survival 1.0.17

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
use pyo3::prelude::*;
#[derive(Debug, Clone)]
#[pyclass]
pub struct RMSTResult {
    #[pyo3(get)]
    pub rmst: f64,
    #[pyo3(get)]
    pub variance: f64,
    #[pyo3(get)]
    pub se: f64,
    #[pyo3(get)]
    pub ci_lower: f64,
    #[pyo3(get)]
    pub ci_upper: f64,
    #[pyo3(get)]
    pub tau: f64,
}
#[pymethods]
impl RMSTResult {
    #[new]
    fn new(rmst: f64, variance: f64, se: f64, ci_lower: f64, ci_upper: f64, tau: f64) -> Self {
        Self {
            rmst,
            variance,
            se,
            ci_lower,
            ci_upper,
            tau,
        }
    }
}
#[derive(Debug, Clone)]
#[pyclass]
pub struct RMSTComparisonResult {
    #[pyo3(get)]
    pub rmst_diff: f64,
    #[pyo3(get)]
    pub rmst_ratio: f64,
    #[pyo3(get)]
    pub diff_se: f64,
    #[pyo3(get)]
    pub diff_ci_lower: f64,
    #[pyo3(get)]
    pub diff_ci_upper: f64,
    #[pyo3(get)]
    pub ratio_ci_lower: f64,
    #[pyo3(get)]
    pub ratio_ci_upper: f64,
    #[pyo3(get)]
    pub p_value: f64,
    #[pyo3(get)]
    pub rmst_group1: RMSTResult,
    #[pyo3(get)]
    pub rmst_group2: RMSTResult,
}
#[pymethods]
impl RMSTComparisonResult {
    #[new]
    #[allow(clippy::too_many_arguments)]
    fn new(
        rmst_diff: f64,
        rmst_ratio: f64,
        diff_se: f64,
        diff_ci_lower: f64,
        diff_ci_upper: f64,
        ratio_ci_lower: f64,
        ratio_ci_upper: f64,
        p_value: f64,
        rmst_group1: RMSTResult,
        rmst_group2: RMSTResult,
    ) -> Self {
        Self {
            rmst_diff,
            rmst_ratio,
            diff_se,
            diff_ci_lower,
            diff_ci_upper,
            ratio_ci_lower,
            ratio_ci_upper,
            p_value,
            rmst_group1,
            rmst_group2,
        }
    }
}
fn norm_cdf(x: f64) -> f64 {
    0.5 * (1.0 + erf(x / std::f64::consts::SQRT_2))
}
fn erf(x: f64) -> f64 {
    let a1 = 0.254829592;
    let a2 = -0.284496736;
    let a3 = 1.421413741;
    let a4 = -1.453152027;
    let a5 = 1.061405429;
    let p = 0.3275911;
    let sign = if x < 0.0 { -1.0 } else { 1.0 };
    let x = x.abs();
    let t = 1.0 / (1.0 + p * x);
    let y = 1.0 - ((((a5 * t + a4) * t + a3) * t + a2) * t + a1) * t * (-x * x).exp();
    sign * y
}
pub fn compute_rmst(time: &[f64], status: &[i32], tau: f64, confidence_level: f64) -> RMSTResult {
    let n = time.len();
    if n == 0 {
        return RMSTResult {
            rmst: 0.0,
            variance: 0.0,
            se: 0.0,
            ci_lower: 0.0,
            ci_upper: 0.0,
            tau,
        };
    }
    let mut indices: Vec<usize> = (0..n).collect();
    indices.sort_by(|&a, &b| {
        time[a]
            .partial_cmp(&time[b])
            .unwrap_or(std::cmp::Ordering::Equal)
    });
    let mut unique_times: Vec<f64> = Vec::new();
    let mut n_events: Vec<f64> = Vec::new();
    let mut n_risk: Vec<f64> = Vec::new();
    let mut total_at_risk = n as f64;
    let mut i = 0;
    while i < n {
        let current_time = time[indices[i]];
        if current_time > tau {
            break;
        }
        let mut events = 0.0;
        let mut removed = 0.0;
        while i < n && time[indices[i]] == current_time {
            removed += 1.0;
            if status[indices[i]] == 1 {
                events += 1.0;
