{ "cells": [ { "cell_type": "markdown", "id": "intro-md", "metadata": {}, "source": [ "# Profile-likelihood CIs — Wald vs. profile vs. sandwich\n", "\n", "The default `confint(level=0.95)` on a `tram` fit returns the *Wald*\n", "interval\n", "\n", "$$\n", "\\hat\\theta_j \\;\\pm\\; z_{1-\\alpha/2}\\,\\sqrt{V_{jj}},\n", "$$\n", "\n", "where $V = \\text{vcov}() = -H^{-1}$ is the inverse observed information.\n", "Two assumptions are baked in: the log-likelihood is locally a\n", "well-conditioned paraboloid around $\\hat\\theta$, and that paraboloid is\n", "*symmetric*. Both can fail — most visibly when the MLE sits on (or near)\n", "an active monotonicity boundary, which is the typical situation for the\n", "Bernstein coefficients of a small-$n$ baseline transformation.\n", "\n", "mltpy 0.4 exposes two non-Wald alternatives on the same `confint()`\n", "method (`type=\"profile\"`) and `sandwich_se()` helper:\n", "\n", "* **Profile likelihood** — `confint(type=\"profile\")` inverts the\n", " $\\chi^2_1$ likelihood-ratio test by re-fitting the constrained model\n", " with $\\theta_j$ pinned to a sweep of values and root-finding for\n", " $2\\,(\\hat\\ell - \\ell_p(v)) = \\chi^2_{1,1-\\alpha}$. Honours likelihood\n", " asymmetry; pays roughly ten constrained refits per parameter.\n", "* **Sandwich** — `sandwich_se()` returns the HC0 estimator\n", " $V_{\\text{sand}} = B\\,M\\,B$ with $B = -H^{-1}$ and\n", " $M = \\sum_i s_i s_i^\\top$, robust to mild mis-specification of the\n", " outcome distribution. We assemble the symmetric CI manually as\n", " $\\hat\\theta_j \\pm z_{1-\\alpha/2}\\sqrt{V_{\\text{sand},jj}}$.\n", "\n", "This vignette compares all three on the right-censored Coxph fixture\n", "from `reference/vcov_coxph_*` — the same dataset that the R-parity\n", "tests in `tests/test_confidence.py` check element-wise against\n", "`tram::Coxph(Surv(y, event) ~ x)`. The Bernstein MLE has\n", "`Bs1 = Bs2 = Bs3` stacked on the monotonicity boundary, so the Wald\n", "approximation breaks down on those baseline coefficients while the\n", "well-identified covariate $\\beta_x$ remains a regular-asymptotics\n", "story where all three agree.\n", "\n", "Below we render two figures: a forest plot of the three intervals\n", "side-by-side, then the profile log-likelihood curve for the most\n", "asymmetric parameter with all CI endpoints annotated." ] }, { "cell_type": "code", "execution_count": 1, "id": "imports", "metadata": { "execution": { "iopub.execute_input": "2026-05-24T00:56:52.604682Z", "iopub.status.busy": "2026-05-24T00:56:52.604496Z", "iopub.status.idle": "2026-05-24T00:56:53.252352Z", "shell.execute_reply": "2026-05-24T00:56:53.251941Z" } }, "outputs": [], "source": [ "import warnings\n", "from pathlib import Path\n", "\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import pandas as pd\n", "from scipy.stats import chi2, norm\n", "\n", "from mltpy.model import ConvergenceWarning\n", "from mltpy.tram import Coxph\n", "from mltpy.variables import CensoredData\n", "\n", "# Profile-CI refits a constrained likelihood ~10× per parameter; the inner\n", "# auglag occasionally hits the outer-iteration cap on Bernstein-boundary\n", "# pins and emits ConvergenceWarning (see CLAUDE.md, _PROFILE_INNER_KKT_THRESHOLD).\n", "# The vignette is informational, not a parity test, so we silence them.