Absolute risk from double nested case-control designs: cause-specific proportional hazards models with and without augmented estimating equations.

We estimate relative hazards and absolute risks (or cumulative incidence or crude risk) under cause-specific proportional hazards models for competing risks from double nested case-control (DNCC) data. In the DNCC design, controls are time-matched not only to cases from the cause of primary interest, but also to cases from competing risks (the phase-two sample). Complete covariate data are available in the phase-two sample, but other cohort members only have information on survival outcomes and some covariates. Design-weighted estimators use inverse sampling probabilities computed from Samuelsen-type calculations for DNCC. To take advantage of additional information available on all cohort members, we augment the estimating equations with a term that is unbiased for zero but improves the efficiency of estimates from the cause-specific proportional hazards model. We establish the asymptotic properties of the proposed estimators, including the estimator of absolute risk, and derive consistent variance estimators. We show that augmented design-weighted estimators are more efficient than design-weighted estimators. Through simulations, we show that the proposed asymptotic methods yield nominal operating characteristics in practical sample sizes. We illustrate the methods using prostate cancer mortality data from the Prostate, Lung, Colorectal, and Ovarian Cancer Screening Trial Study of the National Cancer Institute.

COVID-19 and long-term impact on symptoms and Health-Related Quality of Life in Costa Rica: the RESPIRA cohort study.

BACKGROUND: Evidence continues to accumulate regarding the potential long-term health consequences of COVID-19 in the population. To distinguish between COVID-19-related symptoms and health limitations from those caused by other conditions, it is essential to compare cases with community controls using prospective data ensuring case-control status. The RESPIRA study addresses this need by investigating the lasting impact of COVID-19 on Health-related Quality of Life (HRQoL) and symptomatology in a population-based cohort in Costa Rica, thereby providing a robust framework for controlling HRQoL and symptoms. METHODS: The study comprised 641 PCR-confirmed, unvaccinated cases of COVID-19 and 947 matched population-based controls. Infection was confirmed using antibody tests on enrollment serum samples and symptoms were monitored monthly for 6 months post-enrolment. Administered at the 6-month visit (occurring between 6- and 2-months post-diagnosis for cases and 6 months after enrollment for controls), HRQoL and Self-Perceived Health Change were assessed using the SF-36, while brain fog, using three items from the Mental Health Inventory (MHI). Regression models were utilized to analyze SF-36, MHI scores, and Self-Perceived Health Change, adjusted for case/control status, severity (mild case, moderate case, hospitalized) and additional independent variables. Sensitivity analyses confirmed the robustness of the findings. RESULTS: Cases showed significantly higher prevalences of joint pain, chest tightness, and skin manifestations, that stabilized at higher frequencies from the fourth month post-diagnosis onwards (2.0%, 1.2%, and 0.8% respectively) compared to controls (0.9%, 0.4%, 0.2% respectively). Cases also exhibited significantly lower HRQoL than controls across all dimensions in the fully adjusted model, with a 12.4 percentage-point difference [95%CI: 9.4-14.6], in self-reported health compared to one year prior. Cases reported 8.0% [95%CI: 4.2, 11.5] more physical limitations, 7.3% [95%CI: 3.5, 10.5] increased lack of vitality, and 6.0% [95%CI: 2.4, 9.0] more brain fog compared to controls with similar characteristics. Undiagnosed cases detected with antibody tests among controls had HRQoL comparable to antibody negative controls. Differences were more pronounced in individuals with moderate or severe disease and among women. CONCLUSIONS: PCR-confirmed unvaccinated cases experienced prolonged HRQoL reductions 6 months to 2 years after diagnosis, this was particularly the case in severe cases and among women. Mildly symptomatic cases showed no significant long-term sequelae.

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.

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.

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.

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.

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.

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).

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.

Power of Microbiome Beta-Diversity Analyses Based on Standard Reference Samples.

A simple method to analyze microbiome beta-diversity computes mean beta-diversity distances from a test sample to standard reference samples. We used reference stool and nasal samples from the Human Microbiome Project and regressed an outcome on mean distances (2 degrees-of-freedom (df) test) or additionally on squares and cross-product of mean distances (5-df test). We compared the power of 2-df and 5-df tests with the microbiome regression-based kernel association test (MiRKAT). In simulations, MiRKAT had moderately greater power than the 2-df test for discriminating skin versus saliva and skin versus nasal samples, but differences were negligible for skin versus stool and stool versus nasal samples. The 2-df test had slightly greater power than MiRKAT for Dirichlet multinomial samples. In associating body mass index with beta-diversity in stool samples from the American Gut Project, the 5-df test yielded smaller P values than MiRKAT for most taxonomic levels and beta-diversity measures. Unlike procedures like MiRKAT that are based on the beta-diversity matrix, mean distances to reference samples can be analyzed with standard statistical tools and shared or meta-analyzed without sharing primary DNA data. Our data indicate that standard reference tests have power comparable to MiRKAT's (and to permutational multivariate analysis of variance), but more simulations and applications are needed to confirm this.

