{"id":"7ddab7e7-6927-4702-9146-42c1fd93a8d7","arxiv_id":"2607.29415","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"SoCIFR: a scalar-on-function regression framework that simultaneously handles censored functional predictors and informative observation times, with a matched case-control extension, applied to predicting bot-interaction susceptibility on Twitter/X.","lead":"This paper builds a regression framework that predicts a binary outcome from functional predictors that are both censored and observed at informative times, and applies it to predicting Twitter users' bot interactions. It combines latent-process modeling, inverse-probability weighting, and functional PCA, with simulations and an application to about 9,600 matched user pairs.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (3) is not implied by A1–A3: IPW identity uses p^c=E[R|X,Y=c] but A2 only gives R⊥Z|X; because Y depends on Z, conditioning on Y=c can induce R–Z dependence, biasing the class-specific mean/covariance estimates.","rationale":"The reader's weakest assumption pointed to A2, but the failure is sharper than a possible violation of A2: even when A2 holds exactly, Eq. (3) is not implied. The required conditional independence is R⊥Z | X,Y, and A2 only gives R⊥Z | X. Since Y depends on Z and X through A3, conditioning on Y=c can create dependence between R and Z. The derivation in Eq. (3) explicitly factors E[ZR | X,Y=c], so this is not a minor technicality; it is the central mechanism by which the method claims to recover the latent censored process Z under informative sampling. The simulations in Section 5 may show good prediction, but they do not validate the unbiasedness of the IPW-recovered Z, and the supplement tables would likely reveal systematic bias if true Z is compared with the recovered Z. This raises correctness risk above the reader's 'medium' assessment and means the current manuscript does not establish its central claim. I would move from CONDITIONAL to REJECT, while noting that the flaw is addressable: replacing p^c by p=E[R|X] appears to make the identity valid under the stated A2, or A2 could be strengthened and the estimator re-derived. The open-source code and application are valuable, but the framework's theoretical foundation needs reworking before the paper can be accepted.","tokens_in":20621,"tokens_out":12626,"duration_ms":150739,"concrete_test":"Generate a simple Gaussian/Bernoulli model satisfying A1–A3: X_i~N(0,1); Z_i|X_i~N(X_i,1); R_i|X_i~Bernoulli(expit(X_i)), independent of Z_i given X_i; Y_i|Z_i,X_i~Bernoulli(expit(Z_i+X_i)). For a fixed t (use scalar analogues), compute the true class-specific mean E[Z|Y=c] and the IPW-weighted sample mean sum_i Z_i R_i / p_i^c over subjects with Y_i=c, using the true p_i^c=E[R|X,Y=c]. Repeat for N=100,000 and compare the two values for c=0 and c=1. If they differ by more than 0.01, Eq. (3) fails. As a control, repeat with p_i=E[R|X]; the bias should vanish, isolating the missing conditional independence as the cause.","verdict_should_be":"REJECT","load_bearing_attack":"Section 3.1's key identity, Eq. (3), is the engine for recovering the latent process Z under informative sampling. It asserts E[Z R / p^c | Y=c] = E[Z | Y=c], where p^c = E[R | X, Y=c]. The derivation factors E[Z R | X, Y=c] as E[Z | X,Y=c] E[R | X,Y=c]. That factorization requires R⊥Z | X,Y. Assumption A2 states only R⊥Z | X. Since A3 models Y as a function of Z and X, conditioning on Y=c is a collider-type operation: it generally makes R and Z dependent even when A2 holds. A simple Gaussian/Bernoulli example (X→Z, X→R, Z→Y) confirms the two are not independent given Y. Therefore Eq. (3) is not a consequence of A1–A3, and the class-specific IPW estimates of Z's mean and covariance are biased under the paper's own generative model. The application is not exempt: @-rate Z is only defined on active weeks, so the dependence between activity R and latent @-rate after conditioning on susceptibility is exactly the scenario that breaks the identity. The gap is internal, not a disagreement with consensus; the paper would need either to replace p^c with p=E[R|X] (which makes the identity valid under A2) or to strengthen A2 to R⊥Z|X,Y and re-run the simulations.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes Scalar-on Censored Informative-design Functional Regression (SoCIFR), a framework for binary outcomes when functional predictors are censored and observed under an informative sampling design. It introduces two latent processes — X for the observation mechanism and Z for the latent censored signal — assumes Y is conditionally independent of the observed data given (Z, X), and estimates class-specific observation probabilities p^c via a latent observation-process model. The censored signal's mean and covariance are then recovered using inverse-probability-weighted local censored likelihood (Eqs. 7–9), followed by multivariate functional principal component analysis to extract low-dimensional features that are fed into logistic, additive, or nonlinear predictors. The framework is extended to multiple functional covariates and matched case-control designs. Simulations compare SoCIFR to random forest baselines, and the application predicts bot-interaction susceptibility from Twitter posting trajectories over varying observation windows and horizons.","tokens_in":21078,"tokens_out":6523,"duration_ms":83910,"significance":"If the core identification step were valid, the paper would make a useful contribution to functional data analysis by extending censored functional