (95% CI: 0.68-2.36) with continued antidepressants versus discontinued but decreased if more than two antidepressant prescriptions were refilled. Continued antidepressant use was associated with a 57% reduced likelihood of a postpartum ED visit versus discontinued use in pregnancies with antidepressant prescription refills in the early postpartum.

CONCLUSION

Among women with preexisting ED, there was no association between continued antidepressant use during pregnancy and the likelihood of postpartum psychiatric visits, relative to discontinued antidepressants before pregnancy. Continuation of treatment into the early postpartum is associated with reduced likelihood of postpartum ED visit.

PUBLIC SIGNIFICANCE

Based on data from the Danish registries, we identified 3529 pregnancies among women with preexisting eating disorders before pregnancy. Women with continued antidepressant treatment both before and during pregnancy did not have a lower probability of having postpartum psychiatric visits for an eating disorder or for mood/anxiety disorders (often coexisting with eating disorders), relative to those who discontinued antidepressants before pregnancy. Further continuation of antidepressant treatment into the early postpartum is associated with improved maternal postpartum outcomes. However, residual confounding by disease severity limits confidence in this conclusion.

Association between mental disorders and mortality: A register-based cohort study from the region of Catalonia

We estimated all-cause and cause-specific mortality associated with mental disorder diagnoses using outpatient and inpatient registers from Catalonia. A historical register-based cohort was used, including 516,944 adults diagnosed with psychotic, mood, or anxiety disorders in 2005-2016, and their matched controls. Six psychiatric groups were created using hierarchical rules. Mortality rate ratios (MRRs), calculated with stratified Cox proportional-hazards models adjusted for mental comorbidity, ranged from 2.45 (95%CI = 2.28-2.64) for other non-organic psychoses to 1.11 (95%CI = 1.08-1.15) for anxiety disorders. Higher MRRs were found in males compared to females with non-organic psychoses, other affective and anxiety disorders, and the excess risk of death was higher in younger ages for all the diagnoses except for schizophrenia. Overall, suicide mortality rates were higher for those with mental disorder diagnoses. The highest MRRs due to natural causes were found for metabolic disorders in schizophrenia, infectious diseases in other non-organic psychoses, and respiratory diseases for bipolar, other affective and anxiety disorders. In the most comprehensive study in Southern Europe, excess mortality is observed not only in people with diagnoses of severe mental disorders, but also in those with other mental disorder diagnoses considered less severe, with an important contribution of both natural and unnatural causes.

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.

Learning the Treatment Impact on Time-to-Event Outcomes: The Transcarotid Artery Revascularization Simulated Cohort

Proportional hazard Cox regression models are overwhelmingly used for analyzing time-dependent outcomes. Despite their associated hazard ratio is a valuable index for the difference between populations, its strong dependency on the underlying assumptions makes it a source of misinterpretation. Recently, a number of works have dealt with the subtleties and limitations of this interpretation. Besides, a number of alternative indices and different Cox-type models have been proposed. In this work, we use synthetic data, motivated by a real-world problem, for showing the strengths and weaknesses of some of those methods in the analysis of time-dependent outcomes. We use the power of synthetic data for considering observable results but also utopian designs.

A Review of Causal Inference for External Comparator Arm Studies

Randomized controlled trials (RCTs) are the gold standard design to establish the efficacy of new drugs and to support regulatory decision making. However, a marked increase in the submission of single-arm trials (SATs) has been observed in recent years, especially in the field of oncology due to the trend towards precision medicine contributing to the rise of new therapeutic interventions for rare diseases. SATs lack results for control patients, and information from external sources can be compiled to provide context for better interpretability of study results. External comparator arm (ECA) studies are defined as a clinical trial (most commonly a SAT) and an ECA of a comparable cohort of patients-commonly derived from real-world settings including registries, natural history studies, or medical records of routine care. This publication aims to provide a methodological overview, to sketch emergent best practice recommendations and to identify future methodological research topics. Specifically, existing scientific and regulatory guidance for ECA studies is reviewed and appropriate causal inference methods are discussed. Further topics include sample size considerations, use of estimands, handling of different data sources regarding differential baseline covariate definitions, differential endpoint measurements and timings. In addition, unique features of ECA studies are highlighted, specifically the opportunity to address bias caused by unmeasured ECA covariates, which are available in the SAT.