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.

Efficacy of the bivalent HPV vaccine against HPV 16/18-associated precancer: long-term follow-up results from the Costa Rica Vaccine Trial.

BACKGROUND: Oncogenic human papillomavirus (HPV) infections cause most cases of cervical cancer. Here, we report long-term follow-up results for the Costa Rica Vaccine Trial (publicly funded and initiated before licensure of the HPV vaccines), with the aim of assessing the efficacy of the bivalent HPV vaccine for preventing HPV 16/18-associated cervical intraepithelial neoplasia grade 2 or worse (CIN2+). METHODS: Women aged 18-25 years were enrolled in a randomised, double-blind, controlled trial in Costa Rica, between June 28, 2004, and Dec 21, 2005, designed to assess the efficacy of a bivalent vaccine for the prevention of infection with HPV 16/18 and associated precancerous lesions at the cervix. Participants were randomly assigned (1:1) to receive an HPV 16/18 AS04-adjuvanted vaccine or control hepatitis A vaccine. Vaccines were administered intramuscularly in three 0·5 mL doses at 0, 1, and 6 months and participants were followed up annually for 4 years. After the blinded phase, women in the HPV vaccine group were invited to enrol in the long-term follow-up study, which extended follow-up for 7 additional years. The control group received HPV vaccine and was replaced with a new unvaccinated control group. Women were followed up every 2 years until year 11. Investigators and patients were aware of treatment allocation for the follow-up phase. At each visit, clinicians collected cervical cells from sexually active women for cytology and HPV testing. Women with abnormal cytology were referred to colposcopy, biopsy, and treatment as needed. Women with negative results at the last screening visit (year 11) exited the long-term follow-up study. The analytical cohort for vaccine efficacy included women who were HPV 16/18 DNA-negative at vaccination. The primary outcome of this analysis was defined as histopathologically confirmed CIN2+ or cervical intraepithelial neoplasia grade 3 or worse associated with HPV 16/18 cervical infection detected at colposcopy referral. We calculated vaccine efficacy by year and cumulatively. This long-term follow-up study is registered with ClinicalTrials.gov, NCT00867464. FINDINGS: 7466 women were enrolled in the Costa Rica Vaccine Trial; 3727 received the HPV vaccine and 3739 received the control vaccine. Between March 30, 2009, and July 5, 2012, 2635 women in the HPV vaccine group and 2836 women in the new unvaccinated control group were enrolled in the long-term follow-up study. 2635 women in the HPV vaccine group and 2677 women in the control group were included in the analysis cohort for years 0-4, and 2073 women from the HPV vaccine group and 2530 women from the new unvaccinated control group were included in the analysis cohort for years 7-11. Median follow-up time for the HPV group was 11·1 years (IQR 9·1-11·7), 4·6 years (4·3-5·3) for the original control group, and 6·2 years (5·5-6·9) for the new unvaccinated control group. At year 11, vaccine efficacy against incident HPV 16/18-associated CIN2+ was 100% (95% CI 89·2-100·0); 34 (1·5%) of 2233 unvaccinated women had a CIN2+ outcome compared with none of 1913 women in the HPV group. Cumulative vaccine efficacy against HPV 16/18-associated CIN2+ over the 11-year period was 97·4% (95% CI 88·0-99·6). Similar protection was observed against HPV 16/18-associated CIN3-specifically at year 11, vaccine efficacy was 100% (95% CI 78·8-100·0) and cumulative vaccine efficacy was 94·9% (73·7-99·4). During the long-term follow-up, no serious adverse events occurred that were deemed related to the HPV vaccine. The most common grade 3 or worse serious adverse events were pregnancy, puerperium, and perinatal conditions (in 255 [10%] of 2530 women in the unvaccinated control group and 201 [10%] of 2073 women in the HPV vaccine group). Four women in the unvaccinated control group and three in the HPV vaccine group died; no deaths were deemed to be related to the HPV vaccine. INTERPRETATION: The bivalent HPV vaccine has high efficacy against HPV 16/18-associated precancer for more than a decade after initial vaccination, supporting the notion that invasive cervical cancer is preventable. FUNDING: US National Cancer Institute.

