Latent Transition Analysis

Latent Transition Analysis of Changing Patient States

Latent transition analysis (LTA) estimates how people move between hidden states, such as patterns of adherence, symptom profiles or levels of service use, when each state can only be inferred from several imperfect measures recorded at every wave of a cohort. The method fits the states and the movements between them in one model, so a change in recorded answers is not mistaken for a change in the person. Its main output is a matrix of transition probabilities between latent states, the quantity that drives a Markov cohort model. For health economists the attraction is a set of states built from patient-reported outcomes or claims data, with movement between them corrected for measurement error.

Latent statuses measured at each wave

Lanza and Collins describe LTA as a longitudinal extension of latent class analysis in which change is quantified in a matrix of transition probabilities between two consecutive times. They keep the term latent classes for groups whose membership is fixed and use latent statuses for groups that a person can leave. The basic model has three sets of parameters. These are the status membership probabilities at the first wave (delta), the transition probabilities between statuses (tau) and the item-response probabilities that link each status to the observed answers (rho).

$$P(\mathbf{Y}_i = \mathbf{y}) = \sum_{s_1=1}^{S} \cdots \sum_{s_T=1}^{S} \delta_{s_1} \prod_{t=2}^{T} \tau_{s_t \mid s_{t-1}} \prod_{t=1}^{T} \prod_{m=1}^{M} \prod_{k=1}^{r_m} \rho_{t,m,k \mid s_t}^{I(y_{tm} = k)}$$

where $\mathbf{Y}_i$ is the full set of answers for person $i$ across all waves, $\mathbf{y}$ is one possible set of answers, $S$ is the number of latent statuses, $T$ is the number of waves, $s_t$ is the status at wave $t$, $\delta_{s_1}$ is the probability of being in status $s_1$ at the first wave, $\tau_{s_t \mid s_{t-1}}$ is the probability of being in status $s_t$ at wave $t$ given status $s_{t-1}$ at the previous wave, $M$ is the number of items measured at each wave, $r_m$ is the number of response categories of item $m$, $\rho_{t,m,k \mid s_t}$ is the probability of response $k$ on item $m$ at wave $t$ for a person in status $s_t$, and $I(y_{tm} = k)$ equals 1 when the answer to item $m$ at wave $t$ is $k$ and 0 otherwise.

The rho parameters carry the meaning of each status, since a status is labelled by the answers it makes likely. Within a status and wave the items are assumed independent, as in latent class analysis. The tau parameters depend only on the status at the previous wave, which is the Markov assumption familiar from decision modelling.

Gusinow and colleagues call LTA a type of hidden Markov model, designed to infer latent states and estimate the transition probabilities between them over successive time points. Its forward recursion is given on that page.

How the parameters are estimated

Lanza and Collins report maximum likelihood estimation through the EM algorithm in the SAS procedure PROC LTA. Missing answers on the indicators are handled by dropping them from each person's product, with the data assumed missing at random.

Moore, Quartiroli and Little point out that mixture models have a best global solution and several poorer local maxima of the log likelihood, so each model is run from many random starting values. They cite minimum sample size recommendations of 300 to 500 for mixture models, and report simulation work in which a standard LTA fitted well with 500 participants and two or three time points.

Covariates enter through baseline-category multinomial logit models, one for status membership at the first wave and one for each row of the transition matrix, so exponentiated coefficients are odds ratios, and in each transition row they compare a move with staying in the same status. Lanza and Collins warn that a row whose starting status is small has few people behind it, and they fixed three transition probabilities estimated at 0.009 or smaller to zero before adding a covariate, since group differences in such rare moves would be trivial and the restriction can stop the regression failing.

Choices that shape the states and the transitions

Each modelling decision between the data and the matrix should be reported. Moore and colleagues recommend enumerating the classes at each wave separately before fitting the joint model, and testing measurement invariance before adding covariates.

Number of statuses. Park and Chung compared models with two to five states using the Akaike information criterion, the Bayesian information criterion and entropy, alongside clinical interpretability. Lanza, Patrick and Maggs narrowed the choice on AIC and BIC to three or four statuses and chose four on interpretability.

