survival 1.1.29

A high-performance survival analysis library written in Rust with Python bindings
Documentation
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
use crate::constants::EXP_CLAMP_MIN;
use crate::regression::coxfit6::{CoxFitBuilder, Method as CoxMethod};
use ndarray::{Array1, Array2};
use pyo3::prelude::*;
use rayon::prelude::*;

fn invert_matrix(mat: &[Vec<f64>]) -> Option<Vec<Vec<f64>>> {
    let n = mat.len();
    if n == 0 {
        return None;
    }
    for row in mat {
        if row.len() != n {
            return None;
        }
    }
    let mut aug: Vec<Vec<f64>> = mat
        .iter()
        .enumerate()
        .map(|(i, row)| {
            let mut new_row = row.clone();
            new_row.extend(vec![0.0; n]);
            new_row[n + i] = 1.0;
            new_row
        })
        .collect();
    for i in 0..n {
        let mut max_row = i;
        for k in (i + 1)..n {
            if aug[k][i].abs() > aug[max_row][i].abs() {
                max_row = k;
            }
        }
        aug.swap(i, max_row);
        if aug[i][i].abs() < 1e-12 {
            return None;
        }
        let pivot = aug[i][i];
        for val in aug[i].iter_mut().take(2 * n) {
            *val /= pivot;
        }
        for k in 0..n {
            if k != i {
                let factor = aug[k][i];
                let aug_i_clone: Vec<f64> = aug[i].iter().take(2 * n).copied().collect();
                for (j, aug_i_val) in aug_i_clone.iter().enumerate() {
                    aug[k][j] -= factor * aug_i_val;
                }
            }
        }
    }
    Some(aug.into_iter().map(|row| row[n..].to_vec()).collect())
}
#[derive(Clone)]
#[pyclass]
pub struct Subject {
    #[pyo3(get, set)]
    pub id: usize,
    #[pyo3(get, set)]
    pub covariates: Vec<f64>,
    #[pyo3(get, set)]
    pub is_case: bool,
    #[pyo3(get, set)]
    pub is_subcohort: bool,
    #[pyo3(get, set)]
    pub stratum: usize,
}
#[pymethods]
impl Subject {
    #[new]
    pub fn new(
        id: usize,
        covariates: Vec<f64>,
        is_case: bool,
        is_subcohort: bool,
        stratum: usize,
    ) -> Self {
        Self {
            id,
            covariates,
            is_case,
            is_subcohort,
            stratum,
        }
    }
}
#[pyclass]
pub struct CoxPHModel {
    coefficients: Array2<f64>,
    #[pyo3(get)]
    pub baseline_hazard: Vec<f64>,
    #[pyo3(get)]
    pub risk_scores: Vec<f64>,
    #[pyo3(get, set)]
    pub event_times: Vec<f64>,
    #[pyo3(get, set)]
    pub censoring: Vec<u8>,
    covariates: Array2<f64>,
}
impl Default for CoxPHModel {
    fn default() -> Self {
        Self::new()
    }
}
#[pymethods]
impl CoxPHModel {
    #[new]
    pub fn new() -> Self {
        Self {
            coefficients: Array2::<f64>::zeros((1, 1)),
            baseline_hazard: Vec::new(),
            risk_scores: Vec::new(),
            event_times: Vec::new(),
            censoring: Vec::new(),
            covariates: Array2::<f64>::zeros((1, 1)),
        }
    }
    #[pyo3(signature = (covariates, event_times, censoring))]
    #[staticmethod]
    pub fn new_with_data(
        covariates: Vec<Vec<f64>>,
        event_times: Vec<f64>,
        censoring: Vec<u8>,
    ) -> Self {
        let nrows = covariates.len();
        let ncols = if nrows > 0 { covariates[0].len() } else { 0 };
        let mut cov_array = Array2::<f64>::zeros((nrows, ncols));
        for (i, row) in covariates.iter().enumerate() {
            for (j, &val) in row.iter().enumerate() {
                cov_array[[i, j]] = val;
            }
        }
        Self {
            coefficients: Array2::<f64>::zeros((ncols, 1)),
            baseline_hazard: Vec::new(),
            risk_scores: Vec::new(),
            event_times,
            censoring,
            covariates: cov_array,
        }
    }
    pub fn add_subject(&mut self, subject: &Subject) -> PyResult<()> {
        let n = self.event_times.len();
        let ncols = self.covariates.ncols();
        if ncols != subject.covariates.len() {
            return Err(pyo3::exceptions::PyValueError::new_err(format!(
                "covariate dimension mismatch: expected {}, got {}",
                ncols,
                subject.covariates.len()
            )));
        }
