Variance Estimation Research Articles

Impact of Quitline Services on Tobacco Cessation: An Application of Modern Epidemiological Methods.

This study investigated the effectiveness of quitline service intensity (high vs. low) on past 30-day tobacco abstinence at 7-months follow-up, using observational data from the Oklahoma Tobacco Helpline (OTH) between April 2020 and December 2021. To assess the impact of loss to follow-up and non-random treatment assignment, we fit the parameters of a marginal structural model to estimate inverse probability weights for censoring (IPCW) and treatment (IPTW) and combined (IPCTW). The Risk Ratio (RR) was estimated using modified Poisson regression with robust variance estimator. Of the 4,695 individuals included in the study, 64% received high-intensity cessation services, and 53% were lost to follow-up. Using the conventional complete case analysis (responders only), high-intensity cessation services were associated with abstinence (RR=1.18; 95 CI: 1.04, 1.34). The effect estimate was attenuated after accounting for censoring (RR=1.14; 95% CI: 1.00, 1.30). After adjusting for both baseline confounding and selection bias via IPTCW, high-intensity cessation services were associated with 1.23 times (95% CI: 1.08, 1.41) the probability of abstinence compared to low-intensity services. Despite relatively high loss to follow-up, accounting for selection bias and confounding did not notably impact quit rates or the relationship between intensity of quitline services and tobacco cessation among OTH participants.

Variance Feedback Drift Detection Method for Evolving Data Streams Mining

Learning from changing data streams is one of the important tasks of data mining. The phenomenon of the underlying distribution of data streams changing over time is called concept drift. In classification decision-making, the occurrence of concept drift will greatly affect the classification efficiency of the original classifier, that is, the old decision-making model is not suitable for the new data environment. Therefore, dealing with concept drift from changing data streams is crucial to guarantee classifier performance. Currently, most concept drift detection methods apply the same detection strategy to different data streams, with little attention to the uniqueness of each data stream. This limits the adaptability of drift detectors to different environments. In our research, we designed a unique solution to address this issue. First, we proposed a variance estimation strategy and a variance feedback strategy to characterize the data stream’s characteristics through variance. Based on this variance, we developed personalized drift detection schemes for different data streams, thereby enhancing the adaptability of drift detection in various environments. We conducted experiments on data streams with various types of drifts. The experimental results show that our algorithm achieves the best average ranking for accuracy on the synthetic dataset, with an overall ranking 1.12 to 1.5 higher than the next-best algorithm. In comparison with algorithms using the same tests, our method improves the ranking by 3 to 3.5 for the Hoeffding test and by 1.12 to 2.25 for the McDiarmid test. In addition, they achieve a good balance between detection delay and false positive rates. Finally, our algorithm ranks higher than existing drift detection methods across the four key metrics of accuracy, CPU time, false positives, and detection delay, meeting our expectations.

Hyperalgesia in Patients With a History of Opioid Use Disorder

Short-term and long-term opioid treatment have been associated with increased pain sensitivity (ie, opioid-induced hyperalgesia). Treatment of opioid use disorder (OUD) mainly involves maintenance with methadone and buprenorphine, and observations of heightened cold pain sensitivity among patients are often considered evidence of opioid-induced hyperalgesia. To critically examine the evidence that hyperalgesia in patients with OUD is related to opioid use. Web of Science, PubMed, and Embase between March 1, 2023, and April 12, 2024, were searched. Studies assessing cold pressor test (CPT) pain responses during treatment seeking, pharmacological treatment, or abstinence in patients with OUD history were included. Multilevel random-effects models with robust variance estimation were used for all analyses. Study quality was rated with the JBI checklist. Funnel plots and Egger regression tests were used to assess reporting bias. Main outcomes were pain threshold, tolerance, and intensity in patients and healthy controls, and unstandardized, standardized (Hedges g), and percentage differences (%Δ) in these measures between patients and controls. The association between pain sensitivity and opioid tolerance, withdrawal, and abstinence indices was tested with meta-regression. Thirty-nine studies (1385 patients, 741 controls) met the inclusion criteria. Most studies reported CPT data on patients undergoing opioid agonist treatment. These patients had a mean 2- to 3-seconds lower pain threshold (95% CI, -4 to -1; t test P = .01; %Δ, -22%; g = -0.5) and 29-seconds lower pain tolerance (95% CI, -39 to -18; t test P < .001; %Δ, -52%; g = -0.9) than controls. Egger tests suggested that these differences may be overestimated. There were some concerns of bias due to inadequate sample matching and participant dropout. Meta-regressions yielded no clear support for hyperalgesia being opioid related. Patients receiving opioid agonist treatment for OUD are hypersensitive to cold pain. It remains unclear whether hyperalgesia develops prior to, independent of, or as a result of long-term opioid treatment. Regardless, future studies should investigate the impact of hyperalgesia on patients' well-being and treatment outcomes.

