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Indirect corrections for confounding under multiplicative and additive risk models.

We define a multiplicative model and an additive model for the hazards associated jointly with exposure and with the presence of a confounder like smoking. Under the multiplicative model, the crude relative risk may be adjusted indirectly, by means of a factor proposed by Axelson [1978], and implicitly by Cornfield et al. [1959] and Schlesselman [1978]. We present corresponding indirect correction formulas under the additive risk model for the risk difference and for the excess relative risk. Conditions are established under which these corrections may be applied to age-adjusted rates from composite study populations. We demonstrate that indirect corrections may be no better than crude measures of risk if one assumes the wrong model for the joint action of the exposure and confounding factors. These results are illustrated on an example of occupational exposure to vermiculite. The limitations of the techniques are discussed.

Epidemiologic Methods

Risk Prognostication After Hypomethylating Agents Combined With Venetoclax in AML: The PRISM Risk Model.

PURPOSE: As risk stratification for patients with AML treated with lower-intensity venetoclax-based therapy remains suboptimal, we developed and validated a prognostic model integrating clinical, cytogenetic, and molecular features. METHODS: We assembled a multinational data set comprising 2,092 adults with newly diagnosed AML treated with hypomethylating agents plus venetoclax (HMA + VEN). One thousand nine hundred eighteen patients with complete data were randomly divided into training (70%) and internal validation (30%) cohorts. Two independent external validation cohorts were assembled (n = 500 and n = 222). Modeling overall survival (OS), Elastic Net regression was applied in 1,000 bootstrap samples from the training cohort to select variables for a Ridge regression, which generated a continuous Prognostic Risk Integration for Survival Modeling (PRISM) score and risk categories based on tertiles (PRISM-3: low, moderate, high). These PRISM indices were then computed for the validation cohorts and compared with the 4-gene classifier (based on mutations in FLT3-ITD, N/KRAS, and TP53). RESULTS: PRISM integrated 17 clinical and genomic variables and demonstrated a linear association with OS. PRISM-3 stratified survival consistently across all cohorts (median OS: 25.1-28.8 months for low risk, 12.5-14.7 months for moderate risk, and 5.8-6.7 months for high risk; P < .001). Compared with the 4-gene classifier, PRISM-3 reassigned approximately 40% of patients (and >50% of those with favorable risk) and demonstrated significantly better discrimination in validation cohorts (C-index 0.63-0.65 v 0.59-0.61; P < .05). CONCLUSION: PRISM is a validated prognostic model for patients with AML receiving HMA + VEN that improves survival risk stratification beyond current standard tools and supports individualized, risk-adapted clinical decision making. The model, the PRISM-AML Risk Calculator, is publicly available.

Humans

Alternatives to the BEIR relative risk model for explaining atomic-bomb survivor cancer mortality.

The apparent failure of the BEIR absolute risk model to explain the data on the Japanese atomic-bomb survivors does not imply that the BEIR relative risk model (RRM) is correct. RRM is objectionable in that it fits the data only in conjunction with an assumption not in accord with current knowledge and thinking. Contrary to what is widely believed, RRM is not a consequence of, or consistent with, initiator-promoter theories; models derived from initiator-promoter theories fit the data with fewer adjustable parameters and without requiring unpalatable assumptions. The preferable models give substantially lower radiation risks.

Age Factors

Cell proliferation kinetics and multistage cancer risk models.

Cell-kinetic multistage (CKM) cancer-risk models account for clonal proliferation of postulated intermediate (initiated, premalignant) cell populations during tumorigenesis. To date, almost all CKM models considered have assumed that intermediate, premalignant cells may proliferate exponentially over time in vivo. This "exponential growth" assumption, however, may not always be as biologically plausible as the alternative assumption that cells tend to grow geometrically in time. The general CKM model and applications of it that presume exponential cell growth are reviewed here. Geometric CKM models are then considered, previous erroneous analyses of these models are reviewed, and a corrected mathematical treatment is provided. It is pointed out that the presumption of exponential instead of geometric proliferation kinetics may lead to underestimates of small increments in CKM-predicted cancer risk above background if the geometric assumption is true. An evaluation of pertinent biological evidence is provided, which indicates that precancerous cells may typically proliferate geometrically. Consequently, if CKM models are used for environmental risk assessment, it may be prudent for one to presume geometric cell growth unless specific data support an alternative assumption.

