Prognosis of cancer survivors: estimation based on differential equations.

We present a method for estimating several prognosis parameters for cancer survivors. The method utilizes the fact that these parameters solve differential equations driven by cumulative hazards. By expressing the parameters as solutions to differential equations, we develop generic estimators that are easy to implement with standard statistical software. We explicitly describe the estimators for prognosis parameters that are often employed in practice, but also for parameters that, to our knowledge, have not been used to evaluate prognosis. We then apply these parameters to assess the prognosis of five common cancers in Norway.

Causal inference in continuous time: an example on prostate cancer therapy.

In marginal structural models (MSMs), time is traditionally treated as a discrete parameter. In survival analysis on the other hand, we study processes that develop in continuous time. Therefore, Røysland (2011. A martingale approach to continuous-time marginal structural models. Bernoulli 17, 895-915) developed the continuous-time MSMs, along with continuous-time weights. The continuous-time weights are conceptually similar to the inverse probability weights that are used in discrete time MSMs. Here, we demonstrate that continuous-time MSMs may be used in practice. First, we briefly describe the causal model assumptions using counting process notation, and we suggest how causal effect estimates can be derived by calculating continuous-time weights. Then, we describe how additive hazard models can be used to find such effect estimates. Finally, we apply this strategy to compare medium to long-term differences between the two prostate cancer treatments radical prostatectomy and radiation therapy, using data from the Norwegian Cancer Registry. In contrast to the results of a naive analysis, we find that the marginal cumulative incidence of treatment failure is similar between the strategies, accounting for the competing risk of other death.

Time-dependent mediators in survival analysis: Modeling direct and indirect effects with the additive hazards model.

We discuss causal mediation analyses for survival data and propose a new approach based on the additive hazards model. The emphasis is on a dynamic point of view, that is, understanding how the direct and indirect effects develop over time. Hence, importantly, we allow for a time varying mediator. To define direct and indirect effects in such a longitudinal survival setting we take an interventional approach (Didelez, 2018) where treatment is separated into one aspect affecting the mediator and a different aspect affecting survival. In general, this leads to a version of the nonparametric g-formula (Robins, 1986). In the present paper, we demonstrate that combining the g-formula with the additive hazards model and a sequential linear model for the mediator process results in simple and interpretable expressions for direct and indirect effects in terms of relative survival as well as cumulative hazards. Our results generalize and formalize the method of dynamic path analysis (Fosen, Ferkingstad, Borgan, & Aalen, 2006; Strohmaier et al., 2015). An application to data from a clinical trial on blood pressure medication is given.

Intravenous Patient-controlled Analgesia Versus Thoracic Epidural Analgesia After Open Liver Surgery: A Prospective, Randomized, Controlled, Noninferiority Trial.

OBJECTIVE: We conducted a randomized, controlled, noninferiority trial to investigate if intravenous, multimodal, patient-controlled analgesia (IV-PCA) could be noninferior to multimodal thoracic epidural analgesia (TEA) in patients undergoing open liver surgery. SUMMARY BACKGROUND DATA: The increasing use of minimally invasive techniques and fast track protocols have questioned the position of epidural analgesia as the optimal method of pain management after abdominal surgery. METHODS: Patients operated with open liver resection between February 2012 and February 2016 were randomly assigned to receive either IV-PCA enhanced with ketorolac/diclofenac (IV-PCA, n = 66) or TEA (n = 77) within an enhanced recovery after surgery protocol. Noninferiority would be declared if the mean pain score on the numeric rating scale (NRS) for postoperative days (PODs) 0 to 5 in the IV-PCA group was no worse than the mean pain score in the TEA group by a margin of <1 point on an 11-point scale (0-10). RESULTS: The primary endpoint, mean NRS pain score was 1.7 in the IV-PCA group and 1.6 in the TEA group, establishing noninferiority. Pain scores were lower in the TEA group on PODs 0 and 1, but higher or equal on PODs 2 and 5. Postoperative hospital stay was significantly shorter for patients in the IV-PCA group (74 vs 104 h, P < 0.001). The total opioid consumption during the first 3 days was significantly lower in the IV-PCA group. CONCLUSIONS: IV-PCA was noninferior to TEA for the treatment of postoperative pain in patients undergoing open liver resection.

MetaMass, a tool for meta-analysis of subcellular proteomics data.

We report a tool for the analysis of subcellular proteomics data, called MetaMass, based on the use of standardized lists of subcellular markers. We analyzed data from 11 studies using MetaMass, mapping the subcellular location of 5,970 proteins. Our analysis revealed large variations in the performance of subcellular fractionation protocols as well as systematic biases in protein annotation databases. The Excel and R versions of MetaMass should enhance transparency and reproducibility in subcellular proteomics.