\n", "warnings.filterwarnings(\"ignore\", category=ConvergenceWarning)\n", "\n", "plt.rcParams[\"figure.dpi\"] = 110\n", "REF_DIR = Path(\"../../reference\") # repo-relative path to reference fixtures" ] }, { "cell_type": "markdown", "id": "fit-md", "metadata": {}, "source": [ "## 1. The fitted model\n", "\n", "Right-censored Coxph fit on $n = 200$ observations with one continuous\n", "covariate. Loading the dataset from `reference/` rather than\n", "re-synthesising means the CI tables below are *the same numbers* the\n", "R-parity tests check against — `tram::Coxph` agrees to ~1e-3 on every\n", "row of both `confint(type='wald')` and `confint(type='profile')`." ] }, { "cell_type": "code", "execution_count": 2, "id": "fit", "metadata": { "execution": { "iopub.execute_input": "2026-05-24T00:56:53.253805Z", "iopub.status.busy": "2026-05-24T00:56:53.253712Z", "iopub.status.idle": "2026-05-24T00:56:53.545307Z", "shell.execute_reply": "2026-05-24T00:56:53.545001Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "n = 200, events = 147, censored = 53\n", "log-likelihood at MLE = -168.1675\n", "theta_hat:\n", " Bs0 = -2.4380\n", " Bs1 = +1.1091\n", " Bs2 = +1.1091\n", " Bs3 = +1.1091\n", " Bs4 = +1.8148\n", " x = +0.2383\n" ] } ], "source": [ "y = np.loadtxt(REF_DIR / \"vcov_coxph_y.txt\")\n", "x = np.loadtxt(REF_DIR / \"vcov_coxph_x.txt\").reshape(-1, 1)\n", "event = np.loadtxt(REF_DIR / \"vcov_coxph_event.txt\").astype(int)\n", "a, b = (float(v) for v in np.loadtxt(REF_DIR / \"vcov_coxph_support.txt\"))\n", "\n", "cd = CensoredData.right_censored(y, censored=event == 0)\n", "model = Coxph(support=(a, b), order=4).fit(cd, X=x)\n", "\n", "param_names = [f\"Bs{i}\" for i in range(5)] + [\"x\"]\n", "ll_hat = model.score(cd, X=x)\n", "\n", "print(f\"n = {len(y)}, events = {int(event.sum())}, censored = {(event == 0).sum()}\")\n", "print(f\"log-likelihood at MLE = {ll_hat:.4f}\")\n", "print(\"theta_hat:\")\n", "for name, th in zip(param_names, model.theta_):\n", " print(f\" {name:>4} = {th:+.4f}\")" ] }, { "cell_type": "markdown", "id": "boundary-md", "metadata": {}, "source": [ "Notice `Bs1 = Bs2 = Bs3 ≈ 1.109` — three consecutive Bernstein\n", "coefficients have collapsed onto the monotonicity boundary\n", "$\\theta_{k+1} \\ge \\theta_k$. Equality-active constraints make the\n", "observed information singular along the boundary direction, and the\n", "Wald CI is the diagnostic that catches it most loudly." ] }, { "cell_type": "markdown", "id": "ci-md", "metadata": {}, "source": [ "## 2. Wald, profile, and sandwich side-by-side\n", "\n", "All three share `confint`'s coverage target (95 %) and the same\n", "$\\hat\\theta$. They differ only in how they convert the local\n", "likelihood geometry into an interval:\n", "\n", "* **Wald** — `confint(type=\"wald\")`: symmetric, uses\n", " $\\sqrt{V_{jj}} = \\sqrt{(-H^{-1})_{jj}}$.\n", "* **Profile** — `confint(type=\"profile\")`: inverts the LR test,\n", " asymmetric in general.\n", "* **Sandwich** — assembled by hand as\n", " $\\hat\\theta_j \\pm z_{0.975}\\,\\sqrt{V_{\\text{sand},jj}}$ using\n", " `sandwich_se()`. Still symmetric; the only thing it replaces is\n", " the variance estimator." ] }, { "cell_type": "code", "execution_count": 3, "id": "three-cis", "metadata": { "execution": { "iopub.execute_input": "2026-05-24T00:56:53.546539Z", "iopub.status.busy": "2026-05-24T00:56:53.546486Z", "iopub.status.idle": "2026-05-24T00:57:32.614001Z", "shell.execute_reply": "2026-05-24T00:57:32.613612Z" } }, "outputs": [ { "data": { "text/html": [ "
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theta_hatwald_lowald_hiprof_loprof_hisand_losand_hi
Bs0-2.438-2.819-2.057-2.810-2.092-2.621-2.255
Bs11.1090.4081.8110.8891.3200.4521.767
Bs21.1090.0082.2100.8891.3200.0562.162
Bs31.1090.1452.0730.8891.3730.1522.066
Bs41.8151.1792.4501.3032.5181.4212.208
x0.2380.0770.4000.0800.4000.0720.404
\n", "
