Regression models for censored time-to-event data using infinitesimal jack-knife pseudo-observations, with applications to left-truncation.

Jack-knife pseudo-observations have in recent decades gained popularity in regression analysis for various aspects of time-to-event data. A limitation of the jack-knife pseudo-observations is that their computation is time consuming, as the base estimate needs to be recalculated when leaving out each observation. We show that jack-knife pseudo-observations can be closely approximated using the idea of the infinitesimal jack-knife residuals. The infinitesimal jack-knife pseudo-observations are much faster to compute than jack-knife pseudo-observations. A key assumption of the unbiasedness of the jack-knife pseudo-observation approach is on the influence function of the base estimate. We reiterate why the condition on the influence function is needed for unbiased inference and show that the condition is not satisfied for the Kaplan-Meier base estimate in a left-truncated cohort. We present a modification of the infinitesimal jack-knife pseudo-observations that provide unbiased estimates in a left-truncated cohort. The computational speed and medium and large sample properties of the jack-knife pseudo-observations and infinitesimal jack-knife pseudo-observation are compared and we present an application of the modified infinitesimal jack-knife pseudo-observations in a left-truncated cohort of Danish patients with diabetes.

Bivariate pseudo-observations for recurrent event analysis with terminal events.

The analysis of recurrent events in the presence of terminal events requires special attention. Several approaches have been suggested for such analyses either using intensity models or marginal models. When analysing treatment effects on recurrent events in controlled trials, special attention should be paid to competing deaths and their impact on interpretation. This paper proposes a method that formulates a marginal model for recurrent events and terminal events simultaneously. Estimation is based on pseudo-observations for both the expected number of events and survival probabilities. Various relevant hypothesis tests in the framework are explored. Theoretical derivations and simulation studies are conducted to investigate the behaviour of the method. The method is applied to two real data examples. The bivariate marginal pseudo-observation model carries the strength of a two-dimensional modelling procedure and performs well in comparison with available models. Finally, an extension to a three-dimensional model, which decomposes the terminal event per death cause, is proposed and exemplified.

Cumulative risk regression in case-cohort studies using pseudo-observations.

Case-cohort studies are useful when information on certain risk factors is difficult or costly to ascertain. Particularly, a case-cohort study may be well suited in situations where several case series are of interest, e.g. in studies with competing risks, because the same sub-cohort may serve as a comparison group for all case series. Previous analyses of this kind of sampled cohort data most often involved estimation of rate ratios based on a Cox regression model. However, with competing risks this method will not provide parameters that directly describe the association between covariates and cumulative risks. In this paper, we study regression analysis of cause-specific cumulative risks in case-cohort studies using pseudo-observations. We focus mainly on the situation with competing risks. However, as a by-product, we also develop a method by which absolute mortality risks may be analyzed directly from case-cohort survival data. We adjust for the case-cohort sampling by inverse sampling probabilities applied to a generalized estimation equation. The large-sample properties of the proposed estimator are developed and small-sample properties are evaluated in a simulation study. We apply the methodology to study the effect of a specific diet component and a specific gene on the absolute risk of atrial fibrillation.

New drug candidates for bipolar disorder-A nation-wide population-based study.

OBJECTIVE: Drug repurposing is an increasingly promising idea in many fields of medicine. We systematically used Danish nation-wide population-based registers to investigate whether continued use of non-aspirin non-steroidal anti-inflammatory drugs (NSAIDs), low-dose aspirin, high-dose aspirin, statins, allopurinol, and angiotensin agents decrease the rate of incident mania/bipolar disorder. METHODS: A nation-wide population-based longitudinal study using Poisson regression analyses including all persons in Denmark who purchased the exposure medication of interest and a random sample of 30% of the Danish population. The follow-up period comprised a 10 years period from 2005 to 2015. Two different outcome measures were included, (1) a diagnosis of mania/bipolar disorder at a psychiatric hospital contact as inpatient or outpatient and (2) a combined measure of a diagnosis of mania/bipolar disorder or initiation of lithium use. RESULTS: A total of 1,605,365 subjects were exposed to one of the six drugs of interest during the exposure period from 2005 to 2015, median age 57 years [quartiles: 43;69], and female proportion of 53.1%. Continued use of low-dose aspirin, statins, and angiotensin agents were associated with decreased rates of incident mania/bipolar disorder on both outcome measures. Continued uses of non-aspirin NSAIDs as well as high-dose aspirin were associated with an increased rate of incident bipolar disorder. There were no statistically significant associations for allopurinol. CONCLUSIONS: The study supports the potential of agents acting on inflammation and the stress response system in bipolar disorder and illustrates that population-based registers can be used to systematically identify drugs with repurposing potentials.