Testing for Differences in Survival When Treatment Effects Are Persistent, Decaying, or Delayed

A statistical test for the presence of treatment effects on survival will be based on a null hypothesis (absence of effects) and an alternative (presence of effects). The null is very simply expressed. The most common alternative, also simply expressed, is that of proportional hazards. For this situation, not only do we have a very powerful test in the log-rank test but also the outcome is readily interpreted. However, many modern treatments fall outside this relatively straightforward paradigm and, as such, have attracted attention from statisticians eager to do their best to avoid losing power as well as to maintain interpretability when the alternative hypothesis is less simple. Examples include trials where the treatment effect decays with time, immunotherapy trials where treatment effects may be slow to manifest themselves as well as the so-called crossing hazards problem. We review some of the solutions that have been proposed to deal with these issues. We pay particular attention to the integrated log-rank test and how it can be combined with the log-rank test itself to obtain powerful tests for these more complex situations.

Penalized weighted proportional hazards model for robust variable selection and outlier detection

Identifying exceptional responders or nonresponders is an area of increased research interest in precision medicine as these patients may have different biological or molecular features and therefore may respond differently to therapies. Our motivation stems from a real example from a clinical trial where we are interested in characterizing exceptional prostate cancer responders. We investigate the outlier detection and robust regression problem in the sparse proportional hazards model for censored survival outcomes. The main idea is to model the irregularity of each observation by assigning an individual weight to the hazard function. By applying a LASSO-type penalty on both the model parameters and the log transformation of the weight vector, our proposed method is able to perform variable selection and outlier detection simultaneously. The optimization problem can be transformed to a typical penalized maximum partial likelihood problem and thus it is easy to implement. We further extend the proposed method to deal with the potential outlier masking problem caused by censored outcomes. The performance of the proposed estimator is demonstrated with extensive simulation studies and real data analyses in low-dimensional and high-dimensional settings.

Doubly-robust methods for differences in restricted mean lifetimes using pseudo-observations

In clinical studies or trials comparing survival times between two treatment groups, the restricted mean lifetime (RML), defined as the expectation of the survival from time 0 to a prespecified time-point, is often the quantity of interest that is readily interpretable to clinicians without any modeling restrictions. It is well known that if the treatments are not randomized (as in observational studies), covariate adjustment is necessary to account for treatment imbalances due to confounding factors. In this article, we propose a simple doubly-robust pseudo-value approach to effectively estimate the difference in the RML between two groups (akin to a metric for estimating average causal effects), while accounting for confounders. The proposed method combines two general approaches: (a) group-specific regression models for the time-to-event and covariate information, and (b) inverse probability of treatment assignment weights, where the RMLs are replaced by the corresponding pseudo-observations for survival outcomes, thereby mitigating the estimation complexities in presence of censoring. The proposed estimator is double-robust, in the sense that it is consistent if at least one of the two working models remains correct. In addition, we explore the potential of available machine learning algorithms in causal inference to reduce possible bias of the causal estimates in presence of a complex association between the survival outcome and covariates. We conduct extensive simulation studies to assess the finite-sample performance of the pseudo-value causal effect estimators. Furthermore, we illustrate our methodology via application to a dataset from a breast cancer cohort study. The proposed method is implementable using the R package drRML, available in GitHub.

Comorbidity between eating disorders and psychiatric disorders

OBJECTIVE

Previous literature has established an increased risk of eating disorders among individuals with other psychiatric disorders and vice versa. However, often studies have focused on eating disorders as a single diagnostic entity and/or investigated selected psychiatric comorbidities. We conducted a comprehensive study, exploring bidirectional associations between different types of eating disorders and broad groups of all other psychiatric disorders, to identify patterns of comorbidity.

METHOD

We included all people born in Denmark 1963-2010. We collected information on eating disorders and considered the risk of subsequent psychiatric disorders using Cox-proportional hazards regression. Absolute risks were calculated using competing risks survival analyses. We also considered prior psychiatric disorders and subsequent eating disorders.

RESULTS

An increased risk was seen for almost all disorder pairs of diagnoses evaluated. Following an anorexia nervosa (AN) diagnosis, the median hazard ratio for the different subsequent psychiatric disorders was 3.80 (range 2.48-6.15); following an other eating disorder (OED) diagnosis, it was 3.16 (range 2.05-5.14). After different psychiatric disorder diagnoses, the median hazard ratio was 2.66 for later AN (range 1.21-5.31), and 2.51 for later OED (range 1.25-4.10). Absolute risk of eating disorders was also higher among those with other psychiatric disorders than those without.

