b = coxphfit (X, T) returns the $p$-by-1 vector of coefficients b of the Cox model

$$ h(x_i, t) = h_0(t)\exp\left(\sum_{j=1}^{p} x_{ij} b_j\right) $$

fitted to the $n$-by-$p$ matrix of predictors X and the $n$-by-1 vector of event times T. T may instead be an $n$-by-2 matrix whose rows give a $(start,\; stop]$ interval of exposure, the counting process form, in which an observation joins the risk set only after its start time. $h\_0(t)$ is the baseline hazard, which is left unspecified: the coefficients are estimated by maximizing the Cox partial likelihood, which does not involve it.

X must not contain a column of ones. The model has no constant term, since any constant is absorbed into the baseline hazard. A constant column is detected, reported by a warning, and given a zero coefficient.

Rows of X, T or "Frequency" holding NaN are removed before fitting.

[b, logl, H, stats] = coxphfit (…) additionally returns the maximized partial log-likelihood logl, the estimated baseline cumulative hazard H, and a structure stats of coefficient statistics and residuals.

H is a two-column matrix whose first column holds the distinct event times and whose second holds the estimated cumulative hazard at those times, evaluated at the predictor values given by "Baseline". Its first row is the first event time with a cumulative hazard of zero; an observation censored before any event contributes no row. In a stratified model H gains a third column carrying the stratum, the blocks appear in ascending stratum order, and each block leads with its own zero row at its own first event time. A stratum holding no event contributes a single row of NaN with its label.

The following name/value pairs are accepted:

The fields of stats are:

Two documented deviations, both where R2024a disagrees with itself. The martingale residual is defined as the event indicator minus the cumulative hazard the observation actually experienced, so "csres" and "martres" must sum to that indicator. They do here, always.

Under "efron" ties MATLAB’s do not: its "martres" comes from a cumulative hazard agreeing neither with its own "csres" nor with the H it returns, and the two sum to 1.0437 and $-0.0414$ where they must give 1 and 0.

In the counting process form MATLAB’s "martres" correctly subtracts the hazard accrued before the observation entered, but its "csres" does not, so the two disagree by exactly that amount for any row whose start time follows an event. Here both account for it, so "csres" differs from MATLAB’s by $\backslash Lambda(start)\; \backslash exp\; (x\text{'}b)$ and the identity is preserved.

The score residuals inherit the first of those two deviations, being an integral against the martingale residual: under "efron" ties they differ from MATLAB’s, whose own do not sum to the score at the maximum, while these sum to zero under both tie methods, weighted by "Frequency" where one is given.

Every other output agrees with R2024a to machine precision, across censoring, weights, both tie methods, stratification, and the counting process form.

See also: statset, ecdf, fitlm

Source Code: coxphfit