Parametric regression on cumulative incidence function

We propose parametric regression analysis of cumulative incidence function with competing risks data. A simple form of Gompertz distribution is used for the improper baseline subdistribution of the event of interest. Maximum likelihood inferences on regression parameters and associated cumulative incidence function are developed for parametric models, including a flexible generalized odds rate model. Estimation of the long-term proportion of patients with cause-specific events is straightforward in the parametric setting. Simple goodness-of-fit tests are discussed for evaluating a fixed odds rate assumption. The parametric regression methods are compared with an existing semiparametric regression analysis on a breast cancer data set where the cumulative incidence of recurrence is of interest. The results demonstrate that the likelihood-based parametric analyses for the cumulative incidence function are a practically useful alternative to the semiparametric analyses.     

The influence of competing-risks setting on the choice of hypothesis test for treatment effect

There is considerable debate regarding the choice of test for treatment difference in a randomized clinical trial in the presence of competing risks. This question arose in the study of standard and new antiepileptic drugs (SANAD) trial comparing new and standard antiepileptic drugs. This paper provides simulation results for the log-rank test comparing cause-specific hazard rates and Gray's test comparing cause-specific cumulative incidence curves. To inform the analysis of the SANAD trial, competing-risks settings were considered where both events are of interest, events may be negatively correlated, and the degree of correlation may differ in the 2 treatment groups. In settings where there are effects in opposite directions for the 2 event types, a likely situation for the SANAD trial, Gray's test has greater power to detect treatment differences than log-rank analysis. For the epilepsy application, conclusions were qualitatively similar for both log-rank and Gray's tests.     

Nonparametric estimation of the cumulative incidences of competing risks under double truncation

Registry data typically report incident cases within a certain calendar time interval. Such interval sampling induces double truncation on the incidence times, which may result in an observational bias. In this paper, we introduce nonparametric estimation for the cumulative incidences of competing risks when the incidence time is doubly truncated. Two different estimators are proposed depending on whether the truncation limits are independent of the competing events or not. The asymptotic properties of the estimators are established, and their finite sample performance is investigated through simulations. For illustration purposes, the estimators are applied to childhood cancer registry data, where the target population is peculiarly defined conditional on future cancer development. Then, in our application, the cumulative incidences inform on the distribution by age of the different types of cancer.     

Average risks of breast and ovarian cancer associated with BRCA1 or BRCA2 mutations detected in case Series unselected for family history: a combined analysis of 22 studies

Germline mutations in BRCA1 and BRCA2 confer high risks of breast and ovarian cancer, but the average magnitude of these risks is uncertain and may depend on the context. Estimates based on multiple-case families may be enriched for mutations of higher risk and/or other familial risk factors, whereas risk estimates from studies based on cases unselected for family history have been imprecise. We pooled pedigree data from 22 studies involving 8,139 index case patients unselected for family history with female (86%) or male (2%) breast cancer or epithelial ovarian cancer (12%), 500 of whom had been found to carry a germline mutation in BRCA1 or BRCA2. Breast and ovarian cancer incidence rates for mutation carriers were estimated using a modified segregation analysis, based on the occurrence of these cancers in the relatives of mutation-carrying index case patients. The average cumulative risks in BRCA1-mutation carriers by age 70 years were 65% (95% confidence interval 44%-78%) for breast cancer and 39% (18%-54%) for ovarian cancer. The corresponding estimates for BRCA2 were 45% (31%-56%) and 11% (2.4%-19%). Relative risks of breast cancer declined significantly with age for BRCA1-mutation carriers (P trend.0012) but not for BRCA2-mutation carriers. Risks in carriers were higher when based on index breast cancer cases diagnosed at <35 years of age. We found some evidence for a reduction in risk in women from earlier birth cohorts and for variation in risk by mutation position for both genes. The pattern of cancer risks was similar to those found in multiple-case families, but their absolute magnitudes were lower, particularly for BRCA2. The variation in risk by age at diagnosis of index case is consistent with the effects of other genes modifying cancer risk in carriers.     

Competing risks regression for stratified data

For competing risks data, the Fine-Gray proportional hazards model for subdistribution has gained popularity for its convenience in directly assessing the effect of covariates on the cumulative incidence function. However, in many important applications, proportional hazards may not be satisfied, including multicenter clinical trials, where the baseline subdistribution hazards may not be common due to varying patient populations. In this article, we consider a stratified competing risks regression, to allow the baseline hazard to vary across levels of the stratification covariate. According to the relative size of the number of strata and strata sizes, two stratification regimes are considered. Using partial likelihood and weighting techniques, we obtain consistent estimators of regression parameters. The corresponding asymptotic properties and resulting inferences are provided for the two regimes separately. Data from a breast cancer clinical trial and from a bone marrow transplantation registry illustrate the potential utility of the stratified Fine-Gray model.     