DISCUSSION

In this broad examination, we identified bidirectional increases in risk of comorbidity for those with both eating disorder diagnoses and psychiatric disorder diagnoses. Although our findings indicate different patterns of comorbidity between eating disorders, these variations were generally small.

Novel Use of Patient-Specific Covariates From Oncology Studies in the Era of Biomedical Data Science: A Review of Latest Methodologies

In this article, we review different applications of how to incorporate individual patient variables into clinical research within oncology. These methodologies range from the more traditional use of baseline covariates from randomized clinical trials, as well as observational studies, to using covariates to generalize the results of randomized clinical trials to other populations. Individual patient variables also allow for the consideration of heterogeneity in treatment effects and individualized treatment rules. We primarily consider two treatment groups and mostly focus on time-to-event outcomes where such methodologies have been well established and widely applied. We also discuss more conceptually newer statistical research that has not been widely applied in clinical oncology, but is likely to make an impact in future oncology research. With the increasing amount of biomedical data available for analysis, it is inevitable that more methods are developed to make best use of information, to advance oncology research.

Graphical calibration curves and the integrated calibration index (ICI) for competing risk models

BACKGROUND

Assessing calibration-the agreement between estimated risk and observed proportions-is an important component of deriving and validating clinical prediction models. Methods for assessing the calibration of prognostic models for use with competing risk data have received little attention.

METHODS

We propose a method for graphically assessing the calibration of competing risk regression models. Our proposed method can be used to assess the calibration of any model for estimating incidence in the presence of competing risk (e.g., a Fine-Gray subdistribution hazard model; a combination of cause-specific hazard functions; or a random survival forest). Our method is based on using the Fine-Gray subdistribution hazard model to regress the cumulative incidence function of the cause-specific outcome of interest on the predicted outcome risk of the model whose calibration we want to assess. We provide modifications of the integrated calibration index (ICI), of E50 and of E90, which are numerical calibration metrics, for use with competing risk data. We conducted a series of Monte Carlo simulations to evaluate the performance of these calibration measures when the underlying model has been correctly specified and when the model was mis-specified and when the incidence of the cause-specific outcome differed between the derivation and validation samples. We illustrated the usefulness of calibration curves and the numerical calibration metrics by comparing the calibration of a Fine-Gray subdistribution hazards regression model with that of random survival forests for predicting cardiovascular mortality in patients hospitalized with heart failure.

RESULTS

The simulations indicated that the method for constructing graphical calibration curves and the associated calibration metrics performed as desired. We also demonstrated that the numerical calibration metrics can be used as optimization criteria when tuning machine learning methods for competing risk outcomes.

CONCLUSIONS

The calibration curves and numeric calibration metrics permit a comprehensive comparison of the calibration of different competing risk models.

Censoring-robust time-dependent receiver operating characteristic curve estimators

Time-dependent receiver operating characteristic curves are often used to evaluate the classification performance of continuous measures when considering time-to-event data. When one is interested in evaluating the predictive performance of multiple covariates, it is common to use the Cox proportional hazards model to obtain risk scores; however, previous work has shown that when the model is mis-specified, the estimand corresponding to the partial likelihood estimator depends on the censoring distribution. In this manuscript, we show that when the risk score model is mis-specified, the AUC will also depend on the censoring distribution, leading to either over- or under-estimation of the risk score's predictive performance. We propose the use of censoring-robust estimators to remove the dependence on the censoring distribution and provide empirical results supporting the use of censoring-robust risk scores.

Postpartum psychiatric disorders and subsequent live birth: a population-based cohort study in Denmark

STUDY QUESTION

Are women with a history of first-onset postpartum psychiatric disorders after their first liveborn delivery less likely to have a subsequent live birth?

SUMMARY ANSWER

Women with incident postpartum psychiatric disorders are less likely to go on to have further children.

WHAT IS KNOWN ALREADY

Women are particularly vulnerable to psychiatric disorders in the postpartum period. The potential effects of postpartum psychiatric disorders on the mother's future chances of live birth are so far under-researched.

STUDY DESIGN, SIZE, DURATION

A population-based cohort study consisted of 414 571 women who had their first live birth during 1997-2015. We followed the women for a maximum of 19.5 years from the date of the first liveborn delivery until the next conception leading to a live birth, emigration, death, their 45th birthday or 30 June 2016, whichever occurred first.