            }
            i += 1;
        }
        if events > 0.0 {
            unique_times.push(current_time);
            n_events.push(events);
            n_risk.push(total_at_risk);
        }
        total_at_risk -= removed;
    }
    let m = unique_times.len();
    if m == 0 {
        return RMSTResult {
            rmst: tau,
            variance: 0.0,
            se: 0.0,
            ci_lower: tau,
            ci_upper: tau,
            tau,
        };
    }
    let mut survival = Vec::with_capacity(m);
    let mut surv = 1.0;
    for j in 0..m {
        surv *= 1.0 - n_events[j] / n_risk[j];
        survival.push(surv);
    }
    let mut rmst = 0.0;
    let mut prev_time = 0.0;
    for j in 0..m {
        let prev_surv = if j == 0 { 1.0 } else { survival[j - 1] };
        rmst += prev_surv * (unique_times[j] - prev_time);
        prev_time = unique_times[j];
    }
    let last_surv = survival[m - 1];
    rmst += last_surv * (tau - prev_time);
    let mut variance = 0.0;
    let mut cum_area_after: Vec<f64> = vec![0.0; m];
    for j in (0..m).rev() {
        let area_to_tau = if j == m - 1 {
            survival[j] * (tau - unique_times[j])
        } else {
            survival[j] * (unique_times[j + 1] - unique_times[j]) + cum_area_after[j + 1]
        };
        cum_area_after[j] = area_to_tau;
    }
    for j in 0..m {
        let d = n_events[j];
        let y = n_risk[j];
        if y > d && y > 0.0 {
            let area = cum_area_after[j];
            variance += d * area * area / (y * (y - d));
        }
    }
    let se = variance.sqrt();
    let z = if confidence_level >= 0.99 {
        2.576
    } else if confidence_level >= 0.95 {
        1.96
    } else if confidence_level >= 0.90 {
        1.645
    } else {
        1.28
    };
    let ci_lower = (rmst - z * se).max(0.0);
    let ci_upper = rmst + z * se;
    RMSTResult {
        rmst,
        variance,
        se,
        ci_lower,
        ci_upper,
        tau,
    }
}
pub fn compare_rmst(
    time: &[f64],
    status: &[i32],
    group: &[i32],
    tau: f64,
    confidence_level: f64,
) -> RMSTComparisonResult {
    let mut unique_groups: Vec<i32> = group.to_vec();
    unique_groups.sort();
    unique_groups.dedup();
    if unique_groups.len() < 2 {
        let result = compute_rmst(time, status, tau, confidence_level);
        return RMSTComparisonResult {
            rmst_diff: 0.0,
            rmst_ratio: 1.0,
            diff_se: 0.0,
            diff_ci_lower: 0.0,
            diff_ci_upper: 0.0,
            ratio_ci_lower: 1.0,
            ratio_ci_upper: 1.0,
            p_value: 1.0,
            rmst_group1: result.clone(),
            rmst_group2: result,
        };
    }
    let g1 = unique_groups[0];
    let g2 = unique_groups[1];
    let mut time1 = Vec::new();
    let mut status1 = Vec::new();
    let mut time2 = Vec::new();
    let mut status2 = Vec::new();
    for i in 0..time.len() {
        if group[i] == g1 {
            time1.push(time[i]);
            status1.push(status[i]);
        } else if group[i] == g2 {
            time2.push(time[i]);
            status2.push(status[i]);
        }
    }
    let (rmst1, rmst2) = rayon::join(
        || compute_rmst(&time1, &status1, tau, confidence_level),
        || compute_rmst(&time2, &status2, tau, confidence_level),
    );
    let diff = rmst1.rmst - rmst2.rmst;
