Likelihood analysis of multi-state models for disease incidence and mortality

The role of co-occurring conditions and genetics in the associations of eating disorders with attention-deficit/hyperactivity disorder and autism spectrum disorder

Eating disorders (EDs) commonly co-occur with other psychiatric and neurodevelopmental disorders including attention-deficit/hyperactivity disorder (ADHD) and autism spectrum disorder (ASD); however, the pattern of family history and genetic overlap among them requires clarification. This study investigated the diagnostic, familial, and genetic associations of EDs with ADHD and ASD. The nationwide population-based cohort study included all individuals born in Denmark, 1981-2008, linked to their siblings and cousins. Cox regression was used to estimate associations between EDs and ADHD or ASD, and mediation analysis was used to assess the effects of intermediate mood or anxiety disorders. Polygenic scores (PGSs) were used to investigate the genetic association between anorexia nervosa (AN) and ADHD or ASD. Significantly increased risk for any ED was observed following an ADHD [hazard ratio = 1.97, 95% confidence interval = 1.75-2.22] or ASD diagnosis [2.82, 2.48-3.19]. Mediation analysis suggested that intermediate mood or anxiety disorders could account for 44-100% of the association between ADHD or ASD and ED. Individuals with a full sibling or maternal halfsibling with ASD had increased risk of AN [1.54, 1.33-1.78; 1.45, 1.08-1.94] compared to those with siblings without ASD. A positive association was found between ASD-PGS and AN risk [1.06, 1.02-1.09]. In this study, positive phenotypic associations between EDs and ADHD or ASD, mediation by mood or anxiety disorder, and a genetic association between ASD-PGS and AN were observed. These findings could guide future research in the development of new treatments that can mitigate the development of EDs among individuals with ADHD or ASD.

Diagnosed eating disorders in Danish registers - incidence, prevalence, mortality, and polygenic risk

Eating disorders are a group of severe and potentially enduring psychiatric disorders associated with increased mortality. Compared to other severe mental illnesses, they have received relatively limited research attention. Epidemiological studies often only report relative measures despite these being difficult to interpret having limited practical use. The aims of this study were to evaluate the incidence and prevalence of diagnosed anorexia nervosa (AN), bulimia nervosa, and eating disorder not otherwise specified recorded in Danish hospital registers and estimate both relative and absolute measures of subsequent mortality - both all-cause and cause-specific in a general nationwide population of 1,667,374 individuals. In a smaller, genetically informed case-cohort sample, the prediction of polygenic scores for AN, body fat percentage, and body mass index on AN prevalence and severity was estimated. Despite males being less likely to be diagnosed with an eating disorder, those that do have significantly increased rates of mortality. AN prevalence was highest for individuals with high AN and low body fat percentage/body mass index polygenic scores.

Estimation of the causal effects of time-varying treatments in nested case-control studies using marginal structural Cox models

When estimating the causal effects of time-varying treatments on survival in nested case-control (NCC) studies, marginal structural Cox models (Cox-MSMs) with inverse probability weights (IPWs) are a natural approach. However, calculating IPWs from the cases and controls is difficult because they are not random samples from the full cohort, and the number of subjects may be insufficient for calculation. To overcome these difficulties, we propose a method for calculating IPWs to fit Cox-MSMs to NCC sampling data. We estimate the IPWs using a pseudo-likelihood estimation method with an inverse probability of sampling weight using NCC samples, and additional samples of subjects who experience treatment changes and subjects whose follow-up is censored are required to calculate the weights. Our method only requires covariate histories for the samples. The confidence intervals are calculated from the robust variance estimator for the NCC sampling data. We also derive the asymptotic properties of the estimator of Cox-MSM under NCC sampling. The proposed methods will allow researchers to apply several case-control matching methods to improve statistical efficiency. A simulation study was conducted to evaluate the finite sample performance of the proposed method. We also applied our method to a motivating pharmacoepidemiological study examining the effect of statins on the incidence of coronary heart disease. The proposed method may be useful for estimating the causal effects of time-varying treatments in NCC studies.

Risk factors for anorexia nervosa: A population-based investigation of sex differences in polygenic risk and early life exposures

OBJECTIVE

To examine sex differences in risk factors for anorexia nervosa (AN).

METHOD

This population-based study involved 44,743 individuals (6,239 AN cases including 5,818 females and 421 males, and 38,504 controls including 18,818 females and 19,686 males) born in Denmark between May 1981 and December 2009. Follow-up began on the individual's sixth birthday and ended at AN diagnosis, emigration, death, or December 31, 2016, whichever occurred first. Exposures included socioeconomic status (SES), pregnancy, birth, and early childhood factors based on data from Danish registers, and psychiatric and metabolic polygenic risk scores (PRS) based on genetic data. Hazard ratios were estimated using weighted Cox proportional hazards models stratified by sex (assigned at birth), with AN diagnosis as the outcome.

RESULTS

The effects of early life exposures and PRS on AN risk were comparable between females and males. Although we observed some differences in the magnitude and direction of effects, there were no significant interactions between sex and SES, pregnancy, birth, or early childhood exposures. The effects of most PRS on AN risk were highly similar between the sexes. We observed significant sex-specific effects of parental psychiatric history and body mass index PRS, though these effects did not survive corrections for multiple comparisons.

CONCLUSIONS

Risk factors for AN are comparable between females and males. Collaboration across countries with large registers is needed to further investigate sex-specific effects of genetic, biological, and environmental exposures on AN risk, including exposures in later childhood and adolescence as well as the additive effects of exposures.

PUBLIC SIGNIFICANCE

Sex differences in the prevalence and clinical presentation of AN warrant examination of sex-specific risk factors. This population-based study indicates that the effects of polygenic risk and early life exposures on AN risk are comparable between females and males. Collaboration between countries with large registers is needed to further investigate sex-specific AN risk factors and improve early identification of AN.

Sure Joint Screening for High Dimensional Cox's Proportional Hazards Model Under the Case-Cohort Design

This study develops a sure joint feature screening method for the case-cohort design with ultrahigh-dimensional covariates. Our method is based on a sparsity-restricted Cox proportional hazards model. An iterative reweighted hard thresholding algorithm is proposed to approximate the sparsity-restricted, pseudo-partial likelihood estimator for joint screening. We rigorously show that our method possesses the sure screening property, with the probability of retaining all relevant covariates tending to 1 as the sample size goes to infinity. Our simulation results demonstrate that the proposed procedure has substantially improved screening performance over some existing feature screening methods for the case-cohort design, especially when some covariates are jointly correlated, but marginally uncorrelated, with the event time outcome. A real data illustration is provided using breast cancer data with high-dimensional genomic covariates. We have implemented the proposed method using MATLAB and made it available to readers through GitHub.