Weight calibration to improve the efficiency of pure risk estimates from case-control samples nested in a cohort.

Cohort studies provide information on relative hazards and pure risks of disease. For rare outcomes, large cohorts are needed to have sufficient numbers of events, making it costly to obtain covariate information on all cohort members. We focus on nested case-control designs that are used to estimate relative hazard in the Cox regression model. In 1997, Langholz and Borgan showed that pure risk can also be estimated from nested case-control data. However, these approaches do not take advantage of some covariates that may be available on all cohort members. Researchers have used weight calibration to increase the efficiency of relative hazard estimates from case-cohort studies and nested cased-control studies. Our objective is to extend weight calibration approaches to nested case-control designs to improve precision of estimates of relative hazards and pure risks. We show that calibrating sample weights additionally against follow-up times multiplied by relative hazards during the risk projection period improves estimates of pure risk. Efficiency improvements for relative hazards for variables that are available on the entire cohort also contribute to improved efficiency for pure risks. We develop explicit variance formulas for the weight-calibrated estimates. Simulations show how much precision is improved by calibration and confirm the validity of inference based on asymptotic normality. Examples are provided using data from the American Association of Retired Persons Diet and Health Cohort Study.

On Mendelian randomization analysis of case-control study.

Mendelian randomization (MR) analysis uses genotypes as instruments to estimate the causal effect of an exposure in the presence of unobserved confounders. The existing MR methods focus on the data generated from prospective cohort studies. We develop a procedure for studying binary outcomes under a case-control design. The proposed procedure is built upon two working models commonly used for MR analyses and adopts a quasi-empirical likelihood framework to address the ascertainment bias from case-control sampling. We derive various approaches for estimating the causal effect and hypothesis testing under the empirical likelihood framework. We conduct extensive simulation studies to evaluate the proposed methods. We find that the proposed empirical likelihood estimate is less biased than the existing estimates. Among all the approaches considered, the Lagrange multiplier (LM) test has the highest power, and the confidence intervals derived from the LM test have the most accurate coverage. We illustrate the use of our method in MR analysis of prostate cancer case-control data with vitamin D level as exposure and three single nucleotide polymorphisms as instruments.

Estimating the decision curve and its precision from three study designs.

The decision curve plots the net benefit (NB) of a risk model for making decisions over a range of risk thresholds, corresponding to different ratios of misclassification costs. We discuss three methods to estimate the decision curve, together with corresponding methods of inference and methods to compare two risk models at a given risk threshold. One method uses risks (R) and a binary event indicator (Y) on the entire validation cohort. This method makes no assumptions on how well-calibrated the risk model is nor on the incidence of disease in the population and is comparatively robust to model miscalibration. If one assumes that the model is well-calibrated, one can compute a much more precise estimate of NB based on risks R alone. However, if the risk model is miscalibrated, serious bias can result. Case-control data can also be used to estimate NB if the incidence (or prevalence) of the event ( Y=1 ) is known. This strategy has comparable efficiency to using the full (R,Y) data, and its efficiency is only modestly less than that for the full (R,Y) data if the incidence is estimated from the mean of Y. We estimate variances using influence functions and propose a bootstrap procedure to obtain simultaneous confidence bands around the decision curve for a range of thresholds. The influence function approach to estimate variances can also be applied to cohorts derived from complex survey samples instead of simple random samples.

Using standard microbiome reference groups to simplify beta-diversity analyses and facilitate independent validation.

Motivation: Comparisons of microbiome communities across populations are often based on pairwise distance measures (beta-diversity). Standard analyses (principal coordinate plots, permutation tests, kernel methods) require access to primary data if another investigator wants to add or compare independent data. We propose using standard reference measurements to simplify microbiome beta-diversity analyses, to make them more transparent, and to facilitate independent validation and comparisons across studies. Results: Using stool and nasal reference sets from the Human Microbiome Project (HMP), we computed mean distances (actually Bray-Curtis or Pearson correlation dissimilarities) to each reference set for each new sample. Thus, each new sample has two mean distances that can be plotted and analyzed with classical statistical methods. To test the approach, we studied independent (not reference) HMP subjects. Simple Hotelling tests demonstrated statistically significant differences in mean distances to reference sets between all pairs of body sites (stool, skin, nasal, saliva and vagina) at the phylum, class, order, family and genus levels. Using the distance to a single reference set was usually sufficient, but using both reference sets always worked well. The use of reference sets simplifies standard analyses of beta-diversity and facilitates the independent validation and combining of such data because others can compute distances to the same reference sets. Moreover, standard statistical methods for survival analysis, logistic regression and other procedures can be applied to vectors of mean distances to reference sets, thereby greatly expanding the potential uses of beta-diversity information. More work is needed to identify the best reference sets for particular applications. Availability and implementation: https://github.com/NCI-biostats/microbiome-fixed-reference. Supplementary information: Supplementary data are available at Bioinformatics online.