Animals

Cancer risk models for ionizing radiation.

Risk estimation in radiation carcinogenesis depends primarily on epidemiological data and hazard rate models. The A-bomb survivors follow-up provides information on the complexity of this process. Several hazard rate models are briefly discussed and illustrated using the A-bomb experience.

Dose-Response Relationship, Radiation

Calculating excess lifetime risk in relative risk models.

When assessing the impact of radiation exposure it is common practice to present the final conclusions in terms of excess lifetime cancer risk in a population exposed to a given dose. The present investigation is mainly a methodological study focusing on some of the major issues and uncertainties involved in calculating such excess lifetime risks and related risk projection methods. The age-constant relative risk model used in the recent analyses of the cancer mortality that was observed in the follow-up of the cohort of A-bomb survivors in Hiroshima and Nagasaki is used to describe the effect of the exposure on the cancer mortality. In this type of model the excess relative risk is constant in age-at-risk, but depends on the age-at-exposure. Calculation of excess lifetime risks usually requires rather complicated life-table computations. In this paper we propose a simple approximation to the excess lifetime risk; the validity of the approximation for low levels of exposure is justified empirically as well as theoretically. This approximation provides important guidance in understanding the influence of the various factors involved in risk projections. Among the further topics considered are the influence of a latent period, the additional problems involved in calculations of site-specific excess lifetime cancer risks, the consequences of a leveling off or a plateau in the excess relative risk, and the uncertainties involved in transferring results from one population to another. The main part of this study relates to the situation with a single, instantaneous exposure, but a brief discussion is also given of the problem with a continuous exposure at a low-dose rate.

Age Factors

A competing-risk model based on the life table procedure in epidemiological studies.

In this paper, a new non-parametric competing-risk model is proposed. This model takes relative susceptibility into account, and is thus free from the usual assumption of independence between competing causes of death. Another feature of the model is the adjustments of survivors and deaths as a results of the elimination of one of the causes of death in the previous time interval. The computational procedure of the model is simple and can be incorporated into the regular life table procedures.

Epidemiologic Methods

A retrospective look at Rn-induced lung cancer mortality from the viewpoint of a relative risk model.

The potential contribution to U.S. lung cancer deaths from 1930 to 1987 from indoor 222Rn exposures is investigated from the standpoint of a constant relative risk model. Based on this model, which assumes a Rn risk proportional to the baseline lung cancer risk from other causes, the rate of Rn-induced lung cancer mortality has been increasing sharply since 1930. However, the estimated proportion of lung cancer deaths attributable to Rn has remained fairly constant. Applying the range of coefficients the U.S. Environmental Protection Agency employs in assessing the risk from indoor Rn, it is estimated that 8-25% of all current lung cancer deaths are "attributable to" past Rn exposures. The major sources of uncertainty in the estimates are discussed.

Environmental Exposure

Representativeness of the Framingham risk model for coronary heart disease mortality: a comparison with a national cohort study.

The Framingham Heart Study has been the foundation upon which several national policies regarding risk factors for coronary heart disease mortality are based. The NHANES I Epidemiologic Followup Study is the first national cohort study based upon a comprehensive medical examination of a probability sample of United States adults. The average follow-up time was 10 years. This study afforded an opportunity to evaluate the generalizability of the Framingham risk model, using systolic blood pressure, total cholesterol, and cigarette smoking, to the U.S. population with respect to predicting death from coronary heart disease. The Framingham model predicts remarkably well for this national sample. The major risk factors for coronary heart disease mortality described in previous Framingham analyses are applicable to the United States white adult population.

Adult

Risk modelling: which models to choose?

Using as examples excess lung cancer mortality in coke oven workers and lung tumor induction in rats by inhalation of diesel engine emissions or cadmium chloride aerosol, the maximum likelihood estimate and the upper limit of risk were determined using a set of conventional risk models. The additional safety offered by going to the upper limit of the 95% confidence interval when deriving a unit risk value was found to be less than a factor of 5 in all but one case, and usually much less than 2. It is concluded that the selection of an adequate model is the most critical step in risk assessment, and that an additional safety factor may be required to allow for a better protection of the public in case models other than the most conservative ones come into use.