Adipose tissue n-3/n-6 fatty acids ratios versus n-3 fatty acids fractions as predictors of myocardial infarction

BACKGROUND

Tissue levels of n-3 polyunsaturated fatty acids (PUFAs) have been inversely related with risk of myocardial infarction (MI). Whether ratios of n-3 to n-6 PUFAs, reflecting both dietary intake of n-3 PUFAs and competing n-6 PUFAs, are better predictors of future MI than n-3 PUFA fractions is unclear. We aimed at investigating whether such ratios in adipose tissue better predict MI than n-3 PUFA fractions.

METHODS

Subcutaneous adipose tissue biopsies were obtained in a random sample (n=3,500) of the Diet, Cancer and Health cohort (n=57,053). Adipose tissue content of eicosapentaenoic acid (EPA), docosapentaenoic acid (DPA), docosahexaenoic acid (DHA), alpha-linolenic acid (ALA), arachidonic acid (AA) and linoleic acid (LA) was determined using gas chromatography. Fractions of selected n-3 PUFAs and n-3/n-6 PUFA ratios were correlated to the 15-year occurrence of MI in a case-cohort design.

RESULTS

A total of 2,406 participants experienced an MI during follow-up. Adipose tissue total marine n-3 PUFAs, EPA+DHA, EPA, EPA/AA, DHA/AA and (EPA+DPA+DHA)/AA were all inversely associated with risk of incident MI. Evaluating the predictive power (Harrel's C-index) of the selected metrics, fractions of marine n-3 PUFAs and ratios of EPA/AA, DHA/AA, (EPA+DHA)/AA and (EPA+DPA+DHA)/AA all refined risk prediction over age and sex alone. At multivariable analyses, however, the above ratios were the only metrics providing additional risk prediction. Differences in ratios were related to differences in food intake.

CONCLUSIONS

Both adipose tissue n-3 PUFAs fractions and ratios of n-3 PUFAs/AA were associated with a lower occurrence of MI, but ratios provided superior risk prediction. Dietary strategies affecting n-3/n-6 PUFA ratios should be further investigated for prediction of MI with dietary interventions at the population level and in intervention studies.

A nutritional biomarker score of the Mediterranean diet and incident type 2 diabetes: Integrated analysis of data from the MedLey randomised controlled trial and the EPIC-InterAct case-cohort study

BACKGROUND

Self-reported adherence to the Mediterranean diet has been modestly inversely associated with incidence of type 2 diabetes (T2D) in cohort studies. There is uncertainty about the validity and magnitude of this association due to subjective reporting of diet. The association has not been evaluated using an objectively measured biomarker of the Mediterranean diet.

METHODS AND FINDINGS

We derived a biomarker score based on 5 circulating carotenoids and 24 fatty acids that discriminated between the Mediterranean or habitual diet arms of a parallel design, 6-month partial-feeding randomised controlled trial (RCT) conducted between 2013 and 2014, the MedLey trial (128 participants out of 166 randomised). We applied this biomarker score in an observational study, the European Prospective Investigation into Cancer and Nutrition (EPIC)-InterAct case-cohort study, to assess the association of the score with T2D incidence over an average of 9.7 years of follow-up since the baseline (1991 to 1998). We included 22,202 participants, of whom 9,453 were T2D cases, with relevant biomarkers from an original case-cohort of 27,779 participants sampled from a cohort of 340,234 people. As a secondary measure of the Mediterranean diet, we used a score estimated from dietary-self report. Within the trial, the biomarker score discriminated well between the 2 arms; the cross-validated C-statistic was 0.88 (95% confidence interval (CI) 0.82 to 0.94). The score was inversely associated with incident T2D in EPIC-InterAct: the hazard ratio (HR) per standard deviation of the score was 0.71 (95% CI: 0.65 to 0.77) following adjustment for sociodemographic, lifestyle and medical factors, and adiposity. In comparison, the HR per standard deviation of the self-reported Mediterranean diet was 0.90 (95% CI: 0.86 to 0.95). Assuming the score was causally associated with T2D, higher adherence to the Mediterranean diet in Western European adults by 10 percentiles of the score was estimated to reduce the incidence of T2D by 11% (95% CI: 7% to 14%). The study limitations included potential measurement error in nutritional biomarkers, unclear specificity of the biomarker score to the Mediterranean diet, and possible residual confounding.

CONCLUSIONS

These findings suggest that objectively assessed adherence to the Mediterranean diet is associated with lower risk of T2D and that even modestly higher adherence may have the potential to reduce the population burden of T2D meaningfully.

TRIAL REGISTRATION

Australian New Zealand Clinical Trials Registry (ANZCTR) ACTRN12613000602729 https://www.anzctr.org.au/Trial/Registration/TrialReview.aspx?id=363860.

Omega-3 fatty acids in adipose tissue and risk of atrial fibrillation

BACKGROUND

The aim of the present study was to examine the relation between adipose tissue content of eicosapentaenoic acid (EPA) and docosahexaenoic acid (DHA) and the risk of incident atrial fibrillation (AF).

METHODS

In this case-cohort study based on data from the Danish Diet, Cancer and Health cohort, a total of 5255 incident cases of AF was identified during 16.9 years of follow-up. Adipose tissue biopsies collected at baseline from all cases and from a randomly drawn subcohort of 3440 participants were determined by gas chromatography. Data were analysed using weighted Cox regression.

RESULTS

Data were available for 4741 incident cases of AF (2920 men and 1821 women). Participants in the highest vs. the lowest quintile of EPA experienced a 45% lower risk of AF (men HR 0.55 (95% CI 0.41-0.69); women HR 0.55 (0.41-0.72)). For DHA, no clear association was found in men, whereas in women, participants in the highest quintile of DHA in adipose tissue had a 30% lower risk of incident AF (HR 0.70 (0.54-0.91)) compared to participants in the lowest quintile.

CONCLUSIONS

A monotonous inverse association was found for the content of EPA in adipose tissue and risk of AF in both men and women. The content of DHA was inversely associated with the risk of AF in women, whereas no clear association was found for men.

Conditional screening for ultrahigh-dimensional survival data in case-cohort studies

The case-cohort design has been widely used to reduce the cost of covariate measurements in large cohort studies. In many such studies, the number of covariates is very large, and the goal of the research is to identify active covariates which have great influence on response. Since the introduction of sure independence screening, screening procedures have achieved great success in terms of effectively reducing the dimensionality and identifying active covariates. However, commonly used screening methods are based on marginal correlation or its variants, they may fail to identify hidden active variables which are jointly important but are weakly correlated with the response. Moreover, these screening methods are mainly proposed for data under the simple random sampling and can not be directly applied to case-cohort data. In this paper, we consider the ultrahigh-dimensional survival data under the case-cohort design, and propose a conditional screening method by incorporating some important prior known information of active variables. This method can effectively detect hidden active variables. Furthermore, it possesses the sure screening property under some mild regularity conditions and does not require any complicated numerical optimization. We evaluate the finite sample performance of the proposed method via extensive simulation studies and further illustrate the new approach through a real data set from patients with breast cancer.

