Cox model inference for relative hazard and pure risk from stratified weight-calibrated case-cohort data.

The case-cohort design obtains complete covariate data only on cases and on a random sample (the subcohort) of the entire cohort. Subsequent publications described the use of stratification and weight calibration to increase efficiency of estimates of Cox model log-relative hazards, and there has been some work estimating pure risk. Yet there are few examples of these options in the medical literature, and we could not find programs currently online to analyze these various options. We therefore present a unified approach and R software to facilitate such analyses. We used influence functions adapted to the various design and analysis options together with variance calculations that take the two-phase sampling into account. This work clarifies when the widely used "robust" variance estimate of Barlow (Biometrics 50:1064-1072, 1994) is appropriate. The corresponding R software, CaseCohortCoxSurvival, facilitates analysis with and without stratification and/or weight calibration, for subcohort sampling with or without replacement. We also allow for phase-two data to be missing at random for stratified designs. We provide inference not only for log-relative hazards in the Cox model, but also for cumulative baseline hazards and covariate-specific pure risks. We hope these calculations and software will promote wider use of more efficient and principled design and analysis options for case-cohort studies.

Predicting absolute risk for a person with missing risk factors.

We compared methods to project absolute risk, the probability of experiencing the outcome of interest in a given projection interval accommodating competing risks, for a person from the target population with missing predictors. Without missing data, a perfectly calibrated model gives unbiased absolute risk estimates in a new target population, even if the predictor distribution differs from the training data. However, if predictors are missing in target population members, a reference dataset with complete data is needed to impute them and to estimate absolute risk, conditional only on the observed predictors. If the predictor distributions of the reference data and the target population differ, this approach yields biased estimates. We compared the bias and mean squared error of absolute risk predictions for seven methods that assume predictors are missing at random (MAR). Some methods imputed individual missing predictors, others imputed linear predictor combinations (risk scores). Simulations were based on real breast cancer predictor distributions and outcome data. We also analyzed a real breast cancer dataset. The largest bias for all methods resulted from different predictor distributions of the reference and target populations. No method was unbiased in this situation. Surprisingly, violating the MAR assumption did not induce severe biases. Most multiple imputation methods performed similarly and were less biased (but more variable) than a method that used a single expected risk score. Our work shows the importance of selecting predictor reference datasets similar to the target population to reduce bias of absolute risk predictions with missing risk factors.

Cohort profile: evaluation of immune response and household transmission of SARS-CoV-2 in Costa Rica: the RESPIRA study.

PURPOSE: The RESPIRA cohort aims to describe the nature, magnitude, time course and efficacy of the immune response to SARS-CoV-2 infection and vaccination, population prevalence, and household transmission of COVID-19. PARTICIPANTS: From November 2020, we selected age-stratified random samples of COVID-19 cases from Costa Rica confirmed by PCR. For each case, two population-based controls, matched on age, sex and census tract were recruited, supplemented with hospitalised cases and household contacts. Participants were interviewed and blood and saliva collected for antibodies and PCR tests. Participants will be followed for 2 years to assess antibody response and infection incidence. FINDINGS TO DATE: Recruitment included 3860 individuals: 1150 COVID-19 cases, 1999 population controls and 719 household contacts from 304 index cases. The age and regional distribution of cases was as planned, including four age strata, 30% rural and 70% urban. The control cohort had similar sex, age and regional distribution as the cases according to the study design. Among the 1999 controls recruited, 6.8% reported at enrolment having had COVID-19 and an additional 12.5% had antibodies against SARS-CoV-2. Compliance with visits and specimens has been close to 70% during the first 18 months of follow-up. During the study, national vaccination was implemented and nearly 90% of our cohort participants were vaccinated during follow-up. FUTURE PLANS: RESPIRA will enable multiple analyses, including population prevalence of infection, clinical, behavioural, immunological and genetic risk factors for SARS-CoV-2 acquisition and severity, and determinants of household transmission. We are conducting retrospective and prospective assessment of antibody levels, their determinants and their protective efficacy after infection and vaccination, the impact of long-COVID and a series of ancillary studies. Follow-up continues with bimonthly saliva collection for PCR testing and biannual blood collection for immune response analyses. Follow-up will be completed in early 2024. TRIAL REGISTRATION NUMBER: NCT04537338.