    let diff_var = rmst1.variance + rmst2.variance;
    let diff_se = diff_var.sqrt();
    let z = if confidence_level >= 0.99 {
        2.576
    } else if confidence_level >= 0.95 {
        1.96
    } else if confidence_level >= 0.90 {
        1.645
    } else {
        1.28
    };
    let diff_ci_lower = diff - z * diff_se;
    let diff_ci_upper = diff + z * diff_se;
    let ratio = if rmst2.rmst > 0.0 {
        rmst1.rmst / rmst2.rmst
    } else {
        f64::INFINITY
    };
    let (ratio_ci_lower, ratio_ci_upper) = if rmst1.rmst > 0.0 && rmst2.rmst > 0.0 {
        let log_ratio = ratio.ln();
        let log_ratio_var =
            rmst1.variance / (rmst1.rmst * rmst1.rmst) + rmst2.variance / (rmst2.rmst * rmst2.rmst);
        let log_ratio_se = log_ratio_var.sqrt();
        (
            (log_ratio - z * log_ratio_se).exp(),
            (log_ratio + z * log_ratio_se).exp(),
        )
    } else {
        (0.0, f64::INFINITY)
    };
    let z_stat = if diff_se > 0.0 { diff / diff_se } else { 0.0 };
    let p_value = 2.0 * (1.0 - norm_cdf(z_stat.abs()));
    RMSTComparisonResult {
        rmst_diff: diff,
        rmst_ratio: ratio,
        diff_se,
        diff_ci_lower,
        diff_ci_upper,
        ratio_ci_lower,
        ratio_ci_upper,
        p_value,
        rmst_group1: rmst1,
        rmst_group2: rmst2,
    }
}
#[pyfunction]
#[pyo3(signature = (time, status, tau, confidence_level=None))]
pub fn rmst(
    time: Vec<f64>,
    status: Vec<i32>,
    tau: f64,
    confidence_level: Option<f64>,
) -> PyResult<RMSTResult> {
    let conf = confidence_level.unwrap_or(0.95);
    Ok(compute_rmst(&time, &status, tau, conf))
}
#[pyfunction]
#[pyo3(signature = (time, status, group, tau, confidence_level=None))]
pub fn rmst_comparison(
    time: Vec<f64>,
    status: Vec<i32>,
    group: Vec<i32>,
    tau: f64,
    confidence_level: Option<f64>,
) -> PyResult<RMSTComparisonResult> {
    let conf = confidence_level.unwrap_or(0.95);
    Ok(compare_rmst(&time, &status, &group, tau, conf))
}
#[derive(Debug, Clone)]
#[pyclass]
pub struct MedianSurvivalResult {
    #[pyo3(get)]
    pub median: Option<f64>,
    #[pyo3(get)]
    pub ci_lower: Option<f64>,
    #[pyo3(get)]
    pub ci_upper: Option<f64>,
    #[pyo3(get)]
    pub quantile: f64,
}
#[pymethods]
impl MedianSurvivalResult {
    #[new]
    fn new(
        median: Option<f64>,
        ci_lower: Option<f64>,
        ci_upper: Option<f64>,
        quantile: f64,
    ) -> Self {
        Self {
            median,
            ci_lower,
            ci_upper,
            quantile,
        }
    }
}
pub fn compute_survival_quantile(
    time: &[f64],
    status: &[i32],
    quantile: f64,
    confidence_level: f64,
) -> MedianSurvivalResult {
    let n = time.len();
    if n == 0 {
        return MedianSurvivalResult {
            median: None,
            ci_lower: None,
            ci_upper: None,
            quantile,
        };
    }
    let mut indices: Vec<usize> = (0..n).collect();
    indices.sort_by(|&a, &b| {
        time[a]
            .partial_cmp(&time[b])
            .unwrap_or(std::cmp::Ordering::Equal)
    });
    let mut unique_times: Vec<f64> = Vec::new();
    let mut survival: Vec<f64> = Vec::new();
    let mut ci_lower_vec: Vec<f64> = Vec::new();
    let mut ci_upper_vec: Vec<f64> = Vec::new();
    let mut total_at_risk = n as f64;
    let mut surv = 1.0;