Animals

Risk models for rebleeding and postoperative mortality in bleeding gastric ulcer.

In order to better define management policies we attempted to construct risk models for rebleeding on initial conservative management and mortality after emergency surgery for failure of medical therapy in 387 patients with bleeding gastric ulcer. Several different models were constructed using logistic regression analysis with validation by the 'leaving-one-out' method. However, despite large patient numbers, modelling in this way is difficult because of inherent wide variation between patients. Suitable models for rebleeding were regarded as rather unsatisfactory, for although overall accuracy was 86%, sensitivity was only 54%. More promising was a model for mortality after emergency surgery which had an accuracy of 93% and a sensitivity of 80%. Such mortality models incorporating age, history of previous malignant disease or dyspepsia, the presence or absence of ascites and total transfusion requirements may well prove to be of value in surgical practice. This paper seeks to examine the process of modelling rebleeding and mortality and of interpreting the models produced.

Aged

Model risk analysis of nitrosatable compounds in the diet as precursors of potential endogenous carcinogens.

The potential health risk posed by the endogenous formation of N-nitroso compounds (NOC) from nitrosation of dietary ureas, guanidines, amides, amino acids and amines (primary, secondary and aromatic) was estimated according to the model: Risk = [daily intake of precursor] X [gastric concentration of nitrite]n X [nitrosatability rate constant] X [carcinogenicity of derivative]. The daily intakes of these compound classes span five orders of magnitude (100 g/day amides, top; 1-10 mg/day secondary amines, ureas, bottom); the nitrosation rate constants span seven orders of magnitude (aryl amines, ureas, top; amides, secondary amines, bottom); and the carcinogenicity estimates span a 10,000-fold range from 'very strong' to 'virtually noncarcinogenic'. The resulting risk estimates likewise span an enormous range (nine orders of magnitude): dietary ureas and aromatic amines combined with high nitrite concentration could pose as great a risk as the intake of preformed N-nitrosodimethylamine in the diet. In contrast, the risk posed by the in-vivo nitrosation of primary and secondary amines is probably negligible. The risk contributed by amides (including protein), guanidines and primary amino acids is intermediate between these two extremes.

Amines

Identification of ultrasound-associated gene candidates in myeloid cells and construction of a prognostic risk model for acute myeloid leukemia.

BACKGROUND: Incorporating ultrasound (US) treatment sensitivity analysis may improve the treatment of acute myeloid leukemia (AML). METHODS: This study integrated single-cell and bulk datasets for analysis. Differential expression analysis between US-treated and control samples was performed using limma package. The AUCell package was used to calculate US-associated scores in the single-cell dataset. Differentially expressed genes (DEGs) between the specific groups were identified, followed by intersection analysis with previously identified DEGs. Univariate regression, Least Absolute Shrinkage and Selection Operator (LASSO) analysis (using the glmnet package), and stepwise multivariate regression (using the MASS package) were used to refine the candidate genes and to construct a risk model. The model genes were validated using in vitro experiments. Enrichment analysis was conducted using gene set enrichment analysis (GSEA), and immune infiltration was evaluate by single-sample GSEA (ssGSEA) and ESTIMATE algorithms. The correlations between RiskScores and drug sensitivity were analyzed by oncoPredict package. Finally, tumor mutational burden (TMB) and genomic mutations were compared between the risk groups. RESULTS: Nine prognostic signatures (SPINK2, HNRNPAB, SH3BGRL3, CLEC11A, ITGA4, RPL39L, MX1, HEXIM1, and MAP4K4) were identified. Particularly, low expression of SPINK2 attenuated the activity and invasion of AML cells. High-risk group had higher immune cell infiltration. Eight drugs were predicted to be correlated with the RiskScore model. DNMT3A and RUNX1 showed higher mutation frequencies in the high-risk group, whereas KIT and MUC16 showed higher mutation frequencies in the low-risk group. CONCLUSION: The RiskScore model established in this study provides a theoretical basis for clinically screening responsive populations and optimizing treatment strategies.