Sufficient Cause Interaction for Time-to-event Outcomes.

Methods to assess sufficient cause interactions are well developed for binary outcomes. We extend these methods to handle time-to-event outcomes, which occur frequently in medicine and epidemiology. Based on theory for marginal structural models in continuous time, we show how to assess sufficient cause interaction nonparametrically, allowing for censoring and competing risks. We apply the method to study interaction between intensive blood pressure therapy and statin treatment on all-cause mortality.

On null hypotheses in survival analysis.

The conventional nonparametric tests in survival analysis, such as the log-rank test, assess the null hypothesis that the hazards are equal at all times. However, hazards are hard to interpret causally, and other null hypotheses are more relevant in many scenarios with survival outcomes. To allow for a wider range of null hypotheses, we present a generic approach to define test statistics. This approach utilizes the fact that a wide range of common parameters in survival analysis can be expressed as solutions of differential equations. Thereby, we can test hypotheses based on survival parameters that solve differential equations driven by cumulative hazards, and it is easy to implement the tests on a computer. We present simulations, suggesting that our tests perform well for several hypotheses in a range of scenarios. As an illustration, we apply our tests to evaluate the effect of adjuvant chemotherapies in patients with colon cancer, using data from a randomized controlled trial.

Dynamic susceptibility contrast and diffusion MR imaging identify oligodendroglioma as defined by the 2016 WHO classification for brain tumors: histogram analysis approach.

PURPOSE: According to the revised World Health Organization (WHO) Classification of Tumors of the Central Nervous System (CNS) of 2016, oligodendrogliomas are now defined primarily by a specific molecular signature (presence of IDH mutation and 1p19q codeletion). The purpose of our study was to assess the value of dynamic susceptibility contrast MR imaging (DSC-MRI) and diffusion-weighted imaging (DWI) to characterize oligodendrogliomas and to distinguish them from astrocytomas. METHODS: Seventy-one adult patients with untreated WHO grade II and grade III diffuse infiltrating gliomas and known 1p/19q codeletion status were retrospectively identified and analyzed using relative cerebral blood volume (rCBV) and apparent diffusion coefficient (ADC) maps based on whole-tumor volume histograms. The Mann-Whitney U test and logistic regression were used to assess the ability of rCBV and ADC to differentiate between oligodendrogliomas and astrocytomas both independently, but also related to the WHO grade. Prediction performance was evaluated in leave-one-out cross-validation (LOOCV). RESULTS: Oligodendrogliomas showed significantly higher microvascularity (higher rCBVMean ≥ 0.80, p = 0.013) and higher vascular heterogeneity (lower rCBVPeak ≤ 0.044, p = 0.015) than astrocytomas. Diffuse gliomas with higher cellular density (lower ADCMean ≤ 1094 × 10-6 mm2/s, p = 0.009) were more likely to be oligodendrogliomas than astrocytomas. Histogram analysis of rCBV and ADC was able to differentiate between diffuse astrocytomas (WHO grade II) and anaplastic astrocytomas (WHO grade III). CONCLUSION: Histogram-derived rCBV and ADC parameter may be used as biomarkers for identification of oligodendrogliomas and may help characterize diffuse gliomas based upon their genetic characteristics.

The additive hazard estimator is consistent for continuous-time marginal structural models.

Marginal structural models (MSMs) allow for causal analysis of longitudinal data. The standard MSM is based on discrete time models, but the continuous-time MSM is a conceptually appealing alternative for survival analysis. In applied analyses, it is often assumed that the theoretical treatment weights are known, but these weights are usually unknown and must be estimated from the data. Here we provide a sufficient condition for continuous-time MSM to be consistent even when the weights are estimated, and we show how additive hazard models can be used to estimate such weights. Our results suggest that continuous-time weights perform better than IPTW when the underlying process is continuous. Furthermore, we may wish to transform effect estimates of hazards to other scales that are easier to interpret causally. We show that a general transformation strategy can be used on weighted cumulative hazard estimates to obtain a range of other parameters in survival analysis, and explain how this strategy can be applied on data using our R packages ahw and transform.hazards.

Exploring Selection Bias by Causal Frailty Models: The Magnitude Matters.