        let mut new_covariates = Array2::<f64>::zeros((n + 1, ncols));
        for row_idx in 0..n {
            for col_idx in 0..ncols {
                new_covariates[[row_idx, col_idx]] = self.covariates[[row_idx, col_idx]];
            }
        }
        for col_idx in 0..ncols {
            new_covariates[[n, col_idx]] = subject.covariates[col_idx];
        }
        self.covariates = new_covariates;
        self.event_times.push(0.0);
        self.censoring.push(if subject.is_case { 1 } else { 0 });
        Ok(())
    }
    #[pyo3(signature = (n_iters = 20))]
    pub fn fit(&mut self, n_iters: u16) -> PyResult<()> {
        if self.event_times.is_empty() || self.covariates.nrows() == 0 {
            return Err(pyo3::exceptions::PyValueError::new_err(
                "cannot fit model: no data provided",
            ));
        }
        let n = self.event_times.len();
        let nvar = self.covariates.ncols();
        if nvar == 0 {
            return Err(pyo3::exceptions::PyValueError::new_err(
                "cannot fit model: no covariates provided",
            ));
        }
        let time_array = Array1::from_vec(self.event_times.clone());
        let status_array: Array1<i32> =
            Array1::from_vec(self.censoring.iter().map(|&x| x as i32).collect());
        let strata = Array1::zeros(n);
        let initial_beta: Vec<f64> =
            if self.coefficients.nrows() == nvar && self.coefficients.ncols() > 0 {
                self.coefficients.column(0).to_vec()
            } else {
                vec![0.0; nvar]
            };
        let mut cox_fit = CoxFitBuilder::new(time_array, status_array, self.covariates.clone())
            .strata(strata)
            .method(CoxMethod::Breslow)
            .max_iter(n_iters as usize)
            .eps(1e-5)
            .toler(1e-9)
            .initial_beta(initial_beta)
            .build()
            .map_err(|e| {
                pyo3::exceptions::PyRuntimeError::new_err(format!(
                    "Cox fit initialization failed: {}",
                    e
                ))
            })?;
        cox_fit.fit().map_err(|e| {
            pyo3::exceptions::PyRuntimeError::new_err(format!("Cox fit failed: {}", e))
        })?;
        let (beta, _means, _u, _imat, _loglik, _sctest, _flag, _iter) = cox_fit.results();
        let mut coefficients_array = Array2::<f64>::zeros((nvar, 1));
        for (idx, &beta_val) in beta.iter().enumerate() {
            coefficients_array[[idx, 0]] = beta_val;
        }
        self.coefficients = coefficients_array;
        self.risk_scores.clear();
        for row in self.covariates.outer_iter() {
            let risk_score = self.coefficients.column(0).dot(&row);
            self.risk_scores.push(risk_score.exp());
        }
        self.calculate_baseline_hazard();
        Ok(())
    }
    fn calculate_baseline_hazard(&mut self) {
        let n = self.event_times.len();
        if n == 0 {
            self.baseline_hazard = Vec::new();
            return;
        }
        let mut indices: Vec<usize> = (0..n).collect();
        indices.sort_by(|&i, &j| {
            self.event_times[i]
                .partial_cmp(&self.event_times[j])
                .unwrap_or(std::cmp::Ordering::Equal)
                .then_with(|| self.censoring[j].cmp(&self.censoring[i]))
        });
        let mut cumulative_risk = vec![0.0; n];
        let mut running_sum = 0.0;
        for i in (0..n).rev() {
            running_sum += self.risk_scores[indices[i]];
            cumulative_risk[i] = running_sum;
        }
        let n_events_estimate = self.censoring.iter().filter(|&&c| c == 1).count();
        let mut unique_times = Vec::with_capacity(n_events_estimate);
        let mut baseline_hazard = Vec::with_capacity(n_events_estimate);
        let mut cum_hazard = 0.0;
        let mut i = 0;
        while i < n {
            let idx = indices[i];
            if self.censoring[idx] == 0 {
                i += 1;
                continue;
            }
            let current_time = self.event_times[idx];
            let mut events = 0.0;
            let start_i = i;
            while i < n && (self.event_times[indices[i]] - current_time).abs() < 1e-9 {
                if self.censoring[indices[i]] == 1 {