PARTICIPANTS/MATERIALS, SETTING, METHODS

Postpartum psychiatric disorders were defined as filling a prescription for psychotropic medications or hospital contact for psychiatric disorders for the first time within 6 months postpartum. The outcome of interest was time to the next conception leading to live birth after the first liveborn delivery. Records on the death of a child were obtained through the Danish Register of Causes of Death. Cox regression was used to estimate the hazard ratios (HRs), stratified by the survival status of the first child.

MAIN RESULTS AND THE ROLE OF CHANCE

Altogether, 4327 (1.0%) women experienced postpartum psychiatric disorders after their first liveborn delivery. The probability of having a subsequent live birth was 69.1% (95% CI: 67.4-70.7%) among women with, and 82.3% (95% CI: 82.1-82.4%) among those without, postpartum psychiatric disorders. Women with postpartum psychiatric disorders had a 33% reduction in the rate of having second live birth (HR = 0.67, 95% CI: 0.64-0.69), compared to women without postpartum psychiatric disorders. The association disappeared if the first child died (HR = 1.01, 95% CI: 0.85-1.20). If postpartum psychiatric disorders required hospitalisations, this was associated with a more pronounced reduction in live birth rate, irrespective of the survival status of the first child (HR = 0.54, 95% CI: 0.47-0.61 if the first child survived, and HR = 0.49, 95% CI: 0.23-1.04 if the first child died).

LIMITATIONS, REASONS FOR CAUTION

The use of population-based registers allows for the inclusion of a representative cohort with almost complete follow-up. The large sample size enables us to perform detailed analyses, accounting for the survival status of the child. However, we did not have accurate information on stillbirths and miscarriages, and only pregnancies that led to live birth were included.

WIDE IMPLICATIONS OF THE FINDINGS

Our study is the first study to investigate subsequent live birth after postpartum psychiatric disorders in a large representative population. The current study indicates that postpartum psychiatric disorders have a significant impact on subsequent live birth, as women experiencing these disorders have a decreased likelihood of having more children. However, the variations in subsequent live birth rate are influenced by both the severity of the disorders and the survival status of the first-born child, indicating that both personal choices and decreased fertility may have a role in the reduced subsequent live birth rate among women with postpartum psychiatric disorders.

STUDY FUNDING/COMPETING INTEREST(S)

This work was supported by the Danish Council for Independent Research (DFF-5053-00156B), the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 837180, AUFF NOVA (AUFF-E 2016-9-25), iPSYCH, the Lundbeck Foundation Initiative for Integrative Psychiatric Research (R155-2014-1724), Niels Bohr Professorship Grant from the Danish National Research Foundation and the Stanley Medical Research Institute, the National Institute of Mental Health (NIMH) (R01MH104468) and Fabrikant Vilhelm Pedersen og Hustrus Legat. The authors do not declare any conflicts of interest.

TRIAL REGISTRATION NUMBER

N/A.

A weighted log-rank test and associated effect estimator for cancer trials with delayed treatment effect

The standard log-rank test has been extended by adopting various weight functions. Cancer vaccine or immunotherapy trials have shown a delayed onset of effect for the experimental therapy. This is manifested as a delayed separation of the survival curves. This work proposes new weighted log-rank tests to account for such delay. The weight function is motivated by the time-varying hazard ratio between the experimental and the control therapies. We implement a numerical evaluation of the Schoenfeld approximation (NESA) for the mean of the test statistic. The NESA enables us to assess the power and to calculate the sample size for detecting such delayed treatment effect and also for a more general specification of the non-proportional hazards in a trial. We further show a connection between our proposed test and the weighted Cox regression. Then the average hazard ratio using the same weight is obtained as an estimand of the treatment effect. Extensive simulation studies are conducted to compare the performance of the proposed tests with the standard log-rank test and to assess their robustness to model mis-specifications. Our tests outperform the G^ρ,γ class in general and have performance close to the optimal test. We demonstrate our methods on two cancer immunotherapy trials.

Non-proportional hazards in immuno-oncology: Is an old perspective needed?

A fundamental concept in two-arm non-parametric survival analysis is the comparison of observed versus expected numbers of events on one of the treatment arms (the choice of which arm is arbitrary), where the expectation is taken assuming that the true survival curves in the two arms are identical. This concept is at the heart of the counting-process theory that provides a rigorous basis for methods such as the log-rank test. It is natural, therefore, to maintain this perspective when extending the log-rank test to deal with non-proportional hazards, for example, by considering a weighted sum of the "observed - expected" terms, where larger weights are given to time periods where the hazard ratio is expected to favor the experimental treatment. In doing so, however, one may stumble across some rather subtle issues, related to difficulties in the interpretation of hazard ratios, that may lead to strange conclusions. An alternative approach is to view non-parametric survival comparisons as permutation tests. With this perspective, one can easily improve on the efficiency of the log-rank test, while thoroughly controlling the false positive rate. In particular, for the field of immuno-oncology, where researchers often anticipate a delayed treatment effect, sample sizes could be substantially reduced without loss of power.