" ], "text/plain": [ " theta_hat wald_lo wald_hi prof_lo prof_hi sand_lo sand_hi\n", "Bs0 -2.438 -2.819 -2.057 -2.810 -2.092 -2.621 -2.255\n", "Bs1 1.109 0.408 1.811 0.889 1.320 0.452 1.767\n", "Bs2 1.109 0.008 2.210 0.889 1.320 0.056 2.162\n", "Bs3 1.109 0.145 2.073 0.889 1.373 0.152 2.066\n", "Bs4 1.815 1.179 2.450 1.303 2.518 1.421 2.208\n", "x 0.238 0.077 0.400 0.080 0.400 0.072 0.404" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ci_wald = model.confint(level=0.95, type=\"wald\")\n", "ci_prof = model.confint(level=0.95, type=\"profile\")\n", "se_sand = model.sandwich_se()\n", "z = float(norm.ppf(0.975))\n", "ci_sand = np.column_stack((model.theta_ - z * se_sand, model.theta_ + z * se_sand))\n", "\n", "ci_table = pd.DataFrame(\n", " {\n", " \"theta_hat\": model.theta_,\n", " \"wald_lo\": ci_wald[:, 0],\n", " \"wald_hi\": ci_wald[:, 1],\n", " \"prof_lo\": ci_prof[:, 0],\n", " \"prof_hi\": ci_prof[:, 1],\n", " \"sand_lo\": ci_sand[:, 0],\n", " \"sand_hi\": ci_sand[:, 1],\n", " },\n", " index=param_names,\n", ").round(3)\n", "ci_table" ] }, { "cell_type": "markdown", "id": "table-discussion-md", "metadata": {}, "source": [ "Two patterns to read out of the table:\n", "\n", "1. **Covariate `x` (the proportional-hazards $\\beta$)** — all three\n", " intervals agree to $\\approx 0.01$. $\\beta_x$ is well-identified by\n", " 147 uncensored events, the Hessian is regular in its direction, and\n", " the likelihood is locally quadratic and symmetric. This is the\n", " textbook regularity case.\n", "2. **Bernstein coefficients `Bs1`–`Bs3`** — the Wald widths\n", " (1.40, 2.20, 1.93) are 3–5× wider than the profile widths\n", " ($\\approx 0.43$). Sandwich barely helps: it inherits the same\n", " bread $V$ and only reweights it. When the bread itself is\n", " near-singular along an active monotonicity row, no rescaling will\n", " recover a sensible interval. Profile sidesteps the issue entirely\n", " by *refitting* under the pin, so the active-constraint geometry\n", " propagates correctly." ] }, { "cell_type": "code", "execution_count": 4, "id": "forest", "metadata": { "execution": { "iopub.execute_input": "2026-05-24T00:57:32.615350Z", "iopub.status.busy": "2026-05-24T00:57:32.615285Z", "iopub.status.idle": "2026-05-24T00:57:32.693763Z", "shell.execute_reply": "2026-05-24T00:57:32.693431Z" } }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(7.5, 4.5))\n", "positions = np.arange(len(model.theta_))\n", "offset = 0.22\n", "\n", "\n", "def _band(ax, pos, ci, theta_hat, color, label):\n", " ax.hlines(pos, ci[:, 0], ci[:, 1], color=color, linewidth=2.5, label=label)\n", " ax.plot(theta_hat, pos, \"o\", color=color, markersize=5)\n", "\n", "\n", "_band(ax, positions - offset, ci_wald, model.theta_, \"#1f77b4\", \"Wald\")\n", "_band(ax, positions, ci_prof, model.theta_, \"#d62728\", \"profile\")\n", "_band(ax, positions + offset, ci_sand, model.theta_, \"#2ca02c\", \"sandwich\")\n", "ax.set_yticks(positions)\n", "ax.set_yticklabels(param_names)\n", "ax.invert_yaxis()\n", "ax.axvline(0, color=\"grey\", lw=0.5)\n", "ax.set_xlabel(r\"$\\theta$ (95 % CI)\")\n", "ax.set_title(\"Coxph(y ~ x) — Wald vs. profile vs. sandwich CIs\")\n", "ax.legend(loc=\"lower right\", frameon=False)\n", "fig.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "asym-md", "metadata": {}, "source": [ "## 3. The profile log-likelihood for the most asymmetric parameter\n", "\n", "The forest plot above shows Wald and profile have the same *centre*\n", "($\\hat\\theta$) but different *widths*. A finer diagnostic is whether\n", "the profile interval is itself asymmetric around $\\hat\\theta$ — i.e.\n", "the curvature of $\\ell_p$ differs on either side. Compute the\n", "left / right halves of each profile CI:" ] }, { "cell_type": "code", "execution_count": 5, "id": "asym-compute", "metadata": { "execution": { "iopub.execute_input": "2026-05-24T00:57:32.694853Z", "iopub.status.busy": "2026-05-24T00:57:32.694795Z", "iopub.status.idle": "2026-05-24T00:57:32.698042Z", "shell.execute_reply": "2026-05-24T00:57:32.697727Z" } }, "outputs": [ { "data": { "text/html": [ "