A note on pseudo-observations and left-truncation.

Pseudo-observations have been introduced as a way to perform regression analysis of a mean value parameter related to a right-censored time-to-event outcome, such as the survival probability or the restricted mean survival time. Since the introduction of the approach there have been several extensions from the original setting. However, the proper definition and performance of pseudo-observations under left-truncation has not yet been addressed. Here, we look at two types of pseudo-observations under right-censoring and left-truncation. We explored their performance in a simulation study and applied them to data on diabetes patients with left-truncation.

Lithium in drinking water and the incidence of bipolar disorder: A nation-wide population-based study.

OBJECTIVE: Animal data suggest that subtherapeutic doses, including micro doses, of lithium may influence mood, and lithium levels in drinking water have been found to correlate with the rate of suicide. It has never been investigated whether consumption of lithium may prevent the development of bipolar disorder (primary prophylaxis). In a nation-wide population-based study, we investigated whether long-term exposure to micro levels of lithium in drinking water correlates with the incidence of bipolar disorder in the general population, hypothesizing an inverse association in which higher long-term lithium exposure is associated with lower incidences of bipolar disorder. METHODS: We included longitudinal individual geographical data on municipality of residence, data from drinking water lithium measurements and time-specific data from all cases with a hospital contact with a diagnosis of mania/bipolar disorder from 1995 to 2013 (N=14 820) and 10 age- and gender-matched controls from the Danish population (N= 140 311). Average drinking water lithium exposure was estimated for all study individuals. RESULTS: The median of the average lithium exposure did not differ between cases with a diagnosis of mania/bipolar disorder (12.7 µg/L; interquartile range [IQR]: 7.9-15.5 µg/L) and controls (12.5 µg/L; IQR: 7.6-15.7 µg/L; P=.2). Further, the incidence rate ratio of mania/bipolar disorder did not decrease with higher long-term lithium exposure, overall, or within age categories (0-40, 41-60 and 61-100 years of age). CONCLUSION: Higher long-term lithium exposure from drinking water was not associated with a lower incidence of bipolar disorder. The association should be investigated in areas with higher lithium levels than in Denmark.

Causal inference in survival analysis using pseudo-observations.

Causal inference for non-censored response variables, such as binary or quantitative outcomes, is often based on either (1) direct standardization ('G-formula') or (2) inverse probability of treatment assignment weights ('propensity score'). To do causal inference in survival analysis, one needs to address right-censoring, and often, special techniques are required for that purpose. We will show how censoring can be dealt with 'once and for all' by means of so-called pseudo-observations when doing causal inference in survival analysis. The pseudo-observations can be used as a replacement of the outcomes without censoring when applying 'standard' causal inference methods, such as (1) or (2) earlier. We study this idea for estimating the average causal effect of a binary treatment on the survival probability, the restricted mean lifetime, and the cumulative incidence in a competing risks situation. The methods will be illustrated in a small simulation study and via a study of patients with acute myeloid leukemia who received either myeloablative or non-myeloablative conditioning before allogeneic hematopoetic cell transplantation. We will estimate the average causal effect of the conditioning regime on outcomes such as the 3-year overall survival probability and the 3-year risk of chronic graft-versus-host disease. Copyright © 2017 John Wiley & Sons, Ltd.