Estimating the cumulative incidence of SARS-CoV-2 infection in Costa Rica: modelling seroprevalence data in a population-based cohort.

Background: The true incidence of SARS-CoV-2 infection in Costa Rica was likely much higher than officially reported, because infection is often associated with mild symptoms and testing was limited by official guidelines and socio-economic factors. Methods: Using serology to define natural infection, we developed a statistical model to estimate the true cumulative incidence of SARS-CoV-2 in Costa Rica early in the pandemic. We estimated seroprevalence from 2223 blood samples collected from November 2020 to October 2021 from 1976 population-based controls from the RESPIRA study. Samples were tested for antibodies against SARS-CoV-2 nucleocapsid and the receptor-binding-domain of the spike proteins. Using a generalized linear model, we estimated the ratio of true infections to officially reported cases. Applying these ratios to officially reported totals by age, sex, and geographic area, we estimated the true number of infections in the study area, where 70% of Costa Ricans reside. We adjusted the seroprevalence estimates for antibody decay over time, estimated from 1562 blood samples from 996 PCR-confirmed COVID-19 cases. Findings: The estimated total proportion infected (ETPI) was 4.0 times higher than the officially reported total proportion infected (OTPI). By December 16th, 2021, the ETPI was 47% [42-52] while the OTPI was 12%. In children and adolescents, the ETPI was 11.0 times higher than the OTPI. Interpretation: Our findings suggest that nearly half the population had been infected by the end of 2021. By the end of 2022, it is likely that a large majority of the population had been infected. Funding: This work was sponsored and funded by the National Institute of Allergy and Infectious Diseases through the National Cancer Institute, the Science, Innovation, Technology and Telecommunications Ministry of Costa Rica, and Costa Rican Biomedical Research Agency-Fundacion INCIENSA (grant N/A).

Exposure to polycyclic aromatic hydrocarbons, volatile organic compounds, and tobacco-specific nitrosamines and incidence of esophageal cancer.

BACKGROUND: Studying carcinogens in tobacco and non-tobacco sources may be key to understanding the pathogenesis and geographic distribution of esophageal cancer. METHODS: Golestan Cohort Study (GCS) has been conducted since 2004 in a region with high rates of esophageal squamous cell carcinoma (ESCC). For this nested study, the cases comprised of all incident cases by Jan 1, 2018; controls were matched to the case by age, sex, residence, time in cohort, and tobacco use. We measured urinary concentrations of 33 exposure biomarkers of nicotine, polycyclic aromatic hydrocarbons (PAHs), volatile organic compounds (VOCs), and tobacco-specific nitrosamines (TSNAs). We used conditional logistic regression to calculate odds ratios (OR) and 95% confidence intervals (95%CI) for associations between the 90th versus the 10th percentiles of the biomarker concentrations and incident ESCC. RESULTS: Among individuals who did not currently use tobacco (148 cases/163 controls), two acrolein metabolites, two acrylonitrile metabolites, one propylene oxide metabolite and one 1,3-butadiene metabolite were significantly associated with incident ESCC (adjusted ORs between 1.8 and 4.3). Among tobacco users (57 cases/63 controls), metabolites of two other VOCs (styrene and xylene) were associated with ESCC (ORs= 6.2 and 9.0). In tobacco users, two TSNAs (NNN and N'-Nitrosoanatabine) were also associated with ESCC. Suggestive associations were seen with some PAHs (especially 2-hydroxynaphthalene) in non-users of tobacco products and other TSNAs in tobacco users. CONCLUSION: These novel associations based on individual-level data and samples collected many years before cancer diagnosis, from a population without occupational exposure, have important public health implications.

Behavioral factors and SARS-CoV-2 transmission heterogeneity within a household cohort in Costa Rica.