Linoleic acid in adipose tissue and the risk of myocardial infarction: a case-cohort study

PURPOSE

We investigated risk of myocardial infarction (MI) associated with the content of linoleic acid (LA) in adipose tissue, a biomarker of long-term dietary intake of LA and a marker of endogenous LA exposure.

METHODS

Between 1993 and 1997, 57,053 middle-aged subjects were included in the Danish Diet, Cancer and Health cohort. We performed a case-cohort study that included a random sample of the full cohort (n = 3167) and all incident MI cases appearing during 16 years of follow-up (n = 2819). Information on incident MI cases was obtained by linkage with Danish nationwide registries. Adipose tissue biopsies were taken from the buttocks of the participants, and their fatty acid composition was determined using gas chromatography. HRs (hazard ratios) with 95% confidence intervals (CIs) were used to describe the associations between content of LA in adipose tissue and the risk of MI. HRs were calculated using weighted Cox proportional hazards regression with robust variance.

RESULTS

After adjustment for established risk factors of MI, adipose tissue content of LA was not associated with the risk of MI in men and women combined (quintiles 5 versus 1, HR, 1.03 (95% CI, 0.85-1.25), P-trend = 0.970) or in men and women separately (quintiles 5 versus 1, HR, 1.05 (95% CI, 0.83-1.33), P-trend = 0.871 and quintiles 5 versus 1, HR, 0.99 (95% CI 0.72-1.37), P-trend = 0.928, respectively). Investigating the association between LA and MI with a shorter, 5- or 10-year duration of follow-up provided similar results.

CONCLUSION

Content of LA in adipose tissue was not associated with the risk of MI.

Cumulative risk regression in case-cohort studies using pseudo-observations

Case-cohort studies are useful when information on certain risk factors is difficult or costly to ascertain. Particularly, a case-cohort study may be well suited in situations where several case series are of interest, e.g. in studies with competing risks, because the same sub-cohort may serve as a comparison group for all case series. Previous analyses of this kind of sampled cohort data most often involved estimation of rate ratios based on a Cox regression model. However, with competing risks this method will not provide parameters that directly describe the association between covariates and cumulative risks. In this paper, we study regression analysis of cause-specific cumulative risks in case-cohort studies using pseudo-observations. We focus mainly on the situation with competing risks. However, as a by-product, we also develop a method by which absolute mortality risks may be analyzed directly from case-cohort survival data. We adjust for the case-cohort sampling by inverse sampling probabilities applied to a generalized estimation equation. The large-sample properties of the proposed estimator are developed and small-sample properties are evaluated in a simulation study. We apply the methodology to study the effect of a specific diet component and a specific gene on the absolute risk of atrial fibrillation.

Multiplicative rates model for recurrent events in case-cohort studies

In large prospective cohort studies, accumulation of covariate information and follow-up data make up the majority of the cost involved in the study. This might lead to the study being infeasible when there are some expensive variables and/or the event is rare. Prentice (Biometrika 73(1):1-11, 1986) proposed the case-cohort study for time to event data to tackle this problem. There has been extensive research on the analysis of univariate and clustered failure time data, where the clusters are formed among different individuals under case-cohort sampling scheme. However, recurrent event data are quite common in biomedical and public health research. In this paper, we propose case-cohort sampling schemes for recurrent events. We consider a multiplicative rates model for the recurrent events and propose a weighted estimating equations approach for parameter estimation. We show that the estimators are consistent and asymptotically normally distributed. The proposed estimator performed well in finite samples in our simulation studies. For illustration purposes, we examined the association between prior occurrence of measles on acute lower respiratory tract infections (ALRI) among young children in Brazil.

Adipose tissue content of alpha-linolenic acid and development of peripheral artery disease: a Danish case-cohort study

PURPOSE

The aim of this study was to investigate the association between adipose tissue content of the plant-derived n-3 fatty acid, alpha-linolenic acid, and the rate of incident peripheral artery disease (PAD).

METHODS

We conducted a case-cohort study nested within the Danish Diet, Cancer and Health cohort (n = 57,053), which was established between 1993 and 1997. Potential PAD cases were identified using linkage with The Danish National Patient Register and all potential cases were validated. Adipose tissue samples from the buttock were collected at baseline and fatty acid composition was determined in cases and in a random sample (n = 3500) from the cohort by gas chromatography. Statistical analyses were performed using weighted Cox regression allowing for different baseline hazards among sexes.

RESULTS

During a median of 13.5 years of follow-up, we identified 863 PAD cases with complete information. The median adipose tissue content of ALA in the sub-cohort (n = 3197) was 0.84% (interquartile range 0.73-0.94%) of total fatty acids. In multivariate analyses including adjustment for established risk factors, we observed a U-shaped association between ALA in adipose tissue and rate of PAD, but the association was not statistically significant (P = 0.131). Similar pattern of associations were observed between ALA content in adipose tissue and the rate of PAD among men and women.

CONCLUSIONS

We found indications of a U-shaped association between adipose tissue content of ALA and the rate of PAD, but the association was not statistically significant.

Sampling-based Markov regression model for multistate disease progression: Applications to population-based cancer screening program

To develop personalized screening and surveillance strategies, the information required to superimpose state-specific covariates into the multi-step progression of disease natural history often relies on the entire population-based screening data, which are costly and infeasible particularly when a new biomarker is proposed. Following Prentice's case-cohort concept, a non-standard case-cohort design from a previous study has been adapted for constructing multistate disease natural history with two-stage sampling. Nonetheless, the use of data only from first screens may invoke length-bias and fail to consider the test sensitivity. Therefore, a new sampling-based Markov regression model and its variants are proposed to accommodate additional subsequent follow-up data on various detection modes to construct state-specific covariate-based multistate disease natural history with accuracy and efficiency. Computer simulation algorithms for determining the required sample size and the sampling fraction of each detection mode were developed either through power function or the capacity of screening program. The former is illustrated with breast cancer screening data from which the effect size and the required sample size regarding the effect of BRCA on multistate outcome of breast cancer were estimated. The latter is applied to population-based colorectal cancer screening data to identify the optimal sampling fraction of each detection mode.