    let mut var_sum = 0.0;
    let z = if confidence_level >= 0.99 {
        2.576
    } else if confidence_level >= 0.95 {
        1.96
    } else if confidence_level >= 0.90 {
        1.645
    } else {
        1.28
    };
    let mut i = 0;
    while i < n {
        let current_time = time[indices[i]];
        let mut events = 0.0;
        let mut removed = 0.0;
        while i < n && time[indices[i]] == current_time {
            removed += 1.0;
            if status[indices[i]] == 1 {
                events += 1.0;
            }
            i += 1;
        }
        if events > 0.0 && total_at_risk > 0.0 {
            surv *= 1.0 - events / total_at_risk;
            if total_at_risk > events {
                var_sum += events / (total_at_risk * (total_at_risk - events));
            }
            let se = surv * var_sum.sqrt();
            let lower = (surv - z * se).clamp(0.0, 1.0);
            let upper = (surv + z * se).clamp(0.0, 1.0);
            unique_times.push(current_time);
            survival.push(surv);
            ci_lower_vec.push(lower);
            ci_upper_vec.push(upper);
        }
        total_at_risk -= removed;
    }
    let target = 1.0 - quantile;
    let median = survival
        .iter()
        .position(|&s| s <= target)
        .map(|idx| unique_times[idx]);
    let ci_lower = ci_upper_vec
        .iter()
        .position(|&s| s <= target)
        .map(|idx| unique_times[idx]);
    let ci_upper = ci_lower_vec
        .iter()
        .position(|&s| s <= target)
        .map(|idx| unique_times[idx]);
    MedianSurvivalResult {
        median,
        ci_lower,
        ci_upper,
        quantile,
    }
}
#[pyfunction]
#[pyo3(signature = (time, status, quantile=None, confidence_level=None))]
pub fn survival_quantile(
    time: Vec<f64>,
    status: Vec<i32>,
    quantile: Option<f64>,
    confidence_level: Option<f64>,
) -> PyResult<MedianSurvivalResult> {
    let q = quantile.unwrap_or(0.5);
    let conf = confidence_level.unwrap_or(0.95);
    Ok(compute_survival_quantile(&time, &status, q, conf))
}
#[derive(Debug, Clone)]
#[pyclass]
pub struct CumulativeIncidenceResult {
    #[pyo3(get)]
    pub time: Vec<f64>,
    #[pyo3(get)]
    pub cif: Vec<Vec<f64>>,
    #[pyo3(get)]
    pub variance: Vec<Vec<f64>>,
    #[pyo3(get)]
    pub event_types: Vec<i32>,
    #[pyo3(get)]
    pub n_risk: Vec<usize>,
}
#[pymethods]
impl CumulativeIncidenceResult {
    #[new]
    fn new(
        time: Vec<f64>,
        cif: Vec<Vec<f64>>,
        variance: Vec<Vec<f64>>,
        event_types: Vec<i32>,
        n_risk: Vec<usize>,
    ) -> Self {
        Self {
            time,
            cif,
            variance,
            event_types,
            n_risk,
        }
    }
}
pub fn compute_cumulative_incidence(time: &[f64], status: &[i32]) -> CumulativeIncidenceResult {
    let n = time.len();
    if n == 0 {
        return CumulativeIncidenceResult {
            time: vec![],
            cif: vec![],
            variance: vec![],
            event_types: vec![],
            n_risk: vec![],
        };
    }
    let mut event_types: Vec<i32> = status.iter().filter(|&&s| s > 0).copied().collect();
    event_types.sort();
    event_types.dedup();
    if event_types.is_empty() {
        return CumulativeIncidenceResult {
            time: vec![],
            cif: vec![],
            variance: vec![],
