The Role of Influenza in the Delay between Low Temperature and Ischemic Heart Disease: Evidence from Simulation and Mortality Data from Japan

Many studies have found that cardiovascular deaths mostly occur within a few days of exposure to heat, whereas cold-related deaths can occur up to 30 days after exposure. We investigated whether influenza infection could explain the delayed cold effects on ischemic heart diseases (IHD) as they can trigger IHD. We hypothesized two pathways between cold exposure and IHD: a direct pathway and an indirect pathway through influenza infection. We created a multi-state model of the pathways and simulated incidence data to examine the observed delayed patterns in cases. We conducted cross-correlation and time series analysis with Japanese daily pneumonia and influenza (P&I) mortality data to help validate our model. Simulations showed the IHD incidence through the direct pathway occurred mostly within 10 days, while IHD through influenza infection peaked at 4–6 days, followed by delayed incidences of up to 20–30 days. In the mortality data from Japan, P&I lagged IHD in cross-correlations. Time series analysis showed strong delayed cold effects in the older population. There was also a strong delay on intense days of influenza which was more noticeable in the older population. Influenza can therefore be a plausible explanation for the delayed association between cold exposure and cardiovascular mortality.

. A multi-state competing risk model for influenza infections and ischemic heart diseases (IHD) mortality or morbidity incidence.

Estimations of Event Times
We used previous studies to estimate the rate for the exponential distributions. The mean event time is the inverse of the rate.

Transition 1: Individuals to Stay Healthy
The rate for the exponential distribution was estimated from a study for health-related quality life in Japan. In the study [1], a representative population was examined by the international standard survey called EuroQol (EQ-5D) to measure the different dimensions of health status (e.g., morbidity, pain/discomfort, and anxiety/depression) and 45.6% of the study population reported problems in any dimensions of health status. Therefore, we assume that one can maintain the condition with no health issues is 55% of daily probability.

Transition 2: Individuals Infected with Influenza
The rate for the exponential distribution was estimated from the number of outpatient records diagnosed with influenza infections reported by National Federation of Health Insurance Societies [2]. During the epidemic season 2011-2012, February had the highest number of influenza diagnoses (approximately 410,000) among insurance holders (approximately 1,363,000). Therefore, the daily rate was estimated as 0.0104 (1.04%) ≈ 410,000 ÷ 1,363,000 ÷ 29 days. Since incubation period of influenza is on average 2 days [3], the first 2 days were assumed to be one-fifth of the mean rate.

Transition 3: Individuals to Ischemic Heart Diseases (IHD)
The rate for the exponential distribution was estimated from the patient survey data from the Japanese Ministry of Health, Labor and Welfare [4]. The daily outpatient for ischemic heart diseases (IHD) was approximately 49 per 100,000 (0.00049% or 0.049%) in October, 2011. Given that our mortality data shows an approximate 50% increase of cases when compared with following February in 2012, the outpatient rate was also doubled (0.000735% or 0.0735%).

Transition 4: Influenza Infections to Recovery (Healthy)
With an assumption that recovery takes one week, the rate for the exponential distribution was estimated as 0.14 (14%) ≈ (1 event ÷ 7 days).

Transition 5: Influenza Infections to No Recovery
In Hong's study [5], four cases among 635 laboratory confirmed influenza cases were reported as deaths within an average of 8 days. Therefore, the mean rate for the exponential distribution was estimated as 0.00079(0.079%) ≈ (4 events ÷ 635 events) ÷ 8 days.

Statistics for IHD and Pneumonia and Influenza (P&I) Mortality
Daily minimum (min), maximum (max) and mean mortality are calculated based on the data from 1995-2012 which corresponds the period of ICD-10 (Table S1). The total cases were based on the study period of 1973-2012.  Figure S2. Time series plots for IHD and P&I mortality, and mean temperature in Japan, 1973-2012.

Sensitivity Analysis for the Degrees of Freedom for the Smoothing Function on Time
We examined whether changing the number of degrees of freedom per year could impact on our interaction results. The graphs in Figure S3 show that, regardless of different number of the degrees of freedom, the patterns of different lag responses between intense and non-intense influenza days were consistent, proving the robustness of our results.  Figure S4 shows the cross-correlations in daily P&I and IHD deaths and daily temperatures among the population aged 15-64 in Japan, 1973-2009. Negative lags correspond to P&I deaths before IHD deaths, and positive lags correspond to P&I deaths after IHD deaths. The red vertical line at zero is for the same day. The green vertical line highlights the largest cross-correlation.  Figure S5 show the estimated delayed effects of extreme temperatures on IHD for population aged 65 years or older and age of 15-64. Japan, 1973-2012. As we increased the degrees of freedom from 4 to 8, a secondary peak emerges at approximately day 3 for cold temperatures. Figure S5. Increased degrees of freedom for the splines for lag and temperature.

Lag Responses of a Cold Effect on IHD from Simulation and Empirical Data
The Figure S4 shows the estimates of cold effect on IHD from simulation and mortality data from Japan. Light green bars are simulated relative risks (RR). The blue lines and grey shades are point estimates and 95% confidence intervals from time series analysis with Japanese mortality data. As aged population accounts for most cases of IHD, time series results for IHD among all age and aged population were very similar with simulated results.

Estimations of Event Times for Simulations
The initial simulation for the impact of cold on IHD (as described in Figure S1 above) was projected based on the cold season when influenza epidemics occur. In order to simulate the reference values to compute RR, cases during warm season/non-epidemic season were simulated. For the event probability estimates during non-epidemic seasons, Transition 2 and 3 (transitions to influenza infection and IHD) were restated based on case reports in October 2011 in Japan.

Transition 2: Individuals Infected with Influenza
Based on the diagnosis reports in February 2012, the daily rate during epidemics was estimated as 0.0104 (1.04%) ≈ 410,000 ÷ 1,363,000 ÷ 29 days (as stated in Figure S1). The probability during non-epidemic was then estimated as 0.000029 (0.0029%) ≈ 0.0104 × 0.0028 as the national sentinel surveillance reported that influenza-like illness (ILIs) incidence in the preceding October 2011 was 0.28% of February 2012 [7]. Again, since incubation period of influenza is on average 2 days [3], the first 2 days were assumed to be one-fifth of the mean rate.

Transition 3: Individuals to IHD
The daily rate was estimated 0.00049% or 0.049% based on the outpatient survey which was conducted in October 2011, by the Japanese Ministry of Health, Labor and Welfare [4].

Estimates from Time Series Analysis
Since the cases for non-epidemic season were simulated based on the reports of October 2011, the mean temperature of that time (17.5 °C) was set the reference temperature to cold effect (0 °C) (see Figure S6).