Counter-intuitive associations appear frequently in epidemiology, and these results are often debated. In particular, several scenarios are characterized by a general risk factor that appears protective in particular subpopulations, for example, individuals suffering from a specific disease. However, the associations are not necessarily representing causal effects. Selection bias due to conditioning on a collider may often be involved, and causal graphs are widely used to highlight such biases. These graphs, however, are qualitative, and they do not provide information on the real life relevance of a spurious association. Quantitative estimates of such associations can be obtained from simple statistical models. In this study, we present several paradoxical associations that occur in epidemiology, and we explore these associations in a causal, frailty framework. By using frailty models, we are able to put numbers on spurious effects that often are neglected in epidemiology. We discuss several counter-intuitive findings that have been reported in real life analyses, and we present calculations that may expand the understanding of these associations. In particular, we derive novel expressions to explain the magnitude of bias in index-event studies.

Dynamic path analysis - a useful tool to investigate mediation processes in clinical survival trials.

When it comes to clinical survival trials, regulatory restrictions usually require the application of methods that solely utilize baseline covariates and the intention-to-treat principle. Thereby, much potentially useful information is lost, as collection of time-to-event data often goes hand in hand with collection of information on biomarkers and other internal time-dependent covariates. However, there are tools to incorporate information from repeated measurements in a useful manner that can help to shed more light on the underlying treatment mechanisms. We consider dynamic path analysis, a model for mediation analysis in the presence of a time-to-event outcome and time-dependent covariates to investigate direct and indirect effects in a study of different lipid-lowering treatments in patients with previous myocardial infarctions. Further, we address the question whether survival in itself may produce associations between the treatment and the mediator in dynamic path analysis and give an argument that because of linearity of the assumed additive hazard model, this is not the case. We further elaborate on our view that, when studying mediation, we are actually dealing with underlying processes rather than single variables measured only once during the study period. This becomes apparent in results from various models applied to the study of lipid-lowering treatments as well as our additionally conducted simulation study, where we clearly observe that discarding information on repeated measurements can lead to potentially erroneous conclusions.

Does Cox analysis of a randomized survival study yield a causal treatment effect?

Statistical methods for survival analysis play a central role in the assessment of treatment effects in randomized clinical trials in cardiovascular disease, cancer, and many other fields. The most common approach to analysis involves fitting a Cox regression model including a treatment indicator, and basing inference on the large sample properties of the regression coefficient estimator. Despite the fact that treatment assignment is randomized, the hazard ratio is not a quantity which admits a causal interpretation in the case of unmodelled heterogeneity. This problem arises because the risk sets beyond the first event time are comprised of the subset of individuals who have not previously failed. The balance in the distribution of potential confounders between treatment arms is lost by this implicit conditioning, whether or not censoring is present. Thus while the Cox model may be used as a basis for valid tests of the null hypotheses of no treatment effect if robust variance estimates are used, modeling frameworks more compatible with causal reasoning may be preferrable in general for estimation.

A multi-state model to estimate incidence of heroin use.

BACKGROUND: Existing incidence estimates of heroin use are usually based on one information source. This study aims to incorporate more sources to estimate heroin use incidence trends in Spain between 1971 and 2005. METHODS: A multi-state model was constructed, whereby the initial state "heroin consumer" is followed by transition to either "admitted to first treatment" or to "left heroin use" (i.e. permanent cessation or death). Heroin use incidence and probabilities of entering first treatment ever were estimated following a back-calculation approach. RESULTS: The highest heroin use incidence rates in Spain, around 1.5 per 1,000 inhabitants aged 10-44, occurred between 1985 and 1990; subdividing by route of administration reveals higher incidences of injection between 1980 and 1985 (a mean of 0.62 per 1.000) and a peak for non-injectors in 1990 (0.867 per 1,000). CONCLUSIONS: A simple conceptual model for heroin users' trajectories related to treatment admission, provided a broader view of the historical trend of heroin use incidence in Spain.

Long-Term Outcomes of Invasive vs Conservative Strategies for Older Patients With Non-ST-Segment Elevation Acute Coronary Syndromes.

BACKGROUND: Non-ST-segment elevation acute coronary syndrome (NSTE-ACS) is a frequent cause of hospital admission in older people, but clinical trials targeting this population are scarce. OBJECTIVES: The After Eighty Study assessed the effect of an invasive vs a conservative treatment strategy in a very old population with NSTE-ACS. METHODS: Between 2010 and 2014, the investigators randomized 457 patients with NSTE-ACS aged ≥80 years (mean age 85 years) to an invasive strategy involving early coronary angiography with immediate evaluation for revascularization and optimal medical therapy or to a conservative strategy (ie, optimal medical therapy). The primary endpoint was a composite of myocardial infarction, need for urgent revascularization, stroke, and death. The long-term outcomes are presented. RESULTS: After a median follow up of 5.3 years, the invasive strategy was superior to the conservative strategy in the reduction of the primary endpoint (incidence rate ratio: 0.76; 95% CI: 0.63-0.93; P = 0.0057). The invasive strategy demonstrated a significant gain in event-free survival of 276 days (95% CI: 151-400 days; P = 0.0001) at 5 years and 337 days (95% CI: 123-550 days; P = 0.0001) at 10 years. These results were consistent across subgroups of patients with respect to major cardiovascular prognostic factors. CONCLUSIONS: In patients aged ≥80 years with NSTE-ACS, the invasive strategy was superior to the conservative strategy in the reduction of composite events and demonstrated a significant gain in event-free survival. (The After Eighty Study: a randomized controlled trial; NCT01255540).