Most meta-analyses in oral health do not have conclusive and robust results

ObjectivesIn meta-analyses with few studies, between-study heterogeneity is poorly estimated. The Hartung and Knapp (HK) correction and the prediction intervals can account for the uncertainty in estimating heterogeneity and the range of effect sizes we may encounter in future trials, respectively. The aim of this study was to assess the reported use of the HK correction in oral health meta-analyses and to compare the published reported results and interpretation i) to those calculated using eight heterogeneity estimators and the HK adjustment ii) and to the prediction intervals (PIs). MethodsWe sourced systematic reviews (SRs) published between 2021 and 2023 in eighteen leading specialty and general dental journals. We extracted study characteristics at the SR and meta-analysis level and re-analyzed the selected meta-analyses via the random-effects model and eight heterogeneity estimators, with and without the HK correction. For each meta-analysis, we re-calculated the overall estimate, the P-value, the 95 % confidence interval (CI) and the PI. ResultsWe analysed 292 meta-analyses. The median number of primary studies included in meta-analysis was 8 (interquartile range [IQR] = [5.75–15] range: 3–121). Only 3/292 meta-analyses used the HK adjustment and 12/292 reported PIs. The percentage of statistically significant results that became non-significant varied across the heterogeneity estimators (7.45 %- 16.59 %). Based on the PIs, >60 % of meta-analyses with statistically significant results are likely to change in the future and >40 % of the PIs included the opposite pooled effect. ConclusionsThe precision and statistical significance of the pooled estimates from meta-analyses with at least three studies is sensitive to the HK correction, the heterogeneity variance estimator, and the PIs. Clinical SignificanceUncertainty in meta-analyses estimates should be considered especially when a small number of trials is available or vary notably in their precision. Misinterpretation of the summary results can lead to ineffective interventions being applied in clinical practice.

Robust variance estimators in application to segmentation of measurement data distorted by impulsive and non-Gaussian noise

The paper algorithmizes the problem of regime change point identification for data measured in a system exhibiting impulsive behaviors. This is a fundamental challenge for annotation of measurement data, relevant, e.g., for designing data-driven autonomous systems. The contribution consists in formulation of an offline robust methodology based on the classical approach for structural break detection. The problem of data segmentation for the changing scale is solved as a process variable sensitive to the occurrence of a critical event in a reorganizing physical system. The advantage is that this approach does not require the existence of a variance of the data distribution. Efficiency has been evaluated for simulated data from two distributions and for real-world data sets measured in financial, mechanical, and medical systems. Simulation studies show that in the most challenging case, the error mean absolute in estimating the regime change is 20 times lower for the robust approach compared to the classical approach.

