Some recent developments for regression analysis of multivariate failure time data

Cox's seminal 1972 paper on regression methods for possibly censored failure time data popularized the use of time to an event as a primary response in prospective studies. But one key assumption of this and other regression methods is that observations are independent of one another. In many problems, failure times are clustered into small groups where outcomes within a group are correlated. Examples include failure times for two eyes from one person or for members of the same family. This paper presents a survey of models for multivariate failure time data. Two distinct classes of models are considered: frailty and marginal models. In a frailty model, the correlation is assumed to derive from latent variables ("frailties") common to observations from the same cluster. Regression models are formulated for the conditional failure time distribution given the frailties. Alternatively, marginal models describe the marginal failure time distribution of each response while separately modelling the association among responses from the same cluster. We focus on recent extensions of the proportional hazards model for multivariate failure time data. Model formulation, parameter interpretation and estimation procedures are considered.

Ovarian tumors in a cohort of infertile women

BACKGROUND

Case reports and the results of a recent case-control study have raised questions about the potential neoplastic effects of medications used as treatment for infertility.

METHODS

We examined the risk of ovarian tumors in a cohort of 3837 women evaluated for infertility between 1974 and 1985 in Seattle. Computer linkage with a population-based tumor registry was used to identify women in whom tumors were diagnosed before January 1, 1992. Data on infertility testing and treatment were abstracted from the medical records of women who had ovarian cancer and those of a randomly selected comparison group. The risk of ovarian tumors associated with exposure to ovulation-inducing medications was assessed through an age-standardized comparison with the rate of ovarian tumors in the general population, and Cox regression analysis was used to compare the risk of cancer among women who received these medications with the risk among infertile women who did not receive them.

RESULTS

There were 11 invasive or borderline malignant ovarian tumors, as compared with an expected number of 4.4 (standardized incidence ratio, 2.5; 95 percent confidence interval, 1.3 to 4.5). Nine of the women in whom ovarian tumors developed had taken clomiphene; the adjusted relative risk among these women, as compared with that among infertile women who had not taken this drug, was 2.3 (95 percent confidence interval, 0.5 to 11.4). Five of the nine women had taken the drug during 12 or more monthly cycles. This period of treatment was associated with an increased risk of ovarian tumors among both women with ovarian abnormalities and those without apparent abnormalities (relative risk, 11.1; 95 percent confidence interval, 1.5 to 82.3), whereas treatment with the drug for less than one year was not associated with an increased risk.

CONCLUSIONS

Prolonged use of clomiphene may increase the risk of a borderline or invasive ovarian tumor.

An adaptive weighted log-rank test with application to cancer prevention and screening trials

A class of adaptive weighted log-rank statistics is described where the vector of weights is chosen in a data-dependent way from a family of "smooth" weight vectors. A parametric family of weight vectors is identified which includes most shapes of weighting vectors that will be near optimal in many cancer prevention and screening trials. This family of weight vectors is used in an application of the proposed method to data from a breast cancer screening trial. Results from a small simulation study comparing the power of the adaptive statistic to that of the unweighted log-rank statistic are presented.

On estimating HLA/disease association with application to a study of aplastic anemia

A multiplicative model is described relating HLA typing information to disease incidence. A likelihood-based method for estimating parameters in this model is proposed for use with data sets in which HLA haplotype information is available on a series of cases and their parents. This approach is extended to incorporate information from a matched control series for the purpose of estimating HLA and environmental risk factor effects simultaneously. The method is applied to data from aplastic anemia patients treated by bone marrow transplantation and the results are compared to unmatched case-control analyses using the same case series and several different control series.

The Cox proportional hazards model with change point: an epidemiologic application

In this paper, we develop the Cox proportional hazards model with special structured time-dependent covariates in the context of prospective epidemiologic studies. Our model possesses the following two features: (i) different relative risk parameters are allowed for early versus late onset of the disease of interest; (ii) an additional parameter is introduced so that specification is not required for the time (age) at which a change of the magnitude of the relative risks takes place, the so-called change point. Some difficulties with statistical inference for the proposed model are briefly discussed, and the large-sample distribution of a test for no change point is derived. As an illustration, we apply the model to a set of data gathered on a group of white male medical students of The Johns Hopkins Medical School enrolled between 1948 and 1964. We examine the hypothesis that the effect of reactivity to the cold pressor test may vary with early versus late onset of hypertension.