Joint models for longitudinal and time-to-event data in a case-cohort design

Studies with longitudinal measurements are common in clinical research. Particular interest lies in studies where the repeated measurements are used to predict a time‐to‐event outcome, such as mortality, in a dynamic manner. If event rates in a study are low, however, and most information is to be expected from the patients experiencing the study endpoint, it may be more cost efficient to only use a subset of the data. One way of achieving this is by applying a case‐cohort design, which selects all cases and only a random samples of the noncases. In the standard way of analyzing data in a case‐cohort design, the noncases who were not selected are completely excluded from analysis; however, the overrepresentation of the cases will lead to bias. We propose to include survival information of all patients from the cohort in the analysis. We approach the fact that we do not have longitudinal information for a subset of the patients as a missing data problem and argue that the missingness mechanism is missing at random. Hence, results obtained from an appropriate model, such as a joint model, should remain valid. Simulations indicate that our method performs similar to fitting the model on a full cohort, both in terms of parameters estimates and predictions of survival probabilities. Estimating the model on the classical version of the case‐cohort design shows clear bias and worse performance of the predictions. The procedure is further illustrated in data from a biomarker study on acute coronary syndrome patients, BIOMArCS.

Long-Term Whole Grain Wheat and Rye Intake Reflected by Adipose Tissue Alkylresorcinols and Breast Cancer: A Case-Cohort Study

Whole grain rye (WGR) and whole grain wheat (WGW) have been suggested to protect against the development of breast cancer. In this study, we estimated long-term intake of WGR and WGW, using both a food frequency questionnaire (FFQ) and alkylresorcinol concentrations in adipose tissue biopsies, in relation to the risk of developing invasive breast cancer in a case-cohort study (n = 414 in the case group, n = 933 in the subcohort group) on the Danish “Diet, Cancer and Health” cohort. The median follow-up time of the subcohort was 5.3 years. Total WGR and WGW intake estimated with FFQ or reflected by total alkylresorcinol concentration in adipose tissue was not significantly associated with risk of breast cancer. However, after adjustment for total WGR and WGW intake, women in the highest quartile of relative WGR intake, reflected by the alkylresorcinol C17:0/C21:0 ratio, had a higher risk of overall breast cancer and estrogen-receptor-positive (ER+) breast cancer than women in the lowest quartile of relative WGR intake, while the risk of estrogen-receptor-negative (ER-) breast cancer incidence was unaffected. Similar results were obtained with the FFQ data. Based on these data, further investigation of the role of specific grain types in reducing or increasing breast cancer risk, and their overall impact on health, is warranted.

Marine n-3 Polyunsaturated Fatty Acids and the Risk of Ischemic Stroke

Background and Purpose—

We hypothesized that total marine n-3 polyunsaturated fatty acids (PUFA), in particular eicosapentaenoic acid (EPA) and docosahexaenoic acid (DHA) in the diet and in adipose tissue (biomarkers of long-term intake and endogenous exposure) were inversely associated with the risk of ischemic stroke and its subtypes.

Methods—

The Diet, Cancer and Health cohort consisted of 57 053 participants aged 50 to 65 years at enrolment. All participants filled in a food frequency questionnaire and had an adipose tissue biopsy taken at baseline. Information on ischemic stroke during follow-up was obtained from The Danish National Patient Register, and all cases were validated. Cases and a random sample of 3203 subjects from the whole cohort had their fatty acid composition of adipose tissue determined by gas chromatography.

Results—

During 13.5 years of follow-up 1879 participants developed an ischemic stroke. Adipose tissue content of EPA was inversely associated with total ischemic stroke (hazard ratio [HR], 0.74; 95% CI, 0.62–0.88) when comparing the highest with the lowest quartile. Also, lower rates of large artery atherosclerosis were seen with higher intakes of total marine n-3 PUFA (HR, 0.69; 95% CI, 0.50–0.95), EPA (HR, 0.66; 95% CI, 0.48–0.91) and DHA (HR, 0.72; 95% CI, 0.53–0.99), and higher adipose tissue content of EPA (HR, 0.52; 95% CI, 0.36–0.76). Higher rates of cardioembolism were seen with higher intakes of total marine n-3 PUFA (HR, 2.50; 95% CI, 1.38–4.53) and DHA (HR, 2.12; 95% CI, 1.21–3.69) as well as with higher adipose tissue content of total marine n-3 PUFA (HR, 2.63; 95% CI, 1.33–5.19) and DHA (HR, 2.00; 95% CI, 1.04–3.84). The EPA content in adipose tissue was inversely associated with small-vessel occlusion (HR, 0.69; 95% CI, 0.55–0.88).

Conclusions—

EPA was associated with lower risks of most types of ischemic stroke, apart from cardioembolism, while inconsistent findings were observed for total marine n-3 PUFA and DHA.

Patterns of adipose tissue fatty acids and the risk of atrial fibrillation: A case-cohort study

Fatty acids in adipose tissue share dietary sources and metabolic pathways and therefore occur in patterns. The aim of the present study was to investigate the association between adipose tissue fatty acid patterns identified by the data-driven dimension-reducing method treelet transform and the risk of atrial fibrillation. A total of 57,053 Danish men and women aged 50–64 years participating in the Diet, Cancer and Health cohort had an adipose tissue biopsy taken at baseline. During a median follow-up of 14.6 years, a total of 4,710 participants developed atrial fibrillation or atrial flutter. Adipose tissue biopsies were analysed for fatty acid content by gas chromatography for all cases of atrial fibrillation and for a randomly drawn subcohort (n = 3,500) representative for the entire cohort. Hazard ratios with 95% confidence intervals for atrial fibrillation according to quintiles of factor scores were determined by weighted Cox proportional hazards regression analyses for men and women separately. From the 32 fatty acids measured, 7 major factors/patterns of fatty acids were identified using treelet transform. We found that a pattern consisting of n-6 polyunsaturated fatty acids (PUFA) (except linoleic acid) was associated with a lower hazard of atrial fibrillation. Patterns consisting of marine n-3 PUFA and containing n-9 fatty acids were associated with a lower hazard of atrial fibrillation in women. In conclusion, patterns of fatty acids in adipose tissue identified by treelet transform may be differentially associated with the risk of atrial fibrillation.