Cytology and human papillomavirus testing 6 to 12 months after ASCUS or LSIL cytology in organized screening to predict high-grade cervical neoplasia between screening rounds.

We carried out a prospective study comparing the performance of human papillomavirus (HPV) E6/E7 mRNA (PreTect HPV-Proofer; NorChip, Klokkarstua, Norway) and DNA (Amplicor HPV test; Roche Diagnostics, Basel, Switzerland) triage testing of women 6 to 12 months after atypical-squamous-cells-of-undetermined-significance (ASCUS) or low-grade-squamous-intraepithelial-lesion (LSIL) cytology in organized screening to predict high-grade cervical intraepithelial neoplasia of grade 2 or worse (CIN2+) between screening rounds. Between January 2005 and April 2008, 692 study women with screening-detected ASCUS/LSIL cytology 6 to 12 months earlier returned for HPV mRNA and DNA testing and repeat cytology. The median follow-up time was 3 years, using existing health care facilities. Follow-up test results were available for 625 women. Of the 145 CIN2+ cases detected during the study period, 95 (65.5%) were HPV mRNA positive 6 to 12 months after screening-detected ASCUS/LSIL, 44 (30.4%) were HPV mRNA negative, and 6 (4.1%) were invalid. The corresponding HPV DNA results were 139 (95.9%), 5 (3.4%), and 1 (0.7%), respectively. The cumulative incidences of CIN2+ 3 years after a negative HPV mRNA and DNA test were 10.3% (95% confidence interval [CI], 7.2 to 13.3%) and 1.8% (95% CI, 0.0 to 3.6%), respectively. The cumulative incidences of CIN2+ 3 years after positive HPV mRNA and DNA tests were 52.8% (95% CI, 40.1 to 60.1%) and 41.3% (95% CI, 35.5 to 46.6%), respectively. In conclusion, both positive HPV mRNA and DNA test results have a high enough long-term prediction of CIN2+ risk to consider referral to colposcopy as good practice when performed in delayed triage of women with ASCUS/LSIL cytology. In addition, the low CIN2+ risk among women with a negative Amplicor HPV test in our study confirms its safe use in a clinical setting.

A Comorbidity Index and Pretransplant Physical Status Predict Survival in Older Kidney Transplant Recipients: A National Prospective Study.

Kidney transplantation (KT) is considered the best treatment for end-stage kidney disease (ESKD). In the increasing elderly ESKD population, KT should be reserved for carefully selected candidates who are expected to experience favorable outcomes. We aimed to prospectively evaluate pretransplant recipient factors that may predict patient survival and can eventually guide therapeutic decisions in elderly with ESKD. Methods: Recipient factors were evaluated in KT candidates aged ≥65 y. Comorbidity was assessed at waitlisting according to the Liu comorbidity index (LCI). Health-related quality of life outcomes were measured using the Kidney Disease Quality of Life Short Form, version 1.3. The Cox proportional hazard regression was used to evaluate predictors of patient survival. Results: We included 192 recipients, with a mean age of 72.1 (4.1) y, who were transplanted with kidneys from deceased brain-dead donors. During a median observation period of 4.6 (3.2-6.3) y, 66 recipients died. Elevated LCI consistently predicted poor patient survival. In recipients with LCI ≥4, dialysis >2 y comprised a 2.5-fold increase in mortality risk compared with recipients on dialysis ≤2 y. Self-reported pretransplant physical function was also proven to be a significant positive predictor of survival. Conclusion: The implementation of LCI and a physical function score during the evaluation of older kidney transplant candidates may improve the selection and thereby optimize posttransplant outcomes.

The Risk of Benign Paroxysmal Positional Vertigo After Head Trauma.

