Confidence intervals for survival quantiles in the Cox regression model

Evaluating Additive Interaction Using Survival Percentiles

Evaluation of statistical interaction in time-to-event analysis is usually limited to the study of multiplicative interaction, via inclusion of a product term in a Cox proportional-hazard model. Measures of additive interaction are available but seldom used. All measures of interaction in survival analysis, whether additive or multiplicative, are in the metric of hazard, usually assuming that the interaction between two predictors of interest is constant during the follow-up period. We introduce a measure to evaluate additive interaction in survival analysis in the metric of time. This measure can be calculated by evaluating survival percentiles, defined as the time points by which different subpopulations reach the same incidence proportion. Using this approach, the probability of the outcome is fixed and the time variable is estimated. We also show that by using a regression model for the evaluation of conditional survival percentiles, including a product term between the two exposures in the model, interaction is evaluated as a deviation from additivity of the effects. In the simple case of two binary exposures, the product term is interpreted as excess/decrease in survival time (i.e., years, months, days) due to the presence of both exposures. This measure of interaction is dependent on the fraction of events being considered, thus allowing evaluation of how interaction changes during the observed follow-up. Evaluation of interaction in the context of survival percentiles allows deriving a measure of additive interaction without assuming a constant effect over time, overcoming two main limitations of commonly used approaches.

Simultaneous confidence bands for Cox regression from semiparametric random censorship

Cox regression is combined with semiparametric random censorship models to construct simultaneous confidence bands (SCBs) for subject-specific survival curves. Simulation results are presented to compare the performance of the proposed SCBs with the SCBs that are based only on standard Cox. The new SCBs provide correct empirical coverage and are more informative. The proposed SCBs are illustrated with two real examples. An extension to handle missing censoring indicators is also outlined.

Sleep duration and survival percentiles across categories of physical activity

The association between long sleep duration and death is not fully understood. Long sleep is associated with low physical activity, which is a strong predictor of death. Our aim was to investigate the association between sleep duration and death across categories of total physical activity in a large prospective cohort of Swedish men and women. We followed a population-based cohort of 70,973 participants (37,846 men and 33,127 women), aged 45-83 years, from January 1998 to December 2012. Sleep duration and physical activity levels were assessed through a questionnaire. We evaluated the association of interest in terms of mortality rates by estimating hazard ratios with Cox regression and in terms of survival by evaluating 15th survival percentile differences with Laplace regression. During 15 years of follow-up, we recorded 14,575 deaths (8,436 men and 6,139 women). We observed a significant interaction between sleep duration and physical activity in predicting death (P < 0.001). Long sleep duration (>8 hours) was associated with increased mortality risk (hazard ratio = 1.24; 95% confidence interval: 1.11, 1.39) and shorter survival (15th percentile difference = -20 months; 95% confidence interval: -30, -11) among only those with low physical activity. The association between long sleep duration and death might be partly explained by comorbidity with low physical activity.

Alcohol consumption and mortality: a dose-response analysis in terms of time

PURPOSE

Low-to-moderate alcohol consumption is associated with decreased mortality. However, many aspects of this association are still debated. Our aim was to complement available information by conducting a dose-response analysis of the association between alcohol consumption and survival time.

METHODS

In a Swedish population-based cohort of 67,706 middle-aged and elderly men and women, frequency and amount of drinking were assessed through a self-administrated questionnaire. During 15 years of follow-up, 13,323 participants died. Differences in survival (10th percentile differences, PDs) according to levels of alcohol consumption were estimated using Laplace regression.

RESULTS

We found evidence of nonlinearity between alcohol consumption and survival. Among women, we observed a rapid increase in survival up to 6 g/d of alcohol consumption (0.5 drinks/d) where survival was 17 months longer (PD = 17 months, 95% confidence interval, 10 to 24). After this peak, higher alcohol consumption was progressively associated with shorter survival. Among men, survival improved up to 15 g/d (1.5 drinks/d) where we observed a PD of 15 months (95% confidence interval, 8 to 22).

CONCLUSIONS

Low alcohol consumption was associated with improved survival up to 1.5 years for women with an average consumption of 0.5 drinks per day and to 1.3 years for men with an average consumption of 1.5 drinks per day.