Adipose Tissue Lipophilic Index and Risk of Ischemic Stroke-A Danish Case-Cohort Study

Diet may influence the risk of ischemic stroke by several mechanisms. A potential and hitherto unknown mechanism may relate to an effect on the lipophilic index, which is a new and convenient indicator of membrane fluidity. This study investigated the association between the adipose tissue lipophilic index and ischemic stroke and its subtypes. A case-cohort study was conducted based on the Danish cohort study Diet, Cancer, and Health, which includes 57,053 subjects aged 50–64 years at enrolment. A subcohort (n = 3500) was randomly drawn from the whole cohort. All ischemic stroke cases were validated and categorized into subtypes. The lipophilic index was calculated based on fatty acid profiles in adipose tissue. Subjects were divided into quintiles and a weighted Cox proportional hazards regression model was used to calculate hazard ratios. After appropriate exclusions, a subcohort of 3194 subjects and 1752 cases of ischemic stroke were included. When comparing the fifth quintile of the lipophilic index with the first quintile, the hazard ratio for ischemic stroke was 0.92 (95% confidence interval 0.75, 1.13) and the trend across quintiles was not statistically significant (p = 0.1727). In conclusion, no association was found between the lipophilic index and ischemic stroke or its subtypes.

Bi-level variable selection for case-cohort studies with group variables

The case-cohort design is an economical approach to estimate the effect of risk factors on the survival outcome when collecting exposure information or covariates on all patients is expensive in a large cohort study. Variables often have group structure such as categorical variables and highly correlated continuous variables. The existing literature for case-cohort data is limited to identifying non-zero variables at individual level only. In this article, we propose a bi-level variable selection method to select non-zero group and within-group variables for case-cohort data when variables have group structure. The proposed method allows the number of variables to diverge as the sample size increases. The asymptotic properties of the estimator including bi-level variable selection consistency and the asymptotic normality are shown. We also conduct simulations to compare our proposed method with some existing method and apply them to the Busselton Health data.

Trans fatty acids in adipose tissue and risk of myocardial infarction: A case-cohort study

BACKGROUND

The risk of coronary heart disease associated with intake of individual trans fatty acids (TFAs) is not clear. Adipose tissue content of TFAs is a biomarker of TFA intake and metabolism.

OBJECTIVE

We investigated the rate of myocardial infarction (MI) associated with the adipose tissue content of total 18:1t, isomers of 18:1t (18:1 Δ6-10t and 18:1 Δ11t) and 18:2 Δ9c, 11t.

METHODS

A case-cohort study, nested within the Danish Diet, Cancer and Health cohort (n = 57,053), was conducted, which included a random sample (n = 3156) of the total cohort and all incident MI cases (n = 2148) during follow-up (14 years). Information on MI cases was obtained by linkage with nationwide registers and validated. Adipose tissue was taken from the participants buttocks and the fatty acid composition was determined by gas chromatography.

RESULTS

Women with higher adipose tissue content of total 18:1t had a 57% higher MI rate (quintiles 5 versus 1, hazard ratio, 1.57; 95% confidence interval, 1.12-2.20; P-trend = 0.011) and women with higher content of 18:1 Δ6-10t had a 76% higher MI rate (quintiles 5 versus 1, hazard ratio, 1.76; 95% confidence interval, 1.23-2.51; P-trend = 0.002). No association between 18:1 Δ11t content and MI rate was observed. In men, no associations between adipose tissue content of total 18:1t and 18:1 Δ6-10t and MI rate were observed. However, men with higher content of 18:1 Δ11t had a 48% higher MI rate (quintiles 5 versus 1, hazard ratio, 1.48; 95% confidence interval, 1.17-1.86; P-trend = 0.003). Adipose tissue content of 18:2 Δ9c, 11t was not associated with MI rate in women or men.

CONCLUSIONS

Adipose tissue content of 18:2 Δ9c, 11t was not associated with MI rate in women or men, whereas higher contents of isomers of 18:1t were associated with higher MI rates but the associations for individual 18:1t isomers differed, however, in women and men.

Linoleic Acid in Adipose Tissue and Development of Ischemic Stroke: A Danish Case-Cohort Study

Background

We investigated the association between the content of linoleic acid in adipose tissue, a biomarker of long‐term intake of linoleic acid, and the risk of ischemic stroke and its subtypes.

Methods and Results

The Danish cohort study Diet, Cancer and Health included 57 053 patients aged 50 to 65 years at enrollment. All participants had an adipose tissue biopsy performed at enrollment, while information on ischemic stroke during follow‐up was obtained from the Danish National Patient Register. Stroke diagnoses were all validated and classified according to the Trial of Org 10172 in Acute Stroke Treatment (TOAST) classification. Cases and a randomly drawn subcohort of 3500 patients had their fatty acid composition in adipose tissue determined by gas chromatography. Hazard ratios with 95% confidence intervals were calculated using weighted Cox proportional hazard regression. During 13.5 years of follow‐up, 1879 ischemic stroke cases were identified, for which 1755 adipose biopsies were available, while adipose biopsies were available for 3203 participants in the subcohort. When comparing the highest and the lowest quartiles of adipose tissue content of linoleic acid there was a negative association with the rate of total ischemic stroke (hazard ratio, 0.78; 95% confidence interval, 0.65–0.93) and large artery atherosclerosis (hazard ratio, 0.61; 95% confidence interval, 0.43–0.88), while there was an indication of a negative association with small‐vessel occlusion (hazard ratio, 0.87; 95% confidence interval, 0.69–1.11). There was no clear association with the rate of cardioembolism.

Conclusions

The content of linoleic acid in adipose tissue was inversely associated with the risk of total ischemic stroke and stroke caused by large artery atherosclerosis.

Adipose tissue content of alpha-linolenic acid and the risk of ischemic stroke and ischemic stroke subtypes: A Danish case-cohort study

BACKGROUND

The plant-derived omega-3 fatty acid alpha-linolenic acid (ALA) may reduce the risk of cardiovascular disease.

OBJECTIVE

We have investigated associations between the content of ALA in adipose tissue and the risk of ischemic stroke and its subtypes.

METHODS

Incident cases of ischemic stroke among participants enrolled into the Danish Diet, Cancer and Health cohort (n = 57,053) were identified by linkage with the Danish National Patient Register. Subsequently, all potential cases were validated and classified into ischemic stroke subtypes. The fatty acid composition of adipose tissue was determined by gas chromatography in cases and in a randomly drawn sub-cohort (n = 3500). Statistical analyses were performed using weighted Cox regression.

RESULTS

During a median of 13.4 years of follow-up, 1735 cases of total ischemic stroke were identified including 297 cases of large artery atherosclerosis, 772 cases of small-vessel occlusion, 99 cases of cardio-embolism, 91 cases with stroke of other etiology and 476 cases with stroke of undetermined etiology. The median content of ALA in adipose tissue within the sub-cohort was 0.84% (95% central range: 0.53-1.19%). Multivariable analyses showed a U-shaped association between adipose tissue content of ALA and the rate of total ischemic stroke, but this association was not statistically significant (p = 0.172). In analyses of ischemic stroke subtypes, we observed a statistically significant U-shaped association between ALA and the rate of ischemic stroke due to large artery atherosclerosis (p = 0.017), whereas no appreciable association was observed between ALA and the rate of small-vessel occlusion (p = 0.427). A positive but statistically non-significant association was observed between ALA and the rate of ischemic stroke due to cardio-embolism (p = 0.162).