Estimating a population cumulative incidence under calendar time trends.

BACKGROUND: The risk of a disease or psychiatric disorder is frequently measured by the age-specific cumulative incidence. Cumulative incidence estimates are often derived in cohort studies with individuals recruited over calendar time and with the end of follow-up governed by a specific date. It is common practice to apply the Kaplan-Meier or Aalen-Johansen estimator to the total sample and report either the estimated cumulative incidence curve or just a single point on the curve as a description of the disease risk. METHODS: We argue that, whenever the disease or disorder of interest is influenced by calendar time trends, the total sample Kaplan-Meier and Aalen-Johansen estimators do not provide useful estimates of the general risk in the target population. We present some alternatives to this type of analysis. RESULTS: We show how a proportional hazards model may be used to extrapolate disease risk estimates if proportionality is a reasonable assumption. If not reasonable, we instead advocate that a more useful description of the disease risk lies in the age-specific cumulative incidence curves across strata given by time of entry or perhaps just the end of follow-up estimates across all strata. Finally, we argue that a weighted average of these end of follow-up estimates may be a useful summary measure of the disease risk within the study period. CONCLUSIONS: Time trends in a disease risk will render total sample estimators less useful in observational studies with staggered entry and administrative censoring. An analysis based on proportional hazards or a stratified analysis may be better alternatives.

Familial Clustering of Staphylococcus aureus Bacteremia in First-Degree Relatives: A Danish Nationwide Cohort Study.

BACKGROUND: A genetic predisposition to Staphylococcus aureus bacteremia has been demonstrated in animals, suggesting that genetic differences might influence susceptibility to S aureus in humans. OBJECTIVE: To determine whether a history of S aureus bacteremia in first-degree relatives increases the rate of the disease, and whether this rate is affected by the type of family relationship (that is, parent or sibling) or by how the relative acquired the infection. DESIGN: Register-based nationwide cohort study (1992 to 2011). SETTING: Denmark. PARTICIPANTS: First-degree relatives (children or siblings) of patients previously hospitalized with S aureus bacteremia. MEASUREMENTS: Poisson regression models were used to calculate standardized incidence ratios (SIRs) of S aureus bacteremia, with the incidence rate in the population as a reference. RESULTS: 34 774 individuals (the exposed cohort) with a first-degree relative (index case patient) previously hospitalized with S aureus bacteremia were followed up for a median of 7.8 years (interquartile range, 3.6 to 13.0). A higher rate of S aureus bacteremia was observed among these first-degree relatives (SIR, 2.49 [95% CI, 1.95 to 3.19]) than in the background population. The estimate was significantly higher if the index case patient was a sibling (SIR, 5.01 [CI, 3.30 to 7.62]) than a parent (SIR, 1.96 [CI, 1.45 to 2.67]; interaction P < 0.0001). No interaction was observed regarding the sex of the first-degree relative (interaction P for parents = 0.85; interaction P for siblings = 0.92). Stratifying by disease acquisition revealed the highest rates in individuals exposed to index case patients with non-hospital-acquired infection. Few were infected with genetically identical bacteremia isolates. LIMITATION: The rarity of the outcome limited the number of variables in the multiple regression analysis, and whether nonsignificant interactions were true or caused by insufficient statistical power remains uncertain. CONCLUSION: A significant familial clustering of S aureus bacteremia was found, with the greatest relative rate of disease observed in individuals exposed to siblings with a history of the disease. PRIMARY FUNDING SOURCE: The Danish Heart Foundation and the Christian Larsen and Judge Ellen Larsen Foundation.

The Intracranial Distribution of Gliomas in Relation to Exposure From Mobile Phones: Analyses From the INTERPHONE Study.

