Inverse probability weighted Cox regression for doubly truncated data

Activated phosphoinositide 3-kinase δ syndrome: Update from the ESID Registry and comparison with other autoimmune-lymphoproliferative inborn errors of immunity

BACKGROUND

Activated phosphoinositide-3-kinase δ syndrome (APDS) is an inborn error of immunity (IEI) with infection susceptibility and immune dysregulation, clinically overlapping with other conditions. Management depends on disease evolution, but predictors of severe disease are lacking.

OBJECTIVES

This study sought to report the extended spectrum of disease manifestations in APDS1 versus APDS2; compare these to CTLA4 deficiency, NFKB1 deficiency, and STAT3 gain-of-function (GOF) disease; and identify predictors of severity in APDS.

METHODS

Data was collected from the ESID (European Society for Immunodeficiencies)-APDS registry and was compared with published cohorts of the other IEIs.

RESULTS

The analysis of 170 patients with APDS outlines high penetrance and early onset of APDS compared to the other IEIs. The large clinical heterogeneity even in individuals with the same PIK3CD variant E1021K illustrates how poorly the genotype predicts the disease phenotype and course. The high clinical overlap between APDS and the other investigated IEIs suggests relevant pathophysiological convergence of the affected pathways. Preferentially affected organ systems indicate specific pathophysiology: bronchiectasis is typical of APDS1; interstitial lung disease and enteropathy are more common in STAT3 GOF and CTLA4 deficiency. Endocrinopathies are most frequent in STAT3 GOF, but growth impairment is also common, particularly in APDS2. Early clinical presentation is a risk factor for severe disease in APDS.

CONCLUSIONS

APDS illustrates how a single genetic variant can result in a diverse autoimmune-lymphoproliferative phenotype. Overlap with other IEIs is substantial. Some specific features distinguish APDS1 from APDS2. Early onset is a risk factor for severe disease course calling for specific treatment studies in younger patients.

Testing for an ignorable sampling bias under random double truncation

In clinical and epidemiological research doubly truncated data often appear. This is the case, for instance, when the data registry is formed by interval sampling. Double truncation generally induces a sampling bias on the target variable, so proper corrections of ordinary estimation and inference procedures must be used. Unfortunately, the nonparametric maximum likelihood estimator of a doubly truncated distribution has several drawbacks, like potential nonexistence and nonuniqueness issues, or large estimation variance. Interestingly, no correction for double truncation is needed when the sampling bias is ignorable, which may occur with interval sampling and other sampling designs. In such a case the ordinary empirical distribution function is a consistent and fully efficient estimator that generally brings remarkable variance improvements compared to the nonparametric maximum likelihood estimator. Thus, identification of such situations is critical for the simple and efficient estimation of the target distribution. In this article, we introduce for the first time formal testing procedures for the null hypothesis of ignorable sampling bias with doubly truncated data. The asymptotic properties of the proposed test statistic are investigated. A bootstrap algorithm to approximate the null distribution of the test in practice is introduced. The finite sample performance of the method is studied in simulated scenarios. Finally, applications to data on onset for childhood cancer and Parkinson's disease are given. Variance improvements in estimation are discussed and illustrated.

Cox regression with doubly truncated responses and time-dependent covariates: the impact of innovation on firm survival

The creation of new firms is an important incentive for the economic growth of a country, since it generates employment, it encourages the competition, and promotes innovation. In this work, we investigate the survival of Spanish firms which were created since 2001 and closed down between 2004 and 2012. The information was gathered from Technological Innovation Panel (PITEC), a survey with a focus the technological innovation in Spanish firms. In particular, a Cox regression model with time-dependent covariates was used in order to identify and quantify the determinants of the risk of exit for the firm. The selection bias due to the interval sampling for the firms was corrected by using methods for doubly truncated lifetimes. Interestingly, it is seen how the correction for the selection bias changes both the size and the statistical significance of the effects provided by standard Cox regression.

Estimating a time-to-event distribution from right-truncated data in an epidemic: A review of methods

Time-to-event data are right-truncated if only individuals who have experienced the event by a certain time can be included in the sample. For example, we may be interested in estimating the distribution of time from onset of disease symptoms to death and only have data on individuals who have died. This may be the case, for example, at the beginning of an epidemic. Right truncation causes the distribution of times to event in the sample to be biased towards shorter times compared to the population distribution, and appropriate statistical methods should be used to account for this bias. This article is a review of such methods, particularly in the context of an infectious disease epidemic, like COVID-19. We consider methods for estimating the marginal time-to-event distribution, and compare their efficiencies. (Non-)identifiability of the distribution is an important issue with right-truncated data, particularly at the beginning of an epidemic, and this is discussed in detail. We also review methods for estimating the effects of covariates on the time to event. An illustration of the application of many of these methods is provided, using data on individuals who had died with coronavirus disease by 5 April 2020.

