Study inclusion and exclusion criteria

The examinations were performed on a convenience sample of 76 deceased individuals with a known time point of death who were admitted to the Institute of Legal Medicine (ILM) of the University Medical Center Hamburg-Eppendorf. The study population consisted of individuals who had died at the University Medical Center (n = 53) and individuals who died in public after observed sudden death and unsuccessful out-of-hospital resuscitation (n = 23). In the latter case, the end of resuscitation measures was considered the TOD. Only a maximum uncertainty of 30 min regarding TOD was accepted for inclusion in the study.

The exclusion criteria were age under 18, a previously known infection or sepsis, polytrauma, bleeding, and hyperthermia (rectal temperature at admission to the ILM > 37 °C). There were no signs of putrefaction or suspicion of intoxication in any of the cases. The exact cause of death remained unknown in most cases, with conventional autopsies conducted in a minority of cases.

Study enrolment procedure

Enrolment in the study was conducted by an investigator (ED) who did not perform postmortem examinations or calculate the postmortem interval with knowledge of the TOD. This investigator also determined when the tests were conducted, between 8 and 20 h postmortem. The examinations on the deceased were carried out by another examiner (FR-E, in some cases, in cooperation with SA-L) without knowledge of the TOD. Calculation of the 95% prediction interval for the TSD interval was also carried out without knowing the TOD (SA-L, FR-E). Information on the TOD was unblinded during data analysis.

All deceased were placed on a metal stretcher on a cotton sheet and were unclothed from the time of admission to the Institute of Legal Medicine. Until the examinations, the deceased were stored at a constant room temperature of about 20 °C (n = 21) or about 10 °C (n = 55; large cold-store room) in still air. Assignment to groups with different storage temperatures did not take place at random. Where corpses were already stored in the cooling chamber by the forensic assistants, they were included as cold stored. There is no direct or indirect association with the exposure or outcome; thus, no strong systematic bias is expected.

Study examination procedures

At the time point defined for the examinations (ED), the measurements were performed as described below, analogous to the methodology commonly used in forensic casework [1, 2].

Rectal temperature was measured at a depth of at least 10 cm using a calibrated thermometer with a suitable probe (Testo 110, Testo, Germany). Using the same thermometer, after connecting a probe to measure the air temperature, the ambient temperature was measured where the deceased was stored in the institute.

The degree of rigor mortis was recorded semiquantitatively. The degree was classified according to the degree of expression at the joints of the extremities (elbow, knee). Mild muscular resistance that the examiner could easily overcome through repeated joint movement was classified as moderate. Marked near-maximal joint stiffness was classified as strong. Cases with marked rigor mortis that did not meet the criteria for classification as moderate or strong were classified as intermediate.

Rigor mortis was entirely released by repeated movement of the elbow joints. The reformation of rigor mortis was tested manually 2 h later, according to the practical requirements of forensic casework. The intensity of reformation was recorded semiquantitatively (negative, moderate, intermediate, strong) and was compared with the intensity before the examination. The reformation was recorded as positive if it was graded as moderate, medium, or strong and negative if no renewed increase in muscle resistance was noted after release. Graduation was also graded positive in the case of unilateral reformation.

Livor mortis was classified as moderate or intense by visual inspection. After vigorous thumb pressure in the central area of livor mortis, the degree of fading produced was graduated as negative, incomplete, or complete semiquantitatively.

The mechanical excitability of skeletal muscle (idiomuscular contraction) was tested bilaterally on the muscle belly of the biceps brachii muscle by a single, forceful blow with a rounded metal rod. The local muscular response was recorded visually and by palpation after 20 s and graduated as negative or positive. Graduation as positive was also done in the case of unilateral triggering.

Electrical excitability of the mimic musculature was tested using insertion electrodes and a stimulation device (MD 95/2007, 40 V, Funeralia, Germany) with the placement of the electrodes in the upper eyelid and classified as negative or positive (grade 1 to 6) according to [2].

Due to previous findings suggesting that this method is not suitable for forensic TSD diagnosis [6], postmortem pharmacological susceptibility of pupillomotor function was not included in the methodology of this study. In addition, examinations of the shifting of livor mortis were not performed to not influence the appearance of the deceased during the examinations.

Calculations of the TSD

The TSD interval was calculated using the Deathtime software (AMA Soft, Germany; www.amasoft.de). Since the program sets the time limit for the re-formation of rigor mortis after mechanical release at 9.5 h post-mortem (hpm), this was manually corrected to 20 hpm according to recent results, if relevant [4, 5]. A correction factor 1.0 was used for body weight based on the deceased's storage conditions.