Minimal risk of chronic renal dysfunction in marrow transplant recipients treated with cyclosporine for 6 months

To determine whether 6 months of cyclosporine therapy is associated with chronic renal dysfunction, we evaluated serum creatinine concentrations 1 year post-transplant in 82 marrow transplant recipients randomized to receive either cyclosporine (n = 40) or methotrexate (n = 42) as graft-versus-host disease (GVHD) prophylaxis. Nine patients in the methotrexate group were later given cyclosporine as treatment for acute or chronic GVHD (methotrexate----cyclosporine). Cyclosporine prophylaxis was started on the day before marrow infusion, given at full doses until day 50, then gradually tapered and discontinued by day 180. Methotrexate prophylaxis was started on day 1 and given intermittently until day 102. Patients in the cyclosporine and methotrexate----cyclosporine groups had significantly higher mean serum creatinine values during the first 100 days post-transplant than methotrexate-treated patients, but by 1 year mean serum creatinine values were not significantly different between the three groups. Serum creatinine values at 1 year were also not significantly different from baseline values in each of the groups. None of the patients who had their cyclosporine discontinued by day 180 developed chronic renal dysfunction, defined as a doubling of the baseline serum creatinine at 1 year. We conclude that chronic renal dysfunction occurs rarely in marrow transplant recipients treated with 6 months of cyclosporine and when it does occur, it appears to have minimal clinical significance.

Further results on covariate measurement errors in cohort studies with time to response data

The impact of covariate measurement errors on the estimation of relative risk regression parameters is discussed. First the dependence of the induced relative risk process on the cumulative baseline failure rate function is noted. Next induced relative risk models under some specific failure time and measurement error models are described, including the much simplified models that are appropriate under a 'rare disease' assumption. The presentation then turns to the joint estimation of relative risk parameters of primary interest along with measurement error parameters. A partial likelihood product is proposed for such estimation and asymptotic properties are indicated. Guidance is also presented as to the appropriate size of a 'validation' sample relative to the full cohort size. Finally some more general considerations are presented as to the usefulness and interpretation of deattenuated regression coefficients.

Modelling paired survival data with covariates

The objective of this paper is to consider the parametric analysis of paired censored survival data when additional covariate information is available, as in the Diabetic Retinopathy Study, which assessed the effectiveness of laser photocoagulation in delaying loss of visual acuity. Our first approach is to extend the fully parametric model of Clayton (1978, Biometrika 65, 141-151) to incorporate covariate information. Our second approach is to obtain parameter estimates from an independence working model together with robust variance estimates. The approaches are compared in terms of efficiency and computational considerations. A fundamental consideration in choosing a strategy for the analysis of paired survival data is whether the correlation within a pair is a nuisance parameter or a parameter of intrinsic scientific interest. The approaches are illustrated with the Diabetic Retinopathy Study.

On testing departure from the binomial and multinomial assumptions

This paper is concerned with testing the multinomial (binomial) assumption against the Dirichlet-multinomial (beta-binomial) alternatives. In particular, we discuss the distribution of the asymptotic likelihood ratio (LR) test and obtain the C(alpha) goodness-of-fit test statistic. The inadequacy of the regular chi-square approximation to the LR test is supported by some Monte Carlo experiments. The C(alpha) test is recommended based on empirical significance level and power and also computational simplicity. Two examples are given.