OBJECTIVES: Head trauma may cause dislodgement of otoconia and development of benign paroxysmal positional vertigo (BPPV). The risk of developing BPPV is expected to be highest shortly after the trauma, then decrease and approach the risk seen in the general population. The aim of this study was to estimate the risk-time curve of BPPV development after head trauma. STUDY DESIGN: Prospective observational study. METHODS: Patients with minimal, mild, or moderate head trauma treated at the Department of Neurosurgery or the Department of Orthopedic Emergency at Oslo University Hospital, were interviewed and examined for BPPV using the Dix-Hallpike and supine roll maneuvers. BPPV was diagnosed according to the International diagnostic criteria of the Bárány Society. Telephone interviews were conducted at 2, 6, and 12 weeks after the first examination. RESULTS: Out of 117 patients, 21% developed traumatic BPPV within 3 months after the trauma. The corresponding numbers were 12% with minimal trauma, 24% with mild, and 40% with moderate trauma. The difference in prevalence between the groups was significant (P = .018). During the first 4 weeks after the trauma, it was observed 20, 3, 0, and 1 BPPV onsets, respectively. No BPPV cases were seen for the remainder of the 3-month follow-up. CONCLUSION: The risk of developing BPPV after minimal-to-moderate head trauma is considerable and related to trauma severity. Most cases occur within few days after the trauma, but any BPPV occurring within the first 2 weeks after head trauma are likely due to the traumatic event. LEVEL OF EVIDENCE: 3 Laryngoscope, 132:443-448, 2022.

Analyzing direct and indirect effects of treatment using dynamic path analysis applied to data from the Swiss HIV Cohort Study.

When applying survival analysis, such as Cox regression, to data from major clinical trials or other studies, often only baseline covariates are used. This is typically the case even if updated covariates are available throughout the observation period, which leaves large amounts of information unused. The main reason for this is that such time-dependent covariates often are internal to the disease process, as they are influenced by treatment, and therefore lead to confounded estimates of the treatment effect. There are, however, methods to exploit such covariate information in a useful way. We study the method of dynamic path analysis applied to data from the Swiss HIV Cohort Study. To adjust for time-dependent confounding between treatment and the outcome 'AIDS or death', we carried out the analysis on a sequence of mimicked randomized trials constructed from the original cohort data. To analyze these trials together, regular dynamic path analysis is extended to a composite analysis of weighted dynamic path models. Results using a simple path model, with one indirect effect mediated through current HIV-1 RNA level, show that most or all of the total effect go through HIV-1 RNA for the first 4 years. A similar model, but with CD4 level as mediating variable, shows a weaker indirect effect, but the results are in the same direction. There are many reasons to be cautious when drawing conclusions from estimates of direct and indirect effects. Dynamic path analysis is however a useful tool to explore underlying processes, which are ignored in regular analyses.

A sequential Cox approach for estimating the causal effect of treatment in the presence of time-dependent confounding applied to data from the Swiss HIV Cohort Study.

When estimating the effect of treatment on HIV using data from observational studies, standard methods may produce biased estimates due to the presence of time-dependent confounders. Such confounding can be present when a covariate, affected by past exposure, is both a predictor of the future exposure and the outcome. One example is the CD4 cell count, being a marker for disease progression for HIV patients, but also a marker for treatment initiation and influenced by treatment. Fitting a marginal structural model (MSM) using inverse probability weights is one way to give appropriate adjustment for this type of confounding. In this paper we study a simple and intuitive approach to estimate similar treatment effects, using observational data to mimic several randomized controlled trials. Each 'trial' is constructed based on individuals starting treatment in a certain time interval. An overall effect estimate for all such trials is found using composite likelihood inference. The method offers an alternative to the use of inverse probability of treatment weights, which is unstable in certain situations. The estimated parameter is not identical to the one of an MSM, it is conditioned on covariate values at the start of each mimicked trial. This allows the study of questions that are not that easily addressed fitting an MSM. The analysis can be performed as a stratified weighted Cox analysis on the joint data set of all the constructed trials, where each trial is one stratum. The model is applied to data from the Swiss HIV cohort study.

Recurrent events and the exploding Cox model.

Counting process models have played an important role in survival and event history analysis for more than 30 years. Nevertheless, almost all models that are being used have a very simple structure. Analyzing recurrent events invites the application of more complex models with dynamic covariates. We discuss how to define valid models in such a setting. One has to check carefully that a suggested model is well defined as a stochastic process. We give conditions for this to hold. Some detailed discussion is presented in relation to a Cox type model, where the exponential structure combined with feedback lead to an exploding model. In general, counting process models with dynamic covariates can be formulated to avoid explosions. In particular, models with a linear feedback structure do not explode, making them useful tools in general modeling of recurrent events.