Measurement invariance over time. Constraining the rho parameters to be equal at every wave keeps each status meaning the same thing, so a transition is a change of status and not a change of definition. Lanza and Collins note that the likelihood-ratio difference test is sensitive to slight differences, and kept invariance despite a significant result of 109.3 on 60 degrees of freedom because the statuses read the same at each wave. Park and Chung imposed invariance and accepted that it may hide time-specific clinical detail as death approaches.

Stationarity and lags. A stationary process has the same transition matrix between each pair of waves, which Lanza and Collins test by equating the matrices. Moore and colleagues also test whether a two-lag path, such as wave 1 to wave 3, is needed, which relaxes the first-order Markov assumption.

Stable and changing people. A mover-stayer component separates people who never change status from those who change at least once. The random intercept LTA described by Moore and colleagues adds a person-level mean across waves, so the statuses describe within-person deviations. In the simulations they report, this variant did poorly with two time points even with 4,000 participants.

Why latent transitions differ from recorded changes

Cross-tabulating recorded answers at two waves looks simpler but fails once several items define the state. Lanza, Patrick and Maggs had three substance use items with 12 possible patterns at each wave, so the wave-to-wave table had 144 cells and was too sparse for a test of independence.

The second reason is error. Lanza and Collins note that latent class models estimate and remove measurement error, and in LTA this extends to the transitions. A person who truly stays in one state but gives a noisy answer at a middle wave shows two recorded moves, while the latent model can attribute both to error.

Worked example with medication adherence measured two ways

All numbers in this example are illustrative. A cohort taking a long-term medicine is assessed once a year with two binary indicators, an on-time pharmacy refill and a self-report of taking every dose. The model has two statuses, adherent (A) and non-adherent (N), with measurement invariant across waves.

1. Set the parameters. At wave 1, 70% are adherent and 30% non-adherent. The annual transition probabilities are 0.80 for staying adherent, 0.20 for A to N, 0.25 for N to A and 0.75 for staying non-adherent. An adherent person refills on time with probability 0.90 and reports full adherence with probability 0.85, against 0.30 and 0.40 for a non-adherent person.

2. Status shares at wave 2. Staying adherent contributes 0.70 × 0.80 = 0.56 and recovering contributes 0.30 × 0.25 = 0.075, so the adherent share is 0.635, leaving 0.365 non-adherent.

3. Probability of one patient's answers. The patient is positive on both indicators at wave 1 and negative on both at wave 2. At wave 1 the answers have probability 0.90 × 0.85 = 0.765 if adherent and 0.30 × 0.40 = 0.12 if non-adherent. At wave 2 they have probability 0.10 × 0.15 = 0.015 if adherent and 0.70 × 0.60 = 0.42 if non-adherent. The four status paths give these products.

The total is 0.062883, and each share is the path probability divided by it, for example 0.044982 / 0.062883 = 0.715. The recorded answers look like a clear lapse, yet the model gives an 18% chance that the patient was non-adherent all along.

4. Transitions read from refills alone. Suppose an analyst calls a patient adherent whenever the refill is on time. The share on time at wave 1 is 0.70 × 0.90 + 0.30 × 0.30 = 0.72. The probability of on time at wave 1 and late at wave 2 sums over the four paths as 0.0504 + 0.0882 + 0.00225 + 0.04725 = 0.1881, so the apparent lapse rate is 0.1881 / 0.72 = 0.261 against a true 0.20. The probability of late then on time is 0.0504 + 0.0042 + 0.04725 + 0.04725 = 0.1491, so the apparent recovery rate is 0.1491 / 0.28 = 0.5325 against a true 0.25.