CONCLUSIONS

The content of ALA in adipose tissue was statistically non-significantly U-shaped associated with risk of total ischemic stroke. For ischemic stroke subtypes a statistically significant, U-shaped association with large artery atherosclerosis was observed.

Maternal Thyroid Function in Early Pregnancy and Child Neurodevelopmental Disorders: A Danish Nationwide Case-Cohort Study

BACKGROUND

Maternal thyroid dysfunction may adversely affect fetal brain development, but more evidence is needed to refine this hypothesis. The aim of this study was to evaluate potential fetal programming by abnormal maternal thyroid function on child neurodevelopmental disorders.

METHODS

The design was a case-cohort study within the Danish National Birth Cohort (1997-2003). From the eligible cohort of 71,706 women, a random 12% sub-cohort (n = 7624) was selected, and all women (n = 2276) whose child was diagnosed with seizures, specific developmental disorder (SDD), autism spectrum disorder (ASD), and/or attention-deficit/hyperactivity disorder (ADHD) up to December 31, 2010, were identified. All women had a blood sample drawn in early pregnancy (median week 9), and the stored sample was used for measurement of free thyroxine and thyrotropin. Method- and week-specific reference ranges were used for classification of maternal thyroid function. A weighted Cox proportional hazards model was used to estimate adjusted hazard ratio (aHR) with 95% confidence intervals (CI) for neurodevelopmental disorders in children exposed to maternal thyroid dysfunction.

RESULTS

The overall frequency of abnormal maternal thyroid function was 12.5% in the sub-cohort and significantly higher among cases of ASD (17.9%; aHR = 1.5 [CI 1.1-2.1]), but not among other types of neurodevelopmental disorders (febrile seizures: 12.7%; epilepsy: 13.1%; SDD: 12.6%; and ADHD: 14.0%). However, evaluation of subtypes of maternal thyroid dysfunction showed that maternal overt hypothyroidism (thyrotropin >10 mIU/L) was a risk factor for epilepsy in the child (aHR = 3.5 [CI 1.2-10]), as was overt hyperthyroidism for cases diagnosed within the first year of life (aHR = 3.0 [CI 1.03-8.4]). Furthermore, both maternal hypothyroidism (aHR = 1.8 [CI 1.1-2.7]) and overt hyperthyroidism (aHR = 2.2 [CI 1.1-4.4]) were risk factors for ASD in the child, and isolated low free thyroxine was associated with ASD (aHR = 4.9 [CI 2.03-11.9]) and ADHD (aHR = 2.3 [CI 1.2-4.3]) in girls but not in boys.

CONCLUSIONS

Abnormal maternal thyroid function in early pregnancy was associated with epilepsy, ASD, and ADHD in the child, but associations differed by subtypes of exposure and by child age and sex. More evidence on subtypes and severity of maternal thyroid function is needed, and alternative outcomes of child neurodevelopment may be warranted.

Adipose tissue content of saturated fatty acids and atrial fibrillation: A case-cohort study

OBJECTIVES

The aim of this study was to investigate the association between adipose tissue content of total saturated fatty acids including myristic (C14:0), palmitic (C16:0) and stearic (C18:0) acid, as a measure of exposure to saturated fatty acids and the risk of incident atrial fibrillation.

MATERIALS AND METHODS

A total of 57 053 Danish men and women aged 50-64 years participating in the Diet, Cancer and Health cohort had an adipose tissue biopsy taken at baseline, and this was analysed for saturated fatty acids content by gas chromatography. Follow-up was registry based and in this case-cohort study we used all cases and a randomly drawn subcohort of 3500 participants representative for the entire cohort.

RESULTS

Data were analysed using weighted Cox proportional hazards regression. During a median follow-up of 14.6 years, a total of 4722 cases of incident atrial fibrillation were diagnosed. For both men and women, no association between adipose tissue content of total saturated fatty acids and the risk of atrial fibrillation could be demonstrated.

CONCLUSION

We did not find an association between adipose tissue content of total saturated fatty acids and the risk of incident atrial fibrillation.

Analysis of two-phase sampling data with semiparametric additive hazards models

Under the case-cohort design introduced by Prentice (Biometrica 73:1-11, 1986), the covariate histories are ascertained only for the subjects who experience the event of interest (i.e., the cases) during the follow-up period and for a relatively small random sample from the original cohort (i.e., the subcohort). The case-cohort design has been widely used in clinical and epidemiological studies to assess the effects of covariates on failure times. Most statistical methods developed for the case-cohort design use the proportional hazards model, and few methods allow for time-varying regression coefficients. In addition, most methods disregard data from subjects outside of the subcohort, which can result in inefficient inference. Addressing these issues, this paper proposes an estimation procedure for the semiparametric additive hazards model with case-cohort/two-phase sampling data, allowing the covariates of interest to be missing for cases as well as for non-cases. A more flexible form of the additive model is considered that allows the effects of some covariates to be time varying while specifying the effects of others to be constant. An augmented inverse probability weighted estimation procedure is proposed. The proposed method allows utilizing the auxiliary information that correlates with the phase-two covariates to improve efficiency. The asymptotic properties of the proposed estimators are established. An extensive simulation study shows that the augmented inverse probability weighted estimation is more efficient than the widely adopted inverse probability weighted complete-case estimation method. The method is applied to analyze data from a preventive HIV vaccine efficacy trial.

Recent progresses in outcome-dependent sampling with failure time data

An outcome-dependent sampling (ODS) design is a retrospective sampling scheme where one observes the primary exposure variables with a probability that depends on the observed value of the outcome variable. When the outcome of interest is failure time, the observed data are often censored. By allowing the selection of the supplemental samples depends on whether the event of interest happens or not and oversampling subjects from the most informative regions, ODS design for the time-to-event data can reduce the cost of the study and improve the efficiency. We review recent progresses and advances in research on ODS designs with failure time data. This includes researches on ODS related designs like case-cohort design, generalized case-cohort design, stratified case-cohort design, general failure-time ODS design, length-biased sampling design and interval sampling design.