A signed-rank test for clustered data

Summary .   We consider the problem of comparing two outcome measures when the pairs are clustered. Using the general principle of within-cluster resampling, we obtain a novel signed-rank test for clustered paired data. We show by a simple informative cluster size simulation model that only our test maintains the correct size under a null hypothesis of marginal symmetry compared to four other existing signed rank tests; further, our test has adequate power when cluster size is noninformative. In general, cluster size is informative if the distribution of pair-wise differences within a cluster depends on the cluster size. An application of our method to testing radiation toxicity trend is presented.     

Semiparametric models for cumulative incidence functions

In analyses of time-to-failure data with competing risks, cumulative incidence functions may be used to estimate the time-dependent cumulative probability of failure due to specific causes. These functions are commonly estimated using nonparametric methods, but in cases where events due to the cause of primary interest are infrequent relative to other modes of failure, nonparametric methods may result in rather imprecise estimates for the corresponding subdistribution. In such cases, it may be possible to model the cause-specific hazard of primary interest parametrically, while accounting for the other modes of failure using nonparametric estimators. The cumulative incidence estimators so obtained are simple to compute and are considerably more efficient than the usual nonparametric estimator, particularly with regard to interpolation of cumulative incidence at early or intermediate time points within the range of data used to fit the function. More surprisingly, they are often nearly as efficient as fully parametric estimators. We illustrate the utility of this approach in the analysis of patients treated for early stage breast cancer.     

BRCA1 and BRCA2 mutation analysis of 208 Ashkenazi Jewish women with ovarian cancer

Ovarian cancer is a component of the autosomal-dominant hereditary breast-ovarian cancer syndrome and may be due to a mutation in either the BRCA1 or BRCA2 genes. Two mutations in BRCA1 (185delAG and 5382insC) and one mutation in BRCA2 (6174delT) are common in the Ashkenazi Jewish population. One of these three mutations is present in approximately 2% of the Jewish population. Each mutation is associated with an increased risk of ovarian cancer, and it is expected that a significant proportion of Jewish women with ovarian cancer will carry one of these mutations. To estimate the proportion of ovarian cancers attributable to founding mutations in BRCA1 and BRCA2 in the Jewish population and the familial cancer risks associated with each, we interviewed 213 Jewish women with ovarian cancer at 11 medical centers in North America and Israel and offered these women genetic testing for the three founder mutations. To establish the presence of nonfounder mutations in this population, we also completed the protein-truncation test on exon 11 of BRCA1 and exons 10 and 11 of BRCA2. We obtained a detailed family history on all women we studied who had cancer and on a control population of 386 Ashkenazi Jewish women without ovarian or breast cancer. A founder mutation was present in 41.3% of the women we studied. The cumulative incidence of ovarian cancer to age 75 years was found to be 6.3% for female first-degree relatives of the patients with ovarian cancer, compared with 2.0% for the female relatives of healthy controls (relative risk 3.2; 95% CI 1.5-6.8; P=.002). The relative risk to age 75 years for breast cancer among the female first-degree relatives was 2.0 (95% CI 1.4-3.0; P=.0001). Only one nonfounder mutation was identified (in this instance, in a woman of mixed ancestry), and the three founding mutations accounted for most of the observed excess risk of ovarian and breast cancer in relatives.     

A note on the tests for clustered matched-pair binary data

McNemar's test is used to assess the difference between two different procedures (treatments) using independent matched-pair data. For matched-pair data collected in clusters, the tests proposed by Durkalski et al. and Obuchowski are popular and commonly used in practice since these tests do not require distributional assumptions or assumptions on the structure of the within-cluster correlation of the data. Motivated by these tests, this note proposes a modified Obuchowski test and illustrates comparisons of the proposed test with the extant methods. An extensive Monte Carlo simulation study suggests that the proposed test performs well with respect to the nominal size, and has higher power; Obuchowski's test is most conservative, and the performance of the Durkalski's test varies between the modified Obuchowski test and the original Obuchowski's test. These results form the basis for our recommendation that (i) for equal cluster size, the modified Obuchowski test is always preferred; (ii) for varying cluster size Durkalski's test can be used for a small number of clusters (e.g. K < 50), whereas for a large number of clusters (e.g. K ≥ 50) the modified Obuchowski test is preferred. Finally, to illustrate practical application of the competing tests, two real collections of clustered matched-pair data are analyzed.     