Confidence intervals for the first crossing point of two hazard functions

The phenomenon of crossing hazard rates is common in clinical trials with time to event endpoints. Many methods have been proposed for testing equality of hazard functions against a crossing hazards alternative. However, there has been relatively few approaches available in the literature for point or interval estimation of the crossing time point. The problem of constructing confidence intervals for the first crossing time point of two hazard functions is considered in this paper. After reviewing a recent procedure based on Cox proportional hazard modeling with Box-Cox transformation of the time to event, a nonparametric procedure using the kernel smoothing estimate of the hazard ratio is proposed. The proposed procedure and the one based on Cox proportional hazard modeling with Box-Cox transformation of the time to event are both evaluated by Monte-Carlo simulations and applied to two clinical trial datasets.

Age at diagnosis and age at death in familial prostate cancer

OBJECTIVES

A family history of prostate cancer is associated with a higher risk for prostate cancer to first-degree relatives. If greater surveillance of men at familial risk is considered to be useful, population-based estimates of the differences in the age at diagnosis between familial and sporadic prostate cancer cases are needed.

METHODS

The men in the nationwide Swedish Family-Cancer Database were classified according to the number and type of affected first-degree relatives (father or brother) and according to the relative's age at diagnosis. The cumulative incidence of prostate cancer and cumulative prostate cancer-specific mortality were estimated using a stratified Cox model.

RESULTS

The cumulative incidence was highest for men with multiple affected first-degree relatives, and it was higher for brothers than for sons of prostate cancer patients. The age to reach the same cumulative incidence as the general population at age 55 years decreased with decreasing age at diagnosis of the relative, ranging from 48.7 years (father diagnosed before 60 years of age) to 53.7 years (father diagnosed after 82 years of age). Prostate cancer-specific mortality was also related to the number and type of affected relatives but there was no clear evidence for a dependency on the age at diagnosis of the relative.

CONCLUSIONS

Men with a father or a brother affected by prostate cancer are diagnosed and die at earlier ages than men without a family history of prostate cancer. This study should encourage further analysis in order to assess the risks and benefits of screening for prostate cancer in men at higher risk.

Age of onset in familial breast cancer as background data for medical surveillance

BACKGROUND

Familial breast cancers are known to be of early onset. This article provides differences in the age of onset of breast cancer and death by breast cancer between women with and without a family history.

METHODS

The Swedish Family-Cancer Database was used to estimate the cumulative risk of breast cancer and death by breast cancer according to family history with a stratified Cox model. Family history was defined separately for affected mother or sister considering their diagnostic ages.

RESULTS

The age to reach the same cumulative incidence as women without family history decreased with decreasing diagnostic age of the affected relative. Women with a maternal history reached the risk of women lacking a family history at the age of 50 years between 12.3 (mother affected <40 years) and 3.3 years (mother affected >82 years) earlier. The trend for breast cancer mortality was essentially similar.

CONCLUSIONS

Women with mother or sister affected by breast cancer are diagnosed and die at earlier ages than do women without family history. The differences depend on the diagnostic age of the affected relative. The present data may provide a rationale to derive recommendations for the starting age of screening in women with affected family members.

Age of onset in familial cancer

BACKGROUND

Reliable estimates on the age of onset between familial and sporadic cancers are important for etiological understanding and clinical practice. Specific studies on the age of onset of familial cancer compared with sporadic cancer are less common than studies on familial risks and these are almost lacking for rare cancers.

MATERIALS AND METHODS

The Swedish Family-Cancer Database was used to estimate cumulative risks of all common cancer types according to family history with a stratified Cox model based on Tsiatis' method. We calculated the age at which the cumulative risk of cancer reached 0.1% and 0.5%.

RESULTS

The age to reach a cumulative risk of 0.1% was significantly lower among individuals with a parent or a sibling affected for any of the investigated cancer sites. The age differences ranged from 2.6 years (sons of prostate cancer patients) to 16.3 years (brothers of urinary bladder cancer patients). A cumulative risk of 0.5% was also reached earlier for individuals with a family history, especially for individuals with a parent and a sibling affected.

CONCLUSIONS

Cancers in individuals with a family history occur earlier than in sporadic patients. The derived estimates may be useful for clinical counseling and screening recommendations.