Serum cyclosporine concentration and risk of acute graft-versus-host disease after allogeneic marrow transplantation

To determine the relation between the serum cyclosporine concentration and the risk of acute graft-versus-host disease (GVHD), we studied 179 recipients of bone marrow grafts from HLA-identical sibling donors who received prophylaxis with cyclosporine, either by itself or combined with methotrexate. Cyclosporine was given either orally or intravenously at full doses from the day before transplantation until day 50; it was then tapered off and discontinued on day 180. Trough concentrations of serum cyclosporine were measured by radioimmunoassay. The relation between patients' characteristics and the risk of acute GVHD was analyzed with a relative-risk regression model. In 66 patients (37 percent), grades II to IV of acute GVHD developed 7 to 66 days (median, 13) after transplantation. The trough cyclosporine concentration for a given week was significantly associated with the risk that acute GVHD would develop during the following week. The relative risks were 0.7 (i.e., there was a 30 percent reduction in risk) for every increase of 100 ng per milliliter in cyclosporine concentration and 1.0, 0.60, and 0.20 for concentrations of less than 100, 100 to 199, and 200 or more ng per milliliter, respectively (P less than 0.01). A patient's age, prophylaxis regimen, and year of transplantation also influenced the risk of acute GVHD significantly. These data indicate that low cyclosporine concentrations can be a cause of treatment failure and that concentrations should be monitored in recipients of marrow transplants.

Aspects of the use of relative risk models in the design and analysis of cohort studies and prevention trials

Relative risk regression methods provide a unifying and powerful approach to a range of problems in the design and analysis of cohort studies and prevention trials. Standard partial likelihood-based estimation procedures do not, however, encompass several features that are important in such contexts. Specifically, one may wish to relate disease rates marginally to 'recent' risk factor measurements, whereas a partial likelihood approach requires one to condition on an accumulating risk factor history. Secondly, risk factor values may be ascertained with considerable measurement error, thereby requiring specialized procedures to estimate relative risk parameters. Thirdly, analysis of raw materials to obtain desired covariate (risk factor) histories may involve considerable expense if carried out for the entire cohort. Case-control and case-cohort sampling procedures can avoid much of this expense, but once again partial likelihood estimation procedures require generalization. Such generalizations are described herein.

Monitoring cyclosporin concentrations in marrow transplant recipients: comparison of two assay methods

Renal dysfunction is the major dose-limiting toxicity associated with cyclosporin therapy. We have previously shown in patients undergoing allogeneic bone marrow transplantation that serum cyclosporin concentrations, as measured by radioimmunoassay (RIA), correlate significantly with the development of renal dysfunction. However, since the RIA measures both parent drug and metabolites, the relative role of each in the development of nephrotoxicity could not be determined. Therefore, we re-measured cyclosporin concentrations in the same serum samples by high-performance liquid chromatography (h.p.l.c.). Serum cyclosporin concentrations of less than 50, 50-100 and greater than 100 ng/ml, as measured by h.p.l.c., were considered equivalent to cyclosporin concentrations of less than 150, 150-250 and greater than 250 ng/ml, as measured by RIA. Contrary to results by RIA, cyclosporin concentrations measured by h.p.l.c. did not significantly correlate with renal dysfunction, which suggests that measurement of serum cyclosporin concentrations by h.p.l.c. provides no clinical advantage to RIA for monitoring cyclosporin concentrations to prevent renal dysfunction.

Linear rank tests for interval-censored data with application to PCB levels in adipose tissue of transformer repair workers

Linear rank statistics are described for testing for differences between groups when the data are interval-censored. The statistics are closely related to those described by Prentice (1978, Biometrika 65, 167-179) for right-censored data. Problems in calculating the statistics are discussed and several approaches to computation including estimation of the efficient rank scores are described. Results from a small simulation study are presented. The methods are applied to data from a study relating tissue levels of PCBs to occupational exposure.

Use of robust variance components models to analyse triglyceride data in families

A robust approach for analysis of variance components models is presented which does not rely on the assumption of multivariate normality for its validity. This approach uses the multivariated normal distribution as a 'working model' but obtains standard errors for the final estimators which do not depend on this underlying distribution. By using the observed variance in the first derivatives of the multivariate normal 'working model' to modify the conventional score test, hypotheses regarding specific components can also be tested without relying directly on the assumption of multivariate normality. A special case is presented where both the modified score test and the likelihood ratio test are equally robust, and simulated data are used to illustrate this situation. Measurements of triglyceride levels in 391 individuals in 60 families randomly selected from the membership of a health maintenance organization are used to illustrate this robust approach to variance components.