Model-assisted estimation of domain totals, areas, and densities in two-stage sample survey designs

Model-assisted, two-stage forest survey sampling designs provide a means to combine airborne remote sensing data, collected in a sampling mode, with field plot data to increase the precision of national forest inventory estimates, while maintaining important properties of design-based inventories, such as unbiased estimation and quantification of uncertainty. In this study, we present a comprehensive set of model-assisted estimators for domain-level attributes in a two-stage sampling design, including new estimators for densities, and compare the performance of these estimators with standard poststratified estimators. Simulation was used to assess the statistical properties (bias, variability) of these estimators, with both simple random and systematic sampling configurations, and indicated that (1) all estimators were generally unbiased and (2) the use of lidar in a sampling mode increased the precision of the estimators at all assessed field sampling intensities, with particularly marked increases in precision at lower field sampling intensities. Variance estimators are generally unbiased for model-assisted estimators without poststratification, while variance estimators for model-assisted estimators with poststratification were increasingly biased as field sampling intensity decreased. In general, these results indicate that airborne remote sensing data, collected as an intermediate level of sampling, can be used to increase the efficiency of national forest inventories in remote regions.

Cognitive expertise in esport experts: a three-level model meta-analysis.

The cognitive expertise of experts has been an intriguing theme; there has been rapid growth in cognitive research related to esports. Given the close association between esports activities and cognition, esports holds promise in offering new perspectives for understanding cognitive expertise. This meta-analysis aims at quantitatively delineating the cognitive disparities between esports experts and amateurs. The expert group comprised professional video game players and high-ranking players (top 1%), while amateurs were assigned to the control group. Research studies published between January 2000 and December 2023 were systematically searched in databases. A three-level model with cluster-robust variance estimation was used to calculate the overall effect size. The moderating variables included professional level, cognitive abilities, dependent variable type, game genre, gender and age. A total of 15 studies containing 142 effect sizes and 1085 participants were included in this meta-analysis. The results indicated that, compared to amateurs, video game experts demonstrated superior cognitive abilities with a small effect size (Hedges' g = 0.373, 95% CI [0.055-0.691], p=.012). The differences between experts and amateur players mainly manifest in spatial cognition and attention. Sensitivity analysis, risk of bias, and publication bias results indicated the reliability of these findings. This meta-analysis confirms that esports experts possess superior cognitive abilities compared to amateurs, particularly in aspects of spatial cognition and attention. These can provide an effective reference for future selection and training in esports.

Improving estimation efficiency of case-cohort studies with interval-censored failure time data.

The case-cohort design is a commonly used cost-effective sampling strategy for large cohort studies, where some covariates are expensive to measure or obtain. In this paper, we consider regression analysis under a case-cohort study with interval-censored failure time data, where the failure time is only known to fall within an interval instead of being exactly observed. A common approach to analyzing data from a case-cohort study is the inverse probability weighting approach, where only subjects in the case-cohort sample are used in estimation, and the subjects are weighted based on the probability of inclusion into the case-cohort sample. This approach, though consistent, is generally inefficient as it does not incorporate information outside the case-cohort sample. To improve efficiency, we first develop a sieve maximum weighted likelihood estimator under the Cox model based on the case-cohort sample and then propose a procedure to update this estimator by using information in the full cohort. We show that the update estimator is consistent, asymptotically normal, and at least as efficient asthe original estimator. The proposed method can flexibly incorporate auxiliary variables to improve estimation efficiency. A weighted bootstrap procedure is employed for variance estimation. Simulation results indicate that the proposed method works well in practical situations. An application to a Phase 3 HIV vaccine efficacy trial is provided for illustration.

Estimation of Additive and Dominance Genetic Variances for Growth and Multiple Stress at Different Ages in Pacific White Shrimp Litopenaeus vannamei