                    events += 1.0;
                }
                i += 1;
            }
            let risk_sum = cumulative_risk[start_i];
            if risk_sum > 0.0 {
                let hazard = events / risk_sum;
                cum_hazard += hazard;
            }
            unique_times.push(current_time);
            baseline_hazard.push(cum_hazard);
        }
        if baseline_hazard.is_empty() {
            self.baseline_hazard = vec![0.0; n];
        } else {
            let mut full_baseline = vec![0.0; n];
            for (i, &t) in self.event_times.iter().enumerate() {
                let pos = unique_times.partition_point(|&ut| ut <= t);
                if pos > 0 {
                    full_baseline[i] = baseline_hazard[pos - 1];
                }
            }
            self.baseline_hazard = full_baseline;
        }
    }
    pub fn predict(&self, covariates: Vec<Vec<f64>>) -> Vec<f64> {
        let nrows = covariates.len();
        let ncols = if nrows > 0 { covariates[0].len() } else { 0 };
        covariates
            .par_iter()
            .map(|row| {
                let mut risk_score = 0.0;
                for (col_idx, &val) in row.iter().enumerate().take(ncols) {
                    if col_idx < self.coefficients.nrows() {
                        risk_score += self.coefficients[[col_idx, 0]] * val;
                    }
                }
                risk_score
            })
            .collect()
    }
    #[getter]
    pub fn get_coefficients(&self) -> Vec<Vec<f64>> {
        let mut result = Vec::new();
        for col in self.coefficients.columns() {
            result.push(col.iter().cloned().collect());
        }
        result
    }
    pub fn brier_score(&self) -> f64 {
        let mut score = 0.0;
        let mut count = 0.0;
        for (time, &status) in self.event_times.iter().zip(self.censoring.iter()) {
            let pred = self.predict_survival(*time);
            score += (pred - status as f64).powi(2);
            count += 1.0;
        }
        if count > 0.0 { score / count } else { 0.0 }
    }
    fn predict_survival(&self, time: f64) -> f64 {
        if self.baseline_hazard.is_empty() || self.risk_scores.is_empty() {
            return 0.5;
        }
        let baseline_haz = self
            .baseline_hazard
            .iter()
            .zip(&self.event_times)
            .filter(|&(_, &et)| et <= time)
            .map(|(h, _)| *h)
            .next_back()
            .unwrap_or(0.0);
        let avg_risk = if !self.risk_scores.is_empty() {
            self.risk_scores.iter().sum::<f64>() / self.risk_scores.len() as f64
        } else {
            1.0
        };
        (-baseline_haz * avg_risk).exp()
    }
    pub fn survival_curve(
        &self,
        covariates: Vec<Vec<f64>>,
        time_points: Option<Vec<f64>>,
    ) -> PyResult<(Vec<f64>, Vec<Vec<f64>>)> {
        let nrows = covariates.len();
        let ncols = if nrows > 0 { covariates[0].len() } else { 0 };
        let mut cov_array = Array2::<f64>::zeros((nrows, ncols));
        for (row_idx, row) in covariates.iter().enumerate() {
            for (col_idx, &val) in row.iter().enumerate() {
                cov_array[[row_idx, col_idx]] = val;
            }
        }
        let times = time_points.unwrap_or_else(|| {
            let mut t = self.event_times.clone();
            t.sort_by(|a, b| a.partial_cmp(b).unwrap_or(std::cmp::Ordering::Equal));
            t.dedup();
            t
        });
        let risk_scores: Vec<f64> = (0..nrows)
            .into_par_iter()
            .map(|row_idx| {
                let mut risk = 0.0;
                for col_idx in 0..ncols {
                    risk += self.coefficients[[col_idx, 0]] * cov_array[[row_idx, col_idx]];
                }
                risk.exp()
            })
            .collect();
        let baseline_hazards: Vec<f64> = times
            .iter()
            .map(|&t| {
                self.baseline_hazard
                    .iter()
                    .zip(&self.event_times)
                    .filter(|&(_, et)| *et <= t)
                    .map(|(h, _)| *h)
                    .sum::<f64>()
            })
            .collect();
        let survival_curves: Vec<Vec<f64>> = risk_scores
            .par_iter()