            event_types: vec![],
            n_risk: vec![],
        };
    }
    let n_event_types = event_types.len();
    let mut indices: Vec<usize> = (0..n).collect();
    indices.sort_by(|&a, &b| {
        time[a]
            .partial_cmp(&time[b])
            .unwrap_or(std::cmp::Ordering::Equal)
    });
    let mut unique_times: Vec<f64> = Vec::new();
    let mut n_risk_vec: Vec<usize> = Vec::new();
    let mut events_by_type: Vec<Vec<f64>> = vec![Vec::new(); n_event_types];
    let mut total_at_risk = n;
    let mut i = 0;
    while i < n {
        let current_time = time[indices[i]];
        let mut event_counts = vec![0.0; n_event_types];
        let mut removed = 0usize;
        while i < n && time[indices[i]] == current_time {
            let s = status[indices[i]];
            removed += 1;
            if let Some(idx) = event_types.iter().position(|&e| e == s) {
                event_counts[idx] += 1.0;
            }
            i += 1;
        }
        let has_events = event_counts.iter().any(|&c| c > 0.0);
        if has_events {
            unique_times.push(current_time);
            n_risk_vec.push(total_at_risk);
            for (k, count) in event_counts.into_iter().enumerate() {
                events_by_type[k].push(count);
            }
        }
        total_at_risk -= removed;
    }
    let m = unique_times.len();
    let mut cif: Vec<Vec<f64>> = vec![Vec::with_capacity(m); n_event_types];
    let mut variance: Vec<Vec<f64>> = vec![Vec::with_capacity(m); n_event_types];
    let mut km_survival = 1.0;
    let mut cum_cif = vec![0.0; n_event_types];
    for j in 0..m {
        let y = n_risk_vec[j] as f64;
        let total_events: f64 = events_by_type.iter().map(|ev| ev[j]).sum();
        for k in 0..n_event_types {
            let d_k = events_by_type[k][j];
            if y > 0.0 {
                cum_cif[k] += km_survival * d_k / y;
            }
            cif[k].push(cum_cif[k]);
            variance[k].push(0.0);
        }
        if y > 0.0 {
            km_survival *= 1.0 - total_events / y;
        }
    }
    CumulativeIncidenceResult {
        time: unique_times,
        cif,
        variance,
        event_types,
        n_risk: n_risk_vec,
    }
}
#[pyfunction]
pub fn cumulative_incidence(
    time: Vec<f64>,
    status: Vec<i32>,
) -> PyResult<CumulativeIncidenceResult> {
    Ok(compute_cumulative_incidence(&time, &status))
}
#[derive(Debug, Clone)]
#[pyclass]
pub struct NNTResult {
    #[pyo3(get)]
    pub nnt: f64,
    #[pyo3(get)]
    pub nnt_ci_lower: f64,
    #[pyo3(get)]
    pub nnt_ci_upper: f64,
    #[pyo3(get)]
    pub absolute_risk_reduction: f64,
    #[pyo3(get)]
    pub arr_ci_lower: f64,
    #[pyo3(get)]
    pub arr_ci_upper: f64,
    #[pyo3(get)]
    pub time_horizon: f64,
}
#[pymethods]
impl NNTResult {
    #[new]
    fn new(
        nnt: f64,
        nnt_ci_lower: f64,
        nnt_ci_upper: f64,
        absolute_risk_reduction: f64,
        arr_ci_lower: f64,
        arr_ci_upper: f64,
        time_horizon: f64,
    ) -> Self {
        Self {
            nnt,
            nnt_ci_lower,
            nnt_ci_upper,
            absolute_risk_reduction,
            arr_ci_lower,
            arr_ci_upper,
            time_horizon,
        }
    }
}
pub fn compute_nnt(
    time: &[f64],
    status: &[i32],
    group: &[i32],
    time_horizon: f64,
    confidence_level: f64,