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paramleft_halfright_halfskew
0Bs00.3720.346-0.037
1Bs10.2200.211-0.020
2Bs20.2200.211-0.020
3Bs30.2200.2640.090
4Bs40.5120.7030.157
5x0.1580.1620.012
\n", "
" ], "text/plain": [ " param left_half right_half skew\n", "0 Bs0 0.372 0.346 -0.037\n", "1 Bs1 0.220 0.211 -0.020\n", "2 Bs2 0.220 0.211 -0.020\n", "3 Bs3 0.220 0.264 0.090\n", "4 Bs4 0.512 0.703 0.157\n", "5 x 0.158 0.162 0.012" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "asym = []\n", "for j in range(len(model.theta_)):\n", " th = float(model.theta_[j])\n", " lo, hi = ci_prof[j]\n", " left = th - lo\n", " right = hi - th\n", " skew = (right - left) / (right + left)\n", " asym.append((param_names[j], left, right, skew))\n", "\n", "asym_df = pd.DataFrame(\n", " asym, columns=[\"param\", \"left_half\", \"right_half\", \"skew\"]\n", ").round(3)\n", "asym_df" ] }, { "cell_type": "code", "execution_count": 6, "id": "asym-pick", "metadata": { "execution": { "iopub.execute_input": "2026-05-24T00:57:32.698973Z", "iopub.status.busy": "2026-05-24T00:57:32.698917Z", "iopub.status.idle": "2026-05-24T00:57:32.700597Z", "shell.execute_reply": "2026-05-24T00:57:32.700227Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "most asymmetric parameter: Bs4 (skew = +0.157, right half 1.37× left half)\n" ] } ], "source": [ "j_star = int(np.argmax([abs(s) for *_, s in asym]))\n", "print(\n", " f\"most asymmetric parameter: {param_names[j_star]} \"\n", " f\"(skew = {asym[j_star][3]:+.3f}, \"\n", " f\"right half {asym[j_star][2] / asym[j_star][1]:.2f}× left half)\"\n", ")" ] }, { "cell_type": "markdown", "id": "sweep-md", "metadata": {}, "source": [ "`_profile_loglik_at(j, v)` returns the maximised log-likelihood under\n", "the constraint $\\theta_j = v$, refitting the remaining $p + q - 1$\n", "parameters under the model's monotonicity constraints (see CLAUDE.md\n", "for the contract). It is the building block `_confint_profile` calls\n", "from `confint(type=\"profile\")`; surfacing the curve here is purely a\n", "diagnostic — `_profile_loglik_at` remains private API and the\n", "supported entry point is `confint(type=\"profile\")`. Sweep it on a\n", "fine grid that brackets both the profile and the Wald endpoints:" ] }, { "cell_type": "code", "execution_count": 7, "id": "sweep", "metadata": { "execution": { "iopub.execute_input": "2026-05-24T00:57:32.701471Z", "iopub.status.busy": "2026-05-24T00:57:32.701421Z", "iopub.status.idle": "2026-05-24T00:57:44.948227Z", "shell.execute_reply": "2026-05-24T00:57:44.947719Z" } }, "outputs": [], "source": [ "crit_95 = float(chi2.ppf(0.95, df=1)) # 3.84\n", "lo_p, hi_p = ci_prof[j_star]\n", "lo_w, hi_w = ci_wald[j_star]\n", "pad = 0.15 * (hi_p - lo_p)\n", "v_grid = np.linspace(min(lo_p, lo_w) - pad, max(hi_p, hi_w) + pad, 41)\n", "ll_grid = np.array([model._profile_loglik_at(j_star, float(v)) for v in v_grid])\n", "twice_diff = 2.0 * (ll_hat - ll_grid)" ] }, { "cell_type": "code", "execution_count": 8, "id": "profile-plot", "metadata": { "execution": { "iopub.execute_input": "2026-05-24T00:57:44.949494Z", "iopub.status.busy": "2026-05-24T00:57:44.949437Z", "iopub.status.idle": "2026-05-24T00:57:45.006467Z", "shell.execute_reply": "2026-05-24T00:57:45.006051Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(7.5, 4.5))\n", "ax.plot(v_grid, twice_diff, color=\"#d62728\", lw=2, label=r\"$2\\,(\\hat\\ell - \\ell_p(v))$\")\n", "ax.axhline(crit_95, color=\"grey\", lw=1, ls=\"--\", label=r\"$\\chi^2_{1,0.95} = 3.84$\")\n", "ax.axvline(\n", " model.theta_[j_star],\n", " color=\"black\",\n", " lw=1,\n", " label=rf\"$\\hat\\theta = {model.theta_[j_star]:.3f}$\",\n", ")\n", "ax.axvline(\n", " lo_p, color=\"#d62728\", lw=1, ls=\":\", label=rf\"profile