Humans

Multivariate analysis of prognostic factors in stage IV follicular low-grade lymphoma: a risk model.

We analyzed the records of 96 previously untreated patients with stage IV follicular low-grade lymphoma (FLGL) uniformly treated with cyclophosphamide, doxorubicin, vincristine, prednisone, and bleomycin (CHOP-Bleo) chemotherapy from 1972 to 1982. The overall complete remission (CR) rate was 77%. At a median follow-up of 138 months, the 10-year cause-specific survival rate was 42% with a median survival of 100 months. Failure-free survival (FFS) was 15% at 10 years with a median FFS of 30 months. Multivariate analysis showed peripheral lymph node size (LN), degree of marrow involvement, and sex, in that order, to be important for FFS, while the number of extranodal sites (#ENS), LN, sex, and degree of marrow involvement were important for cause-specific survival. We devised a tumor burden (TB) model, incorporating #ENS, LN, and degree of marrow involvement. Three groups were identified with statistically significant differences in cause-specific survival and FFS. Those with low TB (one ENS exclusive of extensive marrow and nodal disease less than 5 cm) had a 10-year cause-specific survival of 73% compared with 24% for patients with high TB (greater than or equal to two ENS and nodal disease greater than or equal to 5 cm) (P less than .001) and 40% for those with intermediate TB (either greater than or equal to 2 ENS, or extensive marrow only, or nodal disease greater than 5 cm) (P = .050). Patients with low TB had a 10-year FFS rate of 32%, while the intermediate and high TB groups had 10% and 9% FFS, respectively (P = .003). Because sex was a very strong prognostic variable, we created a risk model for survival and FFS based on TB and sex. Females with low TB had the best prognosis (92% survival and 50% FFS at 10 years) and males with high TB had the worst outlook (median survival and FFS, 43 and 12 months, respectively). Other TB-sex combinations defined two groups with statistically significant differences in survival but comparable FFS. This model should aid in the design and analysis of future trials.

Antineoplastic Combined Chemotherapy Protocols

Relative risk models for assessing the joint effects of multiple factors.

A goal of analyses of occupational cohort data is the specification of how covariate information relates to age-specific disease risks. In describing this relationship, certain assumptions or models must be defined. For example, the usual standardized mortality ratio assumes a constant multiplicative increase in the age and calendar period disease rates of an exposed cohort over rates in a unexposed referent group. For analyzing several exposures, some of which may be continuous, such as cumulative dose, dose rate, duration of employment, and smoking patterns, or for analyzing complex associations between disease rate and covariates, flexible regression procedures are required. Using a crossclassification of the data and a Poisson probability model, relative risk regression methods are outlined. Breslow and Storer [1985], Guerrero and Johnson [1982], and Thomas [1981] propose general models for the relative risk as alternatives to, but which include, the usual exponential form. We review these models, discuss some limitations (in particular when there is more than one covariate) and present alternatives. Methods and models are illustrated by examining the joint effects of radon exposure and tobacco use on lung cancer mortality among a group of uranium miners.

Adult

Biologically motivated cancer risk models.

A two-stage dose response model is proposed for use in cancer risk assessment. The model assumes that transformation probabilities and cellular dynamics are exposure- and time-dependent.

Animals

Logistic risk model for the unique effects of inherent aerobic capacity on +Gz tolerance before and after simulated weightlessness.

