Incidence, progression, and regression of AMD and mortality were modeled by using MSMs in continuous time with misclassification, where the observed data are states assumed to be misclassifications of the true, underlying states. We identified mutually exclusive and exhaustive states representing the current status (current AMD severity level or death) of each subject at a given age. The observed AMD level is subject to measurement error. Replicate single gradings of AMD from fundus photographs were used to estimate the matrix of misclassification probabilities, using a latent class model for diagnostic accuracy in the absence of a known gold standard
42,43 ; the extension of Lo's estimator was used to ensure stochastic ordering of the misclassification probabilities.
44,45 To be specific, the likelihood of a set of
k gradings of a single photograph,
g1, g2,…, gk , is given by Σ
s π(
s) p(
g1 |
s) p(
g2 |
s)…p(
gk |
s), where
s is the unknown (latent) true grade for the photograph, π(
s) is the prevalence of grade
s in the reproducibility sample, and p(
g|
s) is the probability of observed grade
g for a photograph with true grade
s. This model assumes that (1) the gradings (
g1, g2,…, gk ) are conditionally independent given the true AMD state (
s) and (2) the (mis)classification probabilities are constant within and across subjects. With these assumptions, the unknown parameters (π(
s), p(
g|s)) can be estimated via maximum likelihood.
The
Figure illustrates the underlying MSM; arrows indicate possible instantaneous transitions. Instantaneous transitions (the next state to which the individual moves and the time of the change) were allowed between adjacent AMD states with one exception; based on clinical observation, regression from late AMD (level 5) to severe early AMD (level 4) was not allowed. Model selection based on the Akaike information criterion (AIC)
46 was used to evaluate the need for covariate effects on other instantaneous transitions (incidence/progression, regression, or mortality).
Transitions are governed by up to 12 transition intensities, one for each possible instantaneous transition between states (represented by arrows in the
Fig.), which represent the hazard of moving between states. Dependence of transition intensities on age, sex, and
CFH Y402H genotype was specified by using log-linear regression models. Age was entered as a linear term and updated annually. Sex and
CFH Y402H genotype were entered by using indicator variables. Covariate effects on transitions within the AMD scale were unconstrained. Covariate effects on transitions to death were constrained to be equal, but intercepts were allowed to vary.
Analyses were conducted in R
47 by using the msm package.
48 Covariate effects on transition intensities are summarized as hazard ratios. We calculated estimated transition probabilities to each AMD state (and death) after 5 years and estimated cumulative incidence of each AMD state (and death) for specified subgroups. Cumulative incidence calculations used annual assessments of AMD status; subjects were assigned to the most severe AMD state observed at or before the current age.