INTRODUCTION: Variability in household secondary attack rates and transmission risks factors of SARS-CoV-2 remain poorly understood. METHODS: We conducted a household transmission study of SARS-CoV-2 in Costa Rica, with SARS-CoV-2 index cases selected from a larger prospective cohort study and their household contacts were enrolled. A total of 719 household contacts of 304 household index cases were enrolled from November 21, 2020, through July 31, 2021. Blood specimens were collected from contacts within 30-60 days of index case diagnosis; and serum was tested for presence of spike and nucleocapsid SARS-CoV-2 IgG antibodies. Evidence of SARS-CoV-2 prior infections among household contacts was defined based on the presence of both spike and nucleocapsid antibodies. We fitted a chain binomial model to the serologic data, to account for exogenous community infection risk and potential multi-generational transmissions within the household. RESULTS: Overall seroprevalence was 53% (95% confidence interval (CI) 48-58%) among household contacts. The estimated household secondary attack rate is 34% (95% CI 5-75%). Mask wearing by the index case is associated with the household transmission risk reduction by 67% (adjusted odds ratio = 0.33 with 95% CI: 0.09-0.75) and not sharing bedroom with the index case is associated with the risk reduction of household transmission by 78% (adjusted odds ratio = 0.22 with 95% CI 0.10-0.41). The estimated distribution of household secondary attack rates is highly heterogeneous across index cases, with 30% of index cases being the source for 80% of secondary cases. CONCLUSIONS: Modeling analysis suggests that behavioral factors are important drivers of the observed SARS-CoV-2 transmission heterogeneity within the household.

When living in the same house with known SARS-CoV-2 cases, household members may change their behavior and adopt preventive measures to reduce the spread of SARS-CoV-2. To understand how behavioral factors affect SARS-CoV-2 spreading in household settings, we focused on household members of individuals with laboratory-confirmed SARS-CoV-2 infections and followed the way SARS-CoV-2 spread within the household, by looking at who had antibodies against the virus, which means they were infected. We also asked participants detailed questions about their behavior and applied mathematical modeling to evaluate its impact on SARS-CoV-2 transmission. We found that mask-wearing by the SARS-CoV-2 cases, and avoiding sharing a bedroom with the infected individuals, reduces SARS-CoV-2 transmission. However, caring for SARS-CoV-2 cases, and prolonged interaction with infected individuals facilitate SARS-CoV-2 spreading. Our study helps inform what behaviors can help reduce SARS-CoV-2 transmission within a household.

Circulating vitamin D and breast cancer risk: an international pooling project of 17 cohorts.

Laboratory and animal research support a protective role for vitamin D in breast carcinogenesis, but epidemiologic studies have been inconclusive. To examine comprehensively the relationship of circulating 25-hydroxyvitamin D [25(OH)D] to subsequent breast cancer incidence, we harmonized and pooled participant-level data from 10 U.S. and 7 European prospective cohorts. Included were 10,484 invasive breast cancer cases and 12,953 matched controls. Median age (interdecile range) was 57 (42-68) years at blood collection and 63 (49-75) years at breast cancer diagnosis. Prediagnostic circulating 25(OH)D was either newly measured using a widely accepted immunoassay and laboratory or, if previously measured by the cohort, calibrated to this assay to permit using a common metric. Study-specific relative risks (RRs) for season-standardized 25(OH)D concentrations were estimated by conditional logistic regression and combined by random-effects models. Circulating 25(OH)D increased from a median of 22.6 nmol/L in consortium-wide decile 1 to 93.2 nmol/L in decile 10. Breast cancer risk in each decile was not statistically significantly different from risk in decile 5 in models adjusted for breast cancer risk factors, and no trend was apparent (P-trend = 0.64). Compared to women with sufficient 25(OH)D based on Institute of Medicine guidelines (50- < 62.5 nmol/L), RRs were not statistically significantly different at either low concentrations (< 20 nmol/L, 3% of controls) or high concentrations (100- < 125 nmol/L, 3% of controls; ≥ 125 nmol/L, 0.7% of controls). RR per 25 nmol/L increase in 25(OH)D was 0.99 [95% confidence intervaI (CI) 0.95-1.03]. Associations remained null across subgroups, including those defined by body mass index, physical activity, latitude, and season of blood collection. Although none of the associations by tumor characteristics reached statistical significance, suggestive inverse associations were seen for distant and triple negative tumors. Circulating 25(OH)D, comparably measured in 17 international cohorts and season-standardized, was not related to subsequent incidence of invasive breast cancer over a broad range in vitamin D status.

Increasing efficiency and reducing bias when assessing HPV vaccination efficacy by using nontargeted HPV strains.