Early labor force exits in patients with treatment-resistant depression: an assessment of work years lost in a Danish nationwide register-based cohort study

BACKGROUND

Depression is one of the leading causes of premature workforce exit in many Western countries, but little is known about the extent to which treatment-resistance reduces number of work-years. We compared the risk of premature workforce exit among patients with treatment-resistant depression (TRD) relative to non-TRD patients and estimated work years lost (WYL) before scheduled retirement age.

METHODS

The study population, identified in the Danish National Prescription Registry, included all individuals born and living in Denmark who redeemed their first antidepressant (AD) prescription for depression at age 18-60 years between 2005 and 2012. TRD was defined as failure to respond to at least two different treatment trials. Premature workforce exit was measured using disability pension records. We used Cox regression to estimate the hazard ratio (HR) for premature workforce exit in TRD relative to non-TRD patients, adjusting for calendar year, psychiatric and somatic comorbidity, and educational level. Differences in WYL in patients with TRD and all depression patients were estimated through a competing risks model.

RESULTS

Out of the total sample of patients with depression (N = 129,945), 7478 (5.75%) were classified as having TRD. During follow up, 17% of patients with TRD and 8% of non-TRD patients received disability pension, resulting in a greater than three-fold larger risk of premature workforce exit [adjusted HR (aHR) 3.23 95% confidence interval (CI) 3.05-3.43]. The TRD group lost on average six work-years (95% CI 5.64-6.47) more than the total sample due to early labor force exit. The association between TRD and age at premature workforce exit was inversely U-shaped; the hazard rate of premature workforce exit for patients with TRD compared with non-TRD patients was highest in the age groups 31-35, 36-40, and 41-45 years.

CONCLUSION

Patients with TRD constitute a small group within depression patients, but contribute disproportionally to societal costs due to premature workforce exit at a young age.

Robust estimation in the nested case-control design under a misspecified covariate functional form

The Cox proportional hazards model is typically used to analyze time-to-event data. If the event of interest is rare and covariates are difficult or expensive to collect, the nested case-control (NCC) design provides consistent estimates at reduced costs with minimal impact on precision if the model is specified correctly. If our scientific goal is to conduct inference regarding an association of interest, it is essential that we specify the model a priori to avoid multiple testing bias. We cannot, however, be certain that all assumptions will be satisfied so it is important to consider robustness of the NCC design under model misspecification. In this manuscript, we show that in finite sample settings where the functional form of a covariate of interest is misspecified, the estimates resulting from the partial likelihood estimator under the NCC design depend on the number of controls sampled at each event time. To account for this dependency, we propose an estimator that recovers the results obtained using using the full cohort, where full covariate information is available for all study participants. We present the utility of our estimator using simulation studies and show the theoretical properties. We end by applying our estimator to motivating data from the Alzheimer's Disease Neuroimaging Initiative.

Explained variation under the additive hazards model

We study explained variation under the additive hazards regression model for right-censored data. We consider different approaches for developing such a measure, and focus on one that estimates the proportion of variation in the failure time explained by the covariates. We study the properties of the measure both analytically, and through extensive simulations. We apply the measure to a well-known survival dataset as well as the linked surveillance, epidemiology, and end results-Medicare database for prediction of mortality in early stage prostate cancer patients using high-dimensional claims codes.

Empirical power comparison of statistical tests in contemporary phase III randomized controlled trials with time-to-event outcomes in oncology

BACKGROUND

More than 95% of recent cancer randomized controlled trials used the log-rank test to detect a treatment difference making it the predominant tool for comparing two survival functions. As with other tests, the log-rank test has both advantages and disadvantages. One advantage is that it offers the highest power against proportional hazards differences, which may be a major reason why alternative methods have rarely been employed in practice. The performance of statistical tests has traditionally been investigated both theoretically and numerically for several patterns of difference between two survival functions. However, to the best of our knowledge, there has been no attempt to compare the performance of various statistical tests using empirical data from past oncology randomized controlled trials. So, it is unknown whether the log-rank test offers a meaningful power advantage over alternative testing methods in contemporary cancer randomized controlled trials. Focusing on recently reported phase III cancer randomized controlled trials, we assessed whether the log-rank test gave meaningfully greater power when compared with five alternative testing methods: generalized Wilcoxon, test based on maximum of test statistics from multiple weighted log-rank tests, difference in t-year event rate, and difference in restricted mean survival time with fixed and adaptive τ.