Is a higher altitude associated with shorter survival among at-risk neonates?

INTRODUCTION

We hypothesize that high altitudes could have an adverse effect on neonatal health outcomes, especially among at-risk neonates. The current study aims to assess the association between higher altitudes on survival time among at-risk neonates.

METHODS

Retrospective survival analysis. Setting: Ecuadorian neonates who died at ≤28 days of life. Patients: We analyzed the nationwide dataset of neonatal deaths from the Surveillance System of Neonatal Mortality of the Ministry of Public Health of Ecuador, registered from 126 public and private health care facilities, between January 2014 to September 2017. Main outcome measures: We retrospectively reviewed 3016 patients. We performed a survival analysis by setting the survival time in days as the primary outcome and fixed and mixed-effects Cox proportional hazards models to estimate hazard ratios (HR) for each altitude stratum of each one of the health care facilities in which those neonates were attended, adjusting by individual variables (i.e., birth weight, gestational age at birth, Apgar scale at 5 minutes, and comorbidities); and contextual variables (i.e., administrative planning areas, type of health care facility, and level of care).

RESULTS

Altitudes of health care facilities ranging from 80 to <2500 m, 2500 to <2750m, and ≥2750 m were associated respectively with 20% (95% CI: 1% to 44%), 32% (95% CI:<1% to 79%) and 37% (95% CI: 8% to 75%) increased HR; compared with altitudes at <80 m.

CONCLUSION

Higher altitudes are independently associated with shorter survival time, as measured by days among at-risk neonates. Altitude should be considered when assessing the risk of having negative health outcomes during neonatal period.

Cox regression model under dependent truncation

Truncation is a statistical phenomenon that occurs in many time-to-event studies. For example, autopsy-confirmed studies of neurodegenerative diseases are subject to an inherent left and right truncation, also known as double truncation. When the goal is to study the effect of risk factors on survival, the standard Cox regression model cannot be used when the survival time is subject to truncation. Existing methods that adjust for both left and right truncation in the Cox regression model require independence between the survival times and truncation times, which may not be a reasonable assumption in practice. We propose an expectation-maximization algorithm to relax the independence assumption in the Cox regression model under left, right, or double truncation to an assumption of conditional independence on the observed covariates. The resulting regression coefficient estimators are consistent and asymptotically normal. We demonstrate through extensive simulations that the proposed estimator has little bias and has a similar or lower mean-squared error compared to existing estimators. We implement our approach to assess the effect of occupation on survival in subjects with autopsy-confirmed Alzheimer's disease.

Nonparametric estimation of the cumulative incidences of competing risks under double truncation

Registry data typically report incident cases within a certain calendar time interval. Such interval sampling induces double truncation on the incidence times, which may result in an observational bias. In this paper, we introduce nonparametric estimation for the cumulative incidences of competing risks when the incidence time is doubly truncated. Two different estimators are proposed depending on whether the truncation limits are independent of the competing events or not. The asymptotic properties of the estimators are established, and their finite sample performance is investigated through simulations. For illustration purposes, the estimators are applied to childhood cancer registry data, where the target population is peculiarly defined conditional on future cancer development. Then, in our application, the cumulative incidences inform on the distribution by age of the different types of cancer.

Inverse probability weighting methods for Cox regression with right-truncated data

Right-truncated data arise when observations are ascertained retrospectively, and only subjects who experience the event of interest by the time of sampling are selected. Such a selection scheme, without adjustment, leads to biased estimation of covariate effects in the Cox proportional hazards model. The existing methods for fitting the Cox model to right-truncated data, which are based on the maximization of the likelihood or solving estimating equations with respect to both the baseline hazard function and the covariate effects, are numerically challenging. We consider two alternative simple methods based on inverse probability weighting (IPW) estimating equations, which allow consistent estimation of covariate effects under a positivity assumption and avoid estimation of baseline hazards. We discuss problems of identifiability and consistency that arise when positivity does not hold and show that although the partial tests for null effects based on these IPW methods can be used in some settings even in the absence of positivity, they are not valid in general. We propose adjusted estimating equations that incorporate the probability of observation when it is known from external sources, which results in consistent estimation. We compare the methods in simulations and apply them to the analyses of human immunodeficiency virus latency.