Design and analysis considerations for combining data from multiple biomarker studies.

Pooling data from multiple studies improves estimation of exposure-disease associations through increased sample size. However, biomarker exposure measurements can vary substantially across laboratories and often require calibration to a reference assay prior to pooling. We develop two statistical methods for aggregating biomarker data from multiple studies: the full calibration method and the internalized method. The full calibration method calibrates all biomarker measurements regardless of the availability of reference laboratory measurements while the internalized method calibrates only non-reference laboratory measurements. We compare the performance of these two aggregation methods to two-stage methods. Furthermore, we compare the aggregated and two-stage methods when estimating the calibration curve from controls only or from a random sample of individuals from the study cohort. Our findings include the following: (1) Under random sampling for calibration, exposure effect estimates from the internalized method have a smaller mean squared error than those from the full calibration method. (2) Under the controls-only calibration design, the full calibration method yields effect estimates with the least bias. (3) The two-stage approaches produce average effect estimates that are similar to the full calibration method under a controls only calibration design and the internalized method under a random sample calibration design. We illustrate the methods in an application evaluating the relationship between circulating vitamin D levels and stroke risk in a pooling project of cohort studies.

Circulating 25-hydroxyvitamin D up to 3 decades prior to diagnosis in relation to overall and organ-specific cancer survival.

While vitamin D has been associated with improved overall cancer survival in some investigations, few have prospectively evaluated organ-specific survival. We examined the accepted biomarker of vitamin D status, serum 25-hydroxyvitamin D [25(OH)D], and cancer survival in the Alpha-Tocopherol, Beta-Carotene Cancer Prevention Study. Of 4616 cancer cases with measured serum 25(OH)D, 2884 died of their cancer during 28 years of follow-up and 1732 survived or died of other causes. Proportional hazards regression estimated hazard ratios (HR) and 95% confidence intervals (CI) for the association between pre-diagnostic 25(OH)D and overall and site-specific survival. Serum 25(OH)D was significantly lower among cases who subsequently died from their malignancy compared with those who did not (medians 34.7 vs. 36.5 nmol/L, respectively; p = 0.01). Higher 25(OH)D was associated with lower overall cancer mortality (HR = 0.76, 95% CI 0.67-0.85 for highest vs. lowest quintile, p-trend < 0.0001). Higher 25(OH)D was related to lower mortality from the following site-specific malignancies: prostate (HR = 0.74, 95% CI 0.55-1.01, p-trend = 0.005), kidney (HR = 0.59, 95% CI 0.35-0.98, p-trend = 0.28), and melanoma (HR = 0.39, 95% CI 0.20-0.78, p-trend = 0.01), but increased mortality from lung cancer (HR = 1.28, 95% CI 1.02-1.61, p-trend = 0.19). Improved survival was also suggested for head and neck, gastric, pancreatic, and liver cancers, though not statistically significantly, and case numbers for the latter two organ sites were small. Higher 25(OH)D status years prior to diagnosis was related to improved survival for overall and some site-specific cancers, associations that should be examined in other prospective populations that include women and other racial-ethnic groups.

Comparison of approaches for incorporating new information into existing risk prediction models.

We compare the calibration and variability of risk prediction models that were estimated using various approaches for combining information on new predictors, termed 'markers', with parameter information available for other variables from an earlier model, which was estimated from a large data source. We assess the performance of risk prediction models updated based on likelihood ratio (LR) approaches that incorporate dependence between new and old risk factors as well as approaches that assume independence ('naive Bayes' methods). We study the impact of estimating the LR by (i) fitting a single model to cases and non-cases when the distribution of the new markers is in the exponential family or (ii) fitting separate models to cases and non-cases. We also evaluate a new constrained maximum likelihood method. We study updating the risk prediction model when the new data arise from a cohort and extend available methods to accommodate updating when the new data source is a case-control study. To create realistic correlations between predictors, we also based simulations on real data on response to antiviral therapy for hepatitis C. From these studies, we recommend the LR method fit using a single model or constrained maximum likelihood. Copyright © 2016 John Wiley & Sons, Ltd.