METHODS

Using manuscripts from cancer randomized controlled trials recently published in high-tier clinical journals, we reconstructed patient-level data for overall survival (69 trials) and progression-free survival (54 trials). For each trial endpoint, we estimated the empirical power of each test. Empirical power was measured as the proportion of trials for which a test would have identified a significant result (p value < .05).

RESULTS

For overall survival, t-year event rate offered the lowest (30.4%) empirical power and restricted mean survival time with fixed τ offered the highest (43.5%). The empirical power of the other types of tests was almost identical (36.2%-37.7%). For progression-free survival, the tests we investigated offered numerically equivalent empirical power (55.6%-61.1%). No single test consistently outperformed any other test.

CONCLUSION

The empirical power assessment with the past cancer randomized controlled trials provided new insights on the performance of statistical tests. Although the log-rank test has been used in almost all trials, our study suggests that the log-rank test is not the only option from an empirical power perspective. Near universal use of the log-rank test is not supported by a meaningful difference in empirical power. Clinical trial investigators could consider alternative methods, beyond the log-rank test, for their primary analysis when designing a cancer randomized controlled trial. Factors other than power (e.g. interpretability of the estimated treatment effect) should garner greater consideration when selecting statistical tests for cancer randomized controlled trials.

Summarizing causal differences in survival curves in the presence of unmeasured confounding

Proportional hazard Cox regression models are frequently used to analyze the impact of different factors on time-to-event outcomes. Most practitioners are familiar with and interpret research results in terms of hazard ratios. Direct differences in survival curves are, however, easier to understand for the general population of users and to visualize graphically. Analyzing the difference among the survival curves for the population at risk allows easy interpretation of the impact of a therapy over the follow-up. When the available information is obtained from observational studies, the observed results are potentially subject to a plethora of measured and unmeasured confounders. Although there are procedures to adjust survival curves for measured covariates, the case of unmeasured confounders has not yet been considered in the literature. In this article we provide a semi-parametric procedure for adjusting survival curves for measured and unmeasured confounders. The method augments our novel instrumental variable estimation method for survival time data in the presence of unmeasured confounding with a procedure for mapping estimates onto the survival probability and the expected survival time scales.

Cancer and Leukemia Group B 90203 (Alliance): Radical Prostatectomy With or Without Neoadjuvant Chemohormonal Therapy in Localized, High-Risk Prostate Cancer

PURPOSE

Radical prostatectomy (RP) alone is often inadequate in curing men with clinically localized, high-risk prostate cancer (PC). We hypothesized that chemohormonal therapy (CHT) with androgen-deprivation therapy plus docetaxel before RP would improve biochemical progression-free survival (BPFS) over RP alone.

PATIENTS AND METHODS

Men with clinically localized, high-risk PC were assigned to RP alone or neoadjuvant CHT with androgen deprivation plus docetaxel (75 mg/m² body surface area every 3 weeks for 6 cycles) and RP. The primary end point was 3-year BPFS. Biochemical failure was defined as a serum prostate-specific antigen level > 0.2 ng/mL that increased on 2 consecutive occasions that were at least 3 months apart. Secondary end points included 5-year BPFS, overall BPFS, local recurrence, metastasis-free survival (MFS), PC-specific mortality, and overall survival (OS).

RESULTS

In total, 788 men were randomly assigned. Median follow-up time was 6.1 years. The overall rates of grade 3 and 4 adverse events during chemotherapy were 26% and 19%, respectively. No difference was seen in 3-year BPFS between neoadjuvant CHT plus RP and RP alone (0.89 v 0.84, respectively; 95% CI for the difference, -0.01 to 0.11; P = .11). Neoadjuvant CHT was associated with improved overall BPFS (hazard ratio [HR], 0.69; 95% CI, 0.48 to 0.99), improved MFS (HR, 0.70; 95% CI, 0.51 to 0.95), and improved OS (HR, 0.61; 95% CI, 0.40 to 0.94) compared with RP alone.

CONCLUSION

The primary study end point, 3-year BPFS, was not met. Although some improvement was seen in secondary end points, any potential benefit must be weighed against toxicity. Our data do not support the routine use of neoadjuvant CHT and RP in patients with clinically localized, high-risk PC at this time.