Studies of vaccine efficacy often record both the incidence of vaccine-targeted virus strains (primary outcome) and the incidence of nontargeted strains (secondary outcome). However, standard estimates of vaccine efficacy on targeted strains ignore the data on nontargeted strains. Assuming nontargeted strains are unaffected by vaccination, we regard the secondary outcome as a negative control outcome and show how using such data can (i) increase the precision of the estimated vaccine efficacy against targeted strains in randomized trials and (ii) reduce confounding bias of that same estimate in observational studies. For objective (i), we augment the primary outcome estimating equation with a function of the secondary outcome that is unbiased for zero. For objective (ii), we jointly estimate the treatment effects on the primary and secondary outcomes. If the bias induced by the unmeasured confounders is similar for both types of outcomes, as is plausible for factors that influence the general risk of infection, then we can use the estimated efficacy against the secondary outcomes to remove the bias from estimated efficacy against the primary outcome. We demonstrate the utility of these approaches in studies of HPV vaccines that only target a few highly carcinogenic strains. In this example, using nontargeted strains increased precision in randomized trials modestly but reduced bias in observational studies substantially.

Discussion of "A formal causal interpretation of the case-crossover design" by Zach Shahn, Miguel A. Hernan, and James M. Robins.

Shahn, Hernan, and Robins give conditions under which estimates from a case-crossover analysis converge to the desired causal relative risk times a bias factor, and they discuss conditions needed to have small bias. To simplify the problem, we discuss only two exposure times and rely on randomized exposure assignments, thereby avoiding the need for potential outcome notation. We identify many, but not all, of the conditions discussed by Shahn et al. in this simple analysis.

Accommodating population differences when validating risk prediction models.

Validation of risk prediction models in independent data provides a more rigorous assessment of model performance than internal assessment, for example, done by cross-validation in the data used for model development. However, several differences between the populations that gave rise to the training and the validation data can lead to seemingly poor performance of a risk model. In this paper we formalize the notions of "similarity" or "relatedness" of the training and validation data, and define reproducibility and transportability. We address the impact of different distributions of model predictors and differences in verifying the disease status or outcome on measures of calibration, accuracy and discrimination of a model. When individual level information from both the training and validation data sets is available, we propose and study weighted versions of the validation metrics that adjust for differences in the risk factor distributions and in outcome verification between the training and validation data to provide a more comprehensive assessment of model performance. We provide conditions on the risk model and the populations that gave rise to the training and validation data that ensure a model's reproducibility or transportability, and show how to check these conditions using weighted and unweighted performance measures. We illustrate the method by developing and validating a model that predicts the risk of developing prostate cancer using data from two large prostate cancer screening trials.

Estimating vaccine effectiveness against SARS-CoV-2 infection, hospitalization and death from ecologic data in Costa Rica.

BACKGROUND: Clinical trials and individual-level observational data in Israel demonstrated approximately 95% effectiveness of mRNA-based vaccines against symptomatic SARS-CoV-2 infection. Individual-level data are not available in many countries, particularly low- and middle- income countries. Using a novel Poisson regression model, we analyzed ecologic data in Costa Rica to estimate vaccine effectiveness and assess the usefulness of this approach. METHODS: We used national data from December 1, 2020 to May 13, 2021 to ascertain incidence, hospitalizations and deaths within ecologic units defined by 14 age groups, gender, 105 geographic areas, and day of the epidemic. Within each unit we used the proportions of the population with one and with two vaccinations, primarily tozinameran. Using a non-standard Poisson regression model that included an ecologic-unit-specific rate factor to describe rates without vaccination and a factor that depended on vaccine effectiveness parameters and proportions vaccinated, we estimated vaccine effectiveness. RESULTS: In 3.621 million persons aged 20 or older, there were 125,031 incident cases, 7716 hospitalizations, and 1929 deaths following SARS-CoV-2 diagnosis; 73% of those aged ≥ 75 years received two doses. For one dose, estimated effectiveness was 59% (95% confidence interval 53% to 64%) for SARS-CoV-2 incidence, 76% (68% to 85%) for hospitalizations, and 63% (47% to 80%) for deaths. For two doses, the respective estimates of effectiveness were 93% (90% to 96%), 100% (97% to 100%), and 100% (97% to 100%). CONCLUSIONS: These effectiveness estimates agree well with findings from clinical trials and individual-level observational studies and indicate high effectiveness in the general population of Costa Rica. This novel statistical approach is promising for countries where ecologic, but not individual-level, data are available. The method could also be adapted to monitor vaccine effectiveness over calendar time.