When investigating the association between brain tumors and use of mobile telephones, accurate data on tumor position are essential, due to the highly localized absorption of energy in the human brain from the radio-frequency fields emitted. We used a point process model to investigate this association using information that included tumor localization data from the INTERPHONE Study (Australia, Canada, Denmark, Finland, France, Germany, Israel, Italy, Japan, New Zealand, Norway, Sweden, and the United Kingdom). Our main analysis included 792 regular mobile phone users diagnosed with a glioma between 2000 and 2004. Similar to earlier results, we found a statistically significant association between the intracranial distribution of gliomas and the self-reported location of the phone. When we accounted for the preferred side of the head not being exclusively used for all mobile phone calls, the results were similar. The association was independent of the cumulative call time and cumulative number of calls. However, our model used reported side of mobile phone use, which is potentially influenced by recall bias. The point process method provides an alternative to previously used epidemiologic research designs when one is including localization in the investigation of brain tumors and mobile phone use.

Misspecified poisson regression models for large-scale registry data: inference for 'large n and small p'.

Poisson regression is an important tool in register-based epidemiology where it is used to study the association between exposure variables and event rates. In this paper, we will discuss the situation with 'large n and small p', where n is the sample size and p is the number of available covariates. Specifically, we are concerned with modeling options when there are time-varying covariates that can have time-varying effects. One problem is that tests of the proportional hazards assumption, of no interactions between exposure and other observed variables, or of other modeling assumptions have large power due to the large sample size and will often indicate statistical significance even for numerically small deviations that are unimportant for the subject matter. Another problem is that information on important confounders may be unavailable. In practice, this situation may lead to simple working models that are then likely misspecified. To support and improve conclusions drawn from such models, we discuss methods for sensitivity analysis, for estimation of average exposure effects using aggregated data, and a semi-parametric bootstrap method to obtain robust standard errors. The methods are illustrated using data from the Danish national registries investigating the diabetes incidence for individuals treated with antipsychotics compared with the general unexposed population.

A three-dimensional point process model for the spatial distribution of disease occurrence in relation to an exposure source.

We study methods for how to include the spatial distribution of tumours when investigating the relation between brain tumours and the exposure from radio frequency electromagnetic fields caused by mobile phone use. Our suggested point process model is adapted from studies investigating spatial aggregation of a disease around a source of potential hazard in environmental epidemiology, where now the source is the preferred ear of each phone user. In this context, the spatial distribution is a distribution over a sample of patients rather than over multiple disease cases within one geographical area. We show how the distance relation between tumour and phone can be modelled nonparametrically and, with various parametric functions, how covariates can be included in the model and how to test for the effect of distance. To illustrate the models, we apply them to a subset of the data from the Interphone Study, a large multinational case-control study on the association between brain tumours and mobile phone use.

The effectiveness of structured personal care of type 2 diabetes on recurrent outcomes: a 19 year follow-up of the study Diabetes Care in General Practice (DCGP).

AIMS/HYPOTHESIS: The estimation of effect size in clinical trials commonly disregards recurrent outcomes. We investigated the effectiveness of a complex intervention on recurrent outcomes in patients with type 2 diabetes. METHODS: In the Diabetes Care in General Practice (DCGP) randomised controlled trial, 1,381 patients newly diagnosed with type 2 diabetes were randomised to 6 years of structured personal care or routine care (ClinicalTrials.gov NCT01074762). The trial had 19 years of registry-based follow-up and was analysed with Cox regression models. Repeated occurrences in the same patient of outcomes (any diabetes-related endpoint, myocardial infarction [MI], stroke, peripheral vascular disease and microvascular disease) were accounted for with the Wei, Lin and Weissfeld method. RESULTS: As previously shown, the intervention reduced the rates of first occurrence of both MI and any diabetes-related endpoint. However, for all outcomes, the HR for a second event showed a statistically non-significant tendency to be increased. We estimated a combined HR for all marginal failure times, regardless of whether they were first, second or later events. This showed that the intervention had no effect on the rate of any of the outcomes, including MI (HR 0.89, 95% CI 0.76, 1.05) and any diabetes-related endpoint (HR 0.98, 95% CI 0.87, 1.09). CONCLUSIONS/INTERPRETATION: In the DCGP study, a smaller proportion of patients who received structured care experienced a first occurrence of MI or any diabetes-related endpoint compared with patients who received routine care. However, the patients who received structured care tended to experience more recurrent outcomes, so the total outcome rate was not affected by the intervention.