Association between Mental Disorders and Subsequent Medical Conditions

BACKGROUND

Persons with mental disorders are at a higher risk than the general population for the subsequent development of certain medical conditions.

METHODS

We used a population-based cohort from Danish national registries that included data on more than 5.9 million persons born in Denmark from 1900 through 2015 and followed them from 2000 through 2016, for a total of 83.9 million person-years. We assessed 10 broad types of mental disorders and 9 broad categories of medical conditions (which encompassed 31 specific conditions). We used Cox regression models to calculate overall hazard ratios and time-dependent hazard ratios for pairs of mental disorders and medical conditions, after adjustment for age, sex, calendar time, and previous mental disorders. Absolute risks were estimated with the use of competing-risks survival analyses.

RESULTS

A total of 698,874 of 5,940,299 persons (11.8%) were identified as having a mental disorder. The median age of the total population was 32.1 years at entry into the cohort and 48.7 years at the time of the last follow-up. Persons with a mental disorder had a higher risk than those without such disorders with respect to 76 of 90 pairs of mental disorders and medical conditions. The median hazard ratio for an association between a mental disorder and a medical condition was 1.37. The lowest hazard ratio was 0.82 for organic mental disorders and the broad category of cancer (95% confidence interval [CI], 0.80 to 0.84), and the highest was 3.62 for eating disorders and urogenital conditions (95% CI, 3.11 to 4.22). Several specific pairs showed a reduced risk (e.g., schizophrenia and musculoskeletal conditions). Risks varied according to the time since the diagnosis of a mental disorder. The absolute risk of a medical condition within 15 years after a mental disorder was diagnosed varied from 0.6% for a urogenital condition among persons with a developmental disorder to 54.1% for a circulatory disorder among those with an organic mental disorder.

CONCLUSIONS

Most mental disorders were associated with an increased risk of a subsequent medical condition; hazard ratios ranged from 0.82 to 3.62 and varied according to the time since the diagnosis of the mental disorder. (Funded by the Danish National Research Foundation and others; COMO-GMC ClinicalTrials.gov number, NCT03847753.).

Reproduction after the loss of a child: a population-based matched cohort study

STUDY QUESTION

Is the death of a child associated with higher subsequent fertility?

SUMMARY ANSWER

Women who had lost a child had higher fertility both shortly after the loss and throughout the entire follow-up, independent of the child's age at the time of death.

WHAT IS KNOWN ALREADY

Women who lose a child in the perinatal period often have another child shortly after. However, to our knowledge no previous study has investigated if the death of an older child affects reproductive behavior.

STUDY DESIGN, SIZE, DURATION

The source population for this matched cohort study consisted of all women who gave birth in Denmark from 1978 to 2004 and in Sweden from 1973 to 2002 (N = 1 979 958). Women were followed through to the end of 2008 in Denmark and the end of 2006 in Sweden.

PARTICIPANTS/MATERIALS, SETTING, METHODS

Women who had lost a child before the age of 45 years during the study period (exposed group; n = 36 511) were matched with up to five women who were from the same country and of similar age and family characteristics and had not lost a child at the time of matching (unexposed group; n = 182 522).

MAIN RESULTS AND THE ROLE OF CHANCE

During follow-up, 74% of exposed and 46% of unexposed women had another birth (live- or stillbirth) after a gestation of 28 weeks or more. Compared with unexposed women, exposed women had a shorter interpregnancy interval and, consequently, a higher rate of conception leading to a birth (HR = 5.5 [95% CI: 5.4-5.6]). Rates for exposed women were higher from the first month following the child's death, but the largest difference was between 2 and 3 months after the event. This pattern was independent of the age of the deceased child. Exposed women had more subsequent children than unexposed, leading to a comparable number of living children at the end of follow-up.

LIMITATIONS, REASONS FOR CAUTION

The use of population-based registers allows for the inclusion of virtually all eligible women and nearly complete follow-up; the potential for selection bias is thus negligible. However, only pregnancies that led to a live birth or a stillbirth could be identified, thus fetal losses occurring before week 28 of gestation were missing.

WIDER IMPLICATIONS OF THE FINDINGS

Our findings corroborate the previous evidence suggesting that women try to conceive again shortly after a perinatal death, and many succeed. In addition, this is the first study to investigate the reproductive trajectory after losing an older child. The current study indicates that most women who lose a child between the ages of 6 months and 5 years conceive shortly after the loss, and they have a comparable number of living children at the end of the follow-up compared to those who do not lose a child.