) -> NNTResult {
    let surv1 = compute_survival_at_time(time, status, group, 0, time_horizon);
    let surv2 = compute_survival_at_time(time, status, group, 1, time_horizon);
    let risk1 = 1.0 - surv1.0;
    let risk2 = 1.0 - surv2.0;
    let arr = risk2 - risk1;
    let z = if confidence_level >= 0.99 {
        2.576
    } else if confidence_level >= 0.95 {
        1.96
    } else if confidence_level >= 0.90 {
        1.645
    } else {
        1.28
    };
    let arr_se = (surv1.1 + surv2.1).sqrt();
    let arr_ci_lower = arr - z * arr_se;
    let arr_ci_upper = arr + z * arr_se;
    let nnt = if arr.abs() > 1e-10 {
        1.0 / arr
    } else {
        f64::INFINITY
    };
    let (nnt_ci_lower, nnt_ci_upper) = if arr_ci_lower > 0.0 && arr_ci_upper > 0.0 {
        (1.0 / arr_ci_upper, 1.0 / arr_ci_lower)
    } else if arr_ci_lower < 0.0 && arr_ci_upper < 0.0 {
        (1.0 / arr_ci_lower, 1.0 / arr_ci_upper)
    } else {
        (f64::NEG_INFINITY, f64::INFINITY)
    };
    NNTResult {
        nnt,
        nnt_ci_lower,
        nnt_ci_upper,
        absolute_risk_reduction: arr,
        arr_ci_lower,
        arr_ci_upper,
        time_horizon,
    }
}
fn compute_survival_at_time(
    time: &[f64],
    status: &[i32],
    group: &[i32],
    target_group: i32,
    t: f64,
) -> (f64, f64) {
    let mut unique_groups: Vec<i32> = group.to_vec();
    unique_groups.sort();
    unique_groups.dedup();
    if unique_groups.len() <= target_group as usize {
        return (1.0, 0.0);
    }
    let g = unique_groups[target_group as usize];
    let mut filtered_time = Vec::new();
    let mut filtered_status = Vec::new();
    for i in 0..time.len() {
        if group[i] == g {
            filtered_time.push(time[i]);
            filtered_status.push(status[i]);
        }
    }
    if filtered_time.is_empty() {
        return (1.0, 0.0);
    }
    let n = filtered_time.len();
    let mut indices: Vec<usize> = (0..n).collect();
    indices.sort_by(|&a, &b| {
        filtered_time[a]
            .partial_cmp(&filtered_time[b])
            .unwrap_or(std::cmp::Ordering::Equal)
    });
    let mut surv = 1.0;
    let mut var_sum = 0.0;
    let mut total_at_risk = n as f64;
    let mut i = 0;
    while i < n {
        let current_time = filtered_time[indices[i]];
        if current_time > t {
            break;
        }
        let mut events = 0.0;
        let mut removed = 0.0;
        while i < n && filtered_time[indices[i]] == current_time {
            removed += 1.0;
            if filtered_status[indices[i]] == 1 {
                events += 1.0;
            }
            i += 1;
        }
        if events > 0.0 && total_at_risk > 0.0 {
            surv *= 1.0 - events / total_at_risk;
            if total_at_risk > events {
                var_sum += events / (total_at_risk * (total_at_risk - events));
            }
        }
        total_at_risk -= removed;
    }
    let variance = surv * surv * var_sum;
    (surv, variance)
}
#[pyfunction]
#[pyo3(signature = (time, status, group, time_horizon, confidence_level=None))]
pub fn number_needed_to_treat(
    time: Vec<f64>,
    status: Vec<i32>,
    group: Vec<i32>,
    time_horizon: f64,
    confidence_level: Option<f64>,
) -> PyResult<NNTResult> {
    let conf = confidence_level.unwrap_or(0.95);
    Ok(compute_nnt(&time, &status, &group, time_horizon, conf))
}