AbstractThis study aimed to estimate the additive and dominance genetic variance in growth and multiple‐stress tolerance traits in 7‐week‐old and 15‐week‐old Pacific white shrimp Litopenaeus vannamei. Four different animal models were studied by including all or different subsets of the following effects: additive genetic effects (A), additive genetic and common environmental effects (A + C), additive genetic and dominance effects (A + D), and additive, common environmental, and dominance effects (A + D + C). Variance components were estimated using the average information restricted maximum likelihood method. In general, estimates of additive genetic variance were inflated under the simple model (A) and decreased remarkably under the more complex models (A + C, A + D, and A + D + C). The genetic parameters of two‐stage (7‐week and 15‐week shrimp) growth and multiple‐stress tolerance traits were more suitable for estimation using the A + C model. The additive effects (0.311–0.754) of seven traits in 7‐week shrimp were greater than the dominance effects (4.950 × 10−7 to 0.201), whereas the additive effects of the same seven traits in adult shrimp ranged from 7.712 × 10−8 to 0.468 and the dominance effects ranged from 0.074 to 0.577. Except for survival time, carapace length, and carapace width, the additive effects of the other traits were smaller than the corresponding dominance effects. Thus, better genetic improvement of 7‐week and 15‐week shrimp growth and multiple‐stress tolerance can be obtained with selective breeding than with crossbreeding and better genetic improvement of 7‐week shrimp growth traits can be obtained with crossbreeding than with selective breeding. Our study further enriches the database for enhancing growth and stress resistance in Pacific white shrimp and provides reference information for growth improvement and multiple‐stress resistance breeding.

Incidence and Risk Factors of Refeeding Syndrome in Preterm Infants.

This study aimed to evaluate the incidence and risk factors associated with refeeding syndrome (RFS) in preterm infants (≤32 weeks gestational age) during their first week of life. Infants (gestational age ≤ 32 weeks; birth weight < 1500 g) who were admitted to the neonatal intensive care unit (NICU), level III, and received parenteral nutrition between January 2015 and April 2024 were retrospectively evaluated. Modified log-Poisson regression with generalized linear models and a robust variance estimator was applied to adjust the relative risk of risk factors. Of the 760 infants identified, 289 (38%) developed RFS. In the multivariable regression analysis, male, intraventricular hemorrhage (IVH), and sodium phosphate significantly affected RFS. Male infants had significantly increased RFS risk (aRR1.31; 95% CI 1.08-1.59). The RFS risk was significantly higher in infants with IVH (aRR 1.71; 95% CI 1.27-2.13). However, infants who received higher sodium phosphate in their first week of life had significantly lower RFS risk (aRR 0.67; 95% 0.47-0.98). This study revealed a notable incidence of RFS among preterm infants aged ≤32 gestational weeks, with sex, IVH, and low sodium phosphate as significant risk factors. Refined RFS diagnostic criteria and targeted interventions are needed for optimal management.

Can supervised deep learning architecture outperform autoencoders in building propensity score models for matching?

PurposePropensity score matching is vital in epidemiological studies using observational data, yet its estimates relies on correct model-specification. This study assesses supervised deep learning models and unsupervised autoencoders for propensity score estimation, comparing them with traditional methods for bias and variance accuracy in treatment effect estimations.MethodsUtilizing a plasmode simulation based on the Right Heart Catheterization dataset, under a variety of settings, we evaluated (1) a supervised deep learning architecture and (2) an unsupervised autoencoder, alongside two traditional methods: logistic regression and a spline-based method in estimating propensity scores for matching. Performance metrics included bias, standard errors, and coverage probability. The analysis was also extended to real-world data, with estimates compared to those obtained via a double robust approach.ResultsThe analysis revealed that supervised deep learning models outperformed unsupervised autoencoders in variance estimation while maintaining comparable levels of bias. These results were supported by analyses of real-world data, where the supervised model’s estimates closely matched those derived from conventional methods. Additionally, deep learning models performed well compared to traditional methods in settings where exposure was rare.ConclusionSupervised deep learning models hold promise in refining propensity score estimations in epidemiological research, offering nuanced confounder adjustment, especially in complex datasets. We endorse integrating supervised deep learning into epidemiological research and share reproducible codes for widespread use and methodological transparency.