regression to informative/MNAR sampling, and by providing an interpretable alternative to black-box predictors in a socially relevant application. The manuscript also offers useful extensions to matched case-control designs and multiple functional covariates, and it ships open-source software. However, the central IPW identity in Eq. (3) is not implied by the stated assumptions, and the application's feature extraction appears to use outcome information before the train–test split. Both issues are load-bearing: the first affects every estimate produced by the method, and the second affects the credibility of the reported application AUCs. The framework's significance can only be assessed after these are resolved.","major_comments":[{"comment":"The identity E[Z_i(t) R_i(t)/p_i^c(t) | Y_i=c] = E[Z_i(t) | Y_i=c] is derived by factoring E[Z_i(t) R_i(t) | X_i, Y_i=c] as E[Z_i(t) | X_i,Y_i=c] E[R_i(t) | X_i,Y_i=c]. This factorization requires R_i ⊥ Z_i | X_i, Y_i=c. Assumption A2 states only R_i ⊥ Z_i | X_i. Because A3 makes Y_i depend on (Z_i, X_i), conditioning on Y_i=c induces dependence between R_i and Z_i even when A2 holds (a collider-type path through the common cause X). Therefore Eq. (3) is not a consequence of A1–A3, and the class-specific IPW estimates in Eqs. (7)–(9) are biased under the paper's own generative model. This is an internal gap, not a disagreement with external consensus. The authors need either to strengthen the assumption to R_i ⊥ Z_i | X_i, Y_i and re-derive and re-run the simulations, or to provide a different identification argument for the class-specific mean/covariance of Z. As written, the central cl","section":"Section 3.1, Eq. (3)"},{"comment":"The application section states that 'Feature extraction used 99% and 95% PVE thresholds... yielding approximately 4–5 features per trajectory', and then that these features were evaluated using 10 random train–test splits. It is not stated whether the class-specific estimation of p^c and Z^c and the PVE-based feature extraction were nested inside the training folds or performed on the full dataset. As written, the outcome Y is used to define the classes for estimating p^c, Z^c, and the MFPCA basis, so test observations' features can depend on their own labels. If full-data feature extraction was used, the reported PR AUCs (0.87 for pair-level prediction and 0.78 for subject-level prediction) are partly circular. The manuscript must clarify the splitting protocol; if features were extracted on the full data, the analysis should be rerun with feature estimation performed only on each train","section":"Section 6, feature extraction and train–test splits"},{"comment":"The simulation study compares SoCIFR to two random forest baselines, but it does not test the motivating claim in Section 1 that 'ignoring either can lead to biased inference'. No comparison is made to estimators that ignore the informative sampling (e.g., treating inactive weeks as missing at random or setting the weights to 1), nor to censored-FPCA methods without the IPW adjustment. Without such an ablation, the simulations do not demonstrate that the IPW component is doing the claimed work; they only show that the full pipeline is competitive with random forests. This is important because the paper's stated novelty is the joint accommodation of censoring and informative sampling, and the simulations should isolate that contribution.","section":"Section 5.1, Table 1"}],"minor_comments":[{"comment":"There are typos and inconsistent formatting, e.g., 'difficult' (p. 2), 'efficient' (p. 14), and 'Guassian' in Eq. (8). These do not affect the substance but should be corrected.","section":"Throughout"},{"comment":"The case labels in the bivariate censored likelihood appear inconsistent. For example, the case 'W1 = b, W2 = a' uses 'Φ^C(a|W1 = b; ...)', while other cases condition on the uncensored variable. Please check that each case uses the correct conditional argument and that the notation is consistently defined.","section":"Eq. (8)"},{"comment":"The text says 'we omit the group-specific notation' after defining p_i^c, but Eq. (7) then uses p̂^{-1}_{ij}. It should be made explicit that these weights are class-specific throughout Section 3.2.2.","section":"Section 3.2.2"},{"comment":"The paragraph on multiple functional covariates repeats itself: 'For the informative group, we jointly recover...' and then 'For the first group, we jointly recover...' say nearly the same thing. Please merge and clarify the grouping logic.","section":"Section 4.2"},{"comment":"The manuscript reports both pair-level and subject-level prediction results and uses PR AUC in the application but AUC in the matched-case simulations (Tables 2–3). A brief explanation of the choice of metric and how prevalence adjustment (King and Zeng, 2001) is applied in Figure 2 would improve comparability.","section":"Section 6 and Figure 2"}],"recommendation":"major_revision","confidential_remarks":"The Eq. (3) issue is the most serious technical obstacle. If the authors can supply a valid identifying assumption and show through simulation that the class-specific IPW estimates are unbiased under that assumption, the paper may be salvageable; otherwise the central contribution is not established. The application's potential circularity must also be addressed before any reported predictive performance can be interpreted."