Constrained parametric model for simultaneous inference of two cumulative incidence functions

We propose a parametric regression model for the cumulative incidence functions (CIFs) commonly used for competing risks data. The model adopts a modified logistic model as the baseline CIF and a generalized odds‐rate model for covariate effects, and it explicitly takes into account the constraint that a subject with any given prognostic factors should eventually fail from one of the causes such that the asymptotes of the CIFs should add up to one. This constraint intrinsically holds in a nonparametric analysis without covariates, but is easily overlooked in a semiparametric or parametric regression setting. We hence model the CIF from the primary cause assuming the generalized odds‐rate transformation and the modified logistic function as the baseline CIF. Under the additivity constraint, the covariate effects on the competing cause are modeled by a function of the asymptote of the baseline distribution and the covariate effects on the primary cause. The inference procedure is straightforward by using the standard maximum likelihood theory. We demonstrate desirable finite‐sample performance of our model by simulation studies in comparison with existing methods. Its practical utility is illustrated in an analysis of a breast cancer dataset to assess the treatment effect of tamoxifen, adjusting for age and initial pathological tumor size, on breast cancer recurrence that is subject to dependent censoring by second primary cancers and deaths.     

Nonparametric testing for DNA copy number induced differential mRNA gene expression

Summary .  The central dogma of molecular biology relates DNA with mRNA. Array CGH measures DNA copy number and gene expression microarrays measure the amount of mRNA. Methods that integrate data from these two platforms may uncover meaningful biological relationships that further our understanding of cancer. We develop nonparametric tests for the detection of copy number induced differential gene expression. The tests incorporate the uncertainty of the calling of genomic aberrations. The test is preceded by a "tuning algorithm" that discards certain genes to improve the overall power of the false discovery rate selection procedure. Moreover, the test statistics are "shrunken" to borrow information across neighboring genes that share the same array CGH signature. For each gene we also estimate its effect, its amount of differential expression due to copy number changes, and calculate the coefficient of determination. The method is illustrated on breast cancer data, in which it confirms previously reported findings, now with a more profound statistical underpinning.     

Testing for differentially expressed genes with microarray data

This paper compares the type I error and power of the one- and two-sample t-tests, and the one- and two-sample permutation tests for detecting differences in gene expression between two microarray samples with replicates using Monte Carlo simulations. When data are generated from a normal distribution, type I errors and powers of the one-sample parametric t-test and one-sample permutation test are very close, as are the two-sample t-test and two-sample permutation test, provided that the number of replicates is adequate. When data are generated from a t-distribution, the permutation tests outperform the corresponding parametric tests if the number of replicates is at least five. For data from a two-color dye swap experiment, the one-sample test appears to perform better than the two-sample test since expression measurements for control and treatment samples from the same spot are correlated. For data from independent samples, such as the one-channel array or two-channel array experiment using reference design, the two-sample t-tests appear more powerful than the one-sample t-tests.     

Risk Prediction for Breast,Endometrial, and Ovarian Cancer in White Women Aged 50 y or Older: Derivation and Validation from Population-Based Cohort Studies

Background

Breast, endometrial, and ovarian cancers share some hormonal and epidemiologic risk factors. While several models predict absolute risk of breast cancer, there are few models for ovarian cancer in the general population, and none for endometrial cancer.

Methods and Findings

Using data on white, non-Hispanic women aged 50+ y from two large population-based cohorts (the Prostate, Lung, Colorectal, and Ovarian Cancer Screening Trial [PLCO] and the National Institutes of Health–AARP Diet and Health Study [NIH-AARP]), we estimated relative and attributable risks and combined them with age-specific US-population incidence and competing mortality rates. All models included parity. The breast cancer model additionally included estrogen and progestin menopausal hormone therapy (MHT) use, other MHT use, age at first live birth, menopausal status, age at menopause, family history of breast or ovarian cancer, benign breast disease/biopsies, alcohol consumption, and body mass index (BMI); the endometrial model included menopausal status, age at menopause, BMI, smoking, oral contraceptive use, MHT use, and an interaction term between BMI and MHT use; the ovarian model included oral contraceptive use, MHT use, and family history or breast or ovarian cancer. In independent validation data (Nurses'' Health Study cohort) the breast and ovarian cancer models were well calibrated; expected to observed cancer ratios were 1.00 (95% confidence interval [CI]: 0.96–1.04) for breast cancer and 1.08 (95% CI: 0.97–1.19) for ovarian cancer. The number of endometrial cancers was significantly overestimated, expected/observed = 1.20 (95% CI: 1.11–1.29). The areas under the receiver operating characteristic curves (AUCs; discriminatory power) were 0.58 (95% CI: 0.57–0.59), 0.59 (95% CI: 0.56–0.63), and 0.68 (95% CI: 0.66–0.70) for the breast, ovarian, and endometrial models, respectively.