The Oral Microbiome and Lung Cancer Risk: An Analysis of 3 Prospective Cohort Studies.

BACKGROUND: Previous studies suggested associations between the oral microbiome and lung cancer, but studies were predominantly cross-sectional and underpowered. METHODS: Using a case-cohort design, 1306 incident lung cancer cases were identified in the Agricultural Health Study; National Institutes of Health-AARP Diet and Health Study; and Prostate, Lung, Colorectal, and Ovarian Cancer Screening Trial. Referent subcohorts were randomly selected by strata of age, sex, and smoking history. DNA was extracted from oral wash specimens using the DSP DNA Virus Pathogen kit, the 16S rRNA gene V4 region was amplified and sequenced, and bioinformatics were conducted using QIIME 2. Hazard ratios and 95% confidence intervals were calculated using weighted Cox proportional hazards models. RESULTS: Higher alpha diversity was associated with lower lung cancer risk (Shannon index hazard ratio = 0.90, 95% confidence interval = 0.84 to 0.96). Specific principal component vectors of the microbial communities were also statistically significantly associated with lung cancer risk. After multiple testing adjustment, greater relative abundance of 3 genera and presence of 1 genus were associated with greater lung cancer risk, whereas presence of 3 genera were associated with lower risk. For example, every SD increase in Streptococcus abundance was associated with 1.14 times the risk of lung cancer (95% confidence interval = 1.06 to 1.22). Associations were strongest among squamous cell carcinoma cases and former smokers. CONCLUSIONS: Multiple oral microbial measures were prospectively associated with lung cancer risk in 3 US cohort studies, with associations varying by smoking history and histologic subtype. The oral microbiome may offer new opportunities for lung cancer prevention.

Tools for Contralateral Prophylactic Mastectomy Decision Making.

PURPOSE: Women with unilateral breast cancer are increasingly opting for the removal of not only the involved breast, but also for the removal of the opposite uninvolved breast (contralateral prophylactic mastectomy [CPM]), although the risk of contralateral breast cancer (CBC) has decreased in recent years. Models to predict the absolute risk of CBC can help a woman decide whether to undergo CPM. Our objective is to illustrate that a better decision can be made if the patient and doctor also have estimates of the absolute risks of regional and distant recurrences and mortality from non-breast cancer causes. MATERIALS AND METHODS: We based our analyses on two published models for CBC and published information on the hazards of regional and distant recurrences and non-breast cancer mortality. Assuming that CPM eliminates CBC but has no effect on other events, we calculated how much CPM reduces a woman's CBC risk and total risk from all these events for 10 hypothetical women with various subtypes of breast cancer and risk factors. RESULTS: The risk of CBC and total risk vary greatly, depending on the breast cancer subtype. In some cases, a decision for or against CPM can be based on CBC risk alone, but in others, additional consideration of total risk may cause a woman to decline CPM. CONCLUSION: There is a potential to develop more informative tools for deciding on CPM. Realizing this potential will require more and better data to validate existing models of absolute CBC risk and to characterize the hazards of regional and distant recurrences and deaths from non-breast cancer causes for women with various subtypes of breast cancers and risk factors.

Performance of Cervical Screening a Decade Following HPV Vaccination: The Costa Rica Vaccine Trial.

BACKGROUND: We investigated the impact of human papillomavirus (HPV) vaccination on the performance of cytology-based and HPV-based screening for detection of cervical precancer among women vaccinated as young adults and reaching screening age. METHODS: A total of 4632 women aged 25-36 years from the Costa Rica HPV Vaccine Trial were included (2418 HPV-vaccinated as young adults and 2214 unvaccinated). We assessed the performance of cytology- and HPV-based cervical screening modalities in vaccinated and unvaccinated women to detect high-grade cervical precancers diagnosed over 4 years and the absolute risk of cumulative cervical precancers by screening results at entry. RESULTS: We detected 95 cervical intraepithelial neoplasia grade 3 or worse (52 in unvaccinated and 43 in vaccinated women). HPV16/18/31/33/45 was predominant (69%) among unvaccinated participants, and HPV35/52/58/39/51/56/59/66/68 predominated (65%) among vaccinated participants. Sensitivity and specificity of cervical screening approaches were comparable between women vaccinated as young adults and unvaccinated women. Colposcopy referral rates were lower in the vaccinated group for HPV-based screening modalities, but the positive predictive value was comparable between the 2 groups. CONCLUSIONS: Among women approaching screening ages, vaccinated as young adults, and with a history of intensive screening, the expected reduction in the positive predictive value of HPV testing, associated with dropping prevalence of HPV-associated lesions, was not observed. This is likely due to the presence of high-grade lesions associated with nonvaccine HPV types, which may be less likely to progress to cancer.