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know. First, this paper really is the first to combine censored functional predictors with an informative observation process in scalar-on-function binary regression, and it adds a matched case-control extension. That fills a genuine gap in the functional data literature, and the overall structure—latent activity process, class-specific IPW likelihood, Monte Carlo score prediction, MFPCA with scaling, conditional logistic regression—is coherent and reasonably well executed. The simulations show the method outperforms random forests at higher signal levels, and the bot-susceptibility application is a sensible motivation. Credit where due: the software is provided, the train-test splits are explicitly described, and sensitivity to PVE thresholds is checked.\n\nThe soft spot is real and load-bearing. Equation (3) asserts E[Z_i(t)R_i(t)/p_i^c(t) | Y_i=c] = E[Z_i(t)|Y_i=c] with p_i^c = E[R_i|X_i,Y_i=c]. The derivation factorizes E[ZR|X,Y=c] as E[Z|X,Y=c]E[R|X,Y=c], which requires R⊥Z | X, Y=c. Assumption A2 only gives R⊥Z | X. Because Y depends on Z and X, conditioning on Y=c generally induces dependence between R and Z even when A2 holds. So the class-specific IPW estimates of Z's mean and covariance are biased under the paper's own generative model. This is not a minor technicality—it is the mechanism that supposedly recovers the latent censored process under informative sampling. The fix is straightforward conceptually: either strengthen A2 to R⊥Z | X,Y, or replace p_i^c with an unconditional p_i = E[R_i|X_i] and re-derive the identity. The paper should say which and rerun the simulations.\n\nSecond soft spot: the class-specific estimation uses Y to estimate the observation process and the censored latent process, so the extracted features are supervised. If the same full-data feature extraction feeds the reported train-test splits, the application PR AUCs (0.87 pair-level, 0.78 subject-level) are partly circular. The paper does not explicitly state that feature extraction is refit within each training fold. That should be clarified and, if necessary, corrected.\n\nSmaller issues: there is no theory for the estimators (no asymptotics), and the treatment of post volume as left-censored at zero is debatable since log(x+1) zero is a true zero. The coefficient functions in the application have no uncertainty quantification.\n\nWho is this for? Functional data analysts working with censored or informatively sampled longitudinal data, and applied social media researchers. It deserves a serious referee, but the referee should push for a corrected IPW derivation and a clean evaluation pipeline before publication. I would not cite the current version without caveats, but I would bring it to a reading group to discuss the assumption trap.","headline":"A useful first combination of censored functional predictors and informative observation processes, but the key IPW identity in Eq. (3) does not follow from the stated assumptions and the application evaluation may be partly circular.","tokens_in":21530,"tokens_out":4915,"would_cite":false,"duration_ms":56452,"reading_group":"yes","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["62R10","62N01"],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper claims that bot-interaction susceptibility can be predicted from a year of censored, informatively sampled posting trajectories by jointly estimating a latent activity process and a latent signal process, and that this recovers un","keywords":["censored functional data","informative observation times","functional regression","inverse probability weighting","matched case-control","functional principal component analysis","missing not at random","social media bot interaction"],"falsifier":"Generate synthetic data where the observation indicator depends directly on the latent signal Z as well as the activity process X, e.g., R_t ~ Bernoulli(logit^{-1}(X_t + γ Z_t)) with γ ≠ 0, then run SoCIFR and compare the estimated class-conditional mean curve E[Z(t)|Y=c] to the known truth. If the paper's claim is right, the inverse-probability-weighted estimates should stay unbiased when γ = 0 and show increasing bias as γ grows, revealing exactly how much A2 violations degrade the recovered trajectories and the resulting predictions.","tokens_in":20523,"feed_emoji":"🤖","tokens_out":6018,"duration_ms":70135,"temperature":0.7,"pith_summary":"Social-media users' risk of interacting with bot accounts can be predicted from a year of weekly posting behavior, even though the key behavioral trajectories are censored and only observed on weeks a user happens to post. The paper introduces SoCIFR, a functional-regression framework that treats observed trajectories as noisy, boundary-clamped views of a latent signal, and treats whether a user posts as a second latent process. The central move is an inverse-probability-weighting identity that recovers unbiased class-specific mean and covariance functions of the censored signal under missing-not-at-random observation times. Those recovered curves are reduced to a few scores and fed into logistic or additive models, with a conditional-logistic extension for matched case-control data. Applied to 9,586 matched Twitter/X pairs, the method predicts bot-interaction susceptibility with PR AUC 0.87 for pairs and 0.78 for individuals, roughly matching random forests while keeping the model interpretable.","feed_headline":"Censored posting data predict bot-interaction risk","feed_subtitle":"Recovers latent posting behavior from censored, irregular weekly tweets to predict which users will engage with bots.","key_machinery":"The engine is the inverse-probability-weighting identity (Eq. 3), which converts censored observations