            .map(|&risk_exp| {
                baseline_hazards
                    .iter()
                    .map(|&bh| (-bh * risk_exp).exp())
                    .collect()
            })
            .collect();
        Ok((times, survival_curves))
    }
    pub fn hazard_ratios(&self) -> Vec<f64> {
        self.coefficients
            .column(0)
            .iter()
            .map(|&beta| beta.exp())
            .collect()
    }
    #[pyo3(signature = (confidence_level = 0.95))]
    pub fn hazard_ratios_with_ci(&self, confidence_level: f64) -> (Vec<f64>, Vec<f64>, Vec<f64>) {
        let coefs: Vec<f64> = self.coefficients.column(0).to_vec();
        let n = coefs.len();
        let z = if confidence_level >= 0.99 {
            2.576
        } else if confidence_level >= 0.95 {
            1.96
        } else {
            1.645
        };
        let se = self.compute_standard_errors();
        let mut hr = Vec::with_capacity(n);
        let mut ci_lower = Vec::with_capacity(n);
        let mut ci_upper = Vec::with_capacity(n);
        for (i, &beta) in coefs.iter().enumerate() {
            let se_i = se.get(i).copied().unwrap_or(0.1);
            hr.push(beta.exp());
            ci_lower.push((beta - z * se_i).exp());
            ci_upper.push((beta + z * se_i).exp());
        }
        (hr, ci_lower, ci_upper)
    }
    fn compute_standard_errors(&self) -> Vec<f64> {
        let n = self.event_times.len();
        let nvar = self.coefficients.nrows();
        if n == 0 || nvar == 0 {
            return vec![0.1; nvar];
        }
        let mut sorted_indices: Vec<usize> = (0..n).collect();
        sorted_indices.sort_by(|&i, &j| {
            self.event_times[j]
                .partial_cmp(&self.event_times[i])
                .unwrap_or(std::cmp::Ordering::Equal)
        });
        let mut cumulative_risk = vec![0.0; n];
        let mut cumulative_weighted_cov = vec![0.0; n * nvar];
        let mut cumulative_weighted_cov_sq = vec![0.0; n * nvar];
        let mut running_risk = 0.0;
        let mut running_weighted_cov = vec![0.0; nvar];
        let mut running_weighted_cov_sq = vec![0.0; nvar];
        for (pos, &idx) in sorted_indices.iter().enumerate() {
            let risk_j = self.risk_scores.get(idx).copied().unwrap_or(1.0);
            running_risk += risk_j;
            for k in 0..nvar {
                let cov_jk = self.covariates.get([idx, k]).copied().unwrap_or(0.0);
                running_weighted_cov[k] += risk_j * cov_jk;
                running_weighted_cov_sq[k] += risk_j * cov_jk * cov_jk;
            }
            cumulative_risk[pos] = running_risk;
            let base = pos * nvar;
            cumulative_weighted_cov[base..base + nvar].copy_from_slice(&running_weighted_cov);
            cumulative_weighted_cov_sq[base..base + nvar].copy_from_slice(&running_weighted_cov_sq);
        }
        let mut index_to_pos = vec![0usize; n];
        for (pos, &idx) in sorted_indices.iter().enumerate() {
            index_to_pos[idx] = pos;
        }
        let event_indices: Vec<usize> = (0..n).filter(|&i| self.censoring[i] == 1).collect();
        let fisher_contributions: Vec<Vec<f64>> = event_indices
            .par_iter()
            .filter_map(|&i| {
                let pos = index_to_pos[i];
                let risk_set_sum = cumulative_risk[pos];
                if risk_set_sum <= 0.0 {
                    return None;
                }
                let base = pos * nvar;
                let contrib: Vec<f64> = (0..nvar)
                    .map(|k| {
                        let weighted_cov = cumulative_weighted_cov[base + k];
                        let weighted_cov_sq = cumulative_weighted_cov_sq[base + k];
                        let mean_cov = weighted_cov / risk_set_sum;
                        weighted_cov_sq / risk_set_sum - mean_cov * mean_cov
                    })
                    .collect();
                Some(contrib)
            })
            .collect();
        let mut fisher_diag = vec![0.0; nvar];
        for contrib in fisher_contributions {
            for (k, &val) in contrib.iter().enumerate() {
                fisher_diag[k] += val;
            }
        }
        fisher_diag
            .iter()
            .map(|&f| if f > 0.0 { (1.0 / f).sqrt() } else { 0.1 })
