Technical note: unsafe rectal temperature measurements due to delayed warming of the thermocouple by using a condom. An issue concerning the estimation of the postmortem interval by using Henßge's nomogram

Technical note: Excel spreadsheet calculation of the Henssge equation as an aid to estimating postmortem interval

In forensic cases for which the time of death is unknown, several methods are used to estimate the postmortem interval. The quotient (Q) defined as the difference between the rectal and ambient temperature (Tr - Ta) divided by the initial difference (T0 - Ta) represents the progress of postmortem cooling: Q = (Tr - Ta)/(T0 - Ta), (1 ≥ Q ≥ 0). Henssge was able to show that with the body weight and its empirical corrective factor, Q can be reasonably predicted as a double exponential decay function of time (Qp(t)). On the other hand, actual Q is determined as Qd by measuring Tr and Ta under an assumption of T0 = 37.2 °C. Then, the t value at which Qp(t) is equal to Qd (Qd=Qp(t)) would be a good estimate of the postmortem interval (the Henssge equation). Since the equation cannot be solved analytically, it has been solved using a pair of nomograms devised by Henssge. With greater access to computers and spreadsheet software, computational methods based on the input of actual parameters of the case can be more easily utilized. In this technical note, we describe two types of Excel spreadsheets to solve the equation numerically. In one type, a fairly accurate solution was obtained by iteration using an add-in program Solver. In the other type (forward calculation), a series of Qp(t) was generated at a time interval of 0.05 h and the t value at which Qp(t) was nearest to Qd was selected as an approximate solution using a built-in function, XLOOKUP. Alternatively, a series of absolute values of the difference between Qd and Qp(t) (|Dq(t)| = |Qd - Qp(t)|) was generated with time interval 0.1 h and the t value that produces the minimum |Dq(t)| was selected. These Excel spreadsheets are available as Supplementary Files.

The experimental design of postmortem studies: the effect size and statistical power

Purpose

The aim is of this study was to show the poor statistical power of postmortem studies. Further, this study aimed to find an estimate of the effect size for postmortem studies in order to show the importance of this parameter. This can be an aid in performing power analysis to determine a minimal sample size.

Methods

GPower was used to perform calculations on sample size, effect size, and statistical power. The minimal significance (α) and statistical power (1 − β) were set at 0.05 and 0.80 respectively. Calculations were performed for two groups (Student’s t-distribution) and multiple groups (one-way ANOVA; F-distribution).

Results

In this study, an average effect size of 0.46 was found (n = 22; SD = 0.30). Using this value to calculate the statistical power of another group of postmortem studies (n = 5) revealed that the average statistical power of these studies was poor (1 − β < 0.80).

Conclusion

The probability of a type-II error in postmortem studies is considerable. In order to enhance statistical power of postmortem studies, power analysis should be performed in which the effect size found in this study can be used as a guideline.