fast.adonis: a computationally efficient non-parametric multivariate analysis of microbiome data for large-scale studies.

Motivation: Nonparametric multivariate analysis has been widely used to identify variables associated with a dissimilarity matrix and to quantify their contribution. For very large studies ( n ≥ 5000 ) and many explanatory variables, existing software packages (e.g. adonis and adonis2 in vegan) are computationally intensive when conducting sequential multivariate analysis with permutations or bootstrapping. Moreover, for subjects from a complex sampling design, we need to adjust for sampling weights to derive an unbiased estimate. Results: We implemented an R function fast.adonis to overcome these computational challenges in large-scale studies. fast.adonis generates results consistent with adonis/adonis2 but much faster. For complex sampling studies, fast.adonis integrates sampling weights algebraically to mimic the source population; thus, analysis can be completed very fast without requiring a large amount of memory. Availability and implementation: fast.adonis is implemented using R and is publicly available at https://github.com/jennylsl/fast.adonis. Supplementary information: Supplementary data are available at Bioinformatics Advances online.

Rationale and design of a double-blind randomized non-inferiority clinical trial to evaluate one or two doses of vaccine against human papillomavirus including an epidemiologic survey to estimate vaccine efficacy: The Costa Rica ESCUDDO trial.

HPV vaccination of adolescent girls is the most effective measure to prevent cervical cancer. The World Health Organization recommends that adolescent girls receive two doses of vaccine but only a small proportion of girls from regions with the highest disease burden are vaccinated because of cost and logistical considerations. Our Costa Rica HPV Vaccine trial suggested that one dose of the bivalent HPV vaccine provides robust and lasting protection against persistent HPV infections for over a decade. Data from a post-licensure trial of the quadrivalent vaccine in India also suggested that a single dose may be effective in reducing cervical cancer risk. To formally compare one versus two doses of the bivalent and nonavalent HPV vaccines, we implemented a large, randomized, double-blind trial to investigate the non-inferiority of one compared to two vaccine doses in the prevention of new HPV16/18 infections that persist 6 or more months. Bivalent and nonavalent vaccines will be evaluated separately. The trial enrolled and randomized (1:1:1:1 to 1- and 2-dose arms of the bivalent and nonavalent vaccines) 20,330 girls 12 to 16 years old residing in Costa Rica. Trial participants are followed every 6 months for up to 5 years. We also aim to estimate vaccine efficacy by comparing the rates of 6 month persistent infection in unvaccinated women with the rates in the follow-up visits of trial participants. We included one survey of unvaccinated women at the start of the study (N = 4452) and will include another survey concomitant with follow up visits of trial participants at year 4.5 (planned N = 3000). Survey participants attend two visits 6 months appart. Herein, we present the rationale, design, and enrolled study population of the ESCUDDO trial. ClinicalTrials.gov Identifier: NCT03180034.

Weight calibration to improve efficiency for estimating pure risks from the additive hazards model with the nested case-control design.

We study the efficiency of covariate-specific estimates of pure risk (one minus the survival function) when some covariates are only available for case-control samples nested in a cohort. We focus on the semiparametric additive hazards model in which the hazard function equals a baseline hazard plus a linear combination of covariates with either time-varying or time-invariant coefficients. A published approach uses the design-based inclusion probabilities to reweight the nested case-control data. We obtain more efficient estimates of pure risks by calibrating the design weights to data available in the entire cohort, for both time-varying and time-invariant covariate coefficients. We develop explicit variance formulas for the weight-calibrated estimates based on influence functions. Simulations show the improvement in precision by using weight calibration and confirm the consistency of variance estimators and the validity of inference based on asymptotic normality. Examples are provided using data from the Prostate, Lung, Colorectal, and Ovarian Cancer Screening Trial Study (PLCO).