5. What the difference does to a model. With a constant transition probability, the expected number of annual cycles spent in a state from entry is one divided by the probability of leaving it.

$$D_s = \frac{1}{1 - \tau_{s \mid s}}$$

where $D_s$ is the expected number of cycles spent in status $s$ after entering it and $\tau_{s \mid s}$ is the probability of staying in status $s$ each cycle. The latent model gives 1 / 0.25 = 4.0 years in non-adherence, against 1 / 0.5325 = 1.878 years from the refill-only rates. If non-adherence carried an illustrative extra GBP 600 a year in avoidable care, ignoring death and discounting, an episode would cost 4.0 × 600 = GBP 2,400 under the latent rates and 1.878 × 600 = GBP 1,127 under the refill-only rates.

6. Interpret. Misclassification by a single indicator inflates movement in both directions, so the recorded-state matrix makes non-adherence look short-lived and cheap. The value of preventing each lapse would be understated.

Uses in health economics and outcomes research

Park and Chung applied it to claims data for all 75,784 people who died of cancer in South Korea in 2016, summarising service use in five binary indicators per interval and finding five end-of-life care states. Persistence was high, with a probability of 0.991 of staying in the high hospice use state between adjacent intervals. Wisk and colleagues used PROMIS-29 subscales to define four health-related quality of life classes after COVID-19-like illness.

For a state-transition model in an economic evaluation, the tau matrix is a candidate input. The cycle length should match the interval between waves, or the matrix must be converted as described on the transition matrix page. Each latent state also needs its own costs and utilities before the matrix can be used, since the classification model does not supply them. Uncertainty in the tau estimates belongs in probabilistic sensitivity analysis, and the number of states is a structural choice for scenario analysis.

Boundaries with neighbouring methods

The nearest methods differ in what is latent and in whether a person's group can change. Latent class analysis supplies the measurement model that LTA repeats at each wave, while multi-state models on recorded states share the transition matrix but take the states as measured without error.

Limitations and common misreadings

Most errors with LTA come from treating the fitted statuses and matrix as more certain than they are. A good fit does not prevent these errors.

Assigned statuses are not known statuses. Counting transitions between each person's most likely status discards classification uncertainty. Lund and Ritz note that their stepwise approach treats first-wave class membership as known without error.

Transitions are not effects. Park and Chung stress that their descriptive design does not allow causal interpretation, and their claims data lacked cancer stage and patient preferences, which may have confounded both the states and the transitions.

A fitted matrix is not automatically a model input. Its probabilities hold only for the spacing of waves in the data. States chosen to describe a cohort may also fail to separate costs.

Sources

• Gusinow R, Górska A, Canziani LM, et al.; ORCHESTRA study group. Latent transition analysis for longitudinal studies of post-acute infection syndromes. Nature Communications. 2026;17:2557. https://doi.org/10.1038/s41467-026-68650-7
• Lanza ST, Collins LM. A new SAS procedure for latent transition analysis: transitions in dating and sexual risk behavior. Developmental Psychology. 2008;44(2):446-456. https://doi.org/10.1037/0012-1649.44.2.446
• Lanza ST, Patrick ME, Maggs JL. Latent transition analysis: benefits of a latent variable approach to modeling transitions in substance use. Journal of Drug Issues. 2010;40(1):93-120. https://doi.org/10.1177/002204261004000106
• Lund L, Ritz C. Flexible and modular latent transition analysis: a tutorial using R. PLoS One. 2025;20(1):e0317617. https://doi.org/10.1371/journal.pone.0317617
• Moore EWG, Quartiroli A, Little TD. Introduction to the best practice recommendations for longitudinal latent transition analysis. International Journal of Psychology. 2025;60(2):e70021. https://doi.org/10.1002/ijop.70021
• Park G, Chung W. Latent transition analysis of end-of-life care trajectories among cancer patients in South Korea: a nationwide cohort study. BMC Health Services Research. 2026;26:911. https://doi.org/10.1186/s12913-026-14949-6
• Wisk LE, Gottlieb M, Chen P, et al. Association of SARS-CoV-2 with health-related quality of life 1 year after illness using latent transition analysis. Open Forum Infectious Diseases. 2025;12(6):ofaf278. https://doi.org/10.1093/ofid/ofaf278