Calibration plots for risk prediction models in the presence of competing risks.

A predicted risk of 17% can be called reliable if it can be expected that the event will occur to about 17 of 100 patients who all received a predicted risk of 17%. Statistical models can predict the absolute risk of an event such as cardiovascular death in the presence of competing risks such as death due to other causes. For personalized medicine and patient counseling, it is necessary to check that the model is calibrated in the sense that it provides reliable predictions for all subjects. There are three often encountered practical problems when the aim is to display or test if a risk prediction model is well calibrated. The first is lack of independent validation data, the second is right censoring, and the third is that when the risk scale is continuous, the estimation problem is as difficult as density estimation. To deal with these problems, we propose to estimate calibration curves for competing risks models based on jackknife pseudo-values that are combined with a nearest neighborhood smoother and a cross-validation approach to deal with all three problems.

Comparing predictions among competing risks models with time-dependent covariates.

Prediction of cumulative incidences is often a primary goal in clinical studies with several endpoints. We compare predictions among competing risks models with time-dependent covariates. For a series of landmark time points, we study the predictive accuracy of a multi-state regression model, where the time-dependent covariate represents an intermediate state, and two alternative landmark approaches. At each landmark time point, the prediction performance is measured as the t-year expected Brier score where pseudovalues are constructed in order to deal with right-censored event times. We apply the methods to data from a bone marrow transplant study where graft versus host disease is considered a time-dependent covariate for predicting relapse and death in remission.

Self-injury, suicidality and eating disorder symptoms in young adults following COVID-19 lockdowns in Denmark.

An aggravation in mental health during the COVID-19 lockdown has been suggested but the impact on self-injury, suicidality and eating disorders (EDs) are less elucidated. Using linear regression in different data set-ups that is longitudinal (n = 7,579) and repeated cross-sectional data (n = 24,625) from the Danish National Birth Cohort, we compared self-reported self-injury, suicidality and symptoms of EDs from before through different pandemic periods until spring 2021. The longitudinal data indicate a reduction in the proportion of self-injury in men (-3.2% points, 95% confidence interval (CI) = -4.3%; -2.2%, P < 0.001, d.f. = 2) and women (5.7% points, 95% CI = -6.6%; -4.8%, P < 0.001, d.f. = 2) and of suicide ideation in men (-3.0% points, 95% CI = -4.6%; -1.4%, P = 0.002, d.f. = 2) and women (-7.4% points, 95% CI = -8.7%; -6.0%, P < 0.001, d.f. = 2), as well as symptoms of EDs in women (-2.3% points, 95% CI = -3.2%; -1.4%, P < 0.001, d.f. = 2). For suicide attempt, indication of an increase was observed in men only (0.4% points, 95% CI = 0.1%; 0.7%, P = 0.019, d.f. = 2). In the repeated cross-sectional data, we observed no changes in any of the outcomes. Our findings provide no support for the increase in self-injury, suicidality and symptoms of EDs after the lockdowns. Key limitations are differential attrition and varying age in pre- and post-lockdown measures in the longitudinal data.

Single-institution long-term outcomes for patients receiving nonmyeloablative conditioning hematopoeitic cell transplantation for chronic lymphocytic leukemia and follicular lymphoma.

Non-myeloablative conditioning hematopoietic cell transplantation (NMC-HCT) has improved the treatment of chronic lymphocytic leukemia (CLL) and follicular lymphoma (FL). In a cohort of 85 patients (45 with CLL and 40 with FL), we observed 5-yr overall survival (OS) and progression-free survival (PFS) of 53% and 38% in the CLL group and 81% and 76% in the FL group. In the both the CLL group and the FL group, a strong trend toward better OS and PFS was observed among patients in complete remission (CR) at HCT. Within the FL group, sixteen patients had at one or more time points in their disease history had transformed FL. In contrast to the poor survival found in patients with transformed FL in previous studies, the 5-yr OS was almost identical in patients with transformed and non-transformed FL, 83% and 78%, respectively. In conclusion, our study supports that NMC-HCT is a safe and efficacious treatment that can provide long-term survival in elderly, heavily pretreated patients with FL and CLL. Especially patients with FL, and also transformed FL, seemed to have a great benefit of NMC-HCT, and CR at the time of HCT was an important prognostic factor.