Conclusions

These models predict absolute risks for breast, endometrial, and ovarian cancers from easily obtainable risk factors and may assist in clinical decision-making. Limitations are the modest discriminatory ability of the breast and ovarian models and that these models may not generalize to women of other races. Please see later in the article for the Editors'' Summary     

Prevalence and contribution of BRCA1 mutations in breast cancer and ovarian cancer: results from three U.S. population-based case-control studies of ovarian cancer.

We investigate the familial risks of cancers of the breast and ovary, using data pooled from three population-based case-control studies of ovarian cancer that were conducted in the United States. We base estimates of the frequency of mutations of BRCA1 (and possibly other genes) on the reported occurrence of breast cancer and ovarian cancer in the mothers and sisters of 922 women with incident ovarian cancer (cases) and in 922 women with no history of ovarian cancer (controls). Segregation analysis and goodness-of-fit testing of genetic models suggest that rare mutations (frequency .0014; 95% confidence interval .0002-.011) account for all the observed aggregation of breast cancer and ovarian cancer in these families. The estimated risk of breast cancer by age 80 years is 73.5% in mutation carriers and 6.8% in noncarriers. The corresponding estimates for ovarian cancer are 27.8% in carriers and 1.8% in noncarriers. For cancer risk in carriers, these estimates are lower than those obtained from families selected for high cancer prevalence. The estimated proportion of all U.S. cancer diagnoses, by age 80 years, that are due to germ-line BRCA1 mutations is 3.0% for breast cancer and 4.4% for ovarian cancer. Aggregation of breast cancer and ovarian cancer was less evident in the families of 169 cases with borderline ovarian cancers than in the families of cases with invasive cancers. Familial aggregation did not differ by the ethnicity of the probands, although the number of non-White and Hispanic cases (N = 99) was sparse.     

The impact of under and over-recording of cancer on death certificates in a competing risks analysis: A simulation study

Background: With linked register and cause of death data becoming more accessible than ever, competing risks methodology is being increasingly used as a way of obtaining “real world” probabilities of death broken down by specific causes. It is important, in terms of the validity of these studies, to have accurate cause of death information. However, it is well documented that cause of death information taken from death certificates is often lacking in accuracy and completeness. Methods: We assess through use of a simulation study the effect of under and over-recording of cancer on death certificates in a competing risks analysis consisting of three competing causes of death: cancer, heart disease and other causes. Using realistic levels of misclassification, we consider 24 scenarios and examine the bias in the cause-specific hazard ratios and the cumulative incidence function. Results: The bias in the cumulative incidence function was highest in the oldest age group reaching values as high as 2.6 percentage units for the “good” cancer prognosis scenario and 9.7 percentage units for the “poor” prognosis scenario. Conclusion: The bias resulting from the chosen levels of misclassification in this study accentuate concerns that unreliable cause of death information may be providing misleading results. The results of this simulation study convey an important message to applied epidemiological researchers.     

Using Lifetime Risk Estimates in Personal Genomic Profiles: Estimation of Uncertainty