Small sample size (n less than 10) and inappropriate analysis of multivariate data have hindered previous attempts to describe which physiologic and demographic variables are most important in determining how long humans can tolerate acceleration. Data from previous centrifuge studies conducted at NASA/Ames Research Center, utilizing a 7-14 d bed rest protocol to simulate weightlessness, were included in the current investigation. After review, data on 25 women and 22 men were available for analysis. Study variables included gender, age, weight, height, percent body fat, resting heart rate, mean arterial pressure, VO2max, and plasma volume. Since the dependent variable was time to greyout (failure), two contemporary biostatistical modeling procedures (proportional hazard and logistic discriminant function) were used to estimate risk, given a particular subject's profile. After adjusting for pre-bed-rest tolerance time, none of the profile variables remained in the risk equation for post-bed-rest tolerance greyout. However, prior to bed rest, risk of greyout could be predicted with 91% accuracy. All of the profile variables except weight, MAP, and those related to inherent aerobic capacity (VO2max, percent body fat, resting heart rate) entered the risk equation for pre-bed-rest greyout. A cross-validation using 24 new subjects indicated a very stable model for risk prediction, accurate within 5% of the original equation. The result for the inherent fitness variables is significant in that a consensus as to whether an increased aerobic capacity is beneficial or detrimental has not been satisfactorily established. We conclude that tolerance to +Gz acceleration before and after simulated weightlessness is independent of inherent aerobic fitness.

Acceleration

EMPEROR-Preserved Risk Model and Outcomes in the FINEARTS-HF Trial: A Prespecified Secondary Analysis of FINEARTS-HF.

IMPORTANCE: Patients with heart failure (HF) and mildly reduced ejection fraction (HFmrEF) or preserved EF (HFpEF) show substantial heterogeneity in prognosis. OBJECTIVES: To evaluate the performance of biomarker-driven prognostic models derived from the Empagliflozin Outcome Trial in Patients With Chronic Heart Failure With Preserved Ejection Fraction (EMPEROR-Preserved) Trial in the Finerenone Trial to Investigate Efficacy and Safety Superior to Placebo in Patients With Heart Failure (FINEARTS-HF) and to examine whether baseline risk modified the therapeutic effect of finerenone. DESIGN, SETTING, AND PARTICIPANTS: This is a prespecified secondary analysis of the FINEARTS-HF trial, which was conducted across 653 sites in 37 countries among adults aged 40 years and older with symptomatic HF and left ventricular EF (LVEF) of 40% or greater. Patients were randomized between September 2020 and January 2023, and data analysis for this study was conducted from September to October 2025. The median (IQR) follow-up period was 32 (23-37) months. INTERVENTION: Finerenone (titrated to 20 mg or 40 mg) or placebo. MAIN OUTCOMES AND MEASURES: EMPEROR-Preserved risk scores for the outcomes of first HF hospitalization or cardiovascular death, cardiovascular death, and all-cause death were calculated in FINEARTS-HF using models incorporating N-terminal pro-B-type natriuretic peptide, high-sensitivity cardiac troponin T, New York Heart Association functional class, history of chronic obstructive pulmonary disease and diabetes, insulin use, and-depending on outcome-age, hemoglobin and albumin levels, HF duration, time from prior HF hospitalization, and sodium-glucose transporter 2 inhibitor use. Estimated risks were compared with observed event rates, and model performance was assessed using Harrell C statistic. Treatment effects were evaluated across risk quintiles (Q1 to Q5) and across the continuous risk distribution. RESULTS: Among 6001 patients (mean [SD] age, 72.0 [9.6] years; 2732 [45.5%] women; 3003 randomized to finerenone and 2998 randomized to placebo), the EMPEROR-Preserved risk model estimated risk of outcomes, with Q5 vs Q1 hazard ratios (HRs) of 10.49 (95% CI, 8.14-13.52) for the composite of HF hospitalization or cardiovascular death and 13.47 (95% CI, 8.79-20.64) for cardiovascular death. The model demonstrated good discrimination. The treatment effect of finerenone was consistent across risk quintiles for first HF hospitalization or cardiovascular death (Q1: HR, 0.93 [95% CI, 0.58-1.49]; Q2: HR, 1.04 [95% CI, 0.76-1.43]; Q3: HR, 0.82 [95% CI, 0.62-1.07]; Q4: HR, 0.81 [95% CI, 0.65-1.01]; and Q5: HR, 0.88 [95% CI, 0.74-1.05]; P for interaction&#x2009;=&#x2009;.68) and remained uniform across the continuous risk spectrum. CONCLUSIONS AND RELEVANCE: The EMPEROR-Preserved risk models demonstrated good performance in FINEARTS-HF. Baseline risk did not modify the relative treatment effect of finerenone. TRIAL REGISTRATION: ClinicalTrials.gov Identifier: NCT04435626.

Humans