CI = [{lo_p:.3f}, {hi_p:.3f}]\"\n", ")\n", "ax.axvline(hi_p, color=\"#d62728\", lw=1, ls=\":\")\n", "ax.axvline(\n", " lo_w, color=\"#1f77b4\", lw=1, ls=\":\", label=rf\"Wald CI = [{lo_w:.3f}, {hi_w:.3f}]\"\n", ")\n", "ax.axvline(hi_w, color=\"#1f77b4\", lw=1, ls=\":\")\n", "ax.set_xlabel(rf\"$v$ (pinned value of $\\theta_{{{j_star}}}$ = {param_names[j_star]})\")\n", "ax.set_ylabel(r\"$2\\,(\\hat\\ell - \\ell_p(v))$\")\n", "ax.set_title(\n", " f\"Profile log-likelihood for {param_names[j_star]} (skew = {asym[j_star][3]:+.2f})\"\n", ")\n", "ax.legend(frameon=False, loc=\"upper center\", fontsize=9)\n", "fig.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "interpret-md", "metadata": {}, "source": [ "Three things to read off the plot:\n", "\n", "* The curve crosses the dashed $\\chi^2_{1,0.95}$ cutoff at the two\n", " *red dotted* lines — these are the profile-CI endpoints by\n", " construction (`_confint_profile` solves exactly\n", " $2\\,(\\hat\\ell - \\ell_p(v)) - 3.84 = 0$ on each side via\n", " `scipy.optimize.brentq`).\n", "* The right arm of the profile curve is visibly flatter than the\n", " left, which is exactly what the positive skew in the table records.\n", " A symmetric Wald paraboloid (blue dotted endpoints) misses this:\n", " the upper Wald endpoint sits *inside* the profile region while the\n", " lower Wald endpoint sits *outside* it.\n", "* On `Bs4`, profile is shifted *to the right* relative to Wald — the\n", " baseline coefficient can take values further above $\\hat\\theta$\n", " than the symmetric approximation allows, because the only thing\n", " shrinking the right tail is the next-up boundary $\\theta_4$ has\n", " little neighbour to push against." ] }, { "cell_type": "markdown", "id": "summary-md", "metadata": {}, "source": [ "## 4. When to prefer each interval type\n", "\n", "| | Cost per parameter | Honours asymmetry | Robust to mis-specified link | Robust to active constraints |\n", "|---|---|---|---|---|\n", "| **Wald** | one inversion of $H$ at $\\hat\\theta$ | no | no | **no** — fails on monotonicity boundaries |\n", "| **Sandwich** | one inversion of $H$ + one $s s^\\top$ accumulation | no | **yes** | no — same singular bread as Wald |\n", "| **Profile** | $\\approx$ 10 constrained refits | **yes** | partially (still uses $\\ell$) | **yes** — refits under the pin |\n", "\n", "Practical rules of thumb that follow from the table:\n", "\n", "* Default to Wald for fast triage and well-identified covariates\n", " ($\\beta_x$ above: all three methods agreed to 0.01).\n", "* Reach for sandwich when you suspect distributional mis-specification\n", " — heavy tails relative to the base distribution, residual\n", " heteroskedasticity not captured by `scaling=`, etc. See also the\n", " [`scaling-terms vignette`](05_scaling_terms.ipynb) for explicit\n", " modelling of heteroskedasticity, which often is the better answer\n", " than sandwiching.\n", "* Reach for profile when (i) the Wald and sandwich CIs disagree on\n", " width despite the link looking right, (ii) the parameter sits near\n", " a boundary (Bernstein coefficients, scaling $\\gamma$ at the\n", " identification frontier, etc.), or (iii) you need to report a CI\n", " that you can defend as inversion of the LR test. Pay the extra\n", " ~10× cost on a `parm=[j]` subset rather than the full vector unless\n", " $p + q$ is small.\n", "\n", "Profile and Wald CIs are R-parity tested against `tram::Coxph` /\n", "`tram::BoxCox` / `tram::Colr` in `tests/test_confidence.py` to\n", "`rtol = 1e-3`; the sandwich estimator is checked against\n", "`sandwich::vcovHC(..., type = \"HC0\")` in the same file." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.13" } }, "nbformat": 4, "nbformat_minor": 5 }