Personal genome tests are now offered direct-to-consumer (DTC) via genetic variants identified by genome-wide association studies (GWAS) for common diseases. Tests report risk estimates (age-specific and lifetime) for various diseases based on genotypes at multiple loci. However, uncertainty surrounding such risk estimates has not been systematically investigated. With breast cancer as an example, we examined the combined effect of uncertainties in population incidence rates, genotype frequency, effect sizes, and models of joint effects among genetic variants on lifetime risk estimates. We performed simulations to estimate lifetime breast cancer risk for carriers and noncarriers of genetic variants. We derived population-based cancer incidence rates from Surveillance, Epidemiology, and End Results (SEER) Program and comparative international data. We used data for non-Hispanic white women from 2003 to 2005. We derived genotype frequencies and effect sizes from published GWAS and meta-analyses. For a single genetic variant in FGFR2 gene (rs2981582), combination of uncertainty in these parameters produced risk estimates where upper and lower 95% simulation intervals differed by more than 3-fold. Difference in population incidence rates was the largest contributor to variation in risk estimates. For a panel of five genetic variants, estimated lifetime risk of developing breast cancer before age 80 for a woman that carried all risk variants ranged from 6.1% to 21%, depending on assumptions of additive or multiplicative joint effects and breast cancer incidence rates. Epidemiologic parameters involved in computation of disease risk have substantial uncertainty, and cumulative uncertainty should be properly recognized. Reliance on point estimates alone could be seriously misleading.     

Marginal Models for Clustered Time‐to‐Event Data with Competing Risks Using Pseudovalues

Summary Many time‐to‐event studies are complicated by the presence of competing risks and by nesting of individuals within a cluster, such as patients in the same center in a multicenter study. Several methods have been proposed for modeling the cumulative incidence function with independent observations. However, when subjects are clustered, one needs to account for the presence of a cluster effect either through frailty modeling of the hazard or subdistribution hazard, or by adjusting for the within‐cluster correlation in a marginal model. We propose a method for modeling the marginal cumulative incidence function directly. We compute leave‐one‐out pseudo‐observations from the cumulative incidence function at several time points. These are used in a generalized estimating equation to model the marginal cumulative incidence curve, and obtain consistent estimates of the model parameters. A sandwich variance estimator is derived to adjust for the within‐cluster correlation. The method is easy to implement using standard software once the pseudovalues are obtained, and is a generalization of several existing models. Simulation studies show that the method works well to adjust the SE for the within‐cluster correlation. We illustrate the method on a dataset looking at outcomes after bone marrow transplantation.     

A computer model to simulate family history of breast/ovarian cancer in BRCA1 mutation carriers

The BRCA1 gene and its relationship to family history of breast/ovarian cancer are difficult to study in a population because of practical and ethical issues. The paucity of information on BRCA1 in the general population was a major theme in a recent review of genetic testing in Canada. We develop a simulation model to mimic genetic inheritance and cancer incidence in the family of someone with a germline BRCA1 mutation. Given someone's age and family structure, our model simulates his or her family history in three steps: (1) determine which family members have the mutation, (2) determine the ages of family members and (3) determine which family members have breast/ovarian cancer. Each step involves random variation. Some parameters in our model are estimated using local (British Columbia, Canada) population data. The breast/ovarian cancer risk associated with BRCA1 mutations is estimated using values published in the literature. An example is provided to illustrate the model's application. The model incorporates results from genetics, demography and epidemiology, but requires several additional assumptions. Research to address these assumptions is recommended.     

Variation in cancer risks, by mutation position, in BRCA2 mutation carriers

Cancer occurrence in 164 families with breast/ovarian cancer and germline BRCA2 mutations was studied to evaluate the evidence for genotype-phenotype correlations. Mutations in a central portion of the gene (the "ovarian cancer cluster region" [OCCR]) were associated with a significantly higher ratio of cases of ovarian:breast cancer in female carriers than were mutations 5' or 3' of this region (P<.0001), extending previous observations. The optimal definition of the OCCR, as judged on the basis of deviance statistics, was bounded by nucleotides 3059-4075 and 6503-6629. The relative and absolute risks of breast and ovarian cancer associated with OCCR and non-OCCR mutations were estimated by a conditional likelihood approach, conditioning on the set of mutations observed in the families. OCCR mutations were associated both with a highly significantly lower risk of breast cancer (relative risk [RR] 0.63; 95% confidence interval (95% CI) 0.46-0.84; P=.0012) and with a significantly higher risk of ovarian cancer (RR = 1.88; 95% CI = 1.08-3.33; P=.026). No other differences in breast or ovarian cancer risk, by mutation position, were apparent. There was some evidence for a lower risk of prostate cancer in carriers of an OCCR mutation (RR = 0.52; 95% CI = 0.24-1.00; P=.05), but there was no evidence of a difference in breast cancer risk in males. By age 80 years, the cumulative risk of breast cancer in male carriers of a BRCA2 mutation was estimated as 6.92% (95% CI = 1.20%-38.57%). Possible mechanisms for the variation in cancer risk are suggested by the coincidence of the OCCR with the RAD51-binding domain.