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400 Good health: Statistical challengesFIGURE 35.4Graphs showing transition probabilities for transient and absorbing states forbreast cancer (single outcome; left graph), and for breast cancer and stroke(two outcomes; right graph). In both graphs death before outcome occurrenceis a competing risk.before breast cancer occurrence. This competing risk of death is illustrated inthe left graph of Figure 35.4. Based on her follow-up during the risk periodshe is classified as: a) outcome-positive (develops breast cancer); b) outcomenegative(dies before breast cancer or is alive and breast-cancer-free at end ofperiod); or c) censored (last observed alive and free of breast cancer beforeend of period). Competing risk theory is needed to estimate her breast cancerprobability in these circumstances. Most risk models assume that mortalityrates depend only on age at risk, sex and race/ethnicity. However covariates forco-morbidities are likely to be available and could be important in risk modelperformance and validation among older cohort subjects. Thus we need toexpand existing risk models to include covariates associated with mortalityrisk, and to examine the effect of this expansion on risk model performance.There also is need to examine the feasibility of expanding existing riskmodels to include multiple outcomes of interest. For example, an osteoporoticwoman might need to weigh the risks and benefits of several fracturepreventiveoptions (e.g., tamoxifen, a bisphosphonate, or no drug). If she hasa strong family history of certain chronic diseases (e.g., breast cancer, stroke)she needs a model that provides accurate estimates of her risks of these outcomesunder each of the options she is considering. Her marginal outcomerisks may be estimable from existing single-outcome risk models, but thesemodels do not accommodate correlated risks for different outcomes. Also theywere calibrated to cohorts with different selection factors and different covariatedistributions, so their estimates may not be comparable. The graph onthe right of Figure 35.4 indicates that the complexity of multi-state modelsfor stochastic processes increases exponentially with the number of outcomesconsidered. (Here breast cancer (B) and stroke (S) are transient states, sincesubjects in these states are at risk for the other outcome, while death (D) anddevelopment of both breast cancer and stroke (BS) are absorbing states.)Work is needed to determine whether the rich body of work on multistatestochastic processes can be applied to cohort data to provide more realisticrisk estimates for multiple, competing and noncompeting outcomes.