observed at informative times into unbiased estimates of the latent signal's class-specific mean and covariance. It is powered by two latent processes: X(t), the activity/observation process whose observation probability p^c(t) is estimated by functional logistic regression of the binary posting indicators, and Z(t), the latent signal underlying the censored measurements, whose mean and covariance are estimated by local weighted likelihood with weights 1/p^c(t). Multivariate functional principal component analysis with standardized scores then produces the low-dimensional features used in t","core_discovery":"SoCIFR's central claim is that you can estimate the class-specific latent signal underlying censored measurements—even when the times at which measurements appear are themselves informative—by writing the observed measurement as a censored view of the latent signal plus noise, modeling whether a subject is observed as a separate latent activity process, and weighting each observation by the inverse of the estimated class-specific observation probability. The identity E[Z(t)R(t)/p^c(t) | Y=c] = E[Z(t) | Y=c] (Eq. 3) is what makes the weighting work; it holds when the observation indicator is independent of the signal given the activity process. From the recovered latent curves, multivariate f","pith_inferences":["Beyond the paper: Because assumption A2 (observation indicator independent of the signal given the activity process) is never stress-tested on the bot data, the recovered @-rate trajectory could still be biased if the users who post most are also those with extreme @-mention behavior; a sensitivity simulation with observation driven directly by Z would quantify that risk.","Beyond the paper: The two-stage matched-pair prediction—conditional likelihood followed by a population-level intercept—implicitly assumes the matching variables are only weakly prognostic; if a future matched study matches on a strong risk factor, the reported collapsibility of the odds ratio would likely break down.","Beyond the paper: The same machinery could be transplanted to health-monitoring settings where app-use intensity drives measurement of symptom scores—another censored, informatively sampled design—though the Gaussian-process assumptions would need adaptation for count or skewed measurements.","Beyond the paper: One testable extension is a simulation in which the observation indicator is generated from the activity process plus a direct dose of the latent signal; the paper's own identity predicts that class-specific mean estimates will drift with the dose, giving a concrete calibration for when weighting alone is insufficient."],"forward_implications":["If SoCIFR is correct, analysts can fit scalar-on-function regression to longitudinal signals that are both censored at boundaries and observed at informative times; ignoring either mechanism biases estimates.","The matched case-control extension removes pair-specific intercepts through conditional likelihood, so large matched studies can be analyzed without incidental-parameter bias and without assuming strong within-pair correlation.","In the bot application, the estimated coefficient functions locate interpretable behavioral shifts: increased volume, length, and @-activity become leading risk signals roughly 6–8 weeks before the reference week.","The method supports prediction at multiple future horizons (H = 0, 4, 8, 12 weeks) from observation windows of varying length, even when the prevalence of susceptible users changes with the horizon.","The same framework extends to multiple functional predictors of mixed type—censored or uncensored, informatively or noninformatively sampled—while sharing a single observation process when appropriate."],"fun_headline_variants":["Censored posts predict bot engagement risk","Informative sampling powers bot-vulnerability forecasts","Censored tweets expose hidden bot-attraction signals","SoCIFR: predict bot interactions from censored trajectories"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The whole weighting identity collapses if whether a user posts at a week depends on the very behavior being measured—for instance, if users with high @-mention rates are also more likely to post during that week.","fun_headline_variants_meta":{"raw":{"variants":["Censored posts predict bot engagement risk","Informative sampling powers bot-vulnerability forecasts","Censored tweets expose hidden bot-attraction signals","SoCIFR: predict bot interactions from censored trajectories"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000303,"raw_usage":{"total_tokens":1539,"prompt_tokens":665,"completion_tokens":874,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":409,"completion_tokens_details":{"reasoning_tokens":824}},"tokens_in":409,"tokens_out":874,"duration_ms":9281,"temperature":1.0,"reasoning_tokens":824,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T07:27:59.614899+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Generate synthetic data where the observation indicator depends directly on the latent signal Z as well as the activity process X, e.g., R_t ~ Bernoulli(logit^{-1}(X_t + γ Z_t)) with γ ≠ 0, then run SoCIFR and compare the estimated class-conditional mean curve E[Z(t)|Y=c] to the known truth. If the paper's claim is right, the inverse-probability-weighted estimates should stay unbiased when γ = 0 and show increasing bias as γ grows, revealing exactly how much A2 violations degrade the recovered trajectories and the resulting predictions.","supporting_citations":[],"review_version":1}