For each of the 76 cases, the following three calculations were made (a-c):

Assuming a constant ambient temperature from death until measurement – compound method

The ambient temperature measured at the deceased's storage site at the Institute (\(_\)) was assumed for the time from death until measurement; non-temperature-based methods were included (i.e., neglecting potentially different ambient temperatures before admission according to Henssge [8]).

Taking a plausible range of ambient temperatures from death until admission into account – temperature-based methods only

Due to the neglect of times and storage conditions before admission, a corrected mean ambient temperature was used for calculation \(\left(_\right)\). An exploratory approach assumed a range of plausible indoor ambient temperatures (\(}}_^}\), a vector of length 11) between 19 and 29 °C from death until admission. The temperature range was chosen considering a clothing and covering state of the deceased; non-temperature-based methods were neglected. A weighted average was calculated as shown in Formula 1.

Formula 1. The formula for calculating the corrected ambient temperature \(\left(_\right)\) as the weighted average of a vector with a plausible range of ambient temperatures before admission \(\left(_^}\right)\) and the storage temperature (\(_\)) at the ILM.

$$_= \frac_*}}_^}+\left(_-_\right)*_\right)}_}$$

, where tprae is the time from death until admission at the ILM [hours] and thpm is the time from death until measurements [hours].

Taking a plausible range of ambient temperatures from death until admission into account – compound method

Due to the neglect of times and storage conditions before admission, a corrected mean ambient temperature was used for calculation \(\left(_\right)\). In part (b), an ambient temperature that optimised compatibility in the actual TOD and the 95% prediction interval for this cohort was obtained. This cohort-specific ambient temperature was used \(\left(_^}\right)\); non-temperature-based methods were considered. A weighted average was calculated as shown in Formula 1.

Exposure

The primary exposure was time from death until measurement.

Outcome

The primary outcome was compatibility between the actual TOD and the 95% prediction interval for the TSD, according to Henssge. Compatibility was defined as an actual TOD within the 95% prediction interval for the TSD.

Collection and recording of potential confounding variables

Confounder variables were defined on a clinical basis. Sex [binary], age [continuous], body mass index [in kg/m2, continuous], body surface area (m2, continuous [20]) time from death until arrival at the ILM [in hours, continuous], and storage time from admission to the ILM until examination [in hours, continuous] were recorded by FR-E and SA-L.

Descriptive statistics

Categorical variables were summarised with numbers and percentages, and continuous variables were summarised using mean and SD or median and IQR, as appropriate. Continuous variables were inspected for approximate normality using Q-Q plots and histograms.

Comparative statistics

Tables were used to compare two categorical variables, and the \(^\) test was used to formally assess the null hypothesis that there was no difference in expected and observed values across groups. Summary statistics and boxplots were used to compare continuous variables across two groups. A Mann–Whitney U test was conducted to compare locations of continuous variables between two groups where substantial violations of the normality assumption were observed, and a location shift was plausible.

Exact binomial 95% confidence intervals were calculated for proportions.

Generalised linear model

Generalised linear models were used to investigate the association between the (i) time from death until admission, (ii) time from admission until measurement, (iii) body mass index, (iv) body surface area and (v) mode of storage, and the odds of compatibility between the actual TOD and the 95% prediction interval for the TSD. A logistic regression was used. Agreement in the actual TOD and the 95% prediction interval for the TSD, defined as compatibility of the actual TOD and the 95% prediction interval for the TSD, was used as the dependent variable in the model [binary]. First, we calculated univariable logistic regressions by including each interest factor separately. Then, we fitted multivariable logistic regression models by including the factor of interest and confounding variables for each exposure-outcome relationship. Confounders were a priori-defined on a clinical basis, as shown in the directed acyclic graphs (DAGs, Supplementary Figs. 1–4). Likewise, interaction terms were included on a clinical basis. The analysis involved testing for misspecification of the linear predictor using the Hosmer–Lemeshow test with ten groups and predicting standardised Pearson residuals. Index plots and scatter plots were used to identify influential values and assess the correct functional form of continuous variables.

Empirical standardisation was used to calculate marginal probabilities. The delta method was used to estimate 95% confidence intervals for marginal probabilities.

The dataset was inspected for missing data using tabulations as appropriate. Missing data proportions yielded below 5% for all variables, and a complete case analysis was employed. Generally, only one missing value was observed for the re-establishment of rigor mortis (n = 1). One case had to be excluded from calculation (b) at assumed ambient temperatures of 26 °C to 29 °C because the body and ambient temperatures were too close to each other to allow determination of the TSD interval (n = 1).

Statistical analyses were performed using STATA/MP 18.0 (StataCorp, Texas, USA). The figures were created using Adobe Illustrator (Adobe Inc, CA, USA) and GraphPad Prism (GraphPad Software, MA, USA). Tests were conducted at a 5% significance level.