Cox proportional hazards

Note that the term censor is introduced in the preceding table. The log-rank test (invoked in SAS with PROC LIFETEST) and the Cox proportional hazards model (invoked in SAS with PROC PHREG) allow for censoring observations in a time-to-event analysis. These tests adjust for the fact that at some point a patient may no longer be able to experience an event. The censor date is the last known time that the patient did not experience a given event and the point at which the patient is no longer considered able to experience the event. Often the censor date is the last known date of patient follow-up, but a patient could be censored for other reasons, such as having taken a protocol-prohibited medication. 

Hazard ratios are created using the Cox proportional hazards model through PROC PHREG. 

Time-to-event analysis in clinical trials is concerned with comparing the distributions of time to some event for various treatment regimens. The two nonparametric tests used to compare distributions are the log-rank test and the Cox proportional hazards model. The Cox proportional hazards model is more useful when you need to adjust your model for covariates. 

In this light, Robinson et al. (206) performed a study of 104 first-episode patients who were followed for a minimum of 2 months (mean, 207 weeks). The protocol was later limited to a maximal 5-year follow-up. Patients who wished to discontinue drug could do so. The rate of relapse was determined by the Cox Proportional Hazard Regression model. The cumulative life table relapse rate at 5 years was 82%. Most importantly, despite use of medication by many, there were only four unrelapsed patients after 5 years. Although medication was not controlled, the patients who discontinued had a fivefold increase in the relapse rate. This finding suggests that almost all first admission patients will relapse within the next 5 years, suggesting that most should be on maintenance medication. 

Figure 1 The relative 6-year mortality hazard ratios are shown for reported usual sleep hr from 2-3 hr/night to 10 or more hr/night, relative to 1.0 assigned to the hazard for 7 hr/night as the reference standard. The solid line with 95% confidence interval bars shows results from a 32-covariate Cox proportional hazards survival model, as reported previously (3). The dotted lines show data from models that excluded subjects who were not initially healthy, i.e., who died within the first year or whose questionnaires reported any cancer, heart disease, stroke, chronic bronchitis, emphysema, asthma, or current illness (a yes answer to the question are you sick at the present time ). The dot-dash lines with X symbols show models controlling only for age, insomnia, and use of sleeping pills. Data were from 635,317 women and 478,619 men. The thin solid lines with diamonds show the percent of subjects with each reported sleep duration (right axis).

It is interesting to examine how control for various comorbid factors influences the mortality hazard associated with sleep durations. Comorbidities aside, in Cox proportional hazards models for each gender, controlling only for age and hours of sleep, the sample excess fractions (20) of deaths related to sleep durations other than 7 hr were 16.4% for women and 19.4% for men. These fractions are the percentage of observed deaths that would not have occurred in the 6-year fol-... 

Methods that involve studying the disposition of some exogenously administered agent (e.g. indocyanine green, antipyrine, galactose or dextromethorphan) have now been superceded by functional (often multicomponent) tests. Mono-ethylglycinexylidide formation has not found wide acceptance. More complicated Cox proportional hazards models may exist for other liver diseases, but are only used specifically for them (e.g. the Mayo Clinic Survival Model for primary biliary cirrhosis see the US FDA Guidance). 

Adjusted rate ratios (and 95 percent confidence intervals [Cl] were derived from the Cox proportional-hazards model after adjustment for age, race, branch of service, and type of unit. 

Ford I, Norrie J, Ahmadi S (199 5) Model inconsistency, illustrated by the Cox proportional hazards model. Statistics in Medicine 14 735-746. 

The appeal is the ease of computation and applicability. The resulting statistics or p-values for the chosen filter method are then ranked and a cutoff chosen to select the most significant features. Examples of filter methods are t-tests, Wdcoxon rank-sum or signed-rank tests, Pearson correlation estimates, log-rank tests, and univariate regression techniques such as linear, logistic, or Cox proportional hazards. 

Vadeby, A., Forsman, A., Kecklund, G., Akerstedt, T., Sandberg, D., and Anund, A. 2010. Sleepiness and prediction of driver impairment in simulator studies using a Cox proportional hazard approach. Accid. Anal. Prev. 42 835-841. 

The same issue exists for time-to-event endpoints. While the most common metric for trials with these endpoints is the hazard ratio evaluated using survival analysis (usually a Cox proportional hazards model), absolute measures, such as the difference in event rates at a fixed follow-up time, are sometimes used. 

Details of statistical analyses for potential toxicities that should be explicitly considered for all products and AEs of special interest Aiialyses for these events will in general be more comprehensive than for standard safety parameters. These analyses may include subject-year adjusted rates, Cox proportional hazards analysis of time to first event, and Kaplan-Meier curves. Detailed descriptions of the models would typically be provided. For example, if Cox proportional hazards analysis is specified, a detailed description of the model(s) that will be used should be provided. This would generally include study as a stratification factor, covariates, and model selection techniques. More advanced methods, such as multiple events models or competing risk analyses, should be described if used (as appropriate). It is recommended that graphical methods also be employed, for example, forest plot and risk-over-time plot (Xia et al., 2011). 

One hundred twenty-five events would provide 90% power, and 95 events would provide 80% power to illustrate the 95% Cl is < 1.8 based on a Cox proportional hazard model. Therefore, in a clinical trial with an expected event rate of 1 event per 100 patient-years and a 5% annual dropout rate, 90% power would be achieved by enrolling 200 patients per month for 24 months and following all enrolled patients for an additional 24 months. The total trial duration would be 48 months. If, however, the true event rate was actually 0.75%, the power would decrease to 80%—a doubling of the type 2 error. Furthermore, if the event rate were actually 0.5%, then the power would drop to 65%, a type 2 error 3.5 times as high. Because it is hard to predict CV event rates in noncardiac populations, such overestimates are not uncommon. Similarly, if the actual event rate... 

The primary analysis will be a Cox proportional hazard model and the corresponding Cls for the treatment group hazard ratio. We use a Bayesian algorithm, based on the predictive probability of success at the final analysis, throughout the accrual stage to determine when to stop accrual. Thus, we use a Bayesian model to predict the likelihood of success for a frequentist test. A fully Bayesian primary analysis could also be performed. 

The predictive probabilities used to stop the trial for futility or for predicted success are calculated using a combination of the current posterior probability, each individual patient s data (follow-up time and whether they ve experienced an event), and simulated data from the current point forward along with the Cox proportional hazard model. 

The difference in overall survival between paracetamol-related and non-paracetamol-related acute liver failure was not statistically significant Patients with paracetamol-related acute liver failure required dialysis before transplantation more often than all the other groups (27% versus 3-10%). Cox proportional hazards regression analysis showed that the independent pre-transplantation predictors of death after transplantation were being on life support, liver failure due to antiepileptic drugs at age under 18 years, and a raised serum creatinine concentration. 

In line with the study described above, a prospective cohort study with 103 women enrolled, compared 1-year continuation rates in women who had immediate postabortion placement to interval placement using Cox proportional hazard models. The study concluded that ETON implant continuation had similar rates for postabortion and interval placement [58 ]. Therefore, women who xmdergo immediate postabortion placement of the subdermal implant have high rates of continuation that are equivalent to women xmdergoing interval insertion. For women who want a contraceptive implant after an abortion, immediate placement should be available in order to decrease the risk of repeat xmplarmed pregnancy [58 ]. 

---