Common Polymorphisms in the 5-Lipoxygenase Pathway and Risk of Incident Myocardial Infarction: A Danish Case-Cohort Study

BACKGROUND

The 5-lipoxygenase pathway (5-LOX) has been implicated in the development of cardiovascular disease and studies have suggested that genetic polymorphisms related to key enzymes in this pathway may confer risk of myocardial infarction (MI). This study investigated the association of pre-selected genetic polymorphisms in four candidate genes of 5-LOX (arachidonate 5-lipoxygenase and its activating protein (ALOX-5 and FLAP), leukotriene A4 hydroxylase (LTA4-H) and leukotriene C4 synthase (LTC4-S)) with incident MI.

METHODS

In a Danish cohort including 57,053 participants, aged 50-64 at enrolment and recruited from 1993-97, we conducted a case-cohort study including cases with incident MI and a randomly selected sub cohort of 3,000 participants. Cases were identified from national registries through July 2013. A total of 22 SNPs were selected and genotyped using the commercially available KASP™ assay. A tandem-repeat polymorphism, located in the ALOX-5 gene, was genotyped by multi-titre plate sequencing. Haplotypes were inferred using PHASE 2.1.

RESULTS

During a median follow-up of 17.0 years we identified 3,089 cases of incident MI. In FLAP, two SNPs were negatively associated with incident MI (rs9551963 & rs17222842) while one SNP (rs2247570) located in LTA4-H, was associated with higher risk of MI when comparing subjects with two copies of the variant allele to homozygotes for the wild type. However, only rs17222842 remained significantly associated with MI after correcting for multiple testing. Furthermore, the promoter polymorphism rs59439148 was associated with risk of MI in men. For male carriers of two variant alleles we found a hazard ratio of 1.63 (95% CI: 1.06;2.52) compared to homozygotes for the wild type. Previously described haplotypes (Hap-A -B, -E and -K) were not associated with MI in our population.

CONCLUSION

In conclusion, some common polymorphisms in the 5-lipoxygenase pathway were modestly associated with incident MI, suggesting a potential role for this pathway in the development of cardiovascular disease.

Estimating hazard ratios in cohort data with missing disease information due to death

In clinical and epidemiological studies information on the primary outcome of interest, that is, the disease status, is usually collected at a limited number of follow-up visits. The disease status can often only be retrieved retrospectively in individuals who are alive at follow-up, but will be missing for those who died before. Right-censoring the death cases at the last visit (ad-hoc analysis) yields biased hazard ratio estimates of a potential risk factor, and the bias can be substantial and occur in either direction. In this work, we investigate three different approaches that use the same likelihood contributions derived from an illness-death multistate model in order to more adequately estimate the hazard ratio by including the death cases into the analysis: a parametric approach, a penalized likelihood approach, and an imputation-based approach. We investigate to which extent these approaches allow for an unbiased regression analysis by evaluating their performance in simulation studies and on a real data example. In doing so, we use the full cohort with complete illness-death data as reference and artificially induce missing information due to death by setting discrete follow-up visits. Compared to an ad-hoc analysis, all considered approaches provide less biased or even unbiased results, depending on the situation studied. In the real data example, the parametric approach is seen to be too restrictive, whereas the imputation-based approach could almost reconstruct the original event history information.

A case-cohort approach for multi-state models in hospital epidemiology

Analysing the determinants and consequences of hospital-acquired infections involves the evaluation of large cohorts. Infected patients in the cohort are often rare for specific pathogens, because most of the patients admitted to the hospital are discharged or die without such an infection. Death and discharge are competing events to acquiring an infection, because these individuals are no longer at risk of getting a hospital-acquired infection. Therefore, the data is best analysed with an extended survival model - the extended illness-death model. A common problem in cohort studies is the costly collection of covariate values. In order to provide efficient use of data from infected as well as uninfected patients, we propose a tailored case-cohort approach for the extended illness-death model. The basic idea of the case-cohort design is to only use a random sample of the full cohort, referred to as subcohort, and all cases, namely the infected patients. Thus, covariate values are only obtained for a small part of the full cohort. The method is based on existing and established methods and is used to perform regression analysis in adapted Cox proportional hazards models. We propose estimation of all cause-specific cumulative hazards and transition probabilities in an extended illness-death model based on case-cohort sampling. As an example, we apply the methodology to infection with a specific pathogen using a large cohort from Spanish hospital data. The obtained results of the case-cohort design are compared with the results in the full cohort to investigate the performance of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.

Variable selection for case-cohort studies with failure time outcome

Case-cohort designs are widely used in large cohort studies to reduce the cost associated with covariate measurement. In many such studies the number of covariates is very large, so an efficient variable selection method is necessary. In this paper, we study the properties of a variable selection procedure using the smoothly clipped absolute deviation penalty in a case-cohort design with a diverging number of parameters. We establish the consistency and asymptotic normality of the maximum penalized pseudo-partial-likelihood estimator, and show that the proposed variable selection method is consistent and has an asymptotic oracle property. Simulation studies compare the finite-sample performance of the procedure with tuning parameter selection methods based on the Akaike information criterion and the Bayesian information criterion. We make recommendations for use of the proposed procedures in case-cohort studies, and apply them to the Busselton Health Study.

On the use of biomarkers for environmental health research

This article discusses the growing interest in the use of biomarker data in environmental health research and considers some of the challenging statistical issues that arise. We specify a modeling framework that links environmental exposure, biomarkers and outcome, and discuss in conceptual terms how such a formulation could be used to inform dose response modeling for the purpose of quantitative risk assessment. We then analyse some biomarker data from a case-control study designed to elucidate the mechanisms of smoking induced lung cancer. Because of sample size limitations, we use a likelihood-based analysis which subsumes both cohort and case-control designs as special cases. Our analysis allows us to 1) investigate the extent to which the markers explain the pathway from exposure to outcome; 2) quantify the degree to which biomarker data can improve on predicting outcome over and above exposure; and 3) estimate the association among multiple markers.

Dietary intake and adipose tissue content of α-linolenic acid and risk of myocardial infarction: a Danish cohort study

BACKGROUND

Intake of the plant-derived ω-3 (n-3) fatty acid α-linolenic acid (ALA, 18:3; n-3) may reduce coronary heart disease (CHD) risk, but the results of previous studies have been inconsistent.

OBJECTIVE

We aimed to investigate the association between dietary intake of ALA, adipose tissue content of ALA, and risk of incident myocardial infarction (MI).

DESIGN

A total of 57,053 participants, aged 50-64 y, were enrolled in the prospective Danish cohort study Diet, Cancer and Health between 1993 and 1997. Dietary intake of ALA was assessed with the use of a validated semiquantitative food-frequency questionnaire in the full cohort, whereas the adipose tissue content of ALA was determined with the use of gas chromatography in all incident MI cases and in a random sex-stratified sample of the total cohort (n = 3500).