STUDY FUNDING/COMPETING INTEREST(S)

This work was supported by Grant ERC-2010-StG-260242 from the European Research Council, 176673 and 186200 from the Nordic Cancer Union, DFF-6110-00019 from the Danish Council for Independent Research, 904414 and 15199 from TrygFonden, Karen Elise Jensens Fond (2016), and the Program for Clinical Research Infrastructure (PROCRIN) established by the Lundbeck Foundation and the Novo Nordisk Foundation. The authors do not declare any conflicts of interests.

TRIAL REGISTRATION NUMBER

N/A.

Parental asthma occurrence, exacerbations and risk of attention-deficit/hyperactivity disorder

OBJECTIVE

To investigate whether intrauterine exposure to maternal asthma or asthma exacerbations increases the risk of attention-deficit/hyperactivity disorder (ADHD).

METHODS

Using Danish register data, this cohort study comprised of 961,202 live singletons born in Denmark during 1997-2012. Children were followed to a maximum of 20.0 years from birth until the first of ADHD-diagnosis/prescription, emigration, death, or 31 December 2016. Cox regression models were used to evaluate the association between maternal or paternal asthma, asthma exacerbations and offspring ADHD.

RESULTS

During 11.4 million person-years of follow-up, 27,780 (2.9%) children were identified as having ADHD. ADHD risk was increased among offspring born to asthmatic mothers (hazard ratio (HR) 1.41, 95% CI: 1.36-1.46) or asthmatic fathers (HR 1.13, 95% CI: 1.08-1.18). Antenatal antiasthma medication treatment did not increase offspring ADHD. However, higher risks were observed among offspring of mothers with asthma exacerbations compared with children of asthmatic mothers with no exacerbations: HR 1.12 (95% CI: 1.00-1.25) for pre-pregnancy exacerbations; 1.21 (95% CI: 1.00-1.47) for exacerbations during pregnancy; and 1.25 (95% CI: 1.08-1.44) for exacerbations after delivery.

CONCLUSIONS

These results support theories regarding shared genetic and environmental risk factors having a role in the development of ADHD.

Quantifying time-varying cause-specific hazard and subdistribution hazard ratios with competing risks data

Various non-proportional hazard models have been developed in the literature for competing risks data. The regression coefficients under these models, however, typically cannot be compared directly. We propose new methods to quantify the average of the time-varying cause-specific hazard ratios and subdistribution hazard ratios through two general classes of transformations and weight functions that are chosen to reflect the relative importance of the hazard ratios in different time periods. We further propose an L∞ -norm type of test statistic that incorporates the test statistics for all possible pairs of the transformation function and weight function under consideration. Extensive simulations are conducted under various settings of the hazards and demonstrate that the proposed test performs well under all settings. An application to a clinical trial in follicular lymphoma is examined in detail.

Maternal Diabetes Mellitus and Genital Anomalies in Male Offspring: A Nationwide Cohort Study in 2 Nordic Countries

BACKGROUND

Pre-existing diabetes has been associated with an increased risk of congenital malformations overall, but studies on genital anomalies in boys are conflicting and possible causal mechanisms are not well understood. Previous studies have mainly assessed pregestational and gestational diabetes in combination. Yet considering the vulnerable time windows for the genital anomalies, associations could well differ between types of diabetes and between the 2 genital anomalies and we therefore aimed to study this further.

METHODS

A population-based cohort study of 2,416,246 singleton live-born boys from Denmark (1978-2012) and Sweden (1987-2012) was carried out using Danish and Swedish register-based data. Using Cox regression models, we estimated hazard ratios for hypospadias and cryptorchidism according to maternal diabetes. We considered type and severity of diabetes, as well as timing of diagnosis in relation to birth.

RESULTS

Pregestational type 1 diabetes was associated with a higher risk of both genital anomalies. The highest risks were seen for boys of mothers with diabetic complications (hazard ratio for hypospadias = 2.33 [95% confidence interval, 1.48, 3.66] and hazard ratio for cryptorchidism = 1.92 [95% confidence interval, 1.39, 2.65]). Gestational diabetes was associated with slightly increased risks of both genital anomalies.

CONCLUSIONS

These results are consistent with the hypothesis that poor glycemic control may interfere with fetal genital development in the critical early period of organogenesis. Given the widespread and increasing occurrence of diabetes, these results are of public health importance.