            .collect()
    }
    pub fn log_likelihood(&self) -> f64 {
        if self.event_times.is_empty() || self.risk_scores.is_empty() {
            return 0.0;
        }
        let n = self.event_times.len();
        let mut sorted_indices: Vec<usize> = (0..n).collect();
        sorted_indices.sort_by(|&i, &j| {
            self.event_times[j]
                .partial_cmp(&self.event_times[i])
                .unwrap_or(std::cmp::Ordering::Equal)
        });
        let mut cumulative_risk = vec![0.0; n];
        let mut running_sum = 0.0;
        for (pos, &idx) in sorted_indices.iter().enumerate() {
            running_sum += self.risk_scores.get(idx).copied().unwrap_or(1.0);
            cumulative_risk[pos] = running_sum;
        }
        let mut index_to_pos = vec![0usize; n];
        for (pos, &idx) in sorted_indices.iter().enumerate() {
            index_to_pos[idx] = pos;
        }
        let event_indices: Vec<usize> = (0..n).filter(|&i| self.censoring[i] == 1).collect();
        event_indices
            .par_iter()
            .map(|&i| {
                let risk_score_i = self.risk_scores.get(i).copied().unwrap_or(1.0).ln();
                let pos = index_to_pos[i];
                let risk_set_sum = cumulative_risk[pos];
                if risk_set_sum > 0.0 {
                    risk_score_i - risk_set_sum.ln()
                } else {
                    0.0
                }
            })
            .sum()
    }
    pub fn aic(&self) -> f64 {
        let k = self.coefficients.nrows() as f64;
        -2.0 * self.log_likelihood() + 2.0 * k
    }
    pub fn bic(&self) -> f64 {
        let k = self.coefficients.nrows() as f64;
        let n = self.event_times.len() as f64;
        -2.0 * self.log_likelihood() + k * n.ln()
    }
    pub fn cumulative_hazard(&self, covariates: Vec<Vec<f64>>) -> (Vec<f64>, Vec<Vec<f64>>) {
        let nrows = covariates.len();
        let ncols = if nrows > 0 { covariates[0].len() } else { 0 };
        let mut cov_array = Array2::<f64>::zeros((nrows, ncols));
        for (row_idx, row) in covariates.iter().enumerate() {
            for (col_idx, &val) in row.iter().enumerate() {
                cov_array[[row_idx, col_idx]] = val;
            }
        }
        let mut unique_times: Vec<f64> = self.event_times.clone();
        unique_times.sort_by(|a, b| a.partial_cmp(b).unwrap_or(std::cmp::Ordering::Equal));
        unique_times.dedup();
        let risk_scores: Vec<f64> = (0..nrows)
            .into_par_iter()
            .map(|row_idx| {
                let mut risk = 0.0;
                for col_idx in 0..ncols {
                    risk += self.coefficients[[col_idx, 0]] * cov_array[[row_idx, col_idx]];
                }
                risk.exp()
            })
            .collect();
        let baseline_hazards: Vec<f64> = unique_times
            .iter()
            .map(|&t| {
                self.baseline_hazard
                    .iter()
                    .zip(&self.event_times)
                    .filter(|&(_, et)| *et <= t)
                    .map(|(h, _)| *h)
                    .sum::<f64>()
            })
            .collect();
        let cumulative_hazards: Vec<Vec<f64>> = risk_scores
            .par_iter()
            .map(|&risk_exp| baseline_hazards.iter().map(|&bh| bh * risk_exp).collect())
            .collect();
        (unique_times, cumulative_hazards)
    }
    #[pyo3(signature = (covariates, percentile = 0.5))]
    pub fn predicted_survival_time(
        &self,
        covariates: Vec<Vec<f64>>,
        percentile: f64,
    ) -> Vec<Option<f64>> {
        let (times, survival_curves) = match self.survival_curve(covariates, None) {
            Ok(result) => result,
            Err(_) => return vec![],
        };
        let target_survival = 1.0 - percentile;
        survival_curves
            .iter()
            .map(|surv| {
                for (i, &s) in surv.iter().enumerate() {
                    if s <= target_survival {
                        if i == 0 {
                            return Some(times[0]);
                        }
                        let s0 = surv[i - 1];
                        let s1 = s;
                        let t0 = times[i - 1];
                        let t1 = times[i];