Fixed-[formula omitted] asymptotics for panel models with two-way clustering

This paper studies a cluster robust variance estimator proposed by Chiang, Hansen and Sasaki (2024) for linear panels. First, we show algebraically that this variance estimator (CHS estimator, hereafter) is a linear combination of three common variance estimators: the one-way unit cluster estimator, the “HAC of averages” estimator, and the “average of HACs” estimator. Based on this finding, we obtain a fixed-b asymptotic result for the CHS estimator and corresponding test statistics as the cross-section and time sample sizes jointly go to infinity. Furthermore, we propose two simple bias-corrected versions of the variance estimator and derive the fixed-b limits. In a simulation study, we find that the two bias-corrected variance estimators along with fixed-b critical values provide improvements in finite sample coverage probabilities. We illustrate the impact of bias-correction and use of the fixed-b critical values on inference in an empirical example on the relationship between industry profitability and market concentration.

The efficacy of cognitive behavioral therapy for mental health and quality of life among individuals diagnosed with cancer: A systematic review and meta-analysis.

It has long been documented that cognitive behavioral therapy (CBT) has positive impacts on improving mental health (MH) and quality of life (QoL) in the general population, but investigations on its effect on cancer survivors remain limited, especially for QoL outcomes. The purpose of this meta-analysis is to investigate the effects of CBT as compared to control on cancer patients' MH and QoL outcomes. Control is defined in this study as standard therapy, waitlist control, and active/alternative therapy. In total, 154 clinical trials creating a sample size of 1627 individuals were collected. Analysis focusing on MH and QoL excluded 29 clinical trials resulting in a final analysis of 132 clinical trials (and 1030 effect sizes). R Statistical Software (version 4.2.2) and the robumeta package were utilized to complete analysis, which entailed robust variance estimation (RVE) in intercept-only meta-regression, and univariate meta-regression (for moderator analysis). Across 132 clinical trials and 1030 effect size estimates, we identified that CBT moderately improves MH and QoL in cancer patients d = 0.388, 95% CI 0.294-0.483, p < 0.001. Additionally, age and delivery format can influence the efficacy of CBT in this patient population. CBT statistically improves the MH and QoL psychosocial parameters in cancer patients with greater efficacy in younger patients. Important clinical and intervention-related factors, that is, age and delivery, should be considered when oncologists consider CBT as a psychotherapeutic intervention for individuals with cancer.

The Causal Roadmap and Simulations to Improve the Rigor and Reproducibility of Real-data Applications.

The Causal Roadmap outlines a systematic approach to asking and answering questions of cause and effect: define the quantity of interest, evaluate needed assumptions, conduct statistical estimation, and carefully interpret results. To protect research integrity, it is essential that the algorithm for statistical estimation and inference be prespecified prior to conducting any effectiveness analyses. However, it is often unclear which algorithm will perform optimally for the real-data application. Instead, there is a temptation to simply implement one's favorite algorithm, recycling prior code or relying on the default settings of a computing package. Here, we call for the use of simulations that realistically reflect the application, including key characteristics such as strong confounding and dependent or missing outcomes, to objectively compare candidate estimators and facilitate full specification of the statistical analysis plan. Such simulations are informed by the Causal Roadmap and conducted after data collection but prior to effect estimation. We illustrate with two worked examples. First, in an observational longitudinal study, we use outcome-blind simulations to inform nuisance parameter estimation and variance estimation for longitudinal targeted minimum loss-based estimation. Second, in a cluster randomized trial with missing outcomes, we use treatment-blind simulations to examine type-I error control in two-stage targeted minimum loss-based estimation. In both examples, realistic simulations empower us to prespecify an estimation approach with strong expected finite sample performance, and also produce quality-controlled computing code for the actual analysis. Together, this process helps to improve the rigor and reproducibility of our research.