Assessing risk model calibration with missing covariates.

When validating a risk model in an independent cohort, some predictors may be missing for some subjects. Missingness can be unplanned or by design, as in case-cohort or nested case-control studies, in which some covariates are measured only in subsampled subjects. Weighting methods and imputation are used to handle missing data. We propose methods to increase the efficiency of weighting to assess calibration of a risk model (i.e. bias in model predictions), which is quantified by the ratio of the number of observed events, $\mathcal{O}$, to expected events, $\mathcal{E}$, computed from the model. We adjust known inverse probability weights by incorporating auxiliary information available for all cohort members. We use survey calibration that requires the weighted sum of the auxiliary statistics in the complete data subset to equal their sum in the full cohort. We show that a pseudo-risk estimate that approximates the actual risk value but uses only variables available for the entire cohort is an excellent auxiliary statistic to estimate $\mathcal{E}$. We derive analytic variance formulas for $\mathcal{O}/\mathcal{E}$ with adjusted weights. In simulations, weight adjustment with pseudo-risk was much more efficient than inverse probability weighting and yielded consistent estimates even when the pseudo-risk was a poor approximation. Multiple imputation was often efficient but yielded biased estimates when the imputation model was misspecified. Using these methods, we assessed calibration of an absolute risk model for second primary thyroid cancer in an independent cohort.

Associations between Biomarkers of Exposure and Lung Cancer Risk among Exclusive Cigarette Smokers in the Golestan Cohort Study.

Biomarkers of tobacco exposure are known to be associated with disease risk but previous studies are limited in number and restricted to certain regions. We conducted a nested case-control study examining baseline levels and subsequent lung cancer incidence among current male exclusive cigarette smokers in the Golestan Cohort Study in Iran. We calculated geometric mean biomarker concentrations for 28 matched cases and 52 controls for the correlation of biomarker levels among controls and for adjusted odds' ratios (ORs) for lung cancer incidence by biomarker concentration, accounting for demographic characteristics, smoking quantity and duration, and opium use. Lung cancer cases had higher average levels of most biomarkers including total nicotine equivalents (TNE-2), 4-(methylnitrosamino)-1-(3-pyridyl)-1-butanol (NNAL), and 3-hydroxyfluorene (3-FLU). Many biomarkers correlated highly with one another including TNE-2 with NNAL and N-Acetyl-S-(2-cyanoethyl)-L-cysteine (2CYEMA), and N-Acetyl-S-(4-hydroxy-2-buten-1-yl)-L-cysteine (t4HBEMA) with N-Acetyl-S-(3-hydroxypropyl-1-methyl)-L-cysteine (3HMPMA) and N-Acetyl-S-(4-hydroxy-2-methyl-2-buten-1-yl)-L-cysteine (4HMBEMA). Lung cancer risk increased with concentration for several biomarkers, including TNE-2 (OR = 2.22, 95% CI = 1.03, 4.78) and NNN (OR = 2.44, 95% CI = 1.13, 5.27), and estimates were significant after further adjustment for demographic and smoking characteristics for 2CYEMA (OR = 2.17, 95% CI = 1.03, 4.55), N-Acetyl-S-(2-carbamoylethyl)-L-cysteine (2CAEMA) (OR = 2.14, 95% CI = 1.01, 4.55), and N-Acetyl-S-(2-hydroxypropyl)-L-cysteine (2HPMA) (OR = 2.85, 95% CI = 1.04, 7.81). Estimates were not significant with adjustment for opium use. Concentrations of many biomarkers were higher at the baseline for participants who subsequently developed lung cancer than among the matched controls. Odds of lung cancer were higher for several biomarkers including with adjustment for smoking exposure for some but not with adjustment for opium use.

Thoughts on "AIDS and COVID-19: A Tale of Two Pandemics and the Role of Statisticians" by Susan S. Ellenberg and Jeffrey S. Morris.

Human immunodeficiency virus and Covid-19 (or SARS-CoV-2) differ in their incubation distributions and in their susceptibility to immunologic defense. These features affect our ability to predict the course of these epidemics and to control them.