                        let frac = (s0 - target_survival) / (s0 - s1);
                        return Some(t0 + frac * (t1 - t0));
                    }
                }
                None
            })
            .collect()
    }
    pub fn restricted_mean_survival_time(&self, covariates: Vec<Vec<f64>>, tau: f64) -> Vec<f64> {
        let (times, survival_curves) = match self.survival_curve(covariates, None) {
            Ok(result) => result,
            Err(_) => return vec![],
        };
        survival_curves
            .iter()
            .map(|surv| {
                let mut rmst = 0.0;
                let mut prev_time = 0.0;
                let mut prev_surv = 1.0;
                for (i, &t) in times.iter().enumerate() {
                    if t > tau {
                        rmst += prev_surv * (tau - prev_time);
                        break;
                    }
                    rmst += prev_surv * (t - prev_time);
                    prev_time = t;
                    prev_surv = surv[i];
                    if i == times.len() - 1 {
                        rmst += prev_surv * (tau - t);
                    }
                }
                rmst
            })
            .collect()
    }
    pub fn martingale_residuals(&self) -> Vec<f64> {
        let n = self.event_times.len();
        let mut residuals = Vec::with_capacity(n);
        for i in 0..n {
            let status = self.censoring[i] as f64;
            let cum_haz = self.baseline_hazard.get(i).copied().unwrap_or(0.0)
                * self.risk_scores.get(i).copied().unwrap_or(1.0);
            residuals.push(status - cum_haz);
        }
        residuals
    }
    pub fn deviance_residuals(&self) -> Vec<f64> {
        let martingale = self.martingale_residuals();
        martingale
            .iter()
            .zip(self.censoring.iter())
            .map(|(&m, &d)| {
                let sign = if m >= 0.0 { 1.0 } else { -1.0 };
                let abs_term =
                    -2.0 * (m - d as f64 + d as f64 * (d as f64 - m).ln().max(EXP_CLAMP_MIN));
                sign * abs_term.abs().sqrt()
            })
            .collect()
    }
    pub fn dfbeta(&self) -> Vec<Vec<f64>> {
        let n = self.event_times.len();
        let nvar = self.coefficients.nrows();
        if n == 0 || nvar == 0 {
            return vec![];
        }
        let martingale = self.martingale_residuals();
        (0..n)
            .into_par_iter()
            .map(|i| {
                let mart_i = martingale[i];
                let risk_i = self.risk_scores.get(i).copied().unwrap_or(1.0);
                (0..nvar)
                    .map(|k| {
                        let cov_ik = self.covariates.get([i, k]).copied().unwrap_or(0.0);
                        let mut weighted_mean = 0.0;
                        let mut risk_sum = 0.0;
                        for j in 0..n {
                            if self.event_times[j] >= self.event_times[i] {
                                let risk_j = self.risk_scores.get(j).copied().unwrap_or(1.0);
                                let cov_jk = self.covariates.get([j, k]).copied().unwrap_or(0.0);
                                weighted_mean += risk_j * cov_jk;
                                risk_sum += risk_j;
                            }
                        }
                        if risk_sum > 0.0 {
                            weighted_mean /= risk_sum;
                        }
                        mart_i * (cov_ik - weighted_mean) / risk_i.max(1e-10)
                    })
                    .collect()
            })
            .collect()
    }
    pub fn n_events(&self) -> usize {
        self.censoring.iter().filter(|&&c| c == 1).count()
    }
    pub fn vcov(&self) -> Vec<Vec<f64>> {
        let nvar = self.coefficients.nrows();
        if nvar == 0 {
            return vec![];
        }
        let fisher_info = self.compute_fisher_information();
        if fisher_info.is_empty() {
            return vec![vec![0.0; nvar]; nvar];
        }
        invert_matrix(&fisher_info).unwrap_or_else(|| vec![vec![0.0; nvar]; nvar])
    }
    pub fn std_errors(&self) -> Vec<f64> {
        self.compute_standard_errors()
    }
    fn compute_fisher_information(&self) -> Vec<Vec<f64>> {