RESULTS

During a median of 17 y of follow-up, we identified 2177 male and 912 female cases of MI. After appropriate exclusions, we included 2124 men and 854 women for analyses of dietary intake of ALA, whereas 1994 men and 770 women were included in the analysis of the adipose tissue content of ALA. In multivariate analyses that were conducted with the use of restricted cubic splines and adjusted for established CHD risk factors, weak positive associations in men and weak U-shaped associations in women were shown between both dietary intake and the adipose tissue content of ALA and risk of MI, but these associations were not statistically significant. Additional adjustments for dietary factors did not influence the observed associations numerically.

CONCLUSION

This study suggests that ALA has no appreciable association with risk of incident MI in either men or women.

Retrospective likelihood-based methods for analyzing case-cohort genetic association studies

The case cohort (CCH) design is a cost-effective design for assessing genetic susceptibility with time-to-event data especially when the event rate is low. In this work, we propose a powerful pseudo-score test for assessing the association between a single nucleotide polymorphism (SNP) and the event time under the CCH design. The pseudo-score is derived from a pseudo-likelihood which is an estimated retrospective likelihood that treats the SNP genotype as the dependent variable and time-to-event outcome and other covariates as independent variables. It exploits the fact that the genetic variable is often distributed independent of covariates or only related to a low-dimensional subset. Estimates of hazard ratio parameters for association can be obtained by maximizing the pseudo-likelihood. A unique advantage of our method is that it allows the censoring distribution to depend on covariates that are only measured for the CCH sample while not requiring the knowledge of follow-up or covariate information on subjects not selected into the CCH sample. In addition to these flexibilities, the proposed method has high relative efficiency compared with commonly used alternative approaches. We study large sample properties of this method and assess its finite sample performance using both simulated and real data examples.

Flexible modelling of simultaneously interval censored and truncated time-to-event data

This paper deals with the analysis of data from a HET-CAM(VT) experiment. From a statistical perspective, such data yield many challenges. First of all, the data are typically time-to-event like data, which are at the same time interval censored and right truncated. In addition, one has to cope with overdispersion as well as clustering. Traditional analysis approaches ignore overdispersion and clustering and summarize the data into a continuous score that can be analysed using simple linear models. In this paper, a novel combined frailty model is developed that simultaneously captures all of the aforementioned statistical challenges posed by the data.

Baseline patterns of adipose tissue fatty acids and long-term risk of breast cancer: a case-cohort study in the Danish cohort Diet, Cancer and Health

BACKGROUND/OBJECTIVES

The evidence regarding fatty acids and breast cancer risk is inconclusive. Adipose tissue fatty acids can be used as biomarkers of fatty acid intake and of endogenous fatty acid exposure. Fatty acids in adipose tissue are correlated owing to common dietary sources and shared metabolic pathways, which group fatty acids into naturally occurring patterns. We aimed to prospectively investigate associations between adipose tissue fatty acid patterns and long-term risk of total breast cancer and breast cancer subtypes characterised by oestrogen and progesterone receptor status (ER and PR).

SUBJECTS/METHODS

This case-cohort study was based on data from the Danish cohort Diet, Cancer and Health. At baseline, a fat biopsy and information on lifestyle and reproductive factors were collected. From the 31 original fatty acids measured, patterns of fatty acids were identified using the treelet transform. During a median follow-up of 5.3 years, 474 breast cancer cases were identified. Hazard ratios and 95% confidence intervals of risk of total breast cancer and of subtypes according to quintiles of factor score were determined by weighted Cox proportional hazards regression.

RESULTS

After adjustment for potential confounders, factor scores for the seven patterns identified by the treelet transform were not associated with risk of total breast cancer, nor with risk of ER+, ER-, PR+ or PR- tumours.

CONCLUSIONS

No clear associations between the patterns of fatty acids at baseline and long-term risk of total breast cancer or ER+, ER-, PR+ or PR- tumours were observed.

A three-protein biomarker panel assessed in diagnostic tissue predicts death from prostate cancer for men with localized disease

Only a minority of prostate cancers lead to death. Because no tissue biomarkers of aggressiveness other than Gleason score are available at diagnosis, many nonlethal cancers are treated aggressively. We evaluated whether a panel of biomarkers, associated with a range of disease outcomes in previous studies, could predict death from prostate cancer for men with localized disease. Using a case-only design, subjects were identified from three Australian epidemiological studies. Men who had died of their disease, “cases” (N = 83), were matched to “referents” (N = 232), those who had not died of prostate cancer, using incidence density sampling. Diagnostic tissue was retrieved to assess expression of AZGP1, MUC1, NKX3.1, p53, and PTEN by semiquantitative immunohistochemistry (IHC). Poisson regression was used to estimate mortality rate ratios (MRRs) adjusted for age, Gleason score, and stage and to estimate survival probabilities. Expression of MUC1 and p53 was associated with increased mortality (MRR 2.51, 95% CI 1.14–5.54, P = 0.02 and 3.08, 95% CI 1.41–6.95, P = 0.005, respectively), whereas AZGP1 expression was associated with decreased mortality (MRR 0.44, 95% CI 0.20–0.96, P = 0.04). Analyzing all markers under a combined model indicated that the three markers were independent predictors of prostate cancer death and survival. For men with localized disease at diagnosis, assessment of AZGP1, MUC1, and p53 expression in diagnostic tissue by IHC could potentially improve estimates of risk of dying from prostate cancer based only on Gleason score and clinical stage.

Sample size/power calculation for stratified case-cohort design

The case-cohort (CC) study design usually has been used for risk factor assessment in epidemiologic studies or disease prevention trials for rare diseases. The sample size/power calculation for a stratified CC (SCC) design has not been addressed before. This article derives such result based on a stratified test statistic. Simulation studies show that the proposed test for the SCC design utilizing small sub-cohort sampling fractions is valid and efficient for situations where the disease rate is low. Furthermore, optimization of sampling in the SCC design is discussed and compared with proportional and balanced sampling techniques. An epidemiological study is provided to illustrate the sample size calculation under the SCC design.

Bootstrap for the case-cohort design

The case-cohort design facilitates economical investigation of risk factors in a large survival study, with covariate data collected only from the cases and a simple random subset of the full cohort. Methods that accommodate the design have been developed for various semiparametric models, but most inference procedures are based on asymptotic distribution theory. Such inference can be cumbersome to derive and implement, and does not permit confidence band construction. While bootstrap is an obvious alternative, how to resample is unclear because of complications from the two-stage sampling design. We establish an equivalent sampling scheme, and propose a novel and versatile nonparametric bootstrap for robust inference with an appealingly simple single-stage resampling. Theoretical justification and numerical assessment are provided for a number of procedures under the proportional hazards model.