Associations of financial strain and unmet social needs with women’s bladder health

ObjectiveFinancial strain and unmet social needs are associated with greater risk for lower urinary tract symptoms. Little research has examined financial strain and unmet social needs in relation to the more holistic concept of bladder health. This study utilizes baseline data from RISE FOR HEALTH: A U.S. Study of Bladder Health to examine whether financial strain, unmet social needs, and meeting specific federal poverty level threshold levels are associated with lower urinary tract symptoms and poorer perceived bladder health, well-being, and function. Study DesignParticipants were 18 years or older, born female or currently identified as a woman, and from the civilian, noninstitutionalized population residing in 50 counties in the United States that included or surrounded nine recruitment centers. Data were collected through mailed or internet-based surveys. To address research questions, the 10-item Lower Urinary Tract Dysfunction Research Network Symptom Index and selected Prevention of Lower Urinary Tract Symptoms Research Consortium bladder health scores were separately regressed on each financial strain, unmet social need, and federal poverty level variable, using linear regression adjusting for covariates (age, race/ethnicity, education, and vaginal parity) and robust variance estimation for confidence intervals. Participants with no missing data for a given analysis were included (range of n=2,564 to 3,170). In separate sensitivity analyses, body mass index, hypertension, and diabetes were added as covariates and missing data were imputed. ResultsThe mean age of participants was 51.5 years (standard deviation=18.4). Not having enough money to make ends meet, housing insecurity, food insecurity, unreliable transportation, and percent federal poverty levels of 300% or less were consistently associated with more reported lower urinary tract symptoms and poorer perceived bladder health. For example, compared to food secure participants, women who worried that their food would run out at the end of the month had a Lower Urinary Tract Dysfunction Research Network - Symptom Index score that was 3.4 points higher (95% CI: 2.5, 4.3), on average. They also had lower mean scores across different bladder health measures, each assessed using a 100-point scale: global bladder health (-8.2, 95% CI: -10.8,-5.7), frequency (-10.2, 95% CI: -13.8,-6.7), sensation (-11.6, 95% CI: -15.1,-8.2), continence (-13.3, 95% CI: -16.7,-9.9), and emotional impact of bladder health status (-13.2, 95% CI: -16.5,-9.9). Across analyses, associations largely remained significant after additional adjustment for body mass index, hypertension, and diabetes. The pattern of results when imputing missing data was similar to that observed with complete case analysis; all significant associations remained significant with imputation. ConclusionFinancial strain and unmet social needs are associated with worse LUTS and poorer bladder health. Longitudinal research is needed to examine whether financial strain and unmet social needs influence the development, maintenance, and worsening of lower urinary tract symptoms; different mechanisms by which financial strain and unmet social needs may impact symptoms; and the degree to which symptoms contribute to financial strain. If supported by etiologic research, prevention research can be implemented to determine whether the amelioration of financial strain and social needs, including enhanced access to preventative care, may promote bladder health across the life course.

Prediction of resistance, virulence, and host-by-pathogen interactions using dual-genome prediction models

Key messageIntegrating disease screening data and genomic data for host and pathogen populations into prediction models provides breeders and pathologists with a unified framework to develop disease resistance.Developing disease resistance in crops typically consists of exposing breeding populations to a virulent strain of the pathogen that is causing disease. While including a diverse set of pathogens in the experiments would be desirable for developing broad and durable disease resistance, it is logistically complex and uncommon, and limits our capacity to implement dual (host-by-pathogen)-genome prediction models. Data from an alternative disease screening system that challenges a diverse sweet corn population with a diverse set of pathogen isolates are provided to demonstrate the changes in genetic parameter estimates that result from using genomic data to provide connectivity across sparsely tested experimental treatments. An inflation in genetic variance estimates was observed when among isolate relatedness estimates were included in prediction models, which was moderated when host-by-pathogen interaction effects were incorporated into models. The complete model that included genomic similarity matrices for host, pathogen, and interaction effects indicated that the proportion of phenotypic variation in lesion size that is attributable to host, pathogen, and interaction effects was similar. Estimates of the stability of lesion size predictions for host varieties inoculated with different isolates and the stability of isolates used to inoculate different hosts were also similar. In this pathosystem, genetic parameter estimates indicate that host, pathogen, and host-by-pathogen interaction predictions may be used to identify crop varieties that are resistant to specific virulence mechanisms and to guide the deployment of these sources of resistance into pathogen populations where they will be more effective.