        let n = self.event_times.len();
        let nvar = self.coefficients.nrows();
        if n == 0 || nvar == 0 {
            return vec![];
        }
        let mut sorted_indices: Vec<usize> = (0..n).collect();
        sorted_indices.sort_by(|&i, &j| {
            self.event_times[j]
                .partial_cmp(&self.event_times[i])
                .unwrap_or(std::cmp::Ordering::Equal)
        });
        let mut risk_sum = 0.0;
        let mut weighted_cov = vec![0.0; nvar];
        let mut weighted_cov_outer = vec![vec![0.0; nvar]; nvar];
        let mut fisher = vec![vec![0.0; nvar]; nvar];
        let mut index_to_pos = vec![0usize; n];
        for (pos, &idx) in sorted_indices.iter().enumerate() {
            index_to_pos[idx] = pos;
        }
        let mut cumulative_data: Vec<(f64, Vec<f64>, Vec<Vec<f64>>)> = Vec::with_capacity(n);
        for &idx in &sorted_indices {
            let risk_i = self.risk_scores.get(idx).copied().unwrap_or(1.0);
            risk_sum += risk_i;
            for k in 0..nvar {
                let cov_ik = self.covariates.get([idx, k]).copied().unwrap_or(0.0);
                weighted_cov[k] += risk_i * cov_ik;
                for (l, outer_row) in weighted_cov_outer[k].iter_mut().enumerate() {
                    let cov_il = self.covariates.get([idx, l]).copied().unwrap_or(0.0);
                    *outer_row += risk_i * cov_ik * cov_il;
                }
            }
            cumulative_data.push((risk_sum, weighted_cov.clone(), weighted_cov_outer.clone()));
        }
        for (i, &censor) in self.censoring.iter().enumerate() {
            if censor != 1 {
                continue;
            }
            let pos = index_to_pos[i];
            let (rs, wc, wco) = &cumulative_data[pos];
            if *rs <= 0.0 {
                continue;
            }
            for k in 0..nvar {
                for l in 0..nvar {
                    let info_kl = wco[k][l] / rs - (wc[k] / rs) * (wc[l] / rs);
                    fisher[k][l] += info_kl;
                }
            }
        }
        fisher
    }
    pub fn n_observations(&self) -> usize {
        self.event_times.len()
    }
    pub fn summary(&self) -> String {
        let nvar = self.coefficients.nrows();
        let n_obs = self.n_observations();
        let n_events = self.n_events();
        let loglik = self.log_likelihood();
        let aic = self.aic();
        let mut result = String::with_capacity(200 + 50 * nvar);
        result.push_str("Cox Proportional Hazards Model\n");
        result.push_str("================================\n");
        result.push_str(&format!("n={}, events={}\n\n", n_obs, n_events));
        result.push_str(&format!("Log-likelihood: {:.4}\n", loglik));
        result.push_str(&format!("AIC: {:.4}\n\n", aic));
        let hrs = self.hazard_ratios();
        let (_, ci_lower, ci_upper) = self.hazard_ratios_with_ci(0.95);
        result.push_str(&format!(
            "{:<10} {:>10} {:>10} {:>10}\n",
            "Variable", "HR", "CI_Lower", "CI_Upper"
        ));
        result.push_str(&format!("{:-<43}\n", ""));
        for i in 0..nvar {
            result.push_str(&format!(
                "var{:<7} {:>10.4} {:>10.4} {:>10.4}\n",
                i,
                hrs.get(i).copied().unwrap_or(f64::NAN),
                ci_lower.get(i).copied().unwrap_or(f64::NAN),
                ci_upper.get(i).copied().unwrap_or(f64::NAN)
            ));
        }
        result
    }
}

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn test_subject_new() {
        let subject = Subject::new(1, vec![1.0, 2.0], true, false, 0);
        assert_eq!(subject.id, 1);
        assert_eq!(subject.covariates, vec![1.0, 2.0]);
        assert!(subject.is_case);
        assert!(!subject.is_subcohort);
        assert_eq!(subject.stratum, 0);
    }

    #[test]
    fn test_coxph_model_default() {
        let model = CoxPHModel::new();
        assert!(model.baseline_hazard.is_empty());
        assert!(model.risk_scores.is_empty());
        assert!(model.event_times.is_empty());
    }

    #[test]
    fn test_coxph_model_getters() {
        let model = CoxPHModel::new();
        assert_eq!(model.n_observations(), 0);
        assert_eq!(model.n_events(), 0);
    }
}