Absolute risk regression for competing risks: interpretation, link functions, and prediction.

In survival analysis with competing risks, the transformation model allows different functions between the outcome and explanatory variables. However, the model's prediction accuracy and the interpretation of parameters may be sensitive to the choice of link function. We review the practical implications of different link functions for regression of the absolute risk (or cumulative incidence) of an event. Specifically, we consider models in which the regression coefficients ß have the following interpretation: The probability of dying from cause D during the next t years changes with a factor exp(ß) for a one unit change of the corresponding predictor variable, given fixed values for the other predictor variables. The models have a direct interpretation for the predictive ability of the risk factors. We propose some tools to justify the models in comparison with traditional approaches that combine a series of cause-specific Cox regression models or use the Fine-Gray model. We illustrate the methods with the use of bone marrow transplant data.

Competing risks and time-dependent covariates.

Time-dependent covariates are frequently encountered in regression analysis for event history data and competing risks. They are often essential predictors, which cannot be substituted by time-fixed covariates. This study briefly recalls the different types of time-dependent covariates, as classified by Kalbfleisch and Prentice [The Statistical Analysis of Failure Time Data, Wiley, New York, 2002] with the intent of clarifying their role and emphasizing the limitations in standard survival models and in the competing risks setting. If random (internal) time-dependent covariates are to be included in the modeling process, then it is still possible to estimate cause-specific hazards but prediction of the cumulative incidences and survival probabilities based on these is no longer feasible. This article aims at providing some possible strategies for dealing with these prediction problems. In a multi-state framework, a first approach uses internal covariates to define additional (intermediate) transient states in the competing risks model. Another approach is to apply the landmark analysis as described by van Houwelingen [Scandinavian Journal of Statistics 2007, 34, 70-85] in order to study cumulative incidences at different subintervals of the entire study period. The final strategy is to extend the competing risks model by considering all the possible combinations between internal covariate levels and cause-specific events as final states. In all of those proposals, it is possible to estimate the changes/differences of the cumulative risks associated with simple internal covariates. An illustrative example based on bone marrow transplant data is presented in order to compare the different methods.

Impact of chronic diseases on effect of breast cancer screening.

BACKGROUND: Although breast cancer screening reduces breast cancer mortality at the population level, subgroups of women may benefit differently. We investigated the impact of health status on the effect of breast cancer screening. METHODS: The study included 181 299 women invited in two population-based screening programs in Denmark and 1 526 446 control subjects, followed from April 1981 to December 2014. Poisson regressions were used to compare the observed breast cancer mortality rate in women invited to screening with the expected rate in the absence of screening among women with and without chronic diseases. Chronic diseases were defined as any diagnosis in the Charlson Comorbidity Index during 4 years before the first invitation to screening. RESULTS: Almost 10% of women had chronic diseases before first invitation to screening. Whereas we observed a reduction in breast cancer mortality following invitation to screening of 28% (95% CI, 20% to 35%) among women without chronic diseases, only a 7% (95% CI, -39% to 37%) reduction was seen for women with chronic diseases (P-value for interaction = .22). For participants, the reduction, corrected for selection bias, was 35% (95% CI 16% to 49%) for women without, and 4% (95% CI -146% to 62%) for women with chronic diseases (P-value for interaction = .43). CONCLUSION: Our data indicate a marginal effect of mammography screening on breast cancer mortality in women with chronic diseases. If our results are confirmed in other populations, the presence of chronic diseases will be an important factor to take into consideration in personalized screening.