Enhancing Precision in Population Variance Vector Estimation: A Two-Phase Sampling Approach with Multi-Auxiliary Information

To enhance precision in estimating unknown population parameters, an auxiliary variable is often used. However, in scenarios where required information on an auxiliary variable is partially or fully unavailable, two-phase sampling is commonly employed. The challenge of estimating the variance vector using multi-auxiliary variables is a less explored area in current literature. This paper addresses the estimation of vector of unknown population variances for multiple study variables by using an estimated vector of variances derived from multi-auxiliary information. This approach is particularly relevant when population variances for the multi-auxiliary variables are not known prior to the survey. The paper introduces a generalized variance and a vector of biases for the proposed multivariate estimator. Special cases of the proposed multivariate variance estimator are provided, accompanied by expressions for mean square errors. Theoretical mathematical conditions are discussed to guide the preference for the proposed estimator. Through the analysis of real-world application-based data, the applicability and efficiency of the proposed multivariate variance estimator are demonstrated, outperforming modified versions of multivariate variance estimators. Additionally, a simulation study validates the superior performance of the proposed estimator compared to its modified estimators.

Adjusted Design Effect Model for Longitudinal Survey Data

In this research, we propose a longitudinal adjusted design effect model that integrates both the design effect and time effect, offering reliable estimators of variance. We investigate the asymptotic properties of certain types of estimators. Through simulation studies, we show the exceptional performance of the proposed method, demonstrating its superiority in producing accurate standard error estimators compared to existing approaches.

How estimating nuisance parameters can reduce the variance (with consistent variance estimation).

We often estimate a parameter of interest when the identifying conditions involve a finite-dimensional nuisance parameter . Examples from causal inference are inverse probability weighting, marginal structural models and structural nested models, which all lead to unbiased estimating equations. This article presents a consistent sandwich estimator for the variance of estimators that solve unbiased estimating equations including which is also estimated by solving unbiased estimating equations. This article presents four additional results for settings where solves (partial) score equations and does not depend on . This includes many causal inference settings where describes the treatment probabilities, missing data settings where describes the missingness probabilities, and measurement error settings where describes the error distribution. These four additional results are: (1) Counter-intuitively, the asymptotic variance of is typically smaller when is estimated. (2) If estimating is ignored, the sandwich estimator for the variance of is conservative. (3) A consistent sandwich estimator for the variance of . (4) If with the true plugged in is efficient, the asymptotic variance of does not depend on whether is estimated. To illustrate we use observational data to calculate confidence intervals for (1) the effect of cazavi versus colistin on bacterial infections and (2) how the effect of antiretroviral treatment depends on its initiation time in HIV-infected patients.

Аппроксимация статистических данных заболеваемости коронавирусной инфекцией с учетом расслоения по сопутствующим диагнозам

The article considers the stratification of concomitant diagnoses of Covid-19 recovery statistics for the city of Irkutsk for 2020-2021. The previous study was conducted without taking into account such stratification. Various options for approximating real statistics by Gaussian and Lorentz functions, gamma distribution, and Johnson curves are considered. It is shown that the stratification of recovery statistics improves the approximation of Gaussian and Lorentz functions in comparison with integral statistics, and the construction of an approximation based on the Lorentz function always describes the real statistics better. Estimates of mathematical expectation and variance based on statistical data are consistent with estimates of these values based on the Gaussian approximation of statistics by the least squares method, i.e. the approaches are equivalent. At the same time, calculations of the Pearson Chi-squared criterion reject the hypothesis that empirical data correspond to the assumed theoretical distribution. Therefore, we cannot talk about finding the distribution function, but only about approximating statistics by certain types of curves. The fitting of empirical data by Gaussian and Lorentz functions was carried out using the least squares method. In general, the approximation error due to the stratification of statistics on concomitant diagnoses decreases from 6% to 3%.